Answer the following:
Report on TWO of the topics from the list below and explain in your OWN words the basic concepts involved:
- Oscillators with RC feedback circuits
- Oscillators with LC feedback circuits
- Piezoelectric materials and their applications
- Why does the FAA require that some passenger devices with oscillators be turned off during takeoff and landing?
Electronic Devices
10th ed.
Chapter 16
Oscillators
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Electronic Devices
10th ed.
◆ Describe the operating principles of an oscillator
◆ Discuss the principle on which feedback oscillators is based
◆ Describe and analyze the operation of RC feedback oscillators
◆ Describe and analyze the operation of LC feedback oscillators
◆ Describe and analyze the operation of relaxation oscillators
◆ Discuss and analyze the 555 timer and use it in oscillator applications
Objectives:
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Electronic Devices
The Oscillator
Oscillators are electronic circuits that produce a periodic waveform with only the dc supply voltage as an input. Common output waveforms are the sine wave, square wave and sawtooth.
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Electronic Devices
The Oscillator
Oscillators are electronic circuits that produce a periodic waveform with only the dc supply voltage as an input. Common output waveforms are the sine wave, square wave and sawtooth.
Two types of oscillators are feedback oscillators and relaxation oscillators.
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Electronic Devices
Feedback Oscillators
In a feedback oscillator, a fraction of the output is returned to the input with no net phase shift. This means that the feedback circuit compensates for any phase shift in the amplifier and the reinforces the input, a condition known as positive feedback.
If the amplifier is a noninverting type, the feedback circuit does not invert the amplifier’s output, producing positive feedback.
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Electronic Devices
Feedback Oscillators
If the amplifier is an inverting type, the feedback circuit inverts the amplifier’s output, again producing positive feedback.
In a feedback oscillator, a fraction of the output is returned to the input with no net phase shift. This means that the feedback circuit compensates for any phase shift in the amplifier and the reinforces the input, a condition known as positive feedback.
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Electronic Devices
Half-Wave Rectifier
Two conditions are required for sustained oscillations:
1. The phase shift around the feedback loop must be effectively 0o.
2. The closed loop voltage gain, Acl, must be ≥ than 1. For a sine
wave oscillator (shown), the closed loop gain = exactly 1.
(Acl = AvB =1).
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Electronic Devices
Half-Wave Rectifier
What is the gain required for the amplifier portion of a sine-wave oscillator if the feedback fraction, B, is 0.05?
Question:
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Electronic Devices
Half-Wave Rectifier
What is the gain required for the amplifier portion of a sine-wave oscillator if the feedback fraction, B, is 0.05?
Answer:
Question:
Acl = AvB
20
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Electronic Devices
Feedback Oscillators
Feedback oscillators require a small disturbance such as that generated by thermal noise to start oscillations. This initial voltage starts the feedback process and oscillations.
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Electronic Devices
Feedback Oscillators
Feedback oscillators require a small disturbance such as that generated by thermal noise to start oscillations. This initial voltage starts the feedback process and oscillations.
Computer simulations, such as Multisim, use digital signals, which do not have thermal noise. This often creates a problem for computer simulations of oscillators.
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Electronic Devices
The Wien-Bridge Oscillator
RC feedback is used in various lower frequency sine-wave oscillators. The text covers three: the Wien-bridge oscillator, the phase-shift oscillator, and the twin-T oscillator.
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Electronic Devices
The Wien-Bridge Oscillator
RC feedback is used in various lower frequency sine-wave oscillators. The text covers three: the Wien-bridge oscillator, the phase-shift oscillator, and the twin-T oscillator.
The feedback circuit in a Wien-bridge uses a lead-lag circuit. When the R’s and C’s have equal values, the output will be ⅓ of the input at only one frequency and the phase shift at this frequency will be 0o.
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Electronic Devices
The Wien-Bridge Oscillator
Because the Wien-bridge lead-lag feedback network attenuates the output by 1/3 (with equal R’s and C’s), the gain of the noninverting amplifier must be exactly 3.0 to produce a loop gain of 1.0.
Voltage-divider
Lead-lag network
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Electronic Devices
The Wien-Bridge Oscillator
Because the Wien-bridge lead-lag feedback network attenuates the output by 1/3 (with equal R’s and C’s), the gain of the noninverting amplifier must be exactly 3.0 to produce a loop gain of 1.0.
The noninverting amplifier gain is set by R1 and R2. If the gain is too little, oscillations will not occur; if it is too much the sine wave will be clipped. In the basic circuit shown, it is nearly impossible to set this gain to the precise value required.
Voltage-divider
Lead-lag network
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Electronic Devices
The Wien-Bridge Oscillator
To produce the precise gain required, the Wien bridge needs some form of automatic gain control (AGC). One popular method is shown here and uses a JFET transistor.
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Electronic Devices
The Wien-Bridge Oscillator
To produce the precise gain required, the Wien bridge needs some form of automatic gain control (AGC). One popular method is shown here and uses a JFET transistor.
The key elements of the AGC circuit are highlighted in yellow. The diode charges C3 to the negative peak of the signal. This develops the gate bias voltage for the JFET that is related to the output level.
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Electronic Devices
The Wien-Bridge Oscillator
The JFET is operated in the ohmic region and can change its resistance rapidly if conditions change.
Ohmic region
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Electronic Devices
The Wien-Bridge Oscillator
The JFET is operated in the ohmic region and can change its resistance rapidly if conditions change.
Recall from Chapter 8 that a JFET acts as a variable resistor in the ohmic region. If the output increases, the bias tends to be larger, and the drain-source resistance increases (and vice-versa). In the Wien-bridge, the JFET drain-source resistance controls the gain of the op-amp and will compensate for any change to the output.
Ohmic region
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Electronic Devices
The Wien-Bridge Oscillator
When the R’s and C’s in the feedback circuit are equal, the frequency of the bridge is given by
10 kW
1.0 kW
10 kW
680 W
680 W
4.7 nF
4.7 nF
1.0 mF
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Electronic Devices
The Wien-Bridge Oscillator
When the R’s and C’s in the feedback circuit are equal, the frequency of the bridge is given by
10 kW
1.0 kW
10 kW
680 W
4.7 nF
4.7 nF
1.0 mF
Example:
What is fr for the Wien bridge?
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Electronic Devices
The Wien-Bridge Oscillator
When the R’s and C’s in the feedback circuit are equal, the frequency of the bridge is given by
10 kW
1.0 kW
10 kW
680 W
680 W
4.7 nF
4.7 nF
1.0 mF
Example:
What is fr for the Wien bridge?
Solution:
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Electronic Devices
The Wien-Bridge Oscillator
When the R’s and C’s in the feedback circuit are equal, the frequency of the bridge is given by
10 kW
1.0 kW
10 kW
680 W
680 W
4.7 nF
4.7 nF
1.0 mF
Example:
What is fr for the Wien bridge?
Solution:
= 48.9 kHz
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Electronic Devices
The Phase-Shift Oscillator
The phase-shift oscillator uses three RC circuits in the feedback path that have a total phase shift of 180o at one frequency – for this reason an inverting amplifier is required for this circuit.
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Electronic Devices
The Phase-Shift Oscillator
Conditions for oscillation with the phase-shift oscillator is that if all R’s and C’s are equal, the amplifier must have a gain of at least 29 to make up for the attenuation of the feedback circuit. This means that Rf /R3 ≥ 29.
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Electronic Devices
The Phase-Shift Oscillator
Conditions for oscillation with the phase-shift oscillator is that if all R’s and C’s are equal, the amplifier must have a gain of at least 29 to make up for the attenuation of the feedback circuit. This means that Rf /R3 ≥ 29.
Under these conditions, the frequency of oscillation is given by
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Electronic Devices
The Phase-Shift Oscillator
Multisim 14 can simulate the phase-shift oscillator; if there is a problem starting the simulation, you can use a switch and a dc voltage source (see next Example).
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Electronic Devices
The Phase-Shift Oscillator
Example:
Design a phase-shift oscillator for a frequency of 800 Hz. The capacitors are to be 10 nF.
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Electronic Devices
The Phase-Shift Oscillator
Example:
Design a phase-shift oscillator for a frequency of 800 Hz. The capacitors are to be 10 nF.
Solution:
Start by solving for the resistors needed in the feedback circuit:
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Electronic Devices
The Phase-Shift Oscillator
Example:
Design a phase-shift oscillator for a frequency of 800 Hz. The capacitors are to be 10 nF.
Solution:
Start by solving for the resistors needed in the feedback circuit:
8.12 kW
(Use 8.2 kW.)
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Electronic Devices
The Phase-Shift Oscillator
Example:
Design a phase-shift oscillator for a frequency of 800 Hz. The capacitors are to be 10 nF.
Solution:
Start by solving for the resistors needed in the feedback circuit:
8.12 kW
(Use 8.2 kW.)
Calculate the feedback resistor needed:
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Electronic Devices
The Phase-Shift Oscillator
Example:
Design a phase-shift oscillator for a frequency of 800 Hz. The capacitors are to be 10 nF.
Solution:
Start by solving for the resistors needed in the feedback circuit:
8.12 kW
(Use 8.2 kW.)
Rf = 29R = 238 kW.
Calculate the feedback resistor needed:
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Electronic Devices
The Phase-Shift Oscillator
Example:
Design a phase-shift oscillator for a frequency of 800 Hz. The capacitors are to be 10 nF.
Solution:
Start by solving for the resistors needed in the feedback circuit:
8.12 kW
(Use 8.2 kW.)
10 nF
10 nF
10 nF
8.2 kW
8.2 kW
8.2 kW
238 kW
Rf = 29R = 238 kW.
Calculate the feedback resistor needed:
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Electronic Devices
The Phase-Shift Oscillator
Example:
Design a phase-shift oscillator for a frequency of 800 Hz. The capacitors are to be 10 nF.
Solution:
Start by solving for the resistors needed in the feedback circuit:
8.12 kW
(Use 8.2 kW.)
10 nF
10 nF
10 nF
8.2 kW
8.2 kW
8.2 kW
238 kW
The following slide shows the Multisim check.
Rf = 29R = 238 kW.
Calculate the feedback resistor needed:
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Electronic Devices
The Phase-Shift Oscillator
Multisim 14 with S1 to start the simulation (close and open S1). The frequency determined by Multisim is 791 Hz.
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Electronic Devices
The Twin-T Oscillator
The basic twin-T oscillator combines a low-pass and high-pass filter to form a notch filter at the oscillation frequency.
R
R
R/2
C
C
2C
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Electronic Devices
The Twin-T Oscillator
The basic twin-T oscillator combines a low-pass and high-pass filter to form a notch filter at the oscillation frequency.
An excellent notch filter can be formed by using R’s and C’s related by a factor of 2 as shown here.
R
R
R/2
C
C
2C
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Electronic Devices
The Twin-T Oscillator
The basic twin-T oscillator combines a low-pass and high-pass filter to form a notch filter at the oscillation frequency.
An excellent notch filter can be formed by using R’s and C’s related by a factor of 2 as shown here.
R
R
R/2
C
C
2C
With this relationship, the oscillation frequency is approximately
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Electronic Devices
The Twin-T Oscillator
Two improvements to the basic circuit are shown here – adding the parallel diodes and R6 significantly reduces distortion by attenuating harmonics. The potentiometer adds output amplitude adjustment.
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Electronic Devices
The Twin-T Oscillator
Two improvements to the basic circuit are shown here – adding the parallel diodes and R6 significantly reduces distortion by attenuating harmonics. The potentiometer adds output amplitude adjustment.
The frequency is a little higher than the predicted value of 1.94 kHz. With ±15 V power supplies, the measured values are:
f = 2.28 kHz @2.0 Vpp
Amplitude = 0 to 27 Vpp
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Electronic Devices
The Colpitts Oscillator
LC feedback oscillators use resonant circuits in the feedback path. A popular LC oscillator is
the Colpitts oscillator. It uses two series capacitors in the resonant circuit. The feedback voltage is developed across C1.
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Electronic Devices
The Colpitts Oscillator
The resonant frequency is found by
If Q > 10, this formula gives good results.
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Electronic Devices
The Colpitts Oscillator
The resonant frequency is found by
If Q > 10, this formula gives good results.
Recall that the total capacitance of two series capacitors is the product-over-sum of the individual capacitors. Therefore,
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Electronic Devices
The Colpitts Oscillator
The resonant frequency is found by
If Q > 10, this formula gives good results.
Recall that the total capacitance of two series capacitors is the product-over-sum of the individual capacitors. Therefore,
For Q < 10, a correction for Q is
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Electronic Devices
The Hartley Oscillator
The Hartley oscillator is similar to the Colpitts oscillator, except the resonant circuit consists of two series inductors (or a single tapped inductor) and a parallel capacitor. The frequency for Q > 10 is
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Electronic Devices
The Hartley Oscillator
The Hartley oscillator is similar to the Colpitts oscillator, except the resonant circuit consists of two series inductors (or a single tapped inductor) and a parallel capacitor. The frequency for Q > 10 is
One advantage of a Hartley oscillator is that it can be tuned by using a variable capacitor in the resonant circuit.
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Electronic Devices
The Crystal Oscillator
Crystal oscillators are highly stable oscillators for demanding circuits such a radio transmitters. Crystals have very high Q.
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Electronic Devices
The Crystal Oscillator
Crystal oscillators are highly stable oscillators for demanding circuits such a radio transmitters. Crystals have very high Q.
Manufacturers prepare natural crystals (usually quartz) by mounting a very thin slab between metal electrodes. When a small ac voltage is applied, the crystal oscillates at its own resonant frequency.
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Electronic Devices
The Crystal Oscillator
Crystal oscillators are highly stable oscillators for demanding circuits such a radio transmitters. Crystals have very high Q.
The crystal acts as the resonant circuit for the modified Colpitts oscillator and stabilizes the oscillations. The capacitors still tap off a feedback signal to the CE amplifier.
Manufacturers prepare natural crystals (usually quartz) by mounting a very thin slab between metal electrodes. When a small ac voltage is applied, the crystal oscillates at its own resonant frequency.
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Electronic Devices
The Relaxation Oscillator
Relaxation oscillators are characterized by an RC timing circuit and a device that periodically changes state.
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Electronic Devices
The Relaxation Oscillator
Relaxation oscillators are characterized by an RC timing circuit and a device that periodically changes state.
The triangular wave oscillator is an example. For this circuit, the device that changes states is a comparator with hysteresis (Schmitt trigger). The RC timing device is an integrator. The comparator output can be used as a square wave output.