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Page 1: EASA PART 66  MODULE (3 ) PART (B)



Page 2: EASA PART 66  MODULE (3 ) PART (B)



1.1.1 Induced emf 1-21.1.2 Output frequency 1-3


1.4 PRACTICAL DC GENERATOR 1-71.4.1 Construction 1-71.4.2 Lap wound generator 1-91.4.3 Wave wound generator 1-101.4.4 Internal resistance 1-111.4.5 Armature reaction 1-111.4.6 Reactive sparking 1-13

1.5 GENERATOR CLASSIFICATIONS 1-151.5.1 Series generator 1-151.5.2 Shunt generator 1-161.5.3 Self excitation 1-161.5.4 Compound generator 1-17


2.3 PRACTICAL DC MOTORS 2-32.3.1 Construction 2-32.3.2 Back emf 2-32.3.3 Starting d.c. motors 2-32.3.4 Torque 2-42.3.5 Armature reaction 2-42.3.6 Reactive sparking 2-42.3.7 Speed control 2-42.3.8 Changing the direction of rotation 2-5

2.4 MOTOR CLASSIFICATIONS 2-52.4.1 Series motor 2-62.4.2 Shunt motor 2-72.4.3 Compound motor 2-92.4.4 Split field motor 2-9

2.5 RATING 2-10



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4.2 THE SINEWAVE 4-24.2.1 Peak and Peak-to-Peak values 4-34.2.2 Average values 4-34.2.3 RMS values 4-44.2.4 Form Factor 4-44.2.5 Periodic time 4-44.2.6 Frequency 4-44.2.7 Angular Velocity 4-54.2.8 Phase Difference (Angular Difference) 4-5

4.3 PHASOR OR VECTOR DIAGRAMS 4-64.3.1 Addition of phasors 4-7


4.5 MEASURING AC USING OSCILLOSCOPES 4-84.5.1 The cathode Ray oscilloscope 4-84.5.2 Types of oscilloscopes 4-114.5.3 using the oscilloscope 4-15

4.6 OTHER TYPES OF WAVEFORMS 4-274.6.1 Square waves 4-274.6.2 Triangular or sawtooth waves 4-27

4.7 AC VOLTAGE & CURRENT 4-284.7.1 Resistive loads 4-284.7.2 Capacitive loads 4-284.7.3 Inductive loads 4-304.7.4 Impedance 4-31

4.8 AC POWER 4-324.8.1 Resistive loads 4-324.8.2 Inductive loads 4-334.8.3 Capacitive loads 4-344.8.4 The total load on a generator 4-354.8.5 Apparent Power & actual current 4-354.8.6 True power & Real Current 4-364.8.7 Reactive power & reactive current 4-374.8.8 Power Factor 4-37

4.9 SERIES L/C/R CIRCUITS 4-384.9.1 Inductance and resistance in series 4-384.9.2 Capacitance and resistance in series 4-394.9.3 Inductance, capacitance and resistance in series .. 4-394.9.4 Series resonance 4-404.9.5 Voltage magnification 4-414.9.6 Selectivity 4-424.9.7 Bandwidth 4-43


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4.10.1 Inductance and capacitance in parallel 4-444.10.2 Parallel resonance 4-454.10.3 Impedance 4-464.10.4 Current magnification 4-474.10.5 Bandwidth 4-474.10.6 Selectivity 4-48



5.3.1 Iron losses 5-45.3.2 Copper losses 5-45.3.3 Flux leakage losses 5-55.3.4 Skin Effect 5-5





5.8 APPLYING LOADS TO A TRANSFORMER 5-75.8.1 No load conditions 5-75.8.2 Resistive loads 5-85.8.3 Inductive load 5-85.8.4 Capacitive load 5-95.8.5 Combination loads 5-9








6.1.1 High pass filters 6-16.1.2 Low pass filters 6-26.1.3 Band pass filters 6-36.1.4 Band stop filters 6-36.1.5 Smoothing & decoupling circuits 6-5

6.2 ATTENUATORS 6-66.2.1 ‘T’ type attenuator 6-76.2.2 Two section attenuator 6-8

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6.2.3 Variable attenuators 6-96.2.4 '' type attenuators 6-96.2.5 Balanced & unbalanced networks 6-106.2.6 Attenuator symbols 6-10


7.1.1 Output voltage 7-27.1.2 Output frequency 7-27.1.3 Effects of a resistive load 7-37.1.4 Effects of an inductive load 7-47.1.5 Effects of a capacitive load 7-4

7.2 PRACTICAL GENERATOR CONSTRUCTION 7-57.2.1 Rotating armature type 7-57.2.2 Rotating field type 7-57.2.3 Single phase generator 7-6Two phase generator 7-77.2.5 Three phase generator 7-7

7.3 STAR & DELTA SYSTEMS 7-87.3.1 Delta connection 7-97.3.2 Star connection 7-97.3.3 Power in ac systems 7-10


8.1.1 Single phase 8-18.1.2 Two phase 8-28.1.3 Three phase 8-3

8.2 TYPES OF AC MOTOR 8-38.2.1 Induction motor 8-38.2.2 Synchronous motor 8-58.2.3 Shaded pole motor 8-68.2.4 Hysteresis motor 8-7

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If a conductor is moved at right angles to a magnetic field, an emf is induced inthe conductor. If an external circuit is then connected to the conductor a currentwill flow. The direction of the current flow depends on two factors, the:

direction of the magnetic field

direction of relative movement between the conductor and

the field

and can be determined by using Fleming’s right hand rule.

The size of the generated emf depends on three factors, the:

strength of the magnetic field - B

effective length of the conductor in the field - l

linear velocity of the conductor - v

The three are related in the formula E = B l v

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In its simplest form, a generator consists of a single loop of wire rotated betweenthe poles of a permanent magnet. The rotating part of the machine is called therotor or armature, it is connected to the stationary external circuit via two sliprings, thus allowing a current flow.


As the loop rotates an emf is induced in both sides of the conductor. UsingFleming’s right hand rule, it can be seen that the resultant currents flow inopposite directions on each side, but in the same direction around the loop.

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An emf is only induced in a conductor when it is moved at right angles to the linesof flux in a magnetic field. Therefore, the loop will only have an emf induced in itwhen it is moving at right angles to the lines of flux, when moving parallel with thelines of flux, no emf will be induced. At any direction in between, there will be aproportion of maximum emf induced in the loop.

The instantaneous value of emf induced in the loop is given by:

e(instant) = E(max) sin

where E(max) = lv and is the angle of the conductor with respect to the linesof flux.

As the loop passes the neutral point, the conductors direction of travel throughthe field reverses. The conductor that was moving upwards through the field isnow moving downwards, therefore, the emf's induced in the conductors mustchange direction, as must the resultant current flow.


As the loop rotates, the emf rises to a maximum in one direction, then falls to zeroand then rises to a maximum in the opposite direction, before once again fallingto zero. One complete revolution is one cycle, the loop having returned to itsstart position.

The number of cycles per second gives the frequency. The faster the loop isrotated, the more cycles per second and the higher the frequency. In this simplegenerator the frequency depends on the number of loop revolutions per second.

The output from this generator changes polarity every time the loop rotates 180degrees and is therefore of little use as a direct current generator.


In order to make the current flow in the same direction through the load, theconnections to the external circuit must be switched every time the loop movespast its neutral position. This can be achieved using a commutator.

The commutator is used in place of the slip rings and connects the rotating loopto the stationary external circuit.

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A commutator has 2 functions:

Firstly, to transfer current from the rotating loop to the stationary externalcircuit.

Secondly, the periodic switching of the external circuit to keep the currentflowing in the same direction through the load. Switching takes place whenthe loop is moving parallel to the field and has no emf induced in it.

Using a single loop generator and two segment commutator, the output will be asshown above.

Although current now flows in the same direction through the external circuit, it isstill of little practical use, because the voltage and current fall the zero twice everycycle. Using several loops and a multi-segment commutator, a more constantoutput can be produced.


The simple construction of the ring wound generator makes it ideal for explainingthe operation of a multi-coil machine.

The rotor consists of a laminated iron cylinder onto which is wound 8 equallyspaced coils. The junction between each pair of coils is connected to a segmentof the commutator. The number of segments equals the number of coils, thisbeing true for all d.c. generator armature windings.

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The brushes are drawn inside for clarity and are positioned so that when theyshort circuit a coil, that coil is moving parallel to the magnetic field and has no emfinduced in it.

The metal used for the rotor has a very low reluctance, therefore the flux of themain field flows through it, rather than through the airgap in the centre. The partsof the coils on the inside of the rotor are therefore not cutting any flux and haveno emf’s induced in them.

The low reluctance rotor creates a radial field in the airgap as shown above. Theradial field means that the conductors are moving at right angles to the flux for alonger period of time and are therefore producing maximum emf for longer. Thisresults in a flat top to the output waveform as shown above.

The 8 coils are split into two parallel paths of four, each group of four coils beingconnected in series, because one set of four coils is moving up through the mainfield and the other set is moving down through the field, the emf's induced in eachset of four coils is in the opposite direction, but it is in the same direction withrespect to the brushes.

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The emf induced in four coils is as shown below. The emf in the other four coilsis in the opposite direction, but in the same direction with respect to the brushes.It can be seen that the emf no longer falls to zero and only has a small ripple onit.

The ring wound generator is no longer used. Although simple in construction,there are difficulties in winding the coils through the rotor, also, half of each coil iswasted because it has no emf induced in it.

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The size and weight of generators vary considerably, but all are constructed in amanner similar to that shown above.

The field assembly consists of a cylindrical frame, or yoke, onto which the polepieces are bolted. Generators generally have at least four pole pieces, althoughsmall machines may have only two. Wound around each pole piece is a fieldcoil. The yoke has a low reluctance and provides a path for the main field of themachine. To reduce eddy currents the yoke is usually laminated.

The armature core also provides a path for the main field and is therefore also oflow reluctance and laminated.

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The armature windings are located in slots cut in the core, being wedged in withinsulation to prevent them being thrown out by centrifugal forces. The coils arenormally wound so they return along a slot in the rotor that is one pole pitch away(see diagram below).

Pole pitch is a term used to describe the angle between one main pole and thenext main pole of the opposite polarity.

The emf induced in each side of the coil is again in opposite directions, butassisting around the coil. This type of winding is called a drum winding and hasthe advantage that the coils can be wound and insulated before being fitted intothe rotor. There are two types of drum winding, Lap wound and wave wound.

The armature windings are connected to risers attached to the commutator. Thecommutator consisting of copper segments separated by mica insulation.

The brush gear assembly consists of a holder and rocker. The holder allowsthe brushes to slide up a down, whilst preventing them from moving laterally. Therocker allows the brushes to be rotated around the commutator so they can bepositioned on the magnetic neutral axis.

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It should be noted that the output power from a d.c. generator is governedprimarily by its ability to dissipate heat. Methods of cooling vary, a large, low

power generator would normally be cooled naturally by convection and radiation.Smaller, higher power generators will need some form of cooling system thatblows or draws air through the generator. The cooling system may use ram airfrom a propeller slipstream or from movement of the aircraft through the air, ormore commonly, a fan attached to the rotor shaft of the generator.


In a lap wound generator, the end of each coil is bent back to the start of the nextcoil, the two ends of any one coil being connected to adjacent segments of thecommutator (see diagram above). This form of construction is used on largeheavy current machines. The number of parallel paths for current always equalsthe number of brushes and the number of field poles (see diagram).

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In a wave wound generator, the end of each coil is bent forward and connected tothe start of another coil located in a similar position under the next pair of mainpoles (see diagram above). The two ends of one coil are connected to segmentstwo pole pitches away. This type of machine has two parallel paths and uses onlytwo brushes irrespective of the number of poles (see diagram).

This type of winding is used in smaller machines and is therefore more commonon aircraft generators.

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A d.c. machine has resistance due to the:

armature windings


brush to commutator surface contact

This is called internal resistance and can be measured across the terminals ofthe generator.

For the purposes of calculation, the internal resistance is represented as a singlevalue in series with the generated emf.

Internal resistance causes the generators terminal voltage to vary with changes inthe load current. As the load current increases, the voltage dropped across theinternal resistance increases and the terminal voltage decreases.

The generated emf E = Ir + V


When armature current is flowing, a field is produced around the armatureconductors. The overall field of the machine is then produced by interactionbetween the main field and the armature field.

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The armature field is at 90 degrees to the main field of the machine and thereforedistorts it as shown below.

This distortion of the field is called armature reaction and has the effect ofweakening the field at points A and strengthening the field at points B.

The machine is working near to saturation and therefore the overall effect is aweakening of the field and a reduction in the generators output voltage.Distortion of the field also means that the magnetic, or electric neutral axis ismoved around in the direction of rotation, away from the machines geometricneutral axis. When the brushes now short an armature coil, it is no longer at thepoint where zero emf is induced in it, therefore the brushes must be moved. Theposition they are moved to depends on the size of the armature current, thegreater the current, the further the brushes must be advanced.

Armature reaction can be reduced by fitting compensating windings.Compensating windings are small windings wound in series with the armatureand fitted into slots cut in the pole faces of the main fields.

When armature current flows, current flows in the compensating windings andproduces a magnetic field that cancels the armature field.

With careful design, correction is applied for all values of armature current,bringing the magnetic neutral axis back onto the geometric neutral axis andrestoring the overall strength of the machines field.

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The diagrams above represent the movement of the commutator under the brush.Prior to being shorted by the brush, current in coil A is at a maximum value left toright. After leaving the brush, current will be flowing at maximum value in theopposite direction through the coil, as shown in coil B. Whilst the coil is shortedby the brush, the current must drop to zero ready for it to go to maximum value inthe opposite direction when it comes off the brush.

Unfortunately, the coil has inductance, when shorted, a back emf is produced thattries to maintain current flow. When the coil comes off the brush, the current hasnot reduced to zero, resulting in an excess of current that jumps as a spark fromthe commutator to the brush. The sparking produced is called reactive sparking.

Not all sparking at the commutator is reactive sparking, sparks may also becaused by:

worn or sticking brushes

incorrect spring tension

commutator flats

proud mica

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One way of overcoming the problem is to increase the resistance of the brushes,this reduces the time constant of the inductive circuit and enables the current tocollapse to zero during commutation. However, increasing the resistance of thebrushes produces a power loss and increases the overall resistance of themachine. The increase in internal resistance causes greater fluctuations inoutput voltage with changes in load current. EMF Commutation

Another way of overcoming reactive sparking is to use emf commutation. Thepurpose of emf commutation is to neutralise the reactance voltages that lead toreactive sparking. One way of achieving this is to advance the brushes beyondthe magnetic neutral axis, this means the coils are under the influence of the nextmain pole before being shorted and will therefore have an emf induced in them.

The induced emf will be of opposite polarity to the reactance voltage and willreduce it, reducing the reactance voltage reduces the current in the coil andallows time for it to drop to zero whilst the coil is shorted.

Unfortunately, advancing the brushes is only good for one value of armaturecurrent, if the current increases, the brushes must be advanced further.

Advancing the brushes also increases the demagnetising effects of armaturereaction.

A better way of applying emf commutation is to fit commutating or interpolesbetween the main poles of the machine. Interpoles have the same polarity as thenext main pole and are connected in series with the armature.

The interpoles induce emf’s in the short circuited coils that exactly cancels theback emf, thus allowing the current to fall to zero instantly. Being in series withthe armature means that the reactance voltage is always eliminated irrespectiveof the value of armature current.

By careful design, the interpoles can also be used to eliminate armature reactionin the interpole region.

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Generators are usually classified by the method of excitation used. There arethree classifications; permanent magnet, separately excited and self excited.

A permanent magnet generator has a limited output power and an output voltagethat is directly proportional to speed.

A separately excited generator has its field supplied from an external source. Theoutput voltage being controlled by varying the field current.

Self excited generators supply their own field current from the generator output,again the output voltage is controlled by varying the field current. This group maybe subdivided into three sub-groups; series, shunt and compound.


The series generator has a field winding consisting of a few turns of heavy gaugewire connected in series with the armature.

On "No-load" there is no armature current and therefore no field current. Theonly voltage generated is due to residual magnetism within the fields.

As the load current increases, the field current increases and the terminal voltagerises, the increase in voltage more than compensating for the loss due toarmature reactance and internal resistance. The voltage continues to rise untilsaturation of the field occurs.

A series generator therefore has a rising characteristic and is generally only usedas a line booster.

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The shunt generator has a field consisting of many turns of fine wire connected inparallel with the armature.

On "No-load" the terminal voltage is a maximum. As the load current increases,the terminal voltage decreases due to the resistance of the armature andarmature reactance.

The shunt generator has a falling characteristic and is used for d.c. generation onaircraft.


For a d.c. generator to self excite, certain conditions must be met:

The generator must have residual magnetism.

The excitation field, when formed, must assist the residual


For shunt generators, additional criteria need to be met:

The field resistance must be below a critical value.

The load resistance must not be too low.Due to the first two points above, the only way to reverse the output voltage of ad.c. generator is to reverse the polarity of the residual magnetism. If the supply tothe field winding, or the drive direction is reversed, the excitation will oppose theresidual magnetism and the field will be lost.

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Compound generators have both series and shunt field windings and fall into oneof two categories:

differential compound generators, in which the two fields are wound so asto oppose each other.

cumulative compound generators, in which the fields are wound so as toassist each other.

Differential compound generators are generally used where a high initial voltageis required, but only a low running voltage. Devices such as arc welders or arclighting may use this form of generator.

Cumulative compound machines can be wound to produce over, level or undercompounding. Under compounding is more common in aircraft generators, theoutput voltage falling as the load current is increased.

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If a current carrying conductor is placed at right angles to a magnetic field, a forcewill be exerted on it, causing it to move.

The direction of the force and the resultant movement depends on two factors,the :

direction of current flow in the conductor

direction of the magnetic field

The direction of the force and the resultant movement can be found by usingFleming’s left hand rule as shown below:

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The simplest form of motor consists of a single loop ofwire able to rotate between the poles of a permanentmagnet.

If current is applied to the loop through slip rings, a motortorque will be produced, and the loop will start to rotate.

As the loop rotates past vertical, the current appears tochange direction, this causes the torque to changedirection, so the direction of rotation changes.

When the loop passes vertical, the current appears tochange direction again, causing rotation to revert to itsoriginal direction.

If left, the loop will simply oscillate back and forth eitherside of the vertical position.


To make the loop rotate, the current must be made to change direction as theloop passes the vertical position, this is achieved using a commutator andbrushes.

When current is applied to the loop a motor torque is produced and the loopstarts to rotate. When the loop is vertical no rotational torque is produced,however, momentum keeps it moving. At the vertical position, the direction ofcurrent in the loop is reversed by the commutator, so that as the vertical positionis passed, the torque produced is in the original direction, thereby maintainingrotation.

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To improve the torque and produce smoother running, more loops or coils areadded to the armature, each having its own commutator segment. Theconstruction is as described earlier in d.c. generators.



Direct current generators are constructed in the same manner as d.c. generators,therefore further description is unnecessary. The similarities are such that onemachine can be operated as the other with only minimal adjustment. In the caseof starter generators, the only adjustment necessary is achieved electrically.

Most motors have some form of rating, this being a limit on their performance.Ratings take various forms depending on the type, size and use of the motor, butare generally based on a limit on the speed, duration or altitude of operation.

As with generators, the limit on a motors performance depends very much on theability of the machine to dissipate heat. Cooling may be natural, by convectionand radiation, or assisted by rotor mounted fans, blast air or slipstream.

2.3.2 BACK EMF

When a conductor moves in a field, an emf is induced in the conductor.

The armature coils of the motor aremoving in a magnetic field and

therefore must have an emf induced inthem, this emf acts against the appliedvoltage and is called back emf.

The resultant of the two voltages iscalled the effective voltage. Thearmature current is due to the effectivevoltage, not the applied voltage.

When running, the back emf is almost equal to the applied voltage, therefore theeffective voltage and the current taken from the supply are both small.


On starting, the rotor is stationary and therefore producing no back emf, thisresults in a high effective voltage and a large current being taken from the supply.To limit the current, a starting resistor is often used, the resistor being removedfrom the circuit once the motor is running.

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2.3.4 TORQUE

The torque produced by a d.c. motor is directly proportional to the armaturecurrent and the magnetic field strength.


Some torque is lost within the motor, especially if a fan is fitted to the rotor shaft.The torque lost is not constant, usually increasing with an increase in speed.


The overall field of a d.c. motor consists of the armature field and the stator field.The two fields react, as in the d.c. generator, producing armature reaction.

Armature reaction causes the magnetic neutral axis of the motor to be movedaround in the opposite direction to that of the generator, against the direction ofrotation. The problem can be overcome as in d.c. generators, by fittingcompensating windings.


d.c. motors also suffer from reactive sparking. For fixed load motors, the problemis overcome simply by moving the brushes onto the magnetic neutral axis. Forvariable load motors, interpoles are used as in d.c. generators.


The effects of back emf make a d.c. motor a self regulating machine. If the loadis increased, load torque exceeds motor torque and the motor slows down, thereduction in speed causing a decrease in back emf and an increase in theeffective voltage across the armature. The increase in effective voltage causesan increase in the current drawn from the supply and an increase in motor torque,which increases the motor speed to cope with the load increase.

The speed of a d.c. motor can be varied by controlling the field current or bycontrolling the armature current.

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With field control, a decrease in field current causes an increase in motor speed;

main field decreases

back emf across armature decreases

effective voltage increases

armature current increases

motor torque increases over load torque

motor speed increases

This occurs because a small change in the main field strength causes a largechange in the armature current. Of course, this cannot continue uncontrolled

because eventually the field will be lost. Field control is generally used for speedcontrol of normal running speed and upwards. Armature control

With armature control, an increase in armature current causes an increase inmotor torque over load torque and an increase in motor speed. A decrease inarmature current causes a decrease in motor speed. Armature control isgenerally used for control of normal running speed and downwards.


To change the direction of rotation it is only necessary to change the direction ofthe main field or the armature current. If both are changed, the motor will rotatein the same direction.

In the majority of cases where a bi-directional d.c. motor is required on an aircraft,a split field motor is used. This motor will be examined in more detail later in thenotes, suffice to say it has two fields windings, one for clockwise rotation, theother for anti-clockwise rotation.


The construction of d.c. motors is the same as d.c. generators, with armaturesbeing either wave wound or lap wound.

Motors are also classified in a similar way to generators - shunt, series andcompound. Each type having its own operating characteristics and uses.

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A series motor has a low resistance, heavy gauge field winding in series with thearmature winding. On light loads its speed is high, the armature current is lowand the field is weak. On heavy loads. speed is low, the armature current is largeand the field is strong. Series motors have a wide speed variation with load.

The armature torque is proportional to the field strength and armature current. Inseries motors the field strength depends on the armature current, so the torqueproduced is approximately proportional to the square of the armature current. Inpractice it is slightly less (particularly on heavy loads) due to armature reactionand saturation of the magnetic circuit.

As speed increases, the torque decreases, until the load torque and motor torquebalance. If the load of a series motor is removed, the speed may becomedangerously high. It is not normal practice to run series motors off-load .

When starting a series motor, it is normally connected straight to the supply, theinitial current being limited by the combined resistance of the field and armaturewindings and by the inductance of field winding. The field strength builds upquickly, giving a high starting torque, a fast acceleration and a rapid back-emfbuild up. There is a short period of high current drain on the supply.

Where a large change in operating speed is required, as in turbine enginestarting, a starter resistor is initially connected in series with the motor and

removed when the motor is required to increase speed. The starter resistor mustbe able to withstand the large initial current. Applications include starter motors,winches and aircraft actuators.

Some series motors are fitted with two separate windings. This enables motorrotation to be quickly reversed. Applications include fuel valves and landinglights.

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Shunt wound motors have a high resistance field winding connected in parallelwith the armature. The field current will be constant if the input voltage isconstant and no field control resistor is used.

When the load torque is increased, the motor slows down. The decrease inspeed, causes a fall in the back-emf and an increase in armature current whichproduces more motor torque. When the motor torque and load torque are againbalanced, the speed becomes constant.

Small decreases in speed cause relatively large increases in armature current.Between no-load and full-load, the variation in speed of a d.c. shunt motor with alow resistance armature is small enough for it to be considered a constant speedmotor. With a high resistance armature, there is a more noticeable variation inspeed with load.

When a shunt motor has a constant input voltage:

on light loads, the magnetic field is constant and the torque is directlyproportional to the armature current.

on heavy loads the magnetic field is reduced by armature reaction and thetorque does not rise in direct proportion to the armature current.

If a shunt motor does not increase speed when connected to the supply, then noback-emf is produced. This results in a very high armature current, a largearmature reaction and a reduced torque and the motor will not start.

Several options are available to overcome the problem:

use the motor only on a small load

start the motor with no load connected to it

increase the armature resistance

use a starter resistor

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A low resistance shunt motor is normally started with a variable resistor, set tomaximum resistance, placed in series with the armature. This reduces thearmature current and armature reaction, thereby increasing the starting torque.

As the speed increases, the back emf increases and armature current decreases.As the speed builds, the resistance is gradually decreased until at normal runningspeed it is totally removed from the circuit.

An automatic method used to insert a resistor is series with the armature forstarting, and to remove it once the back-emf has been developed is referred to asa 'T’ Start circuit.

At the instant the motor is switched ‘on’, the armature is stationary and producingno back-emf, therefore the voltage at A is almost zero and the relay is de-energized. The resistance is in circuit limiting the current.

As the rotor starts to turn and the back-emf increases, the potential at point Astarts to increase.

At a pre-determined speed the potential at point A and the current through therelay coil will be sufficient to cause the relay to energize, removing the resistorfrom the armature circuit.

Speed control - The speed of a shunt motor isnormally controlled by a variable resistor placed inseries with the field winding. When the resistance isincreased, the field current is reduced, the back-emfdecreases and the effective voltage increases. Theincrease in effective voltage produces an increase inarmature current and an increase in speed. Whenrequired to reduce the speed of the motor, the fieldresistance is decreased.

Separately excited shunt motors - Separately excited d.c. shunt motors havethe same operating characteristics as self excited shunt motors and thereforerequire no additional consideration.

Applications - Shunt motors are used where a constant speed is required andwill be found in inverter drives and windscreen wipers.

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These are used to meet specific requirements, we may require a motor:

that has a high starting torque, but will not race off-load.

to increase, decrease or maintain speed as the load on it varies.

These requirements can be met with suitable compounding. As with generators,there are two forms of compound motor.

Differential compound - fields connected to oppose each other

Cumulative compound - fields connected to assist each other


In certain applications it is necessary to change the direction of rotation of amotor. Typical examples would be in valves and actuators. We have already

seen that this can be achieved by reversing the direction of the armature or fieldcurrent, however, there is also a special form of reversible series motor known asa split field motor.

A split field motor is simply a series motor with two field windings. The fields arewound in opposite directions, with one being used for each direction of rotation.The direction is usually controlled by a single pole, double throw switch as shownabove.

The circuit above is in fact that of an actuator and includes not only a split fieldmotor, but also a selector switch, limit switches and a brake solenoid.

The motor is shown as having driven to position 1, this can be seen because limitswitch A is not connected to the field winding. Whether this position is fully open,fully closed, extended or retracted depends on the device being driven.

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When it is required that the actuator drive to position 2, the selector switch ismoved to position 2. Current flows through the field winding, brake solenoid andarmature winding. The brake is released and the motor starts to turn. As soonas the motor moves, it is no longer in position 1, so switch A moves across. Thisallows the direction to be reversed (by returning the selector switch to position 1)should the need dictate. When the motor reaches the limit of travel at position 2,switch B moves across, removing the motor power supply. The brake solenoid,field winding and armature de-energise, the brake is applied and the motor stops.

If the selector switch is now moved to position 1, the upper field winding, brakesolenoid and armature are energised. The brake is released and the motor runsin the opposite direction towards position 1. Again as soon as the motor turns, itis no longer at position 2 so the lower switch moves over to contact the fieldwinding.


Most motors have a rating - a limit on performance or operation. Ratings takevarious forms - output, time, speed, altitude. As with generators, the outputdepends very much on the machines ability to dissipate heat. All machinesrequire some form of cooling. Low output motors, or those that are not used forcontinuous operation may be cooled naturally. Others may be fitted withcentrifugal or straight fans to drive air through machine, this being usual on smallmachines. Others use air ducted from slipstream.

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Many gas turbine aircraft are equipped with starter-generator systems. Thesestarting systems use a combination starter-generator which operates as a startermotor to drive the engine during starting, and after the engine has reached a self-sustaining speed, operates as a generator to supply the electrical system power.

The starter-generator unit shown below left, is basically a shunt generator with anadditional heavy series winding. This series winding is electrically connected toproduce a strong field and a resulting high torque for starting.

Starter-generator units are desirable from an economical standpoint, since oneunit performs the functions of both starter and generator. Additionally, the totalweight of starting system components is reduced, and fewer spare parts arerequired.

The starter-generator shown below right has four windings; (1) series field, (2)shunt field, (3) compensating, and (4) interpole. During starting, the series,

compensating, and interpole windings are used. The unit is operating in a similarmanner to a direct-cranking starter, since all the of the windings used duringstarting are in series with the source. While acting as a starter, the unit makes nopractical use of its shunt field. A source of 24 volts and 1,500 amperes is usuallyrequired for starting.

When operating as a generator, the shunt, compensating and interpole windingsare used. The output voltage is controlled in the conventional manner, byconnecting the shunt field in the voltage regulator circuit. The compensating andinterpole windings provide almost sparkless commutation from no-load to full-load.

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The following diagram illustrates the external circuit of a starter-generator with anundercurrent controller. This unit controls the starter-generator when it is used asa starter. Its purpose is to ensure positive action of the starter and to keep itoperating until the engine is rotating fast enough to sustain combustion. Thecontrol block of the undercurrent controller contains two relays; one is the motorrelay which controls the input to the starter, the other, the undercurrent relay,controls the operation of the motor relay.

To start an engine equipped with an undercurrent relay, it is first necessary toclose the engine master switch. This completes the circuit from the aircraft's busto the start switch, the fuel valves, and the throttle relay. Energising the throttlerelay starts the fuel pumps, and completing the fuel valve circuit provides thenecessary fuel pressure for starting the engine.

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When the battery and start switches are turned on, three relays close. They arethe motor relay, ignition relay and battery cut-out relay. The motor relay closesthe circuit from the power source to the starter motor; the ignition relay closes thecircuit to the ignition units; and the battery cut-out relay disconnects the battery.On this particular aircraft opening the battery circuit is necessary because theheavy drain of the starter motor would damage the battery, this is not the generalcase. The majority of aircraft are designed to be started using the battery so asto make the aircraft independent of ground resources, the battery will however bedisconnected from the bus when ground power is connected and care must betaken to ensure the ground power unit is capable of supplying the currentrequired by the starter motor.

Closing the motor relay allows a very high current to flow to the motor. Since thiscurrent flows through the coil of the undercurrent relay, it closes. Closing theundercurrent relay completes a circuit from the positive bus to the motor relaycoil, ignition relay coil, and battery cut-out relay coil. The start switch is allowedto return to its normal "off" position and all units continue to operate.

As the motor builds up speed, the current draw by the motor begins to decrease,as it decreases to less than 200 amps, the undercurrent relay opens. This actionbreaks the circuit from the positive bus to the coils of the motor, ignition andbattery cut-out relays. The de-energising of these relay coils halts the startoperation.

After the procedures described are completed, the engine should be operatingefficiently and ignition should be self-sustaining. If however, the engine fails toreach sufficient speed, the stop switch may be used to break the circuit from thepositive bus to the main contacts of the undercurrent relay, thereby halting thestart operation.

On a typical aircraft installation, one starter-generator is mounted on each enginegearbox. During starting, the starter-generator unit functions as a d.c. startermotor until the engine has reached a predetermined self-sustaining speed.Aircraft equipped with two 24 volt batteries can supply the electrical load requiredfor starting by operating the batteries in a series configuration.

The following description of the starting procedure used on a four-engine turbojetaircraft equipped with starter-generator units is typical of most starter-generatorstarting systems.

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Starting power, which can be applied to only one starter-generator at a time, isconnected to a terminal of the selected starter-generator through a correspondingstarter relay. Engine starting is controlled from an engine start panel. A typicalstart panel (see diagram below) contains an air start switch and a normal startswitch.

The engine selector switch shown has five positions ('1, 2, 3, 4, and off'), and isturned to the position corresponding to the engine to be started. The powerselector switch is used to select the electrical circuit applicable to the powersource being used (ground power unit or battery). The air-start switch, whenplaced in the "normal" position, arms the ground starting circuit. When placed inthe "air-start" position, the igniters can be energised independently of the throttleignition switch. The start switch, when in the "start" position, completes thecircuit to the starter-generator of the engine selected, and causes the engine torotate. The engine start panel shown above also includes a battery switch.

When an engine is selected with the engine selector switch, and the start switchis held in the "start" position, the starter relay corresponding to the selectedengine is energised and connects that engine's starter-generator to the starterbus. When the start switch is placed in the "start" position, a start lock-in relay isalso energised. Once energised, the start lock-in relay provides its own holdingcircuit and remains energised providing closed circuits for various start functions.

An overvoltage lockout relay is provided for each start-generator. During groundstarting, the overvoltage lockout relay for the elected start-generator is energisedthrough the starting control circuits. When an overvoltage lockout relay isenergised, overvoltage protection for the selected started- generator issuspended. A bypass of the voltage regulator for the selected starter-generatoris also provided to remove undesirable control and resistance from the startingshunt field.

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On some aircraft a battery lockout switch is installed in the external powerreceptacle compartment. When the door is closed, activating the switch, the

ground starting control circuits function for battery starting only. When the door isopen, only external power ground starts can be accomplished.

A battery series relay is also necessary in this starting system. When energised,the battery is connected in series to the starter bus, providing an initial startingvoltage of 48 volts. The large voltage drop which occurs in delivering the currentneeded for starting, reduces the voltage to approximately 20 volts at the instant ofstarting. The voltage gradually increases as the starter current decreases withengine acceleration and the voltage on the starter bus eventually approaches itsoriginal maximum of 48 volts.

Some multi-engine aircraft equipped with starter-generators include a parallelstart relay in their starting system. After the first two engines of a four-engineaircraft are started, current for starting each of the last two engines passesthrough a parallel start relay. When starting the first two engines, the startingpower requirement necessitates connecting the batteries in series. After two ormore generators are providing power, the combined power of the batteries inseries is not required. Thus, the battery circuit is shifted from series to parallelwhen the parallel start relay is energised.

To start an engine with the aircraft batteries, the start switch is placed in the"start" position. This completes a circuit through a circuit breaker, the throttleignition switch and the engine selector switch to energise the start lock-in relay.Power then has a path from the start switch through the "bat start" position of thepower selector, to energise the battery series relay, which connects the aircraftbatteries in series to the starter bus.

Energising the No 1 engine's starter relay directs power from the starter bus tothe No. 1 starter-generator, which then cranks the engine.

At the time the batteries are connected to the starter bus, power is also routed tothe appropriate bus for the throttle ignition switch. The ignition system isconnected to the starter bus through an overvoltage relay, which does notbecome energised until the engine begins accelerating and the starter busvoltage reaches about 30 volts.

As the engine is turned by the starter to approximately 10% r.p.m. the throttle isadvanced to the "idle" position. This action actuates the throttle ignition switch,energising the igniter relay/ When the igniter relay is closed, power is provided toexcite the igniters and fire the engine.

When the engine reaches about 25 to 30% r.p.m., the start switch is released tothe "off" position. This removes the start and ignition circuits from the enginestart cycles, and the engine accelerates under its own power.

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The only practical way of generating an electromotive force (emf) by mechanicalmeans is to rotate a conductor in a magnetic field. As the conductor rotates inthe magnetic field, its direction of motion relative to the magnetic field iscontinually changing, therefore, the emf induced in the conductor is continuouslychanging. The emf will start at zero when the conductor is moving parallel withthe lines of flux, it will rise to a maximum value when the conductor is moving at90° to the lines of flux, before decaying back to zero rising to a maximum value inthe opposite direction. In this way, an alternating emf is produced which, whenconnected to a circuit, produces an alternating current flow.

By making the conductor in the form of a loop, we have the basis of the simple acgenerator.

All generators, both dc and ac, have this basic design. In a dc machine theoutput to the load is continually switched by the commutator, so that the load

current always flows in one direction. In an ac machine the output to the load iscontinually reversing it direction.

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If the generated emf of the loop is measured and plotted as the loop rotates, theresult will be as shown in the diagram below.

It can be seen that when the conductors are moving parallel to the lines of flux,and not cutting them, the induced emf is zero. When the conductors are cuttingthe lines of flux at right angles, maximum emf is induced in them. By convention,the part of the waveform above the zero line is labelled positive and the partbelow the line is labelled negative.


If the conductor is rotated at uniform speed in a uniform magnetic field, the outputwaveform is said to be ‘sinusoidal’ and we refer to this type of waveform as asine wave. There are many other wave shapes that can be generated ordeveloped, but it is the sine wave that is used for main power supply systems. Itis therefore necessary for the engineer to be very familiar with this particularwaveform and he is expected to be able to remember and use the various figuresand formulae associated with it.

The wave generated is called a sine wave because its amplitude (height) at anyinstant can be calculated from sine tables, i.e. by plotting the sine’s of all anglesbetween 0º and 360º.

When the conductor has completed 360º of rotation, it is said to have completedone cycle.

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Amplitude values and their calculation apply equally to current and voltagemeasurement.

The Peak or Maximum Value. The maximum value attained by the wave ineither direction is called the maximum value, or more usually, the peak value.

The Peak-to-Peak Value. The maximum value in one direction, to the maximumin the other direction is called the Peak-to-Peak value. It must not be confusedwith peak value, which is measured in one direction only. Peak-to-peak valuesare often used on oscilloscopes because it is easier to measure from top tobottom of the waveform, but the majority of calculations require the use of thepeak value. It must be remembered to divide the peak-to-peak value by two inorder to obtain the peak value for calculations.

The Instantaneous Value. As previously stated, the value at any instant can becalculated by multiplying the peak value by the sine of the angle (from 0º) throughwhich the conductor has rotated.


The amplitude of an ac waveform may be defined in terms of its average values.Over one complete cycle, this would mathematically be zero (the wave goes asfar positive as it does negative) If the pulses of voltage or current are always inone direction, the average value can be calculated from:

For single-phase full-wave rectification

Average Value = Peak Value × 0.637

For single-phase half-wave rectification

Average Value = Peak Value × 0.318

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Whilst the Peak and Average values of ac have their place and uses, they are nota lot of use for everyday work on ac. What is required is a value of ac whichrelates to an equivalent value of dc. Suppose an electric fire is operating with 5amperes of d.c. current flowing through it and it is giving out a certain amount ofheat. We want to know the value of a.c. which will produce the same amount ofheat. Such a value is given by the Root Mean Square (rms) value of an a.c.current.

For a sinusoidal waveform, the rms value = peak value × 0.707.

In other words, a sine wave of peak value ‘y’ produces a certain amount of heatwhen passed through a given resistor. To produce the same heating effect, inthe same resistor using d.c., would require a d.c. with a steady current of only

0.707 of ‘y’.

By convention, it is not necessary to add ‘rms’ to a voltage or current value but, ifpeak or average values are being referred to, then the word ‘peak’ (Pk) or‘average’ (Av) must be added after the value.


The form factor of a waveform is a number which indicates its shape:

Form Factor = rms valueaverage value

For a sine waveform, this works out at 0.707 / 0.637 = 1.11. For any otherwaveform, the values will be different and so the Form Factor will be a different

number. (This is given in these notes for information only as the aircraft engineershould not have to concern himself with the form factor).


The time taken to complete one cycle is called the ‘periodic time’ (t). It ismeasured in seconds or fractions of a second.


In electrical terms, frequency is the number of cycles completed in one second(cycles per second) and is expressed in Hertz (Hz).

1 Hz = 1 cycle / sec.

10 Hz = 10 cycles / sec. etc.

1,000 Hz (103 Hz) = 1 Kilo-Hertz (1 kHz)

1,000,000 Hz (106 Hz) = 1 Mega-Hertz (1 MHz)

1,000,000,000 Hz (109 Hz) = 1 Giga-Hertz (1GHz)

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Periodic time and frequency are related.

T = 1/f and f = 1/T


The velocity at which a phasor rotates is very important and can be calculatedfrom:

Speed =DistanceTime

Distance (one revolution) = 2 radians.

Time (periodic time) = 1/f.

Angular Velocity () (omega) = 21/f radians per second

= 2f radians per second.

(A proper understanding of this formula is essential as it is used in otherformulae).

Referring back to our simple loop it can be seen that, if the loop was rotating at120 revolutions per second, the output frequency would be 120 Hz. It thereforefollows, that the frequency of the output of an ac generator is directly proportionalto its speed of rotation.


If two conductors are caused to rotate at the same angular velocity, then twowaves would be generated. Any angle between them is said to be their phasedifference. In the following diagram, the phase difference is 90º. As theconductors rotate in an anti-clockwise direction, the dotted wave is said to leadthe solid wave by 90º.

When two waves are 90º apart, they are said to be in ‘quadrature’ with eachother.

When two waves are 180º apart, they are said to be in ‘antiphase’ with eachother.

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Waveform diagrams are difficult to visualise and engineers have devised adiagrammatic method known as a phasor or vector diagram to simplify theproblem.

The terms vector and phasor are interchangeable, however, the term vector ismore general, being used to denote any quantity that has both magnitude anddirection, whereas the term phasor, tends to be associated with electricalengineering. To avoid repetition, the word phasor will be used in these notes.

Imagine a phasor of length of Vm rotating in an anticlockwise direction, rather likethe conductor rotating in the magnetic field. If you plot the vertical displacementof the tip of the line at various angular intervals, the curve traced out is asinewave.

When the line is horizontal, the vertical displacement of the tip of the line is zero,corresponding to the start of the sinewave at point A. After the line has rotated90 in an anti-clockwise direction, the line points vertically upwards, point B onthe diagram. After 180 of rotation the line points to the left of the page, and thevertical displacement is again zero. Rotation through a further 180 returns theline to its start point.

A phasor is a line representing the rotating line Vm, frozen at some point in time.Although line Vm was drawn to represent the maximum values, a phasor isnormally scaled to represent r.m.s. values, and can be used to represent voltagecurrent, power or indeed flux. One rotation of the phasor produces one cycle ofthe waveform, therefore the number of rotations completed per second gives thefrequency.

The 3 'o-clock position on a phasor diagram is considered to be the referencepoint of the diagram. Whether the current, voltage, mmf or flux is drawn pointingin this direction depends on the circuit under consideration. If two or more phasedisplaced waveforms are to be drawn on the same phasor diagram they musthave the same frequency, their angular displacement is indicated by the anglebetween the phasors. It must be remembered that phasors rotate anti-clockwise,therefore if a voltage leads a current by 90, the two phasors should be drawn sothat as they are rotated, the voltage phasor is leading.

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The addition of sine waves is greatly simplified by the use of phasor addition,however it should be remembered that, phasors can only be used to addsinewaves of the same frequency.

To add two phasors, a parallelogram is produced, the two extra sides beingdrawn parallel to the phasor already present.

Each extra side should start at the end of each phasor as shown. Once theparallelogram has been produced, the resultant voltage is represented by a linefrom the origin to the intersection of the two new lines. The length of this newphasor represents the magnitude of the new voltage and the angle between itand the other phasor is the phase angle between them. When adding more thantwo phasors, it is simply a matter of reducing pairs to a single phasor, asdescribed, until a single resultant remains.

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It is possible for both ac and dc to exist in the same circuit or conductor. In suchcases the ac is said to be superimposed on the dc, or the dc has an ac ripple.The resultant waveform depends on the relative values of ac and dc, as shown inthe diagrams above.



Cathode ray oscilloscopes are analogue-graphical instruments which enableelectrical waveforms to be displayed for analysis and measurement purposes. Atypical instrument is represented in the diagram below.

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With reference to the above diagram, the grids g1, g2 and g3 of the cathode raytube (CRT) form an electron gun which projects a stream of electrons betweendeflecting plates onto the screen. The screen is coated with a phosphorescentmaterial so that a luminous spot is produced on the screen. A property of thescreen coating material allows the spot to persist for a period of time when thestream of electrons is moved or interrupted. The amount of illumination dependson the quantity of electrons in the stream and their velocity on impact with thescreen.

The potential at grid g1, which is negative with respect to the cathode, controlsthe quantity of electrons emitted from the cathode. Adjusting R1 varies thepotential at g1, hence R1 controls the brightness of the illuminated spot. Positivepotentials at g2 and g3 accelerate the electrons towards the screen. The potentialdifference between g2 and g3, varied by adjusting R2, sets up an electrostatic fieldwhich enables the electron stream to be focused at the screen.

The position of the spot on the screen is determined by the simultaneous effect ofvoltages applied to the X and Y deflecting plates. A potential difference betweenthe X deflecting plates causes the spot to move across the screen in thehorizontal direction, through a distance proportional to the potential difference. Apotential difference between the Y deflecting plates exerts a similar control overthe vertical movement of the spot.

The outputs of the X and Y amplifiers establish the potential differences betweencorresponding pairs of deflecting plates. If these voltages vary in magnitude thespot moves over the screen to produce a continuous trace. Since one voltagecontrols horizontal deflection and the other controls vertical deflection, the traceforms a graphical representation of one voltage as a function of the other. The Time Base

Most applications require that a signal waveform isdisplayed as a function of time. To meet this

requirement a time base circuit supplies a voltagewhich varies linearly with time, usually, to the

horizontal (X) deflecting plates whilst the signal to beobserved is usually applied to the vertical (Y)deflecting plates. A time base (sawtooth) voltagesynchronised with a time dependent signal aredepicted in the diagram.

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The period t1, is the sweep, that is the time the spot takes to move linearly from

left to right across the screen. During the much shorter period t2, called the

flyback time, the spot returns rapidly to the left of the screen to start a new cycle.

During flyback the screen may blacked out by a negative pulse generated by the

time base circuit and applied to g1, the control grid.

If the sweep period (T) of the time base is equal to, or is a multiple of, the periodic

time of the signal applied to the Y deflecting plates, a stationary display of the

signal voltage variations with time will be obtained. In the diagram above, the

sweep period (T) equals the periodic time1 of the signal waveform. In practicef

the time base is adjusted so that signals over a wide frequency range may be

displayed against a convenient time scale. Synchronisation

The time base and the displayed waveform may be synchronised by employing a

trigger circuit actuated by the signal itself, that is, by using the output of the Y

amplifier. Alternatively, an external signal source or the mains supply may be

used for this purpose.

The trigger circuit generates a pulse to initiate one sweep of the time base when

the voltage applied to the circuit reaches a predetermined value. The circuit is

adjustable so that a particular trigger point on either the positive or negative half

cycle of the displayed waveform may be selected.

Where the signal to be observed is non-

periodic, or when the signal appears

infrequently, the time base is triggered by the

signal, performs one sweep and then waits for

the next signal to appear. In order that the

beginning of a non-periodic signal can also be

examined, the vertical deflecting voltage is

delayed relative to the trigger pulse so that the

time base is started before the signal to be

observed appears on the screen. The time

relationship is shown in the diagram. MOD

On many oscilloscopes, a terminal marked Z MOD is provided. The terminal is

connected through a blocking capacitor, to the control grid(g1) of the cathode ray

tube. The facility enables a suitable voltage pulse to be applied to the grid so that

selected portions of the display can be blacked out or brightened for the duration

of the pulse.

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The X and Y amplifiers and attenuators provide the voltage scaling required toensure that the instrument and the measured signal are compatible. Since theoscilloscope is required to display complex voltage waveforms, it is essential thatfundamental and harmonic frequencies must undergo the same amplification orattenuation, and that the time relationships between different frequencies must bemaintained. It therefore follows that both the amplifier and the attenuators, musthave flat amplitude against frequency and transit time against frequency,characteristics.

4.5.2 TYPES OF OSCILLOSCOPES Sampling Oscilloscopes

At very high frequencies, say above 300MHz, it is not possible using existingtechniques to produce a continuous display on an oscilloscope. To obtain asatisfactory display a sampling technique must be used.

As shown in the diagram below, in a sampling oscilloscope the time base circuitproduces a stepped voltage waveform to deflect the electron beam in thehorizontal direction. Prior to each step, a pulse is generated which initiates thesampling process.

The input signal is sampled later during each successive cycle to produce thevertical deflection of an illuminated spot. In this way the display, which mayconsist of 1,000 spots, is progressively built up over a number of cycles of theinput signal. An obvious limitation of the sampling oscilloscope is that it cannotbe used to display transient waveforms.

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Oscilloscopes equipped with multiple trace facilities enable two or more signals tobe displayed simultaneously. Essential features of these instruments are aseparate input channel for each signal and a means of separating the electronbeams for display. The most widely used instruments enable two signals to becompared, although four beam instruments are quite common.

Cathode ray tubes equipped with two electron guns and two sets of deflectingplates, so that each channel is completely independent, are employed ininstruments known as Dual Beam Oscilloscopes. Alternatively, a single gunmay be used to produce two traces by switching the Y deflecting plates from oneinput signal to the other for alternate sweeps of the screen. Although the signalsare sampled, the display appears to the eye as a continuous, simultaneous,display of both signals. Oscilloscopes employing this techniques, which is calledthe alternate mode, can only be used as single channel instruments toinvestigate transient waveforms. Dual Trace CRO Alternate Mode

The electronic switch alternately connect the main vertical amplifier to the twovertical preamplifiers. The switching takes place at the start of each sweep. Theswitching rate of the electronic switch is synchronised to the sweep rate, so thatthe CRO spot traces channel 1 signal on one sweep and channel 2 signal on thenext sweep. This is used for viewing high frequency signals.

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The electronic switch is free running at 100 - 500KHz and is independent of thefrequency of the sweep generator. The switch successively connects smallsegments of the 1 and 2 waveforms to the vertical amplifier. If the chopping rateis much faster than the horizontal sweep rate, the individual little segments fed tothe vertical amplifier reconstitute the original 1 and 2 waveforms on the screen,without visible interruptions in the two images. Delayed Sweep

Both time bases in operation.

A - delaying sweep

B - delayed sweep

Either or both (alternate) signals can be fed to X plates. This allows a closerexamination of part of the waveform. CRO contains two linear calibrated sweeps,a main sweep and a delayed sweep. The main sweep is initiated by its triggerpulse at time t0. The delayed sweep will be triggered at time t1, intensifying theoriginal display.

If the CRO sweep control is now set to delay position, the intensified portion willbe shown expanded on the screen.

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The dielectric storage sheet consists of a layer of scattered phosphor particlescapable of having any portion of its surface area written to. This dielectric sheetis deposited on a conductive coated glass faceplate called the "storage targetbackplate".

The flood electrons are distributed evenly over the entire surface area of thestorage target.

After the write gun has written a charge image on the storage target, the floodguns will store the image. The written portions of the target are bombarded byflood electrons that transfer energy to the phosphor layer in the form of visiblelight. This light pattern can be viewed through the glass faceplate. The Digital Storage CRO

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The digital storage CRO stores the data representing the waveforms in a digitalmemory. The input signal is "digitised", i.e. it is sampled and then converted intobinary numbers by the A/D converter.

The resolution of the system depends on the number of bits used by theconverter. Converters are said to have a resolution of 1 part in 2 or 'n bit

resolution' where n is the number of bits, i.e. 10 bit resolution would digitise to 210

(1024) discrete levels: the resolution would be 1 part in 1024 or 0.098%.

This digitised input is then converted back to an analogue signal for display bythe D/A converter.

(1-2MHz which may be extended to 200MHz using sampling techniques).


An oscilloscope is an extremely comprehensive and versatile item of testequipment which can be used in a variety of measuring applications, the most

important of which is the display of time related voltage waveforms. Such an itemprobably represents the single most costly item in the average service shop and itis therefore important that full benefit is derived from it.

The oscilloscope display is provided by a cathode ray tube (CRT) which has atypical screen area of 8cm 10cm. The CRT is fitted with a graticule which maybe an integral part of the tube face or on a separate translucent sheet. Thegraticule is usually ruled with a 1cm grid to which further bold lines may be addedto mark the major axes on the central viewing area. Accurate voltage and timemeasurements may be made with reference to the graticule, applying a scalefactor derived from the appropriate range switch.

A word of caution is appropriate at this stage. Before taking meaningfulmeasurements from the CRT screen it is absolutely essential to ensure that thefront panel variable controls are set in the calibrate (CAL) position. Results willalmost certainly be inaccurate if this is not the case!

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The use of the graticule is illustrated by the following example:

An oscilloscope screen is depicted below. This diagram is reproduced actual sizeand the fine graticule markings are shown every 2mm along the central verticaland horizontal axes. The oscilloscope is operated with all relevant controls in the'CAL' position. The timebase (horizontal deflection) is switched to the 1ms/cmrange and the vertical attenuator (vertical deflection) is switched to the 1V/cmrange. The overall height of the trace is 5cm 1V = 5V. The time for onecomplete cycle (period) is 4 1ms = 4ms. One further important piece ofinformation is the shape of the waveform, which in this case is sinusoidal.

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Page 56: EASA PART 66  MODULE (3 ) PART (B) Layout of Controls

Layouts of the controls and display provided by a typical dual-channeloscilloscope are shown in the diagrams above and below. The majority of thecontrols identified in the above diagram are those associated with the positionand appearance of the display (e.g. vertical shift horizontal shift, intensity andfocus) whilst those shown in the diagram below include the vertical gain andattenuator controls.

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The dual-channel oscilloscope has three BNC coaxial input connectors:

Channel 1. This is the primary vertical input, but it is also used for thehorizontal (X) input when the mode switch is set to the 'X-Y' position.

Channel 2. This is the second vertical input which is also used for the verticalinput (Y) when the mode switch is set to the 'X-Y' position.

External trigger. This input is only used when the trace is to be locked to anexternal trigger signal (both 'CH1' and 'CH2' trigger selector buttons must bedepressed on the trigger selector).

In addition, a voltage calibrator test point is provided (marked 'CAL 1V' on thefront panel). This connector provides an accurate 1V square wave signal whichmay be used to calibrate the two vertical deflection channels.

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Page 58: EASA PART 66  MODULE (3 ) PART (B) Basic Adjustments

The basic adjustments for single-channel waveform measurements are shown inthe diagram below. The sequence of adjustments is as follows:

1. The input signal is applied, via a suitable probe, to the Channel 1 (CH1) inputconnector.

2. The intensity and focus controls are adjusted for a satisfactory display.3. The display is centred on the graticule using the vertical and horizontal shift


4. The variable gain (Var) and variable sweep (Var Sweep) controls are set tothe calibrate (Cal) positions.

5. The trigger selector (TRIGGER) is set the Channel 1 (CH1).6. Positive edge trigger is selected '+' (note that negative edge trigger may also

be selected - in practice the sharpest edge of the waveform will produce themost effective triggering).

7. The display mode switch (MODE) is set to Channel 1 (CH1).

8. The Channel 1 input selector is set to 'AC'.9. The vertical attenuator (VOLTS/CM) control is adjusted to produce a suitable

height display.

10. The trigger level control (Trig Level) is adjusted to obtain a stable (locked)display.

11. The timebase selector (TIME/CM) control is adjusted to produce a suitablenumber of cycles on the display (usually two to five cycles).

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The basic adjustments for dual-channel waveform measurements are shown inthe diagram below. The sequence of adjustments is as follows:1. The first input signal is applied, via a suitable probe, to the Channel 1 (CH1)

input connector.

2. The second input signal is applied, via a suitable probe, to the Channel 2(CH2) input connector.

3. The intensity and focus controls are adjusted for a satisfactory display.4. The displays are centred using the horizontal shift control.

5. The displays are adjusted (vertically separated into the upper and lower partsof the display) using the two vertical shift controls.

6. The two variable gain (Var) and variable sweep (Var Sweep) controls are setto the calibrate (Cal) positions.

7. The trigger selector (TRIGGER) is set to either Channel 1 (CH1), or Channel2 (CH2), as necessary.

8. Positive or negative edge triggering is selected as required.

9. The display mode switch (MODE) is set to dual-channel (Dual).

10. Both input selectors are set to 'AC'.11. The vertical attenuator (VOLTS/CM) controls are adjusted to produce displays

of a suitable height.

12. The trigger level control (Trig Level) is adjusted to obtain a stable (locked)display.

13. The timebase selector (TIME/CM) control is adjusted to produce a suitablenumber of cycles on the display (usually two to five cycles).

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The basic adjustments for measurement of DC offset voltages are shown in thediagram below. The sequence of adjustments is as follows:1. The input signal is applied, via a suitable probe, to the Channel 1 (CH1) input


2. The intensity and focus controls are adjusted for a satisfactory display.

3. The display is centred on the graticule using the horizontal shift control.4. The variable gain (Var) and variable sweep (Var Sweep) controls are set to

the calibrate (Cal) positions.

5. The trigger selector (TRIGGER) is set to Channel 1 (CH1).

6. Positive edge trigger is selected '+' (note that negative edge trigger may bealso be selected - in practice the sharpest edge of the waveform will producethe most effective triggering).

7. The display mode switch (MODE) is set to Channel 1 (CH1).

8. The Channel 1 input selector is set to 'GND'.

9. The vertical shift control is adjusted so that the trace is exactly aligned withthe horizontal axis of the graticule (this line will then correspond to 0V)

10. The Channel 1 input selector is set to 'DC'.11. The vertical attenuator (VOLTS/CM) control is adjusted to produce a suitable

height display.

12. The trigger level control (Trig Level) is adjusted to obtain a stable (locked)display.

13. The timebase selector (TIME/CM) control is adjusted to produce a suitablenumber of cycles on the display (usually two to five cycles).

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Page 61: EASA PART 66  MODULE (3 ) PART (B) Waveform Measurements

Examples of some basic waveformmeasurements using an oscilloscope areshown in the diagram to the left. In (a), asquare wave is displayed. One completecycle of this waveform occupies 2cm onthe display. Since the timebase rangeselector (TIME/CM) is set to 1ms/cm, thetime for one complete cycle of the

waveform is 2 1ms = 2ms. The verticalsize of the waveform (i.e. its peak-peakvalue) measures 2cm on the graticule.Since the vertical attenuator (VOLTS/CM)is set to 1V/cm the peak-peak voltage is 2 1V = 2V.

A sine wave is shown in (b). Onecomplete cycle of this waveform occupies

2.5cm on the display. Since the timebaserange selector (TIME/CM) is set to2ms/cm, the time for one complete cycleof the waveform is 2.5 2ms = 5ms. Thevertical size of the waveform (i.e. its peak-peak value) measures 3cm on thegraticule. Since the vertical attenuator(VOLTS/CM) is set to 50mV/cm the peak-peak voltage is 3 50mV = 150mV.

An irregular pulse is shown in (c). The display is 'low' for 3.4cm measured on thegraticule. Since the timebase range selector (TIME/CM) is set to 0.1s/cm, the'low' time shown on the display is 3.4 0.1s = 0.34s. Similarly, the period forwhich the wave next goes 'high' is 1.5 0.1s = 0.15s. The vertical size of thewaveform (i.e. its peak-peak value) measures 4cm on the graticule. Since the

vertical attenuator (VOLTS/CM) is set to 1V/cm the peak-peak voltage is 4 1V = 4V, equally distributed either side of 0V.

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Page 62: EASA PART 66  MODULE (3 ) PART (B) Pulse Rise and Fall Times

The rise and fall of a pulse can beeasily measured using thetechniques previously described(note that this measurement is onlyvalid if the oscilloscope is fitted witha properly compensated probe). Thediagram shows the parameters of apulse including:

Rise time (10% to 90%)

Fall time (90% to 10%)

On time (time above 50%)

Off time (time below 50%) Pulse Delay

A dual-channel oscilloscope can beeasily used to measure pulse delay(see diagram below). Note that thismeasurement should be performedwith the timebase mode switch set to'CHOP' rather than 'ALTERNATE' onoscilloscopes that offer an alternatesweep facility.

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Page 63: EASA PART 66  MODULE (3 ) PART (B) Wave Performance checks

An oscilloscope can provide a very rapidassessment of the performance of anamplifier. A pure sinewave (of appropriatefrequency and amplitude) is applied to theinput of the amplifier (or other system undertest) and the output is displayed on thescreen of the oscilloscope. The effects ofnon-linearity, clipping noise, distortion, etc.and be easily seen (see diagram). Square Wave PerformanceChecks

An alternative, but equally revealingassessment of an amplifier can be madeusing a square wave test. An accuratesquare wave (of appropriate frequencyand amplitude) is applied to the input ofthe amplifier (or other system under test)and the output is once again displayedon the screen. The effects of poorfrequency response, 'ringing', etc. can beeasily detected (see diagram).

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Page 64: EASA PART 66  MODULE (3 ) PART (B) Phase Measurement

A number of useful measurements can bemade with an oscilloscope in X-Y mode. It ispossible to carry out reasonably accuratemeasurements of phase angle usingLissajous figures (see diagram to the left).In order to obtain these displays, the twosignals must be applied with identicalgain/attenuation and it is usually necessaryto calibrate the instrument by applying thesame sine wave signal to the X and Y inputsand adjust the gain controls to obtain astraight line at exactly 45º (see diagram).Thereafter, the signal to be measured isapplied to vertical channel (Y) whilst thereference signal is applied to the horizontalchannel (X). The shape of the displayindicates the phase shift between the twosignals. This technique is ideal for rapidlychecking the phase shift produced by anetwork, filter or amplifier. Frequency Measurement

Lissajous figures can also be used todetermine the frequency relationship

between two signals (see diagram). Thefrequency ratio is given by the ratio of thenumber of 'peaks' produced in thehorizontal direction to the number of'peaks' produced in the vertical direction.

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Page 65: EASA PART 66  MODULE (3 ) PART (B) Modulation Measurement

Finally, the depth of amplitude modulation(AM) can be easily determined using anoscilloscope (see diagram). The depth ofmodulation (per cent) is given by therelationship:

Modulation depth = VM 100%VC Do's and Don'ts of using an Oscilloscope

Do ensure that the vertical gain and variable time/cm controls are placed inthe calibrate (CAL) positions before making measurements based on theattenuator/timebase settings and graticule.

Do ensure that you have the correct trigger source selected for the type ofwaveform under investigation.

Do remember to align the trace with the horizontal axis of the graticule withthe input selector set to 'GND' before making measurements of DC levels.

Do make use of the built-in calibrator facility (where available).

Do use a properly compensated oscilloscope probe.

Don't leave the intensity control set at a high level for any length of time.

Don't leave a bright spot on the display for even the shortest time (this mayvery quickly burn the screen's phosphor coating).

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Fourier (1768-1830), a French mathematician was one of the first to realise thatall periodic waves could be built-up by combining sinewaves of the appropriateamplitude, frequency and phase.

When considering waveforms made up of a number of sinewaves it is customaryto call the sinewave with the lowest frequency, the fundamental. The resultantwaveform will have the same frequency as the fundamental frequency.

The harmonics are those sine waves with frequencies that are twice, three-times,four times etc. the harmonic frequency.


A perfect square wave has vertical sides and a flat top. Such a theoreticallyperfect wave has an infinite number of odd harmonics and no even harmonics.Such a waveform is not possible to achieve in electronic circuits, however, byusing the fundamental and the lowest nine odd harmonics (3rd to 19th) a goodresemblance can be obtained. Limiting the number of harmonics causes asloping of the sides of the wave.

A voltage with a square waveform is often used as a test signal applied to theinput of a system. If the system does not respond well to higher frequencies, thesides will slope, if it does not respond well to lower frequencies the flat portionswill become curved.

If an amplifier does not function correctly when a square wave is applied to theinput, it is unlikely to function correctly when other periodic waves are applied. Askilled experimenter can make deductions about the response of an amplifier byobserving the output waveforms.


A perfect sawtooth wave contains an infinitenumber of both odd and even harmonics,again this is not possible practically. Thelower harmonics affect the rising portion ofthe wave, the higher harmonics, the decaytime.

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The type of load (resistive, capacitive or inductive) placed on an a.c. powersupply affects the phase angle relationship between the voltage and current.

Each type of load produces a different effect, so they are examined individually.


When a pure resistance is placed in an a.c. circuit, the instantaneous current isgiven by the instantaneous voltage divided by the resistance (i.e. it follows OhmsLaw). This means that the current waveform is in-phase with the voltagewaveform. If the voltage and current values are known, then resistance may be

calculated from VPKIPK



The diagram shows a pure capacitance or capacitorconnected in an ac circuit. This cannot actuallyhappen in practice as there must always be someresistance, but we will introduce the resistive elementlater in these notes.

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A capacitor will always charge up to, or discharge down to, the voltage which isbeing applied to it. In other words, it follows the supply voltage. If we take thepoint where the capacitor is charged in one direction, when connected across anac supply and the ac supply voltage starts decreasing, then a discharge currentwill flow (conventionally) from the capacitor’s positive plate through the supplysource to the negative plate. This current flow will be small at first as the supplyvoltage starts to drop but will increase to a maximum value when the supply is atzero volts. It will continue to flow in the same direction but decrease as thecapacitor is charged up in the reverse direction, becoming zero at the point of fullcharge. The following diagram illustrates this point and it can be seen that thecurrent is leading the supply voltage by 90º.

The operation of the capacitor produces an opposition to the flow of current. Itwill therefore act in a similar manner to a resistance in a circuit. It is a form of ‘acresistance’. The word ‘resistance’ is kept for the physical resistance as wealready know it, so this form of ‘ac resistance’ is called ‘reactance’. It iscalculated in Ohms and is given the symbol X. The opposition to current flowproduced by a capacitor is known as capacitive reactance and given the symbolXC. Capacitive reactance is dependent on frequency, such that XC variesinversely with frequency. If frequency increases, XC decreases and so thecurrent flow increases. If frequency decreases, XC increases and so the currentflow decreases. (This is why, after the initial charge current, no current flowsthrough a capacitor on dc).

Capacitive reactance, XC =1

2fC ohms

Ohms Law still applies XC = V/I ohms

It should be clearly understood that, although we refer to alternating currents andsignals flowing ‘through’ capacitors, no current actually passes through thedielectric between the plates. Electrons circulate from plate to plate through thecircuit, being affected by the electrostatic fields on the plates.

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The diagram shows a pure inductanceor inductor connected across an acsupply. The notes assume that there isno resistance in the circuit. This isa situation which cannot exist inpractice, but we shall introduce theresistive element later.

An inductance always opposes any change in current flow. When the current isa.c. and constantly changing in value, the result is that it always lags behind thesupply voltage. For a pure inductance the angle of lag is 90º.

The constantly changing current means that the magnetic field produced by theinductance is also constantly changing. This gives rise to an emf being inducedinto the inductor’s own windings in such a direction as to oppose the applied emf.This self-induced emf is therefore known as a back-emf. The back-emf isdependent on the rate of change of current and on the value of the inductor (inHenrys).

Back-emf= -L × Rate of Change of Current

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Note that, the ‘minus’ sign indicates that the back-emf is in opposition to theapplied emf. Note also that point F on the following diagram is a maximum‘negative’ value because the current at that instant (point A) is changing atmaximum rate.

The appearance of this back-emf in the circuit means that there is an oppositionto the flow of current from the supply. The opposition due to an inductance, L, iscalled inductive reactance, and given the symbol XL

It has already been stated that back-emf and therefore reactance, depends onthe rate of change of current in the circuit, but this is obviously dependent on thefrequency of the a.c. supply. As frequency increases, XL will increase and socurrent flow will decrease. As frequency decreases, XL will decrease and socurrent flow will increase. It can thus be seen that equipment marked ‘For use ona.c. only’ is depending on the reactance to control the current flow. If it was usedon dc at the same voltage, XL would not exist, the current flow would be too highand the equipment would burn out.

Inductive Reactance, XL = 2fL ohms.

Ohms Law still applies XL = V/I


When inductance, capacitance and resistance appear together in an a.c. circuit,in any combination, the total opposition to current flow is referred to asimpedance and given the symbol Z.

Resistance, inductance and capacitance in a circuit can be represented byphasors in the same way as currents and voltages. The position of each phasorrelative to the reference position (3 o'clock) depends on whether a series orparallel circuit is being considered.

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For the purpose of deriving theimpedance formula shown, it isonly necessary to understandthat phasors for XL and R or XC

and R are at 90 to each otherand as such form a right angledtriangle.

In a circuit containing all three components, the values of XL and XC oppose eachother, leaving one dominant value that again forms a right angled triangle with R.The resultant in each case is the circuit impedance, which can be calculated quiteeasily using Pythagoras.

The total impedance in a circuit containing resistance R, inductance L andcapacitance C, is calculated using the formula:

Impedance Z = R2 + (X L - XC )2


Alternating current power also needs to be examined under the three headings ofresistive loads, inductive loads and capacitive loads, as the calculation of powerin each type of load produces different results.


Power in a Resistive Circuit. When the instantaneous values of voltage andcurrent are multiplied, the resultant power waveform is as shown in this diagrambelow.

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It can be seen that all of the power waveform is above the ‘zero’ line, indictingthat it is all being dissipated in the resistance. The shaped area under the powergraph is the product of power × time and represents the electrical energyconsumed in the circuit.

Peak Power = V(Pk) × I(Pk)

Average Power = Peak Power


= V(Pk) × I(Pk)


= V(Pk) × I(Pk)

2 2

= V(rms) × I(rms)

= VI watts


Power in a purely inductive circuit. No power is developed in a pureinductance. Power is calculated by multiplying the instantaneous values of

voltage and current. If this is done for the two waveforms when they are 90º out-of-phase , then the resultant power waveform will be as shown below.

It can be seen from the above diagram that each half-cycle of voltage and currentproduces one full cycle of power. (Power wave frequency is twice the supplyvoltage frequency).

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When the power curve is ‘positive’, the inductor takes power from the supplysource. When the power curve is ‘negative’, the inductor returns power to thesupply source.

Over a complete cycle, the net absorption of power is zero watts. It must be fullyunderstood that current is flowing in the circuit but that no work is being donewhen that current is 90º out-of-phase with the voltage.


As with pure inductance, a pure capacitance also produces a current flow whichdoes ‘no work’. On one half-cycle, power is delivered to the capacitor (charging)from the supply source but the on the next half-cycle the capacitor returns powerto the supply source (discharging).

Each half cycle of the voltage and current again produces a full cycle of power.When the power curve is positive, the capacitor takes power from the supplysource. When the power curve is negative the capacitor returns power to thesupply source.

Over a complete cycle, the net absorption of power is zero watts. Again it mustbe understood that the current is flowing in the circuit, but no work is being done.

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The following facts regarding power in a.c. circuits have already been establishedin these notes:

In a purely resistive circuit, all of the current does work.

In a purely inductive circuit, none of the current does work.

In a purely capacitive circuit, none of the current does work.

We have also established that, depending on the relative values of resistance,inductance and capacitance, the current can be at any angle, from 0º to 90º,leading or lagging the supply voltage.

If any number of individual loads are switched onto an a.c. generator, theindividual currents will all combine to give one load current on the generator atone particular angle of lead or lag. As the angle is usually designed to be one inwhich the current lags the voltage, we will concentrate on that, but the samearguments we are going to use also apply to a leading current.

If the instantaneous values of two sinewaves are added together, the result willbe another sinewave. Conversely, any sinewave can be thought of as beingcomprised of two separate sinewaves. If therefore, we assume the generator’sload current is lagging the voltage by an angle , we can say that (irrespective ofthe individual loads that produced it) it is comprised of one current which is inphase with the voltage and one current which is 90º lagging the voltage.


The load current (lagging the voltage by ) is called the actual current. This isthe current that would be indicated on an ammeter inserted into the circuit, orwould be detected by a current transformer (see transformer notes). If the supplyvoltage is multiplied by this current, the power that is ‘apparently’ being dissipatedis found. This however, is not the true power being dissipated and so it is calledthe ‘apparent power’ and is given the units of volts-amps.

Apparent power = V × I(actual) volts amps

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If the rating plate on an a.c. generator is examined, it will be seen that thegenerator is rated at, say 200 volts (rms); 30 kVA. The rating is not given in wattsbecause the designer has no way of knowing what the phase angle will be whenit is loaded.


The component of the actual current that is in phase with the voltage is known asthe ‘Active’ or ‘Real’ load current, because it is the part of the load current that isdoing all the work. This component can only be calculated, as it is not possiblefor a device such as an ammeter or current transformer to measure anythingother than actual current. In order to find the real load current, it is necessary tomultiply the actual current by the Cosine of the angle . If the supply voltage ismultiplied be the real load current, the ‘true power’ being dissipated in the circuitis found. The unit of true power is the watt (as in d.c.).

True power = V × I(actual) × Cos Watts.

= V × I(real) Watts.

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The component of the actual current that is lagging the supply voltage by 90º isknown as the ‘Reactive’ or ‘Wattless’ load current, because it is the part of theload current that does no work at all, even though it exists and has to be carriedby the cables, etc. It is brought into being by the nature of the capacitive andinductive loads. Again, it can only be calculated by multiplying the actual loadcurrent by the sine of the angle . If the supply voltage is multiplied by the

reactive load current, the reactive power is found, reactive power is given theunits of Volt Amps Reactive (VAR).

Reactive power = V × I(actual) × Sin VARs

= V × I(reactive) VARs.


The angle which the actual load current makes with the supply voltage is knownas the power factor of the circuit. The power factor is given by the Cosine of theangle .

When the current is in phase with the voltage, the angle is 0º.The Cosine of 0º = 1 and so the power factor = unity (1).

When the current is in quadrature with the voltage, the angle is 90º. The Cosineof 90º = 0 and so the power factor = zero (0).

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Because of considerations of automatic control over varying conditions, thepower factor in aircraft systems is kept well away from unity. It is usual to operateat power factors in the order of 0.75 or 0.8 on aircraft.

Power factor can be obtained from anything that gives the Cosine of the angle.For example, Power factor = R/Z (resistance divided by impedance).

It is also given by Power Factor =True Power

Apparent Power

It also follows that True Power = Apparent Power × Power Factor.


It has already been stated that it is not possible to have an ac circuit consistingonly of inductance, or only capacitance. There must be some resistance in eachof these circuits and this resistance can be thought of as being in series with theinductance, or in series with the capacitance. Of course, many circuits haveresistors deliberately inserted in series with the other components and somecircuits have all three components in series. It is these combinations of seriescircuits that we will now consider:


As L and R are in series, the current I is the same through each component. Thecurrent passing through the inductance gives rise to a potential across it, whichleads the current by 90º. At the same time, the voltage developed across theresistor is in phase with the current. As I is the common value in the circuit, it iscalled the ‘reference phasor’ and is usually drawn horizontally when drawing thephasor diagram. This is shown below, along with the circuit diagram.

The applied voltage V is the phasor sum of VL and VR and leads I by phase angle, which can be any angle between 0º and 90º depending upon the ratio of XL toR. If required, the phasor diagram could now be re-drawn with the supply voltageV in the horizontal position and showing the current lagging this voltage.

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Z(ohms) = R2 + XL2 = V/I = Total opposition to the flow of current.


As C and R are in series, the current through each component is the same. Thecurrent applied to the capacitance gives rise to a potential across the capacitancewhich lags the current by 90º. At the same time, the voltage developed acrossthe resistor is in phase with the current. As I is the common value in the circuit, itis called the reference phasor and is drawn horizontally when drawing the phasordiagram. This is shown below, along with the circuit diagram.

The applied voltage V is the phasor sum of VC and VR and lags I by the phaseangle , which can be any angle between 0º and 90º depending upon the ratio ofXC to R. If required, the phasor diagram could now be re-drawn with the supplyvoltage V in the horizontal position and showing the current lagging this voltage.In this instance:

Z(ohms) = R2 + XC2 = V/I = Total opposition to the flow of current


As in the paragraphs above, the current is again common all three componentsand so is used as the reference phasor when drawing the phasor diagram. Thiswill obviously be a combination of the two diagrams shown previously and isdrawn above, along with the circuit.

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In this example, XL is greater than XC and therefore VL is greater than VC.Resolution of the diagram results in the applied voltage V being shown to lead thecurrent I by phase angle . The circuit is therefore acting as though it wereinductive. The opposite effect would be obtained if XC was greater than XL andthe circuit would then act as though it were capacitive. In this instance, theimpedance (Z) is given by:

Z(ohms) =R2 + (XL - XC )2 = V/I = Total opposition to current flow


It has already been shown that XL varies directly with frequency and that XC

varies inversely with frequency. If therefore, the frequency applied to the abovecircuit was altered to decrease XL and at the same time increase XC, then at oneparticular frequency XL would be equal to XC. This frequency is called theresonant frequency and is denoted by the symbol fo. At the resonant frequency,the applied voltage and the circuit current are in phase, as shown in this phasordiagram below and the impedance of the circuit equals the resistance.

In a Series Circuit at Resonant Frequency (fO):



VL and VC are in antiphase and therefore cancel each other out.

VR = Applied Voltage V.

Z = R. The only opposition to the flow of current comes from the resistiveelement of the circuit, therefore current rises to a maximum value.

Because I is a maximum, this series resonant circuit is known as an‘acceptor circuit’.

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Also, because I is at a maximum value, VL and VC rise to very high values.They can be far higher than the supply voltage and can therefore be verydangerous. For this reason, it is very rare for this type of circuit to beoperated continuously at resonant frequency.

Because XL = XC, then 2 foL =1 1

2foC by transposition fo = 2 LC

If graph of current against frequency is made for a series circuit containingboth inductance and capacitance, the result is as shown below.


At resonance, VL and VC can rise to very large values and be greater than thesupply voltage. This is known as voltage magnification and given the symbol QO.Off resonance the magnification factor is represented by the symbol Q. The

amount of magnification is expressed by the fractions XLR

equals VL

, XC, VLR VS or VC which S

VR or VCR since VS = VR and is sometimes called the ‘Q’ factor of thecircuit.

Qo =XL






Thus QO2 =

And QO = 1R C


R 1



R2 × C

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The actual increase in voltage depends on the resistive element of the circuit.

Below fO the circuit is capacitive, at resonance it is resistive and above fO



Selectivity is the ability of a tuned circuit to respond strongly to its resonantfrequency and to give a poor response to nearby frequencies. A sharp responsecurve indicates high selectivity, a flat response curve indicates low selectivity.

High selectivity may be obtained by:

Either making XL and XC large, that is by using large L and small C, or in

other words using a large L C ratio.

This increases the circuit impedance off-resonance.

Or by making R smaller. This reduces Z at resonance.

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Therefore selectivity L, 1C , R

Since both selectivity and QO are proportional to L and inversely proportional to Cand R the QO may be used as a measure of selectivity.


The bandwidth (B) of a circuit is the difference between two frequencies eitherside of the resonant frequency at which the power has fallen to half its value atresonance, i.e. the half power points (these are also called the -3db points: seeDecibel notation later in the course). If the power has fallen to half its value atresonance, then since:

P I2


P2 2

P2 I2 × I2 (I2 = 0.707I)

The current has fallen to 0.707 of its value at resonance.

By definition Bandwidth (B) = f1 - f2

The narrower the bandwidth of a circuit, the higher the selectivity. Thusbandwidth may also be used as a measure of selectivity, as well as themagnification factor (QO).

fO A useful relationship is: B =QO

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The effects of connecting these three components in series was studied in theprevious section, they can however be connected in parallel. This section studiesthe effects of connecting the three components in parallel.


As with the series circuit, changes of frequency will again effect the inductivereactance and the capacitive reactance and there will again be one particular

frequency at which the two will be equal for a given capacitor and inductor. Thisis the resonant frequency of the circuit. The formula for this is the same as forthe series circuit, providing that the resistive element of the circuit is small. Atresonant frequency, the current circulating between the capacitor and theinductor is high, but the current drawn from the supply is low. This type of circuitis therefore commonly known as a ‘rejector circuit’.

The best way of understanding its operation is to imagine a capacitor and aninductor connect as shown in the diagram.

Imagine also that the capacitor is charged to a given voltage and that there is noresistance in the circuit. When the switch is closed, the capacitor will dischargethrough the inductor, transferring energy to it. The inductor field will thencollapse, charging the capacitor up in the reverse direction. This action willrepeat itself ad infinitum and the current will continue to circulate backwards andforwards at a natural frequency which, of course, is the resonant frequency of thecircuit. This ideal condition would need no external force to keep operating.

In practice, however, there must be some resistance in our circuit and so thecurrent will oscillate at resonant frequency, but will gradually die away as power islost across the resistance. In order to keep our circuit oscillating, it is onlynecessary to keep the circulating current ‘topped-up’ from the supply. Thecurrent drawn from the supply at resonant frequency is therefore very small. Atsupply frequencies less than resonance, the current through the inductorincreases and that through the capacitor decreases. The reverse occurs atsupply frequencies above resonance.

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If a graph is drawn of supply current (or line current, as it is sometimes known)against frequency, the result will be as shown below.

The very high impedance at resonanceassociated with parallel circuits is most

often used in the tuning circuits of radio ortelevision receivers. When tuned to aparticular frequency, that frequency will notpass through the parallel circuit. It istherefore available for the amplifier toamplify and use. All the other (unwanted)frequencies coming in at the aerial arepassed through the parallel circuit to thechassis, thereby by-passing the amplifier.At frequencies above resonance, thecircuit acts as though it were capacitiveand at frequencies below resonance, asthough it were inductive.


Unlike the series tuned circuit, the resistance does have an effect on the resonantfrequency of a parallel tuned circuit, the equation being:


fo =1 1

22 LC - L

However, if R is very small, the term involving resistance may be ignored and formost practical purposes the resonant frequency is given by:

1fo = 2 LC

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At resonance, the supply current (IS) is a minimum and is in phase with the

applied voltage. The value of the resonant current, as shown in the diagram

below, is given by VsZD or VsLR

In a Parallel Circuit at Resonant Frequency (fO):


VL = VC and are in antiphase and therefore cancel each other out

VR = Applied Voltage V.

L Z =

CR and current is a minimum.

Because the impedance is a maximum, the parallel resonant circuit is

known as a ‘rejecter circuit’.


The impedance of a parallel circuit can be calculated using the formula shown

below, although knowledge of this formula is not essential on this course.




12R X L XC

At resonance, the impedance is a maximum and called the dynamic impedance

(ZD) of the circuit. If the supply frequency is increased above or decreased below

fO then the circuit impedance will decrease.

The dynamic impedance is given by the equation: ZD =L


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In a parallel tuned circuit at resonance, current magnification occurs, that is IL andIC will be very large compared with IS. At any instant IL and IC act in the samedirection round the ‘internal’ circuit, and IS flowing in the ‘external’ circuit is thedifference between IL and IC. Thus, if IL and IC are large and very nearly equal, IS

will be small.

At any instant Kirchoff’s first law applies, that is:

IS = IL + LC

The circulating current is the smaller of the two currents (IL or IC) and IS is themake-up current.

Remember that QO for a series tuned circuit is its voltage magnification whereasQO for a parallel tuned circuit is its current magnification at the resonantfrequency.

QO = 1R C


Bandwidth is defined as the difference between two frequencies f1 and f2, oneeither side of resonance, at which the impedance has fallen to 0.707 of themaximum value.

As for the series circuit:

fO LBandwidth B = QO where QO = R C

If R is increased, or the ratio LC decreased, then the impedance at resonance isdecreased, QO is decreased and hence bandwidth increased.

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As for the series circuit, selectivity is the ability of the tuned circuit to respondstrongly to its resonant frequency and to give a poor response to nearbyfrequencies. Again, as for the series circuit, QO is used as a measure ofselectivity.

Below fO Above fO

1. Z small due to small 1. Z small due to smallXL XC

2. XC > XL 2. XL > XC

3. Thus IL > IC 3. Thus IC > IL

4. Thus circuit inductive 4. Thus circuit capacitive

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Transformers have no moving parts and are very efficient pieces of electricalequipment. Transformers operate by mutual inductance, the flux from one coil ofwire linking with another coil. Because the flux must be changing state, statictransformers can only be used on alternating current. In order for a transformerto be used on direct current, part of the transformer must be rotated.


The main elements of a power transformer are:

The primary and secondary windings

A laminated core and coil former

A mounting and terminal strip

The windings consist of insulated wire wound onto a former. The secondarywinding is generally wound on top of the primary winding, the two being

separated by a layer of insulating material. The wire gauge used depends on thecurrent rating of the transformer. The ends of both primary and secondarywindings are connected to the terminal strip for connection into the circuit.

The core is made up of thin strips of iron approximately 0·7mm to 3mm thick, thethickness being determined by the intended frequency of operation. Each sheetis insulated from the next. This laminated form of construction is used to preventeddy currents joining together and producing large circulating current within thecore.

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The core is invariably one of two types, core or shell. A core type core has ‘U’shaped and either ‘I’ or ‘L’ shaped laminations , staggered when assembled toprovide a single circular magnetic circuit. The windings may be wound on onelimb or split between the two. The laminations of a shell type core are usually‘T’ and ‘U’ shaped, staggered when assembled to produce a three-limbed core.When made for single phase operation, both windings are wound on the centrelimb, when made for three phase operation, each phase is wound on a separatelimb. Whilst more expensive, the provision of two magnetic paths make the shelltype former more suitable for large current use.

All of the energy transferred from the primary winding to the secondary must bestored in the magnetic field created in the core, therefore, sufficient iron must beprovided to store the energy of each half cycle of the a.c. waveform.

If the total power is kept the same, there will be less energy in half a highfrequency cycle than in half a low frequency cycle, therefore, the higher thesupply frequency, the smaller and lighter the transformer.


The basic symbol used for a transformer with one primary winding and onesecondary winding is as shown below. The two dots are used to indicate the

phase relationship between the two windings, the terminals marked with a dot arealways in phase with each other. In the diagram shown, when the top of the leftwinding is positive, the bottom of the right winding is positive and vice versa.

Whilst it should be understood that there is a phase shift of 180º between theprimary and secondary voltages, the polarity of the secondary winding (at anyinstant in time) with respect to the primary, depends purely on the way thetransformer is wound.

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To indicate the type of core material used, additional markings are added to thebasic transformer symbol. The core material is determined primarily by thefrequency of the supply on which the transformer is to be operated.

Three lines drawn between the primary and secondary windings on thetransformer below indicate that it has a laminated iron core. As such, the

transformer would be used at low frequencies and may be found on a.c. powersupply systems. The two coils drawn on the right show that this transformer hastwo secondary windings, and the dot notation indicates that these two windingsare wound in opposite directions. The top of one winding being positive whilst thetop of the other is negative.

The dashed lines drawn between the windings of the transformer below indicatethat it has a ferrite core and as such it would be used on medium to highfrequencies.

When there are no lines between the two windings, the transformer is air coredand as such would be used on very high frequencies (VHF) and above.

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Transformer losses are very small, 98% efficiency being easily attained, howeversome losses occur in all transformers. Generally the losses can be divided intothree groups; copper losses, iron or core losses and flux leakage losses.


Iron or core losses are divided into two groups; hysteresis and eddy current.

Hysteresis losses arise through continually magnetising and demagnetisingthe transformer core, the energy required for this is dissipated as heat.Hysteresis loss is dependent on the operating frequency and type of materialused for making the core. The higher the frequency, or the greater the fluxdensity within the core, the greater the loss. Transformers are thereforedesigned to operate on a specific frequency and the material used to make thecore has a narrow hysteresis loop. Typical materials used are stalloy,permalloy or mumetal.

Eddy current loss is due to the formation of eddy currents within thetransformer core, the energy again being dissipated as heat. Any metal

located within the field of a transformer has emf's induced in it, these emf'sproduce small circulating currents called eddy currents. The core of the

transformer is metallic and therefore has eddy currents flowing in it. Providingthe currents are small, loss is minimal, but if they are able to join together,large circulating currents are produced. These large circulating currents resultin a power loss, the loss being proportional to the square of the supplyfrequency.

Eddy currents are kept to a minimum by laminating the transformer core, thuspreventing the small eddy currents joining into large circulating currents.


Copper losses are the I2R losses in the windings. Part of the applied voltage isused to overcome the resistance of the primary winding, this reduces the fluxavailable for inducing an emf in the secondary winding. Also, when thesecondary circuit is connected, the secondary voltage falls due to the resistanceof the secondary winding.

Copper losses are dependent on the primary and secondary currents and theresistance of the windings and are independent of the supply frequency.

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Flux leakage losses as the name implies, result from the fact that not all of theprimary flux links with all of the secondary coils. The reduction in flux linkagesresults in a reduced secondary voltage. With modern production methods thisloss is negligible.


Another loss that occurs at high frequencies is caused by skin effect. Any currentcarrying conductor has a field around it. In a conductor carrying a.c. current, thefield expands from and collapses to the centre of the conductor, and alsochanges direction every half cycle. This alternating flux induces a back-emf inthe conductor. As the field is denser at the centre of the conductor, the back emfat the centre of the conductor is larger than the back-emf at the surface of theconductor. Consequently, the current tends to flow in the surface region of theconductor rather than the centre, almost as thought the cable were a hollow tube.The higher the frequency the greater the skin effect.

Although skin effect cannot be eliminated, the associated problems can bereduced by using Litz wire (multiple stranded cable - the current being dividedbetween the strands), or by reducing the resistance of the surface region of thecable, this can be achieved by silver plating the conductor.


A simple transformer consists of two coils, a primary and a secondary, wound ona high permeability, soft iron core. The changing current in the first coil creates achanging magnetic field that induces an alternating voltage in the secondary coil.

The size of the secondary voltage compared to the voltage applied to the primarydepends on turns ratio, or transformation ratio. That is, the number of turns ofwire in the secondary winding compared to number of turns in the primary.

If losses are small, the turns ratio may be expressed as:


VPr imary

N Secondary

NPr imary T (transformatio n ratio)

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If the number of turns on the secondary is less than the number of turns on theprimary, the output voltage will be less than the input voltage, and the transformeris called a step-down transformer.

If the number of turns on the secondary is greater than the number of turns on theprimary, the transformer is a step-up type and the output voltage will be greaterthan the input voltage.

By convention, when writing the transformation ratio, the secondary voltageis put before the primary, therefore a 4:1 transformer is a step-up transformer,the secondary voltage being 4 times the primary voltage.


If losses are ignored, the power in the secondary winding equals the power in theprimary winding.

IPrimary = ISecondary T

therefore: IPrimary VPrimary

but T = VSecondaryVPrimary

= ISecondary VSecondary

In practice there are some losses in a transformer and the output power cannever equal the input power.


A transformers efficiency, , is given by the ratio of output power to input power.

(eta) = output power 100%input power

The value of eta ranges from about 90% for small power transformers inreceivers, to 98-99% for large power transformers.


As the load on the secondary is increased, the output voltage falls. The amountby which the voltage falls is expressed as a percentage of the no-load voltage,and is termed the % regulation.

% regulation = no load voltage - full load voltage 100%no load voltage

Regulation of power transformers is generally less than 4%.

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In a practical transformer there are losses in theprimary winding due to; resistance, hysteresis andeddy currents. These losses produce a current flowwithin the primary winding that is in phase with theapplied voltage, and is termed loss current.

The iron core and coils of the primary winding makethe circuit highly inductive. The resistance of theprimary winding is by comparison very small. Themagnetising current therefore lags the appliedvoltage by 90 degrees.

The total current flowing in the primary, with the secondary winding off-load, is thevector sum of the magnetising current and the loss current.

Due to the large reactance of the primary circuit, the primary current is very small.If however, the transformer is operated at a lower than rated frequency, theinductive reactance will be less, and a larger primary current will flow, therefore,

transformers should not be operated below their rated minimum frequencywithout reducing the applied voltage.

It is the magnetising current that produces the primary field, and it is thisalternating field that induces an emf in the secondary winding. The induced emfdepends on the rate of change of flux, and therefore lags the primary field by 90.As the primary field already lags the applied (primary) voltage by 90, the emfinduced in the secondary winding will lag the applied voltage by 180. Thesecondary voltage is anti-phase with respect to the applied voltage.

When a load is connected to the transformer, a current is set up in the secondarywinding and a flux is produced. The secondary flux opposes the primary flux andeffectively decreases the inductance of the primary winding. If the appliedvoltage is kept constant, the decrease in inductance results in an increase in theprimary current. This increase in current is known as the load component ofprimary current.

The load current in the primary winding sets up a flux that is equal and oppositeto the secondary flux. The ampere turns of the primary flux equalling the ampereturns of the secondary flux.

NPrimary IPrimary = NSecondary ISecondary

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NSecondary= T (the transformation or turns ratio)

The total primary current is the vector sum of the no-load current and the load

current. The larger the secondary current, the larger the primary current. Under

normal conditions, the load current is so much larger than the no-load current that

the latter can be ignored.


If the load on the secondary is purely resistive, the

secondary voltage and secondary current are in

phase. The secondary current decreases the

inductance of the primary circuit and the primary

current increases, the increase being the load

element of primary current.

The load element of primary current is anti-phase

with respect to the secondary current and equal to

the secondary current the turns ratio. The primary

current consists of the vector sum of the no-load

and load current.

From the diagram it can be seen that the primary

voltage and current become more in phase as the

resistive load applied to the secondary is increased.

It appears as though the secondary load has been

reflected back into the primary winding.


If a purely inductive load is applied to the

secondary winding, the secondary current will

lag the secondary voltage by 90. The load

element of primary current, equal to the

secondary current T, will still be anti-phase

with respect to the secondary current and will

therefore be in phase with the magnetising


The primary current is again the vector sum of

the no-load and load currents. From the

diagram it can be seen that the primary current

now lags the applied voltage by almost 90.

Again it appears as though the load on the

secondary has been reflected back into the

transformer primary winding.

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If a purely capacitive load is applied to thesecondary, the load will again appear to bereflected back into the primary winding, andthe primary current will lead the appliedvoltage by 90.


Introducing resistance into the purelyinductive and capacitive circuits examined,simply has the effect of reducing the phaseangle between the primary voltage andcurrent. The greater the resistance, thegreater the reduction in the angle. Or putanother way. The more resistance there is inthe secondary circuit, the more in phase theprimary voltage and current.


The load placed on the secondary winding of a transformer always affects theprimary current by altering its phase angle in relation to the primary voltage.

Neglecting losses the reflected values of L / R / C can be shown to depend on thetransformation or turns ratio.

Iprimary Vprimary = Isecondary Vsecondary (1)

now Vsecondary = Isecondary Zsecondary (2)

where Z equals the load applied to the secondary winding. Substituting (2) in (1)

Iprimary Vprimary = I2secondary Zsecondary

NPrimarybut ISecondary = IPrimary NSecondary

2Nso 2I V I

primaryZprimary primary Primary 2Nsecondary


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therefore V Iprimary primary

N primary

2N secondaryZsecondary

But the effective impedance in the primary is given by:

Z primary






soZ primary



primaryZ secondary

N secondary

writing the transformation ratio NSecondary = TNPrimary

ZPrimary =1

T2 ZSecondary

ZPrimary = ZSeT2dary

T2 = ZSecondaryZPrimary

In a step down transformer T is less than unity and Z primary is greater than Zsecondary.

The fact that the impedance reflected from the secondary winding into theprimary winding depends on the transformers turns ratio, makes it useful forimpedance matching.


Maximum power is transferred from the source to the load only when the loadimpedance is equal to the internal impedance of the source. If this is not thecase, an impedance matching transformer can be used. The necessary turnsratio being calculated using the formula:

T2 = ZSecondaryZPrimary

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For example a transformer could be used to match a pre-amplifier of 20 000ohms input impedance to a moving coil microphone of 200 ohms. The turns ratiorequired would be calculated as follows:

T2 = ZSecondaryZPrimary = 20000200 = 1001

Therefore T = 10 = NSecondary1NPrimary


Auto transformers have only one winding, this serving as both the primary andsecondary. They may be used as "step up" or "step down" transformers.

When the primary terminals are connected to an a.c. source, current flowsbetween P1 and P2. The alternating flux produced, links with all of the turns on

the former, inducing a voltage in each. The output is taken from terminals S1 andS2.

The voltage ratio is calculated from the turns ratio:


VPrimary= NSecondaryNPrimary

In the step up transformer shown, the number of turns on the primary are thosebetween points A and B, the turns on the secondary, those between points A andC. If the transformer were a step down type, the input and output terminals wouldbe reversed.

The effects of different loads on the transformer are as for the power transformer,however it should be noted that the primary and secondary currents oppose eachother in the common portion of the winding. This enables smaller conductors tobe used in the common portion of the transformer, producing a weight saving,especially if the input and output voltages are almost the same.

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Auto transformers are used for:

line boosters to compensate for the voltage drops in long cable runs

motor starting. Several tappings being used in sequence to apply anincreasing voltage to the motor

impedance matching

to step the 115V a.c. aircraft supply down to 26V for lighting circuits

The major disadvantage of auto transformers, especially step down types, is thatshould the common portion of the winding go open circuit, the primary voltage isapplied directly to the load on the secondary. It was for this reason thatautotransformers were rarely used on aircraft, however, improved reliabilitythrough modern manufacturing methods has made them increasingly morecommon.


Mutual reactors or Quadrature transformers are devices that have been knownabout for many years, however, until the introduction of constant frequency, little use was made of them.

In order to detect the difference between the real and reactive loads on an a.c.generator, there was a requirement for a device that produced a voltage signal,that was at 90 to the current being sensed in a circuit.

For all practical purposes this is achieved in a mutual reactor or quadraturetransformer. When a current is passed through the primary winding, the voltageacross the secondary lags the primary current by almost 90.

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In order to explain the operation of a mutual reactor, it is necessary to examinethe "off-load" vector diagram of a basic power transformer. Under no-loadconditions a small, lagging current flows in the primary winding. If an air-gap iscut in the former, the reluctance of the magnetic circuit is increased and morecurrent is required to magnetise the core. The magnetising element of theprimary current lags the primary voltage by 90. Therefore, as the magnetisingcurrent is increased, the total "no-load" current is increased and moved arounduntil almost at 90 to the primary voltage. It also follows that the primary currentleads the secondary voltage by almost 90.

In understanding the mutual reactor it is best to forget the applied voltage, andremember that, the voltage across the secondary will be in quadrature (at 90)with any current passed through the primary winding.

When physically examining a quadrature transformer it looks very much like apower transformer. The air-gap has to be of optimum size and is normallylocated under the windings. Unlike power transformers, mutual reactors can onlybe used to produce signal voltages and cannot be used supply a load.


Current transformers (CT's) are designed to enable circuit currents to bemeasured without breaking the circuit. The outputs are applied directly to

instruments, or used in control circuits. Although working on the same principlesas power transformers their construction and operation are vastly different.

Some have a primary winding comprising a few turns of wire capable of carryingthe load current that is to be measured, others known as bar primary currenttransformers use the load supply cable as the primary. The bar primary type ismore common on aircraft.

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The secondary former consists of a continuous strip of metal wound on itself toform a ring, although not laminated in the true sense, this gives the effect oflaminations. The secondary winding is toroidally wound on the former, with thetwo ends brought out for connection to the load. When a power transformer isdesigned, the designer only needs to know the:

supply on which the transformer will operate

the output voltage required

maximum current that the transformer will be expected to supply

This is not the case with a CT. A CT is designed to operate on one particularload, if a different load is attached, it will give a false indication. The CT designerneeds to know the load and the supply source, and then designs a CT to link thetwo together.

When writing the turns ratio, the primary is written before the secondary, theopposite to a power transformer. A 400:1 CT will have 1 ampere flowing in itssecondary winding and load, if 400 amps is flowing through the primary cable. Abar primary counts as a single turn.

When a current passes through the supply cable it causes a magnetic field alongits entire length, this flux induces an emf into the coils of the secondary winding.The ring former and the secondary winding only take up a very short length of theprimary conductor, therefore whatever happens to the secondary will havevirtually no effect on the primary.

The voltage induced in the secondary winding causes a current to flow through itsload, this produces a secondary flux that opposes the primary flux, keeping thecore flux to a very low level.

If the primary is operated with the secondary disconnected from its load, there willbe no secondary flux to oppose the primary flux, this results in; a high core flux,increased eddy currents, and increased voltages in the individual secondary coils,which can result in the CT overheating and burning out. Even if the CT isswitched off before it burns out, the core may become pre-magnetised or biased,resulting in an inaccurate output. If it is necessary to operate a CT off-load, thesecondary terminals must be shorted.

If a CT is supplying a load such as an ammeter, the polarity of the connectionsmay not matter, this is not however the case when used in control circuits. If theconnections are crossed, or the CT is fitted the wrong way around on the primary,the output is phase shifted by 180. This will cause control circuits to operate inthe opposite sense.

A CT should never be operated on anything other than its designed load, in someinstances the CT and its load are a matched pair and may have the same serialnumber, in this case they must be changed as a pair.

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Although it is possible to use three, interconnected, single phase transformers forthree phase a.c. it is more common to use a single, three limbed, transformer.Using a three limbed transformer, the primary and secondary windings for eachphase are allocated a single limb.

Once the layout of the transformer has been established, it is only necessary todecide how to interconnect the primary and secondary windings. There are fourpossible alternatives:

The preferred methods of connection are the last two, however, the requirementsof the circuit must come first.

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Linear variable differential transformers (LVDT's), rotary variable differentialtransformers (RVDT's) and E and I bar transducers all use transformer principlesto produce electrical signals from mechanical movement. The magnitude of thesignals produced is dependent on the amount of movement, and the phase of thesignal on the direction of movement. All three devices are used in controlsystems, and will be studied in more detail in module 4.

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Filter circuits are four terminal networks designed to pass a band of frequenciesfrom the input to the output terminals, and to filter-off or attenuate, the remainingunwanted frequencies present at the input terminal. Such circuits are made fromcapacitors and inductors whose reactance changes with change in frequency.

Filter circuits take four main forms:

High pass

Low pass




High pass filters allow all frequencies above a certain cut-off frequency to bepassed from the input terminals to the output terminals. All frequencies below thecut-off frequency are filtered off or attenuated. The diagrams above show asimple high pass filter together with its circuit symbol.

The capacitor C allows the high frequencies to pass onto the output terminals, butoffers a high reactance to the low frequencies. The inductance L offers a lowreactance to low frequencies, so they are filtered off through it, but it offers a highreactance to the high frequencies and thus does not filter them off. A typicalattenuation/frequency graph for a simple high pass filter is shown below.

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In practice a number of high-pass filter circuits are used in succession (cascade)as shown. This improves the attenuation of the lower frequencies and so the cut-off region becomes more abrupt and clearly defined.


Low pass filters allow all frequencies below a certain cut-off frequency to bepassed from the input terminals to the output terminals. All frequencies abovethe cut-off frequency are filtered off or attenuated. The circuit symbol and anattenuation / frequency graph for a simple low pass filter are shown below.

In this circuit, L offers a low reactance to the low frequencies, allowing them topass easily onto the output terminals, but offers a high reactance to the higherfrequencies. The capacitor C offers a low reactance to the high frequencies, sothey are filtered off through it, but it offers a high reactance to the required lowfrequencies and therefore does not attenuate them appreciably.

In practice a number of these filter circuits are used in succession. This improvesthe attenuation of the higher frequencies, and so the cut off region becomes moresharply defined.

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These circuit be passed onto theoutput termin ove and below this

band. A simp

Rejecter circuit L1 C1 and acceptor circuit L2 C2 are tuned to the same frequency,the centre frequency of the required band. No mutual coupling exists between L1

and L2.

The acceptor circuit offers low impedance to the resonant frequencies andpasses them onto the output terminals, but offers high impedance to all the otherinput frequencies. The rejecter circuit offers low impedance to the unwantedfrequencies either side of the band and so they are filtered off through it. Thecircuit symbol and attenuation / frequency curve for a band pass filter are shownbelow.

A more practical band pass filter circuit is shown above. This ' type' band passfilter circuit will give more clearly defined cut off regions.


These circuits pass onto the output terminals all frequencies except a certainnarrow band which is attenuated or filtered off. The circuit below is a simplebandstop filter.

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Acceptor circuit L1C1 and rejecter circuit L2C2 are tuned to the same frequencies;the midpoint frequency of the unwanted band. No mutual coupling existsbetween L1 and L2.

The rejecter circuit offers low impedance to all the required frequencies andtherefore passes them onto the output terminals, but it offers a high impedance tothe unwanted band of frequencies.

The acceptor circuit L1C1 offers a low impedance to the unwanted band offrequencies and so they are filtered off through it. The acceptor circuit offers highimpedance to the wanted frequencies and so, does not attenuate themappreciably.

The circuit symbol and frequency / attenuation graph for a simple band stop filterare shown below.

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A more practical ' type' band stop filter is shown above, again this will give moreclearly defined cut-off regions.


Smoothing and Decoupling circuits are special applications of filters.

A smoothing circuit changes a pulsating d.c. to a smooth d.c. in power supplycircuits. In order to achieve this, the filter circuit offers a high reactance to a.c.and a low reactance to d.c.

A Decoupling circuit removes any unwanted a.c. from a d.c. voltage. Such acircuit offers a high reactance to d.c. and a low reactance to a.c.

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When a source is connected to and supplying power to a load, it may benecessary to reduce the voltage, current or power in the load. This process iscalled ‘attenuation’.

Attenuation can be achieved by adding a resistor in series with the load. Theaddition of the attenuator section (ABCC) in the circuit below, results in the loadvoltage and current being reduced by half, and the power in the load beingreduced to a quarter.

This simple method of attenuation however causes a mismatch. To the source,(terminals AC) the load appears to be 180. The load (terminals BC) sees apower source with an internal impedance of 180. For proper matching, thesupply should see a load of 60 and the load should see a supply with aninternal impedance of 60.

This mismatch may cause a deterioration in the performance of the source and/orload, eg; the frequency response may be affected, particularly where impedanceswith reactance are involved.

To avoid mismatch, an attenuator must match the load and the sourceimpedances, ie; the source must ‘see’ an impedance equal to its own internalresistance and the load must ‘see’ an impedance, looking back into theattenuator, equal to its own value. Such attenuators are called matchingattenuators and different types now follow, although only the first will beexamined in the course.

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If the output terminals of the circuit above are open-circuited, the impedanceacross the input terminals AC is 100 (Ra and Rc in series) or Zoc.

If the output terminals are short-circuited, the impedance at the input terminals is36 (Ra plus parallel combination Rb and Rc) or Zsc.

The impedance of the input terminals can be any value between 36 and 100,depending on the load placed across BC. The geometric means of these valuesis equal to:

ZSC x ZOC = 36 x 100 = 60

and is called the ‘characteristic impedance (Zo) of the network.

By suitable choice of resistor values, a network with any value of characteristicimpedance can be built.

The significance of Characteristic Impedance may be seen if the ‘T’ typeattenuator above is connected between the source and the load in the firstdiagram. This arrangement is shown below, with the appropriate values ofvoltage, current and power shown.

The source (of 60 internal resistance) will ‘see’ a load of 60, ie; it will bematched (Load + Rb in parallel with 80, in series with Ra = 60).

Looking back, the load will ‘see’ an impedance of 60, ie; will be matched(Source resistance + Ra in parallel with 80, then in series with Rb = 60).

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Action. Across the input terminals AC, the impedance is 60: 60V , and 601AWatts is applied as input power to the attenuator. However, at the load, the

power has reduced to 15 W (30V × 0.5A) i.e. one quarter of the input power. (Inunits of decibels, which will be discussed later in the course, this is a reduction of6 dBs). The source and load are matched; only a controlled reduction of power,voltage and current has occurred at the load. Being matched, the performance ofthe source and the load has not been affected in any other way.


Two identical attenuators may be used to reduce the input power by 1/16 at theload. i.e. attenuation of 12 dBs. Such an arrangement is below.

It will be seen that the input power is progressively reduced and that theimpedance at each of the junctions X, Y and Z is the same. Calculated valuesare shown in the table below.

Voltage Current Impedance Power

At X 60V 1A 60 60W

At Y 30V 0.5A 60 15W

At Z 15V 0.25A 60 3.75W

Any number of such sections may be added to give the required attenuation. Theextra sections may be switched in, to give manual control of the amount ofattenuation.

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Fine adjustment of an attenuator may be achieved by having a section with allthree resistors variable as shown below. If the attenuator resistors were changedto the values

Ra = 36 ; Rb = 36 ; Rc = 32

The impedances across AC and BC would be 60 as before.

If Ra and Rb were varied from 20 to 36 and at the same time Rc is varied from80 to 32, the attenuator would reduce the input power from 1/4 to 1/16 at the

load, i.e. attenuation would vary from 6dBs to 12dBs, whilst the impedances seenby the load and the source would remain constant.


In the type attenuator, the components are arranged to form the Greek letter (Pi), as shown below. The same general principles apply to this network, as tothe T type.

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All the attenuators shown so far have a common line (the bottom line in thediagrams), such as earth.

These networks are said to be ‘unbalanced’ because the voltages in each line aredifferent due to the different impedances in each line.

In a balanced network, the two lines have equal anti-phase voltages andtherefore should have equal impedances in each line. Balanced attenuators areshown below.


Functional diagram symbols for a fixed loss attenuator (pad) and a variableattenuator are shown below.

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The generation of an alternating current has already been examined in thesection on d.c. generation. The rules concerning the size of the generated emfand the direction of current flow are as previously described.

Instead of a commutator being used to ensure the current flows in one directionthrough the load, the load is connected via slip rings and the current flow isalternating, as shown below.

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The instantaneous value of emf induced in the loop is given by:

e(instant)= E(max) sin

where E(max) = lv and is the angle of the conductor with respect to thefield.


Referring back to our simple single loop generator, it can be seen that, if the loopwere to rotate at 120 revolutions per second, the output frequency would be 120Hz. It therefore follows that the frequency of the output of an ac generator isdirectly proportional to its speed of rotation.

Another factor which determines the output frequency of an a.c. generator is itsphysical construction. A generator with 4 field poles will produce two completecycles of output for each revolution of the shaft.

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Similarly, a generator with six field poles will produce three complete cycles foreach revolution and so on. A cycle is complete whenever a conductor haspassed under the influence of two dissimilar magnetic poles.

So the output frequency of an ac generator is given by:

Frequency = Revolutions per second × No. of pairs of poles

The speed of rotation is normally given in revolutions per minute (rpm), thereforethe output frequency is actually calculated from using:

Frequency = NP60

Where: N is the speed of rotor rotation in RPM

P is the number of pairs of poles

From the foregoing, it will be seen that one cycle is completed in:

360 mechanical degrees for a two-pole machine,

180 mechanical degrees for a four-pole machine,

120 mechanical degrees for a six-pole machine,

90 mechanical degrees for an eight-pole machine, and so on.

It is therefore necessary to use electrical degrees when referring to angularmotion in the cycle. One cycle = 360 (electrical) degrees. It is not usual to usethe word ‘electrical’ in this respect, but the concept should be clearly understood.


When a resistive load is placed on an a.c. generator, armature reaction occurs. Ifthe generator is a rotating field type, the field is distorted against the direction ofrotation as shown below. If the load is increased, armature reaction is increasedand the field is distorted further.

A resistive load also places a physical load on the generator causing it to slowdown, this results in both the output frequency and voltage decreasing. The onlyway to restore the output is to provide more drive torque to overcome the extraload.

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If an inductive load is placed on an a.c. generator, the current in the stator lagsthe voltage by 90, causing the stator field to move around 90. The stator fieldnow opposes the main field, resulting in a weaker main field and a reduction inoutput voltage.

The voltage is restored by increasing the field current, however this doesgenerate additional heat in the machine.


If a capacitive load is placed on an a.c. generator, the stator field is advanced by90 and now assists the main field, this increases the main field strength andincreases the generators output voltage.

This can be corrected without adverse affects, by decreasing the field current.

Most aircraft systems have inductive loads and a lagging power factor.

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There are two types of alternating current generator, a rotating field type and arotating armature type. These names stem from the way they are bothconstructed. Although the rotating field type generator is the one mostcommonly used for the production of a.c. power on aircraft, both types will be metlater in the course.


A rotating armature generator is constructed in a similar manner to a d.c.generator. The field is located on the stationary part of the machine (stator) andthe emf is induced in windings located on a rotating armature (rotor). The outputis then taken from the generator using slip rings as previously described.


It is possible however, to obtain the same output by rotating the field insidestationary armature (stator) windings located around the frame of the machine.The output is then taken from the stationary armature.

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This type of generator is called a ‘rotating field generator’. It has severaladvantages over the rotating armature type:

Because the output windings are now stationary they are no longer subject tohigh centrifugal forces and can therefore be larger.

By having the output windings on the outside of the machine there is moreroom for good insulation and higher voltages can be used.

With the output windings on the outside of the machine they are more easilycooled and can therefore carry larger currents.

Using a rotating field only requires the use of two slip rings and two brushes,also the current required is relatively small.

These advantages mean a larger output can be obtained from a smaller machine.


A single phase a.c. generator consists of a single output winding wound on a pairof stationary poles and a rotor fitted either with a permanent magnet or anelectromagnet. The electromagnet is energised from a d.c. supply via twobrushes and slip rings.

When the rotor is driven, emf's are induced in the stator windings. When theoutput windings are connected to a load, load current flows. The output

frequency is dependent on the speed of rotor rotation and the number of poles onthe rotor.

If the generator shown was rotated at the same speed, but had two pairs of fieldpoles, the frequency would double.

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A two phase generator has two output windings wound on separate pairs of polespositioned 90 degrees apart as shown. A single, common rotor comprising apermanent or electromagnet is still used.

The 90 angle between the to two output windings means that when maximumemf is induced in one winding, zero emf is induced in the other winding and viceversa.

The output from the generator will be two voltages of equal amplitude andfrequency, but phase displaced from each other by 90.


A three phase a.c. generator has three sets of output windings, each physicallydisplaced from the other two by 120. The rotor is the same as that used in asingle phase or two phase generator.

The Three phase a.c. generator is really three single phase generators on onestator, all using a common field. Due to the construction of the machine, theemf's generated in each of the windings is phase displaced by 120 degrees, asshown below.

The normal order of rotation is:

Red Yellow Blue

1 2 3


If two phases are reversedthen motors and controlcircuits will try to operate inreverse.

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If required, the three single phases can be used independently, however this isnot common practice. The windings are normally connected together in one oftwo ways, called star or delta. Whether star or delta depends on the way thewindings are connected at the generator output terminals.


The three armature windings of a three phase generator can be connected in twoways. Firstly, the end of one winding can be connected to the start of the next, sothat the three windings are connected in series to form a triangle. This form ofconnection if called a Delta system. The delta system is a three wire system, asingle wire being taken from each of the three points of interconnection.

The alternative, is to connect the same end of each armature winding to acommon point and take the other end of each winding to an output terminal. Thisform of connection is called a Star system. The star system is a four wire system,as a wire is also taken from the common point to an output terminal.

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A Delta system is a three wire system,one wire coming from each of thearmature winding interconnectionpoints. In a delta connected system:




A delta connected system has no neutral line and is generally used on smallgenerators supplying virtually fixed, balanced loads. Balanced loads

If the currents in each phase are equal in size and phase displaced from oneanother by 120 degrees, the loads are said to be balanced. Under balancedconditions, the loads on each phase are identical Symmetrical loads

If the phase voltages are the same in magnitude, and phase displaced from oneanother by 120 degrees, the system is said to be symmetrical. Aircraft systemsare naturally symmetrical.


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Although a star connected system is considered to be a four wire system, if theloads are balanced, the neutral line need not be connected. The neutral line onlycarries out of balance currents.

The neutral, although connected to earth, should not be confused with the earthin a three pin mains plug which is there for protection. Under the majority ofconditions, a star connected aircraft power system will have current flowing in theneutral line.

The voltage from the neutral line, or star point, to the other end of each phasewinding is called the phase voltage, the voltage from one phase to another iscalled the line voltage.

In a star connected system:



The frequency is always expressed as the frequency of a single phase.

In aircraft a.c. systems, the phase voltage is 115V and the line voltage is 200V.On some aircraft systems the frequency is variable (wild), however, on themajority of modern aircraft, the frequency is kept constant at 400 Hz.

With a star connected a.c. power system, two possible systems are available:

three single phase systems each operating at the phase voltage

a single three phase system operating at line voltage

If the instantaneous values of two phases are added together to produce a linevoltage and the process is repeated for the other phases, three line voltages willbe produced. Each line voltage is displaced 120 degrees from the other two.One point to note is that, there is a 90 degree phase angle between a phasevoltage and its opposite line voltage, this relationship is used in several aircraftcontrol and monitoring systems.


In star and delta connected systems, the power dissipated in each phase is givenby the formula:

PPhase = VPhase x IPhase Cos Watts

If the system is balanced and symmetrical then the total power is three times theabove value.

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With few exceptions, the operation of an a.c. motor relies on the production of arotating magnetic field, therefore, we will examine the production of a rotatingfield first.


Alternating current supplies are generally available in one of three forms, singlephase, two phase or three phase. Any of these three supplies can be used toproduce a rotating magnetic field, but there are differences in how it is achieved,so they will be examined individually.


To produce a rotating field from a single phase a.c. supply requires a minimum oftwo pairs of field windings and a four pole stator, as shown below. However, asingle phase supply connected to the windings shown, will only produce analternating field positioned at 45 degrees to the pole pieces.

To create a rotating field, the current in one pair of field windings must be 90degrees out of phase with the current in the other pair of field windings. This canbe achieved by placing an inductor or capacitor in series with one pair of fieldwindings, whilst connecting the other directly to the supply. A capacitor isgenerally used because it is more efficient.

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The direction of rotation of the magnetic field depends on the order in which thepoles become magnetised.

The direction of rotation of the field can be reversed either by swapping thesupply to one pair of field windings, or by switching the capacitor from one fieldwinding to the other. The latter method is often used on aircraft motors.

If the supply to both field windings is reversed, the motor will run in the samedirection.


To produce a rotating field from a two phase supply also requires a minimum offour field poles and two pairs of field windings. A two phase supply comprisestwo voltages phase displaced from one another by 90 degrees. Therefore nocapacitor is required.

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The only way to reverse the direction of rotation of such a motor is to swap thepower supply connections to one pair of field windings.

A two phase supply can be obtained from a three phase a.c. supply, byusing one phase voltage and the opposite line voltage.


To produce a rotating field from a three phase a.c. supply requires the use of asix pole stator and three pairs of field windings. The stator of a three phase a.c.motor is the same as that of a rotating field a.c. generator.

The direction of rotation of the field depends on the order in which the windingsare energised. To reverse the direction of rotation, it is only necessary to swapthe connection to any two of the field windings.


The two main types of a.c. motor used on aircraft systems are the induction motorand the synchronous motor. Hysteresis and shaded pole motors are howeveroften found in instruments, and as they are both a.c. motors, they will also beexamined at this time


The rotor of an induction motor consists of a number of copper or aluminium barsconnected by two end rings to form a cage. The cage is enclosed in a laminatediron core to reduce its reluctance. This construction is very simple but verystrong.

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When the rotor is placed in a rotating magnetic field, the bars are cut by therotating flux, causing emf's to be induced in them, because the bars are shortedby the end rings, currents then flow in the bars. Current flow in the bars producesa magnetic field around them, which reacts with the main field of the machine,causing the rotor to turn.

At switch-on, the emf's induced in the rotor bars are at the same frequency as thesupply voltage and because the circuit is highly inductive the current lags thevoltage by almost 90 degrees. This means, that by the time the rotor field hasbeen produced, the main field has moved on by almost 90 degrees and the rotorfield can only react with the trailing edge of the main field, resulting in a smallstarting torque.

As the rotor speed increases, the frequency of the emf's in the rotor decrease,reducing the inductive reactance. The brings the current more in-phase with theinduced emf's, producing a good running torque.

It is not possible for the rotor to rotate at synchronous speed (the speed of thefield), because there would be no emf’s induced in the rotor bars, no current flowand no magnetic field produced. The difference between synchronous speed androtor speed is called ‘slip speed’ and is usually expressed as a percentage ofthe synchronous speed.

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When running, the field around the rotor bars induces an emf into the statorwindings, this ‘back-emf’ is almost 180 degrees out of phase with the applied

voltage and therefore opposes it, resulting in a small effective voltage across thefield and a low current drawn from the power supply. If the load on the motor isincreased, it slows down, this causes the phase angle of the back-emf to change,increasing the effective voltage, the current from the supply and the motor torque.The increase in motor torque accelerates the motor back to its original runningspeed.

When first started, the back-emf is almost at 90 degrees to the applied voltageand therefore not opposing the supply voltage. The effective voltage is thereforealmost equal to the supply voltage and the current demand is high. In order toreduce the starting current, some motors are designed to be started with the fieldwindings connected in star and run with them connected in delta. This increasesthe impedance during starting and reduces the current drawn from the supply, butit does not improve the poor starting torque.

If it is required that an induction motor be started ‘on-load’, then the poor startingtorque must be improved. To achieve this, the rotor current must be made toappear more in phase with the voltage. This can be achieved by increasing theresistance of the rotor windings, however, if the resistance is left in the rotorcircuit once the motor is running, there will be:

an increase in the slip speed

a greater speed variation with load changes

an increase the current taken from the supply

A compromise often used on aircraft induction motors is to fit a second, highresistance, cage into the rotor. This gives an improved starting torque, withminimal running problems.


The synchronous motor gets its name from the fact that the rotor runs atsynchronous speed (the speed of the field), for it to do this, the rotor must be apermanent magnet or an electro-magnet.

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In order for the magnet to lock-on to the field, it must be brought up to about 75%of synchronous speed, to achieve this the majority of synchronous motors havethe cage of an induction motor built into them. The motor starts as an inductionmotor and when sufficient speed has been attained, the electromagnet isenergised, allowing the rotor to lock onto the field. Once running, no emf's areinduced in the rotor bars, however, they are useful in holding the rotor and rotorwindings in place and also assist in smooth running during load changes.

The rotor, although running at synchronous speed, will lag behind the field, theangle of lag is proportional to the load placed on the motor.

If whilst running the load is increased, the angle of lag increases, changing theangle of the back-emf and increasing the effective voltage. This increase ineffective voltage increases the current taken from the supply, producing anincrease in torque to cope with the load increase. Should the angle become toogreat, the magnetic link will snap, the motor will run down, stop, and possibly burnout due to the high current taken from the supply as a result of the loss of backemf.


The shaded pole motoruses only a single set ofpoles to create theappearance of a rotatingmagnetic field. The polesare each cut into twosections. One section ofeach pole is then shadedby a copper or aluminiumring, or a shorted coil.

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When the field winding is energised, an alternating flux appears across the mainpoles. The alternating main field induces emf's in the shaded ring or shortedwinding and causes a current flow within it that produces a second alternatingmagnetic field. The field in the shorted ring lags the main field by approximately90 degrees. The overall effect is to produce a field that appears to move throughan angle determined by the relative positions of the two sections of each mainpole. The field is not fully rotating, only moving through a small angle, thereforethe starting torque is low and the motor can only be used for small, fixed loads.

The operation of the rotor is as for an induction motor.


The construction of hysteresis motors vary. The motor is so named because thematerial used for the rotor has a large hysteresis loop. This type of motorrequires a two phase a.c. supply and is often used as a servo motor, one phasebeing supplied from a reference source, the other from a control circuit. Thecurrent in the control phase is made to either lead or lag the reference phase by

90 degrees, depending on the direction of rotation required.

The motor shown employs a cobalt steel ring rotor. When the field is energised,a North pole appears at A and a South pole at A1. Poles B and B1 are notmagnetised. The field across A-A1 induces a South pole in the rotor at X and aNorth pole in the rotor at Y.

As the supply changes, A and A1 die away as B becomes a North pole and B1becomes a South pole. The retention of flux by the rotor causes the south pole atX to be attracted by the North pole at B and the North pole at Y to be attracted bythe South pole at B1. This causes the rotor to rotate. As the rotor moves to alignwith the field, the field has moved on, so the rotor moves again to try and align.The rotor continues to rotate following the field.

If the phase of the control supply is reversed (made to lag the reference supplyinstead of lead it), the motor will change direction

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