Oscillators

ELECTRONICS 3

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Objectives:1. To determine the fundamentals of an

oscillator 2. To perform analysis and design of a Wien-

Bridge Oscillator, Voltage-Controlled Oscillator, Variable-Duty Cycle, Triangle-Wave Oscillator, and Multivibrators

Oscillator FundamentalsAn oscillator is essentially an amplifier that produces its own input. That is, if we connect an oscillator circuit to a DC power supply, it will generate a signal without having a similar signal available as an input. One of the most fundamental ways to classify oscillator circuits is by the shape of the waveform generated. In this chapter, we will study oscillator circuits that produce waveforms such as sine wave, rectangular wave, ramp wave, and triangular wave.

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Objectives:1. To determine the fundamentals of an oscillator 2. To perform analysis and design of a Wien-


In general, in order for a circuit to operate as an oscillator, three basic factors must be provided in the circuit. They are Amplification, Positive feedback, and Frequency determining network.

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Wien-Bridge Oscillator

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A Wien-bridge oscillator produces sine waves and uses an RC network as the frequency-determining portion of the circuit. The gain of the op amp portion of the circuit is determined by the ratio of the RF and the effective resistance of the FET in parallel with R1. The FET’sresistance is determined by the amount of bias voltage on the gate. As the voltage on the gate becomes more negative, the channel resistance in the FET is increased.

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The gate voltage of the FET is obtained from the output of a half-wave rectifier and filter combination. The input to the rectifier is provided by the output of the oscillator. In short, if the output amplitude tried to increase, the output of the rectifier circuit would become more negative. This increased negative voltage would bias the FET more toward cutoff (i.e. higher channel resistance). The increased FET resistance would cause the gain of the op amp circuit to decrease and thus prevent the output amplitude from increasing. A similar, but opposite, effect would occur if the output amplitude tried to increase.

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The output signal is also returned to the (+) input terminal (positive feedback) via the R1C1 and R2C2network. This is the frequency selective portion of the oscillator. At the desired frequency of oscillation, the RC network will have a voltage gain of one-third and a phase shift of zero (i.e. no phase shift). At all other frequencies, the loss will be even greater and the input/output signals will differ in phase.

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Numerical Analysis• Operating Frequency

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• Effective resistance of FET

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Voltage-Controlled OscillatorA voltage-controlled oscillator (VCO) is an oscillator circuit whose frequency can be controlled or varied by a DC input voltage. This type of circuit is also called a voltage-to-frequency converter (VFC). The output waveform of the VCO may be sine, square, or other wave shape depending on the circuit design.

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The first stage is an integrator. Let us assume that D4is reverse-biased and acting as an open. Under these conditions, +VIN and R1 will determine the value of feedback current for A1. Since VIN is DC and R1 does not change, the value of input current and, therefore, the feedback current will be constant. The feedback current must flow through C1.

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From basic electronics theory, if a capacitor is charged with a constant current source, the resulting voltage will increase linearly. Because the charging current for C1is constant, we can expect a linear ramp of voltage across C1. And because the left end of C1 is connected to a virtual ground point, the other end (output of the op amp) will reflect the linear ramp voltage. The input voltage VIN is positive, so we know that the output ramp that the output ramp will be increasing in the negative direction.

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A2 is configured as a voltage comparator circuit with the upper and lower thresholds being established by diodes D1 and D2. As long as the ramp voltage is above the lower threshold point (established by D1), the output of amplifier A2 will remain at its negative limit (-VSAT).

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Amplifier A3 is connected as an inverting summing amplifier. One input comes from A2 and receives a gain of -2. The other input is provided by +VIN and receives a gain of -1. As long as the output of A2 is at its –VSAT level, diode D3 will be forward-biased and this voltage will be coupled to the input of A3. Clearly, this high-negative voltage will drive amplifier A3 into saturation. That is, the output of A3 will be at the +VSATlevel regardless of the value of +VIN. It is this +VSATlevel on the output of A3 that causes D4 to remain in a reversed-biased state. This circuit condition remains constant as long as the ramp voltage on the output of A1 is above the lower threshold of A2.

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Once the decreasing ramp voltage of A1 falls below the VLT of comparator A2, the output of A2 changes to its +VSAT level. This reverse-biases diode D3 and causes A3 to act as a simple inverting amplifier with regard to the +VIN. A voltage level that is equal (but opposite polarity) to +VIN is felt at the right end of R4. Since R4 is half as large as R1 and has the same voltage applied, we can expect the current flow through R4 to be twice as large as that through R1 and in the opposite direction.

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The current provided by R4 not only cancels the input current provided via R1 but supplies an equal (but opposite) current to C1. That is, C1 will now continue to charge at the same linear rate but in the opposite direction. The ramp voltage at the output of A1 will rise linearly until it exceeds the upper threshold of A2. Once the upper threshold has been exceeded, the output of A2 switches to the –VSAT level. This forces the output of A3 to +VSAT and reverse-biases D4. We are now back to the original circuit state, and the cycle repeats.

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The frequency of operation is determined by the time it takes C1 to charge to the threshold levels of A2. Once the circuit components have been fixed, the only thing that determines frequency is the value of +VIN. This, of course, gives rise to the name voltage-controlled oscillator.Numerical Analysis• Upper Threshold Voltage

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• Lower Threshold Voltage

These threshold values are particularly important because they will determine the charging limits of capacitor C1.

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• Operation of A3

Range of output voltages for A3 as a result of +VIN:

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Output voltage of A3 as a result of the output from A2:

at –VSAT input,

at +VSAT input,

vO = 0 V (since D3 will be reverse-biased)

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Combined effects of two inputs to A3:at –VSAT input and +VIN = 5 V,

at +VSAT input,

vO = -16 V to -5.6 V

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• Operation of A1

Current through R1:

: Since the current is constant, capacitor C1 will charge linearly

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Current through R4:

C1 will charge at the same rate but in opposite polarity

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Frequency of oscillation for a given input voltage +VIN:

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Variable-Duty Cycle

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The figure shows a rectangular wave oscillator with independently controllable alternation providing both frequency and duty-cycle control. The duration of each alternation is independently adjustable, which means that the duty cycle of the output can be adjusted from a small to a very high value.Let us assume that the output is at +VSAT level. This voltage will be regulated down to a lower value by D3and returned to the (+) input as a reference voltage. The positive output voltage is also regulated to a lower level by D5. This latter voltage provides a stable charging voltage for C1.

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C1 charges from ground through D2, R3, and R4 to the regulated positive voltage provided by D5. C1 will charge exponentially toward the D5 voltage. As long as the voltage on C1 is less than the reference voltage on the (+) input of the op amp, the circuit will be stable and C1 will continue to charge.

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Once the voltage of C1 reaches the reference voltage on the (+) input, the output of the op amp quickly switches to its –VSAT level. Diode D4 regulates this negative voltage and provides a new reference voltage for the (+) input. Similarly, D6 regulates the –VSATvoltage and provides a new charging source for C1. The new source is negative, so C1 will discharge and then recharge in the opposite polarity. The charging path is from the negative source provided by D6through R2, R1, D1, and C1 to ground.

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Again, this is an exponential charging action and will continue as long as the voltage on C1 remains more positive than the negative reference voltage on the (+) input. Once the voltage C1 falls below the reference voltage on the (+) input, the circuit quickly switches back to its original state and the cycle repeats.

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The time it takes C1 to charge during the positive output alternation is determined by the values of C1, R3, R4, and D5. Since R3 is adjustable, it can be used to control the period of the positive alternation without affecting the negative alternation. The values of C1, R1, R2, and D6 determine the charge of C1 during the negative output alternation as well. Resistor R1 can be used to control this time period without affecting the positive alternation.Resistors R5 and R6 are current limiting resistors for the two sets of back-to-back zener regulators.

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Numerical Analysis• Reference Voltage

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• Duration of positive output alternation

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• Duration of negative output alternation

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• Frequency of operation

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• Duty cycle

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Triangle-Wave Oscillator

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It shows the schematic of an oscillator circuit that generates a dual ramp (triangle) output. The heart of the circuit is amplifier A1 which uses a capacitor as the feedback element (integrator).Let us assume that the output of A2 is at its –VSAT level. Under these conditions, electrons will flow from the negative potential at the output of A2, through R1 and then C1 as a charging current. The value of this current is determined by the voltage at the output of A2 and the value of R1. Since neither of these is changing at the moment, we assume the charging current is constant.

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Whenever a capacitor is charged from a constant current source, the voltage across it accumulates linearly. Therefore, the voltage across C1 will be increasing linearly, with the right side becoming more positive. Since the left side of C1 is connected to virtual ground point, the right side has a positive-going ramp with reference to ground. This is, of course, our output signal.When the positive-going ramp exceeds the upper threshold voltage of A2, which you should recognize as a non-inverting voltage comparator, the output of A2 will quickly switch to its +VSAT level.

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The electron flow through C1 now reverses and flows from C1 through R1 toward the positive potential at the A2 output. Again, the value of the current is constant and determined by R1 and the voltage at the output of A2. The voltage across C1 will decay linearly until it passes through 0. It will then begin to charge at the same rate in the opposite polarity, producing the negative slope of our output.The output of A1 continues to become more negative until it falls below the lower threshold voltage of A2. At this time, the output of A2 switches to its –VSAT level and the cycle repeats.

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Numerical Analysis• Threshold voltages of comparator A2

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• Duration of each alternation

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• Frequency of operation

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MultivibratorsMultivibrators are a very important classification of relaxation oscillator. This type of circuit employs an RC network in its physical makeup. A rectangular-shaped wave is developed by the output. Astablemultivibrators are commonly used in television receivers to control the electron-beam deflection of the picture tube. Computers use this type of generator to develop timing pulses.

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Multivibrators are considered to be either triggered devices or free running. A triggered multivibratorrequires an input signal or timing pulse to be made operational. The output of this multivibrator is controlled or synchronized by an input signal. Free-running oscillators are self-starting. They operate continuously as long as electrical power is supplied. The shape and frequency of the waveform is determined by component section.

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Astable MutivibratorA free-running or astablemutivibrator is a square-wave generator. The circuit shown is a multivibrator circuit and looks something like a comparator with hysteresis, except that the input voltage is replaced by a capacitor. When VO is at +Vsat, the feedback voltage is called the upper-threshold voltage VUT.

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When VO is at –Vsat, the feedback voltage is called the lower-threshold voltage VLT.

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Free-running multivibrator action is summarized as follows:• When VO = -Vsat, C discharges from VUT to VLT and switches

VO to +Vsat.• When VO = +Vsat, C charges from VLT to VUT and switches

VO to –Vsat.The time needed for C to charge and discharge determines the frequency of the multivibrator.

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Monostable MultivibratorAlso called as one-shot multivibrator.It generates a single output pulse in response to an input signal. The length of the output pulse depends only on external components (resistors and capacitors) connected to the op amp.

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• The duration of the input pulse can be longer or shorter than the expected output pulse. The duration of the output pulse is represented by τ. Since τcan be changed by changing resistors and capacitors, the one-shot can be considered as pulse stretcher. This is because the width of the pulse can be longer than the input pulse.

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If R2 is made about one-fifth of R1, then the duration of the output pulse is given by

The exact equation is

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IC Waveform GeneratorThe 555 IC is a multifunction device that is widely used today. It can be modified to respond as a monostableor astable multivibrator. The internal circuitry of a 555 IC is generally viewed with functional blocks. In this regard, the chip has two comparators, a bistable flip-flop, a resistive divider, a discharge transistor, and an output stage as shown in the figure.

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Operating Modes of a 555 timer

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Monostable Operation

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In the standby mode, the control flip-flop holds Q1 ON, thus clamping the external timing capacitor C to ground. The output (pin 3) during this time is at ground potential, or LOW. The three 5 kΩ internal resistors act as voltage dividers, providing bias voltages of 2/3 VCCand 1/3 VCC respectively. Since these two voltages fix the necessary comparator threshold voltages, they also aid in determining the timing interval.

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Since the “lower” comparator is biased at 1/3 VCC, it remains in the standby state as long as the trigger input (pin 2) is held above 1/3 VCC. When triggered only by a negative-going pulse, the lower comparator sets the internal flip-flop which reverses the short circuit across the timing capacitor, thus turning Q1 OFF, and the output goes HIGH (approximately equal to VCC).

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Since the timing capacitor is now unclamped, the voltage across it now rises exponentially through Ratowards VCC, with a time constant of RaC. After a period of time, the capacitor voltage will equal 2/3 VCC, and the “upper” comparator resets the internal flip-flop, which in turn discharges the capacitor rapidly to ground potential, turning Q1 ON. As a consequence, the output now returns to the standby state, or ground.

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Since the external capacitor voltage changes exponentially from 0 to 2/3 VCC,

or

so that the time width that the output is HIGH is then equal to

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Astable Operation

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Here the timing resistor is now split into two sections, Ra and Rb, with the discharge transistor (pin 7) connected to the junction of Ra and Rb. When the power supply is connected, the timing capacitor C charges towards 2/3 VCC through Ra and Rb. When the capacitor voltage reaches 2/3 VCC, the upper comparator triggers the flip-flop and the comparator starts to discharge towards ground through Rb. When the discharge reaches 1/3 VCC, the lower comparator is triggered and a new cycle is started.

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The output state is HIGH during the charging cycle for a time period t1, so that

or

The output state is LOW during the discharge cycle for a time period t2, given by

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Thus, the total period charge and discharge is

so that the output frequency is given as

Duty cycle• The duty cycle D of a recurring output is defined as the ratio

of the HIGH time to the total cycle, or

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QUESTIONS

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Oscillators

Documents

wienbridge oscillator

oscillator circuits

trianglewave oscillator

trianglewave oscillator

voltage gain

gate voltage

variableduty cycle

bias voltage