-
Issue 1 - 1 January 2002 Page 1
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
Index
1 DC GENERATION
........................................................................
1-1
1.1 SIMPLE SINGLE LOOP GENERATOR
........................................... 1-2 1.1.1 Induced emf
........................................................... 1-2
1.1.2 Output frequency
................................................... 1-3
1.2 COMMUTATION
......................................................................
1-3
1.3 RING WOUND GENERATOR
...................................................... 1-4
1.4 PRACTICAL DC GENERATOR
.................................................... 1-7 1.4.1
Construction
........................................................... 1-7
1.4.2 Lap wound generator
............................................. 1-9 1.4.3 Wave wound
generator .......................................... 1-10 1.4.4
Internal resistance
.................................................. 1-11 1.4.5
Armature reaction
.................................................. 1-11 1.4.6
Reactive sparking
.................................................. 1-13
1.5 GENERATOR CLASSIFICATIONS
................................................ 1-15 1.5.1 Series
generator .................................................... 1-15
1.5.2 Shunt generator
..................................................... 1-16 1.5.3
Self excitation
......................................................... 1-16
1.5.4 Compound generator
............................................. 1-17
2 DC MOTORS
................................................................................
2-1
2.1 SIMPLE SINGLE LOOP MOTOR
.................................................. 2-2
2.2 COMMUTATION
......................................................................
2-2
2.3 PRACTICAL DC MOTORS
.......................................................... 2-3
2.3.1 Construction
........................................................... 2-3
2.3.2 Back emf
................................................................
2-3 2.3.3 Starting d.c. motors
................................................ 2-3 2.3.4
Torque....................................................................
2-4 2.3.5 Armature reaction
.................................................. 2-4 2.3.6
Reactive sparking
.................................................. 2-4 2.3.7 Speed
control .........................................................
2-4 2.3.8 Changing the direction of rotation
.......................... 2-5
2.4 MOTOR CLASSIFICATIONS
....................................................... 2-5 2.4.1
Series motor
........................................................... 2-6
2.4.2 Shunt motor
........................................................... 2-7
2.4.3 Compound motor
................................................... 2-9 2.4.4 Split
field motor ......................................................
2-9
2.5 RATING
.................................................................................
2-10
3 STARTER GENERATORS
........................................................... 3-1
4 AC THEORY
.................................................................................
4-1
-
Issue 1 - 1 January 2002 Page 2
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
4.1 PRODUCTION OF A SINEWAVE
.................................................. 4-1
4.2 THE SINEWAVE
......................................................................
4-2 4.2.1 Peak and Peak-to-Peak values
.............................. 4-3 4.2.2 Average values
...................................................... 4-3 4.2.3
RMS values
............................................................ 4-4
4.2.4 Form Factor.
........................................................... 4-4
4.2.5 Periodic time
.......................................................... 4-4
4.2.6 Frequency
.............................................................. 4-4
4.2.7 Angular Velocity.
.................................................... 4-5 4.2.8
Phase Difference (Angular Difference). .................. 4-5
4.3 PHASOR OR VECTOR DIAGRAMS
.............................................. 4-6 4.3.1 Addition
of phasors ................................................ 4-7
4.4 ADDITION OF AC & DC
.............................................................
4-8
4.5 MEASURING AC USING OSCILLOSCOPES
................................... 4-8 4.5.1 The cathode Ray
oscilloscope ............................... 4-8 4.5.2 Types of
oscilloscopes ........................................... 4-11
4.5.3 using the oscilloscope
............................................ 4-15
4.6 OTHER TYPES OF WAVEFORMS
................................................ 4-27 4.6.1 Square
waves ........................................................ 4-27
4.6.2 Triangular or sawtooth waves ................................
4-27
4.7 AC VOLTAGE & CURRENT
........................................................ 4-28 4.7.1
Resistive loads
....................................................... 4-28 4.7.2
Capacitive loads
..................................................... 4-28 4.7.3
Inductive loads
....................................................... 4-30 4.7.4
Impedance
.............................................................
4-31
4.8 AC POWER
............................................................................
4-32 4.8.1 Resistive loads
....................................................... 4-32 4.8.2
Inductive loads
....................................................... 4-33 4.8.3
Capacitive loads
..................................................... 4-34 4.8.4
The total load on a generator .................................
4-35 4.8.5 Apparent Power & actual current
........................... 4-35 4.8.6 True power & Real
Current .................................... 4-36 4.8.7 Reactive
power & reactive current ......................... 4-37 4.8.8
Power Factor
.......................................................... 4-37
4.9 SERIES L/C/R CIRCUITS
........................................................... 4-38
4.9.1 Inductance and resistance in series .......................
4-38 4.9.2 Capacitance and resistance in series
..................... 4-39 4.9.3 Inductance, capacitance and
resistance in series .. 4-39 4.9.4 Series resonance
................................................... 4-40 4.9.5
Voltage magnification .............................................
4-41 4.9.6 Selectivity
...............................................................
4-42 4.9.7 Bandwidth
..............................................................
4-43
4.10 PARALLEL L/C/R CIRCUITS
....................................................... 4-44
-
Issue 1 - 1 January 2002 Page 3
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
4.10.1 Inductance and capacitance in parallel ..................
4-44 4.10.2 Parallel resonance
................................................. 4-45 4.10.3
Impedance
............................................................. 4-46
4.10.4 Current magnification
............................................. 4-47 4.10.5 Bandwidth
.............................................................. 4-47
4.10.6 Selectivity
...............................................................
4-48
5 TRANSFORMERS
........................................................................
5-1
5.1 POWER TRANSFORMERS
........................................................ 5-1
5.2 CIRCUIT SYMBOLS & DOT CODES
............................................. 5-2
5.3 LOSSES
................................................................................
5-4 5.3.1 Iron losses
.............................................................. 5-4
5.3.2 Copper losses
........................................................ 5-4 5.3.3
Flux leakage losses ...............................................
5-5 5.3.4 Skin Effect
..............................................................
5-5
5.4 TURNS RATIO
........................................................................
5-5
5.5 POWER TRANSFERENCE
......................................................... 5-6
5.6 TRANSFORMER EFFICIENCY
.................................................... 5-6
5.7 TRANSFORMER
REGULATION...................................................
5-6
5.8 APPLYING LOADS TO A TRANSFORMER
..................................... 5-7 5.8.1 No load conditions
................................................. 5-7 5.8.2
Resistive loads
....................................................... 5-8 5.8.3
Inductive load
......................................................... 5-8 5.8.4
Capacitive load
...................................................... 5-9 5.8.5
Combination loads .................................................
5-9
5.9 REFLECTED IMPEDANCE
......................................................... 5-9
5.10 IMPEDANCE MATCHING TRANSFORMERS
.................................. 5-10
5.11 AUTOTRANSFORMERS
............................................................
5-11
5.12 MUTUAL REACTORS
...............................................................
5-12
5.13 CURRENT TRANSFORMERS
..................................................... 5-13
5.14 THREE PHASE TRANSFORMERS
............................................... 5-15
5.15 DIFFERENTIAL TRANSFORMERS
............................................... 5-16
6 FILTERS & ATTENUATORS
........................................................ 6-1
6.1 FILTERS
................................................................................
6-1 6.1.1 High pass filters
..................................................... 6-1 6.1.2 Low
pass filters ......................................................
6-2 6.1.3 Band pass filters
.................................................... 6-3 6.1.4 Band
stop filters .....................................................
6-4 6.1.5 Smoothing & decoupling circuits
............................ 6-5
6.2 ATTENUATORS
......................................................................
6-6 6.2.1 T type attenuator
.................................................. 6-7 6.2.2 Two
section attenuator ...........................................
6-8
-
Issue 1 - 1 January 2002 Page 4
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
6.2.3 Variable attenuators
............................................... 6-9
6.2.4 '' type attenuators
................................................. 6-9 6.2.5
Balanced & unbalanced networks .......................... 6-10
6.2.6 Attenuator symbols
................................................ 6-10
7 AC GENERATION
........................................................................
7-1
7.1 PRINCIPLES
...........................................................................
7-1 7.1.1 Output voltage
........................................................ 7-2 7.1.2
Output frequency
.................................................... 7-2 7.1.3
Effects of a resistive load .......................................
7-3 7.1.4 Effects of an inductive load
.................................... 7-4 7.1.5 Effects of a
capacitive load ..................................... 7-4
7.2 PRACTICAL GENERATOR CONSTRUCTION
.................................. 7-5 7.2.1 Rotating armature type
........................................... 7-5 7.2.2 Rotating
field type .................................................. 7-5
7.2.3 Single phase generator
.......................................... 7-6 Two phase generator
.......................................................... 7-7
7.2.5 Three phase generator
........................................... 7-7
7.3 STAR & DELTA SYSTEMS
......................................................... 7-8 7.3.1
Delta connection
.................................................... 7-9 7.3.2 Star
connection ......................................................
7-9 7.3.3 Power in ac systems
.............................................. 7-10
8 AC MOTORS
................................................................................
8-1
8.1 PRODUCTION OF A ROTATING FIELD
......................................... 8-1 8.1.1 Single phase
.......................................................... 8-1
8.1.2 Two phase
.............................................................. 8-2
8.1.3 Three phase
........................................................... 8-3
8.2 TYPES OF AC MOTOR
.............................................................. 8-3
8.2.1 Induction motor
...................................................... 8-3 8.2.2
Synchronous motor ................................................
8-5 8.2.3 Shaded pole motor
................................................. 8-6 8.2.4
Hysteresis motor
.................................................... 8-7
-
Issue 1 - 1 January 2002 Page 1-1
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
1 DC GENERATION
If a conductor is moved at right angles to a magnetic field, an
emf is induced in the conductor. If an external circuit is then
connected to the conductor a current will 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 Flemings 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
-
Issue 1 - 1 January 2002 Page 1-2
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
1.1 SIMPLE SINGLE LOOP GENERATOR
In its simplest form, a generator consists of a single loop of
wire rotated between the poles of a permanent magnet. The rotating
part of the machine is called the rotor or armature, it is
connected to the stationary external circuit via two slip rings,
thus allowing a current flow.
1.1.1 INDUCED EMF
As the loop rotates an emf is induced in both sides of the
conductor. Using Flemings right hand rule, it can be seen that the
resultant currents flow in opposite directions on each side, but in
the same direction around the loop.
-
Issue 1 - 1 January 2002 Page 1-3
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
An emf is only induced in a conductor when it is moved at right
angles to the lines of flux in a magnetic field. Therefore, the
loop will only have an emf induced in it when it is moving at right
angles to the lines of flux, when moving parallel with the lines of
flux, no emf will be induced. At any direction in between, there
will be a proportion 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 lines of flux.
As the loop passes the neutral point, the conductors direction
of travel through the field reverses. The conductor that was moving
upwards through the field is now moving downwards, therefore, the
emf's induced in the conductors must change direction, as must the
resultant current flow.
1.1.2 OUTPUT FREQUENCY
As the loop rotates, the emf rises to a maximum in one
direction, then falls to zero and then rises to a maximum in the
opposite direction, before once again falling to zero. One complete
revolution is one cycle, the loop having returned to its start
position.
The number of cycles per second gives the frequency. The faster
the loop is rotated, the more cycles per second and the higher the
frequency. In this simple generator the frequency depends on the
number of loop revolutions per second.
The output from this generator changes polarity every time the
loop rotates 180 degrees and is therefore of little use as a direct
current generator.
1.2 COMMUTATION
In order to make the current flow in the same direction through
the load, the connections to the external circuit must be switched
every time the loop moves past its neutral position. This can be
achieved using a commutator.
The commutator is used in place of the slip rings and connects
the rotating loop to the stationary external circuit.
-
Issue 1 - 1 January 2002 Page 1-4
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
A commutator has 2 functions:
Firstly, to transfer current from the rotating loop to the
stationary external circuit.
Secondly, the periodic switching of the external circuit to keep
the current flowing in the same direction through the load.
Switching takes place when the 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 as shown above.
Although current now flows in the same direction through the
external circuit, it is still of little practical use, because the
voltage and current fall the zero twice every cycle. Using several
loops and a multi-segment commutator, a more constant output can be
produced.
1.3 RING WOUND GENERATOR
The simple construction of the ring wound generator makes it
ideal for explaining the operation of a multi-coil machine.
The rotor consists of a laminated iron cylinder onto which is
wound 8 equally spaced coils. The junction between each pair of
coils is connected to a segment of the commutator. The number of
segments equals the number of coils, this being true for all d.c.
generator armature windings.
-
Issue 1 - 1 January 2002 Page 1-5
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
The brushes are drawn inside for clarity and are positioned so
that when they short circuit a coil, that coil is moving parallel
to the magnetic field and has no emf induced in it.
The metal used for the rotor has a very low reluctance,
therefore the flux of the main field flows through it, rather than
through the airgap in the centre. The parts of the coils on the
inside of the rotor are therefore not cutting any flux and have no
emfs induced in them.
The low reluctance rotor creates a radial field in the airgap as
shown above. The radial field means that the conductors are moving
at right angles to the flux for a longer period of time and are
therefore producing maximum emf for longer. This results 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 being connected in series, because one set of
four coils is moving up through the main field and the other set is
moving down through the field, the emf's induced in each set of
four coils is in the opposite direction, but it is in the same
direction with respect to the brushes.
-
Issue 1 - 1 January 2002 Page 1-6
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
The emf induced in four coils is as shown below. The emf in the
other four coils is 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 on it.
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 is wasted because it has no emf
induced in it.
-
Issue 1 - 1 January 2002 Page 1-7
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
1.4 PRACTICAL DC GENERATOR
1.4.1 CONSTRUCTION
The size and weight of generators vary considerably, but all are
constructed in a manner similar to that shown above.
The field assembly consists of a cylindrical frame, or yoke,
onto which the pole pieces are bolted. Generators generally have at
least four pole pieces, although small machines may have only two.
Wound around each pole piece is a field coil. The yoke has a low
reluctance and provides a path for the main field of the machine.
To reduce eddy currents the yoke is usually laminated.
The armature core also provides a path for the main field and is
therefore also of low reluctance and laminated.
-
Issue 1 - 1 January 2002 Page 1-8
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
The armature windings are located in slots cut in the core,
being wedged in with insulation to prevent them being thrown out by
centrifugal forces. The coils are normally 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 the next main pole of the opposite polarity.
The emf induced in each side of the coil is again in opposite
directions, but assisting around the coil. This type of winding is
called a drum winding and has the advantage that the coils can be
wound and insulated before being fitted into the rotor. There are
two types of drum winding, Lap wound and wave wound.
The armature windings are connected to risers attached to the
commutator. The commutator consisting of copper segments separated
by mica insulation.
The brush gear assembly consists of a holder and rocker. The
holder allows the brushes to slide up a down, whilst preventing
them from moving laterally. The rocker allows the brushes to be
rotated around the commutator so they can be positioned on the
magnetic neutral axis.
-
Issue 1 - 1 January 2002 Page 1-9
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
It should be noted that the output power from a d.c. generator
is governed primarily 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 that blows or
draws air through the generator. The cooling system may use ram air
from a propeller slipstream or from movement of the aircraft
through the air, or more commonly, a fan attached to the rotor
shaft of the generator.
1.4.2 LAP WOUND GENERATOR
In a lap wound generator, the end of each coil is bent back to
the start of the next coil, the two ends of any one coil being
connected to adjacent segments of the commutator (see diagram
above). This form of construction is used on large heavy current
machines. The number of parallel paths for current always equals
the number of brushes and the number of field poles (see
diagram).
-
Issue 1 - 1 January 2002 Page 1-10
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
1.4.3 WAVE WOUND GENERATOR
In a wave wound generator, the end of each coil is bent forward
and connected to the start of another coil located in a similar
position under the next pair of main poles (see diagram above). The
two ends of one coil are connected to segments two pole pitches
away. This type of machine has two parallel paths and uses only two
brushes irrespective of the number of poles (see diagram).
This type of winding is used in smaller machines and is
therefore more common on aircraft generators.
-
Issue 1 - 1 January 2002 Page 1-11
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
1.4.4 INTERNAL RESISTANCE
A d.c. machine has resistance due to the:
armature windings
brushes
brush to commutator surface contact
This is called internal resistance and can be measured across
the terminals of the generator.
For the purposes of calculation, the internal resistance is
represented as a single value in series with the generated emf.
Internal resistance causes the generators terminal voltage to
vary with changes in the load current. As the load current
increases, the voltage dropped across the internal resistance
increases and the terminal voltage decreases.
The generated emf E = Ir + V
1.4.5 ARMATURE REACTION
When armature current is flowing, a field is produced around the
armature conductors. The overall field of the machine is then
produced by interaction between the main field and the armature
field.
-
Issue 1 - 1 January 2002 Page 1-12
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
The armature field is at 90 degrees to the main field of the
machine and therefore distorts it as shown below.
This distortion of the field is called armature reaction and has
the effect of weakening 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 a weakening of the field and a reduction in the
generators output voltage. Distortion of the field also means that
the magnetic, or electric neutral axis is moved around in the
direction of rotation, away from the machines geometric neutral
axis. When the brushes now short an armature coil, it is no longer
at the point where zero emf is induced in it, therefore the brushes
must be moved. The position they are moved to depends on the size
of the armature current, the greater 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 armature and fitted into slots cut in the pole faces of
the main fields.
When armature current flows, current flows in the compensating
windings and produces 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 and restoring the overall strength of the
machines field.
-
Issue 1 - 1 January 2002 Page 1-13
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
1.4.6 REACTIVE SPARKING
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 to right. After leaving the
brush, current will be flowing at maximum value in the opposite
direction through the coil, as shown in coil B. Whilst the coil is
shorted by the brush, the current must drop to zero ready for it to
go to maximum value in the opposite direction when it comes off the
brush.
Unfortunately, the coil has inductance, when shorted, a back emf
is produced that tries to maintain current flow. When the coil
comes off the brush, the current has not reduced to zero, resulting
in an excess of current that jumps as a spark from the commutator
to the brush. The sparking produced is called reactive
sparking.
Not all sparking at the commutator is reactive sparking, sparks
may also be caused by:
worn or sticking brushes
incorrect spring tension
commutator flats
proud mica
-
Issue 1 - 1 January 2002 Page 1-14
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
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 to collapse to zero during
commutation. However, increasing the resistance of the brushes
produces a power loss and increases the overall resistance of the
machine. The increase in internal resistance causes greater
fluctuations in output voltage with changes in load current.
1.4.6.1 EMF Commutation
Another way of overcoming reactive sparking is to use emf
commutation. The purpose of emf commutation is to neutralise the
reactance voltages that lead to reactive sparking. One way of
achieving this is to advance the brushes beyond the magnetic
neutral axis, this means the coils are under the influence of the
next main 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 will reduce it, reducing the reactance voltage reduces
the current in the coil and allows time for it to drop to zero
whilst the coil is shorted.
Unfortunately, advancing the brushes is only good for one value
of armature current, if the current increases, the brushes must be
advanced further.
Advancing the brushes also increases the demagnetising effects
of armature reaction.
A better way of applying emf commutation is to fit commutating
or interpoles between the main poles of the machine. Interpoles
have the same polarity as the next main pole and are connected in
series with the armature.
The interpoles induce emfs in the short circuited coils that
exactly cancels the back emf, thus allowing the current to fall to
zero instantly. Being in series with the armature means that the
reactance voltage is always eliminated irrespective of the value of
armature current.
By careful design, the interpoles can also be used to eliminate
armature reaction in the interpole region.
-
Issue 1 - 1 January 2002 Page 1-15
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
1.5 GENERATOR CLASSIFICATIONS
Generators are usually classified by the method of excitation
used. There are three classifications; permanent magnet, separately
excited and self excited.
A permanent magnet generator has a limited output power and an
output voltage that is directly proportional to speed.
A separately excited generator has its field supplied from an
external source. The output 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 may be subdivided into three
sub-groups; series, shunt and compound.
1.5.1 SERIES GENERATOR
The series generator has a field winding consisting of a few
turns of heavy gauge wire connected in series with the
armature.
On "No-load" there is no armature current and therefore no field
current. The only voltage generated is due to residual magnetism
within the fields.
As the load current increases, the field current increases and
the terminal voltage rises, the increase in voltage more than
compensating for the loss due to armature reactance and internal
resistance. The voltage continues to rise until saturation of the
field occurs.
A series generator therefore has a rising characteristic and is
generally only used as a line booster.
-
Issue 1 - 1 January 2002 Page 1-16
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
1.5.2 SHUNT GENERATOR
The shunt generator has a field consisting of many turns of fine
wire connected in parallel 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 and armature reactance.
The shunt generator has a falling characteristic and is used for
d.c. generation on aircraft.
1.5.3 SELF EXCITATION
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
magnetism.
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 a d.c. generator is to reverse the polarity of
the residual magnetism. If the supply to the field winding, or the
drive direction is reversed, the excitation will oppose the
residual magnetism and the field will be lost.
-
Issue 1 - 1 January 2002 Page 1-17
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
1.5.4 COMPOUND GENERATOR
Compound generators have both series and shunt field windings
and fall into one of two categories:
differential compound generators, in which the two fields are
wound so as to oppose each other.
cumulative compound generators, in which the fields are wound so
as to assist each other.
Differential compound generators are generally used where a high
initial voltage is required, but only a low running voltage.
Devices such as arc welders or arc lighting may use this form of
generator.
Cumulative compound machines can be wound to produce over, level
or under compounding. Under compounding is more common in aircraft
generators, the output voltage falling as the load current is
increased.
-
Issue 1 - 1 January 2002 Page 1-18
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
Blank Page
-
Issue 1 - 1 January 2002 Page 2-1
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
2 DC MOTORS
If a current carrying conductor is placed at right angles to a
magnetic field, a force will 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 using Flemings left hand rule as shown below:
-
Issue 1 - 1 January 2002 Page 2-2
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
2.1 SIMPLE SINGLE LOOP MOTOR
The simplest form of motor consists of a single loop of wire
able to rotate between the poles of a permanent magnet.
If current is applied to the loop through slip rings, a motor
torque will be produced, and the loop will start to rotate.
As the loop rotates past vertical, the current appears to change
direction, this causes the torque to change direction, so the
direction of rotation changes.
When the loop passes vertical, the current appears to change
direction again, causing rotation to revert to its original
direction.
If left, the loop will simply oscillate back and forth either
side of the vertical position.
2.2 COMMUTATION
To make the loop rotate, the current must be made to change
direction as the loop passes the vertical position, this is
achieved using a commutator and brushes.
When current is applied to the loop a motor torque is produced
and the loop starts to rotate. When the loop is vertical no
rotational torque is produced, however, momentum keeps it moving.
At the vertical position, the direction of current in the loop is
reversed by the commutator, so that as the vertical position is
passed, the torque produced is in the original direction, thereby
maintaining rotation.
-
Issue 1 - 1 January 2002 Page 2-3
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
To improve the torque and produce smoother running, more loops
or coils are added to the armature, each having its own commutator
segment. The construction is as described earlier in d.c.
generators.
2.3 PRACTICAL DC MOTORS
2.3.1 CONSTRUCTION
Direct current generators are constructed in the same manner as
d.c. generators, therefore further description is unnecessary. The
similarities are such that one machine can be operated as the other
with only minimal adjustment. In the case of 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, but are 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 the ability of the machine to dissipate heat. Cooling
may be natural, by convection and 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 are moving in a magnetic field
and therefore must have an emf induced in them, this emf acts
against the applied voltage and is called back emf.
The resultant of the two voltages is called the effective
voltage. The armature current is due to the effective voltage, not
the applied voltage.
When running, the back emf is almost equal to the applied
voltage, therefore the effective voltage and the current taken from
the supply are both small.
2.3.3 STARTING D.C. MOTORS
On starting, the rotor is stationary and therefore producing no
back emf, this results 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 removed from
the circuit once the motor is running.
-
Issue 1 - 1 January 2002 Page 2-4
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
2.3.4 TORQUE
The torque produced by a d.c. motor is directly proportional to
the armature current and the magnetic field strength.
T = IARMATURE
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.
2.3.5 ARMATURE REACTION
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 moved around in the opposite direction to that of the
generator, against the direction of rotation. The problem can be
overcome as in d.c. generators, by fitting compensating
windings.
2.3.6 REACTIVE SPARKING
d.c. motors also suffer from reactive sparking. For fixed load
motors, the problem is overcome simply by moving the brushes onto
the magnetic neutral axis. For variable load motors, interpoles are
used as in d.c. generators.
2.3.7 SPEED CONTROL
The effects of back emf make a d.c. motor a self regulating
machine. If the load is increased, load torque exceeds motor torque
and the motor slows down, the reduction in speed causing a decrease
in back emf and an increase in the effective voltage across the
armature. The increase in effective voltage causes an 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 by controlling the armature current.
-
Issue 1 - 1 January 2002 Page 2-5
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
2.3.7.1 Field control
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 large change in the armature current. Of course, this
cannot continue uncontrolled because eventually the field will be
lost. Field control is generally used for speed control of normal
running speed and upwards.
2.3.7.2 Armature control
With armature control, an increase in armature current causes an
increase in motor torque over load torque and an increase in motor
speed. A decrease in armature current causes a decrease in motor
speed. Armature control is generally used for control of normal
running speed and downwards.
2.3.8 CHANGING THE DIRECTION OF ROTATION
To change the direction of rotation it is only necessary to
change the direction of the main field or the armature current. If
both are changed, the motor will rotate in 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 the notes, suffice to say
it has two fields windings, one for clockwise rotation, the other
for anti-clockwise rotation.
2.4 MOTOR CLASSIFICATIONS
The construction of d.c. motors is the same as d.c. generators,
with armatures being either wave wound or lap wound.
Motors are also classified in a similar way to generators -
shunt, series and compound. Each type having its own operating
characteristics and uses.
-
Issue 1 - 1 January 2002 Page 2-6
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
2.4.1 SERIES MOTOR
A series motor has a low resistance, heavy gauge field winding
in series with the armature winding. On light loads its speed is
high, the armature current is low and the field is weak. On heavy
loads. speed is low, the armature current is large and 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. In series motors the field strength depends on
the armature current, so the torque produced is approximately
proportional to the square of the armature current. In practice it
is slightly less (particularly on heavy loads) due to armature
reaction and saturation of the magnetic circuit.
As speed increases, the torque decreases, until the load torque
and motor torque balance. If the load of a series motor is removed,
the speed may become dangerously 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, the initial current being limited by the combined
resistance of the field and armature windings and by the inductance
of field winding. The field strength builds up quickly, giving a
high starting torque, a fast acceleration and a rapid back-emf
build 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 engine starting, a starter resistor is initially connected
in series with the motor and removed when the motor is required to
increase speed. The starter resistor must be 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 motor rotation to be quickly reversed. Applications include
fuel valves and landing lights.
-
Issue 1 - 1 January 2002 Page 2-7
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
2.4.2 SHUNT MOTOR
Shunt wound motors have a high resistance field winding
connected in parallel with the armature. The field current will be
constant if the input voltage is constant and no field control
resistor is used.
When the load torque is increased, the motor slows down. The
decrease in speed, causes a fall in the back-emf and an increase in
armature current which produces more motor torque. When the motor
torque and load torque are again balanced, 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 a low resistance armature is small
enough for it to be considered a constant speed motor. With a high
resistance armature, there is a more noticeable variation in speed
with load.
When a shunt motor has a constant input voltage:
on light loads, the magnetic field is constant and the torque is
directly proportional to the armature current.
on heavy loads the magnetic field is reduced by armature
reaction and the torque does not rise in direct proportion to the
armature current.
If a shunt motor does not increase speed when connected to the
supply, then no back-emf is produced. This results in a very high
armature current, a large armature 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
-
Issue 1 - 1 January 2002 Page 2-8
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
A low resistance shunt motor is normally started with a variable
resistor, set to maximum resistance, placed in series with the
armature. This reduces the armature 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 running speed it is totally removed from
the circuit.
An automatic method used to insert a resistor is series with the
armature for starting, and to remove it once the back-emf has been
developed is referred to as a 'T Start circuit.
At the instant the motor is switched on, the armature is
stationary and producing no 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 A starts to increase.
At a pre-determined speed the potential at point A and the
current through the relay coil will be sufficient to cause the
relay to energize, removing the resistor from the armature
circuit.
Speed control - The speed of a shunt motor is normally
controlled by a variable resistor placed in series with the field
winding. When the resistance is increased, the field current is
reduced, the back-emf decreases and the effective voltage
increases. The increase in effective voltage produces an increase
in armature current and an increase in speed. When required to
reduce the speed of the motor, the field resistance is
decreased.
Separately excited shunt motors - Separately excited d.c. shunt
motors have the same operating characteristics as self excited
shunt motors and therefore require no additional consideration.
Applications - Shunt motors are used where a constant speed is
required and will be found in inverter drives and windscreen
wipers.
-
Issue 1 - 1 January 2002 Page 2-9
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
2.4.3 COMPOUND MOTOR
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
2.4.4 SPLIT FIELD MOTOR
In certain applications it is necessary to change the direction
of rotation of a motor. 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 field current, however,
there is also a special form of reversible series motor known as a
split field motor.
A split field motor is simply a series motor with two field
windings. The fields are wound 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 shown
above.
The circuit above is in fact that of an actuator and includes
not only a split field motor, 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 limit switch 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.
-
Issue 1 - 1 January 2002 Page 2-10
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
When it is required that the actuator drive to position 2, the
selector switch is moved to position 2. Current flows through the
field winding, brake solenoid and armature winding. The brake is
released and the motor starts to turn. As soon as the motor moves,
it is no longer in position 1, so switch A moves across. This
allows 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, brake solenoid and armature are energised. The brake
is released and the motor runs in the opposite direction towards
position 1. Again as soon as the motor turns, it is no longer at
position 2 so the lower switch moves over to contact the field
winding.
2.5 RATING
Most motors have a rating - a limit on performance or operation.
Ratings take various forms - output, time, speed, altitude. As with
generators, the output depends very much on the machines ability to
dissipate heat. All machines require some form of cooling. Low
output motors, or those that are not used for continuous operation
may be cooled naturally. Others may be fitted with centrifugal or
straight fans to drive air through machine, this being usual on
small machines. Others use air ducted from slipstream.
-
Issue 1 - 1 January 2002 Page 3-1
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
3 STARTER GENERATORS
Many gas turbine aircraft are equipped with starter-generator
systems. These starting systems use a combination starter-generator
which operates as a starter motor 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 an additional heavy series winding. This
series winding is electrically connected to produce a strong field
and a resulting high torque for starting.
Starter-generator units are desirable from an economical
standpoint, since one unit performs the functions of both starter
and generator. Additionally, the total weight of starting system
components is reduced, and fewer spare parts are required.
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 similar manner to a
direct-cranking starter, since all the of the windings used during
starting are in series with the source. While acting as a starter,
the unit makes no practical use of its shunt field. A source of 24
volts and 1,500 amperes is usually required for starting.
When operating as a generator, the shunt, compensating and
interpole windings are used. The output voltage is controlled in
the conventional manner, by connecting the shunt field in the
voltage regulator circuit. The compensating and interpole windings
provide almost sparkless commutation from no-load to full-load.
-
Issue 1 - 1 January 2002 Page 3-2
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
The following diagram illustrates the external circuit of a
starter-generator with an undercurrent controller. This unit
controls the starter-generator when it is used as a starter. Its
purpose is to ensure positive action of the starter and to keep it
operating until the engine is rotating fast enough to sustain
combustion. The control block of the undercurrent controller
contains two relays; one is the motor relay 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 to close the engine master switch. This completes
the circuit from the aircraft's bus to the start switch, the fuel
valves, and the throttle relay. Energising the throttle relay
starts the fuel pumps, and completing the fuel valve circuit
provides the necessary fuel pressure for starting the engine.
-
Issue 1 - 1 January 2002 Page 3-3
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
When the battery and start switches are turned on, three relays
close. They are the motor relay, ignition relay and battery cut-out
relay. The motor relay closes the circuit from the power source to
the starter motor; the ignition relay closes the circuit to the
ignition units; and the battery cut-out relay disconnects the
battery. On this particular aircraft opening the battery circuit is
necessary because the heavy drain of the starter motor would damage
the battery, this is not the general case. The majority of aircraft
are designed to be started using the battery so as to make the
aircraft independent of ground resources, the battery will however
be disconnected from the bus when ground power is connected and
care must be taken to ensure the ground power unit is capable of
supplying the current required by the starter motor.
Closing the motor relay allows a very high current to flow to
the motor. Since this current flows through the coil of the
undercurrent relay, it closes. Closing the undercurrent relay
completes a circuit from the positive bus to the motor relay coil,
ignition relay coil, and battery cut-out relay coil. The start
switch is allowed to 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 action breaks the circuit from the
positive bus to the coils of the motor, ignition and battery
cut-out relays. The de-energising of these relay coils halts the
start operation.
After the procedures described are completed, the engine should
be operating efficiently and ignition should be self-sustaining. If
however, the engine fails to reach sufficient speed, the stop
switch may be used to break the circuit from the positive bus to
the main contacts of the undercurrent relay, thereby halting the
start operation.
On a typical aircraft installation, one starter-generator is
mounted on each engine gearbox. During starting, the
starter-generator unit functions as a d.c. starter motor until the
engine has reached a predetermined self-sustaining speed. Aircraft
equipped with two 24 volt batteries can supply the electrical load
required for starting by operating the batteries in a series
configuration.
The following description of the starting procedure used on a
four-engine turbojet aircraft equipped with starter-generator units
is typical of most starter-generator starting systems.
-
Issue 1 - 1 January 2002 Page 3-4
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
Starting power, which can be applied to only one
starter-generator at a time, is connected to a terminal of the
selected starter-generator through a corresponding starter relay.
Engine starting is controlled from an engine start panel. A typical
start panel (see diagram below) contains an air start switch and a
normal start switch.
The engine selector switch shown has five positions ('1, 2, 3,
4, and off'), and is turned to the position corresponding to the
engine to be started. The power selector switch is used to select
the electrical circuit applicable to the power source being used
(ground power unit or battery). The air-start switch, when placed
in the "normal" position, arms the ground starting circuit. When
placed in the "air-start" position, the igniters can be energised
independently of the throttle ignition switch. The start switch,
when in the "start" position, completes the circuit to the
starter-generator of the engine selected, and causes the engine to
rotate. The engine start panel shown above also includes a battery
switch.
When an engine is selected with the engine selector switch, and
the start switch is held in the "start" position, the starter relay
corresponding to the selected engine is energised and connects that
engine's starter-generator to the starter bus. When the start
switch is placed in the "start" position, a start lock-in relay is
also energised. Once energised, the start lock-in relay provides
its own holding circuit and remains energised providing closed
circuits for various start functions.
An overvoltage lockout relay is provided for each
start-generator. During ground starting, the overvoltage lockout
relay for the elected start-generator is energised through the
starting control circuits. When an overvoltage lockout relay is
energised, overvoltage protection for the selected started-
generator is suspended. A bypass of the voltage regulator for the
selected starter-generator is also provided to remove undesirable
control and resistance from the starting shunt field.
-
Issue 1 - 1 January 2002 Page 3-5
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
On some aircraft a battery lockout switch is installed in the
external power receptacle compartment. When the door is closed,
activating the switch, the ground starting control circuits
function for battery starting only. When the door is open, 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 starting voltage of 48 volts. The
large voltage drop which occurs in delivering the current needed
for starting, reduces the voltage to approximately 20 volts at the
instant of starting. The voltage gradually increases as the starter
current decreases with engine acceleration and the voltage on the
starter bus eventually approaches its original maximum of 48
volts.
Some multi-engine aircraft equipped with starter-generators
include a parallel start relay in their starting system. After the
first two engines of a four-engine aircraft are started, current
for starting each of the last two engines passes through a parallel
start relay. When starting the first two engines, the starting
power requirement necessitates connecting the batteries in series.
After two or more generators are providing power, the combined
power of the batteries in series is not required. Thus, the battery
circuit is shifted from series to parallel when 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 throttle ignition 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
the power selector, to energise the battery series relay, which
connects the aircraft batteries in series to the starter bus.
Energising the No 1 engine's starter relay directs power from
the starter bus to the No. 1 starter-generator, which then cranks
the engine.
At the time the batteries are connected to the starter bus,
power is also routed to the appropriate bus for the throttle
ignition switch. The ignition system is connected to the starter
bus through an overvoltage relay, which does not become energised
until the engine begins accelerating and the starter bus voltage
reaches about 30 volts.
As the engine is turned by the starter to approximately 10%
r.p.m. the throttle is advanced to the "idle" position. This action
actuates the throttle ignition switch, energising the igniter
relay/ When the igniter relay is closed, power is provided to
excite the igniters and fire the engine.
When the engine reaches about 25 to 30% r.p.m., the start switch
is released to the "off" position. This removes the start and
ignition circuits from the engine start cycles, and the engine
accelerates under its own power.
-
Issue 1 - 1 January 2002 Page 3-6
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
Blank Page
-
Issue 1 - 1 January 2002 Page 4-1
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
4 AC THEORY
4.1 PRODUCTION OF A SINEWAVE
The only practical way of generating an electromotive force
(emf) by mechanical means is to rotate a conductor in a magnetic
field. As the conductor rotates in the magnetic field, its
direction of motion relative to the magnetic field is continually
changing, therefore, the emf induced in the conductor is
continuously changing. The emf will start at zero when the
conductor is moving parallel with the lines of flux, it will rise
to a maximum value when the conductor is moving at 90 to the lines
of flux, before decaying back to zero rising to a maximum value in
the opposite direction. In this way, an alternating emf is produced
which, when connected 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 ac generator.
All generators, both dc and ac, have this basic design. In a dc
machine the output 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 is continually reversing it
direction.
-
Issue 1 - 1 January 2002 Page 4-2
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
If the generated emf of the loop is measured and plotted as the
loop rotates, the result 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 cutting the 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 part
below the line is labelled negative.
4.2 THE SINEWAVE
If the conductor is rotated at uniform speed in a uniform
magnetic field, the output waveform is said to be sinusoidal and we
refer to this type of waveform as a sine wave. There are many other
wave shapes that can be generated or developed, but it is the sine
wave that is used for main power supply systems. It is therefore
necessary for the engineer to be very familiar with this particular
waveform and he is expected to be able to remember and use the
various figures and formulae associated with it.
The wave generated is called a sine wave because its amplitude
(height) at any instant can be calculated from sine tables, i.e. by
plotting the sines of all angles between 0 and 360.
When the conductor has completed 360 of rotation, it is said to
have completed one cycle.
-
Issue 1 - 1 January 2002 Page 4-3
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
4.2.1 PEAK AND PEAK-TO-PEAK VALUES
Amplitude values and their calculation apply equally to current
and voltage measurement.
The Peak or Maximum Value. The maximum value attained by the
wave in either 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 maximum in the other direction is called the Peak-to-Peak
value. It must not be confused with peak value, which is measured
in one direction only. Peak-to-peak values are often used on
oscilloscopes because it is easier to measure from top to bottom of
the waveform, but the majority of calculations require the use of
the peak value. It must be remembered to divide the peak-to-peak
value by two in order to obtain the peak value for
calculations.
The Instantaneous Value. As previously stated, the value at any
instant can be calculated by multiplying the peak value by the sine
of the angle (from 0) through which the conductor has rotated.
4.2.2 AVERAGE VALUES
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 as far positive as it does negative) If the
pulses of voltage or current are always in one 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
-
Issue 1 - 1 January 2002 Page 4-4
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
4.2.3 RMS VALUES
Whilst the Peak and Average values of ac have their place and
uses, they are not a lot of use for everyday work on ac. What is
required is a value of ac which relates to an equivalent value of
dc. Suppose an electric fire is operating with 5 amperes of d.c.
current flowing through it and it is giving out a certain amount of
heat. We want to know the value of a.c. which will produce the same
amount of heat. 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 heat when passed through a given resistor. To produce the
same heating effect, in the 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, if peak or average values are being referred to,
then the word peak (Pk) or average (Av) must be added after the
value.
4.2.4 FORM FACTOR.
The form factor of a waveform is a number which indicates its
shape:
Form Factor = rms value average value
For a sine waveform, this works out at 0.707 / 0.637 = 1.11. For
any other waveform, 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 engineer should not have to
concern himself with the form factor).
4.2.5 PERIODIC TIME
The time taken to complete one cycle is called the periodic time
(t). It is measured in seconds or fractions of a second.
4.2.6 FREQUENCY
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)
-
Issue 1 - 1 January 2002 Page 4-5
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
Periodic time and frequency are related.
T = 1/f and f = 1/T
4.2.7 ANGULAR VELOCITY.
The velocity at which a phasor rotates is very important and can
be calculated from:
Speed =Distance
Time
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 other formulae).
Referring back to our simple loop it can be seen that, if the
loop was rotating at 120 revolutions per second, the output
frequency would be 120 Hz. It therefore follows, that the frequency
of the output of an ac generator is directly proportional to its
speed of rotation.
4.2.8 PHASE DIFFERENCE (ANGULAR DIFFERENCE).
If two conductors are caused to rotate at the same angular
velocity, then two waves would be generated. Any angle between them
is said to be their phase difference. In the following diagram, the
phase difference is 90. As the conductors rotate in an
anti-clockwise direction, the dotted wave is said to lead the solid
wave by 90.
When two waves are 90 apart, they are said to be in quadrature
with each other.
When two waves are 180 apart, they are said to be in antiphase
with each other.
-
Issue 1 - 1 January 2002 Page 4-6
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
4.3 PHASOR OR VECTOR DIAGRAMS
Waveform diagrams are difficult to visualise and engineers have
devised a diagrammatic method known as a phasor or vector diagram
to simplify the problem.
The terms vector and phasor are interchangeable, however, the
term vector is more general, being used to denote any quantity that
has both magnitude and direction, whereas the term phasor, tends to
be associated with electrical engineering. 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 like the conductor rotating in the magnetic
field. If you plot the vertical displacement of the tip of the line
at various angular intervals, the curve traced out is a
sinewave.
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 rotated
90 in an anti-clockwise direction, the line points vertically
upwards, point B on the diagram. After 180 of rotation the line
points to the left of the page, and the vertical displacement is
again zero. Rotation through a further 180 returns the line 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 is normally scaled to represent r.m.s.
values, and can be used to represent voltage current, power or
indeed flux. One rotation of the phasor produces one cycle of the
waveform, therefore the number of rotations completed per second
gives the frequency.
The 3 'o-clock position on a phasor diagram is considered to be
the reference point of the diagram. Whether the current, voltage,
mmf or flux is drawn pointing in this direction depends on the
circuit under consideration. If two or more phase displaced
waveforms are to be drawn on the same phasor diagram they must have
the same frequency, their angular displacement is indicated by the
angle between 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 so that as they are rotated, the voltage phasor is
leading.
-
Issue 1 - 1 January 2002 Page 4-7
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
4.3.1 ADDITION OF PHASORS
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 add sinewaves of the same frequency.
To add two phasors, a parallelogram is produced, the two extra
sides being drawn parallel to the phasor already present.
Each extra side should start at the end of each phasor as shown.
Once the parallelogram has been produced, the resultant voltage is
represented by a line from the origin to the intersection of the
two new lines. The length of this new phasor represents the
magnitude of the new voltage and the angle between it and the other
phasor is the phase angle between them. When adding more than two
phasors, it is simply a matter of reducing pairs to a single
phasor, as described, until a single resultant remains.
-
Issue 1 - 1 January 2002 Page 4-8
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
4.4 ADDITION OF AC & DC
It is possible for both ac and dc to exist in the same circuit
or conductor. In such cases 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 in the diagrams
above.
4.5 MEASURING AC USING OSCILLOSCOPES
4.5.1 THE CATHODE RAY OSCILLOSCOPE
Cathode ray oscilloscopes are analogue-graphical instruments
which enable electrical waveforms to be displayed for analysis and
measurement purposes. A typical instrument is represented in the
diagram below.
-
Issue 1 - 1 January 2002 Page 4-9
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
With reference to the above diagram, the grids g1, g2 and g3 of
the cathode ray tube (CRT) form an electron gun which projects a
stream of electrons between deflecting plates onto the screen. The
screen is coated with a phosphorescent material so that a luminous
spot is produced on the screen. A property of the screen coating
material allows the spot to persist for a period of time when the
stream of electrons is moved or interrupted. The amount of
illumination depends on the quantity of electrons in the stream and
their velocity on impact with the screen.
The potential at grid g1, which is negative with respect to the
cathode, controls the quantity of electrons emitted from the
cathode. Adjusting R1 varies the potential at g1, hence R1 controls
the brightness of the illuminated spot. Positive potentials at g2
and g3 accelerate the electrons towards the screen. The potential
difference between g2 and g3, varied by adjusting R2, sets up an
electrostatic field which enables the electron stream to be focused
at the screen.
The position of the spot on the screen is determined by the
simultaneous effect of voltages applied to the X and Y deflecting
plates. A potential difference between the X deflecting plates
causes the spot to move across the screen in the horizontal
direction, through a distance proportional to the potential
difference. A potential difference between the Y deflecting plates
exerts a similar control over the vertical movement of the
spot.
The outputs of the X and Y amplifiers establish the potential
differences between corresponding pairs of deflecting plates. If
these voltages vary in magnitude the spot moves over the screen to
produce a continuous trace. Since one voltage controls horizontal
deflection and the other controls vertical deflection, the trace
forms a graphical representation of one voltage as a function of
the other.
4.5.1.1 The Time Base
Most applications require that a signal waveform is displayed as
a function of time. To meet this requirement a time base circuit
supplies a voltage which varies linearly with time, usually, to the
horizontal (X) deflecting plates whilst the signal to be observed
is usually applied to the vertical (Y) deflecting plates. A time
base (sawtooth) voltage synchronised with a time dependent signal
are depicted in the diagram.
-
Issue 1 - 1 January 2002 Page 4-10
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
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 time
1
f of the signal waveform. In practice
the time base is adjusted so that signals over a wide frequency
range may be displayed against a convenient time scale.
4.5.1.2 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.
4.5.1.3 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.
-
Issue 1 - 1 January 2002 Page 4-11
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
4.5.1.4 Amplifiers & Attenuators
The X and Y amplifiers and attenuators provide the voltage
scaling required to ensure that the instrument and the measured
signal are compatible. Since the oscilloscope is required to
display complex voltage waveforms, it is essential that fundamental
and harmonic frequencies must undergo the same amplification or
attenuation, and that the time relationships between different
frequencies must be maintained. It therefore follows that both the
amplifier and the attenuators, must have flat amplitude against
frequency and transit time against frequency, characteristics.
4.5.2 TYPES OF OSCILLOSCOPES
4.5.2.1 Sampling Oscilloscopes
At very high frequencies, say above 300MHz, it is not possible
using existing techniques to produce a continuous display on an
oscilloscope. To obtain a satisfactory display a sampling technique
must be used.
As shown in the diagram below, in a sampling oscilloscope the
time base circuit produces a stepped voltage waveform to deflect
the electron beam in the horizontal direction. Prior to each step,
a pulse is generated which initiates the sampling process.
The input signal is sampled later during each successive cycle
to produce the vertical deflection of an illuminated spot. In this
way the display, which may consist of 1,000 spots, is progressively
built up over a number of cycles of the input signal. An obvious
limitation of the sampling oscilloscope is that it cannot be used
to display transient waveforms.
-
Issue 1 - 1 January 2002 Page 4-12
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
4.5.2.2 Multiple Trace Display
Oscilloscopes equipped with multiple trace facilities enable two
or more signals to be displayed simultaneously. Essential features
of these instruments are a separate input channel for each signal
and a means of separating the electron beams for display. The most
widely used instruments enable two signals to be compared, although
four beam instruments are quite common.
Cathode ray tubes equipped with two electron guns and two sets
of deflecting plates, so that each channel is completely
independent, are employed in instruments known as Dual Beam
Oscilloscopes. Alternatively, a single gun may be used to produce
two traces by switching the Y deflecting plates from one input
signal to the other for alternate sweeps of the screen. Although
the signals are sampled, the display appears to the eye as a
continuous, simultaneous, display of both signals. Oscilloscopes
employing this techniques, which is called the alternate mode, can
only be used as single channel instruments to investigate transient
waveforms.
4.5.2.3 Dual Trace CRO
4.5.2.3.1 Alternate Mode
The electronic switch alternately connect the main vertical
amplifier to the two vertical preamplifiers. The switching takes
place at the start of each sweep. The switching rate of the
electronic switch is synchronised to the sweep rate, so that the
CRO spot traces channel 1 signal on one sweep and channel 2 signal
on the next sweep. This is used for viewing high frequency
signals.
-
Issue 1 - 1 January 2002 Page 4-13
JAR 66 CATEGORY B1
MODULE 3 (part B)
ELECTRICAL
FUNDAMENTALS
engineering
uk
4.5.2.3.2 Chopped Mode
The electronic switch is free running at 100 - 500KHz and is
independent of the frequency of the sweep generator. The switch
successively connects small segments of the 1 and 2 waveforms to
the vertical amplifier. If the chopping rate is much faster than
the horizontal sweep rate, the individual little segments fed to
the vertical amplifier reconstitute the original 1 and 2 waveforms
on the screen, without visible interruptions in the two images.
4.5.2.4 Delayed Sweep
Both time bases in operation.
A - delaying sweep
B - delayed sweep
Either or both (alternate) signals can be fed