This document discusses feedback and oscillator circuits. It begins by explaining the theory of sinusoidal oscillation, where positive feedback in a circuit can produce oscillations without any external input signal. It then covers various oscillator circuits like the phase shift oscillator, Wien bridge oscillator, and tuned oscillator circuits like the Colpitts and Hartley oscillators. It also discusses crystal oscillators, noting characteristics of quartz crystals like their series and parallel resonance frequencies which make them useful for stable frequency generation. Worked examples are provided to illustrate calculating oscillator frequencies and component values.

1. MODULE 4
FEEDBACK AND
OSCILLATOR CIRCUITS
ANALOG ELECTRONIC CIRCUITS
(ECE34)

2. 16/10/2017
after
2Aravinda K., Dept. of E&C, NHCE

3. 16/10/2017 3Aravinda K., Dept. of E&C, NHCE

4. Theory of sinusoidal oscillation
If the amplifier is provided with positive feedback,
and if the feedback signal is in correct phase with the
previous input, then there will be an output signal
without any external input signal.
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With respect to the input, the gain
of the amplifier is –A, due to the
phase shift of 180°. If the feedback
circuit also produces an additional
phase shift of 180°, then B is +ve,
and the overall gain equation is:
Af=A/(1-AB)
4Aravinda K., Dept. of E&C, NHCE

5. 16/10/2017
AB < 1 AB > 1 AB = 1
Barkhausen criterion for oscillation: Magnitude of
Loop gain should be unity, at a phase angle of 180°.
The starting signal is the infinitesimal noise voltage,
which is always present, and contains all the frequencies,
due to the random movement of the free electrons. The
amplified noise drives the resonant feedback circuit, and
hence oscillations build up at the desired frequency.
5Aravinda K., Dept. of E&C, NHCE

6. • Bypass circuit, Lag circuit, Low pass circuit
• Coupling circuit, Lead circuit, High pass circuit
• These are examples of phase-shifting circuits,
from 0° till 90°, depending on the frequency.
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7. PHASE SHIFT OSCILLATOR
Here, B = 1/29 and hence A ≥ 29. Each RC stage
provides a phase-shift of 60° at a specific frequency,
provided the loading effect is taken care of.
16/10/2017
IC phase shift
oscillator
7Aravinda K., Dept. of E&C, NHCE

8. FET phase-shift
oscillator
In general, Ri is much
larger. Further, impedance
of the feedback network
is also much larger when
compared to RL.
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9. Exercise - 1
• An FET has gm = 5mS and rd = 50 KΩ. Obtain
the value of C and RD for the phase-shift
oscillator’s frequency of 10 KHz, choosing
R = 4.7 KΩ.
Solution:
C = 1/(2x3.14x2.45x4.7Kx10K) = 1.38 nF.
As A ≥ 29, let A = 40.  RL = 40/5m = 8 KΩ.
Hence, RD = rd RL / (rd - RL) = 9.52 KΩ ≈ 10 KΩ.
16/10/2017 9Aravinda K., Dept. of E&C, NHCE

10. BJT phase-shift
oscillator
Here, Ri is much lesser.
Hence, one solution is to
use an Emitter-follower
at the input stage, and
the other solution is to
use an additional resistor
R′ in series with Ri, such
that, R′ + Ri = R.
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11. Wien-Bridge
Oscillator
• This is the standard oscillator circuit used for general
applications, in the range of 5 Hz till 1 MHz.
• It uses the lead-lag circuit as the resonant feedback.
The series capacitor blocks LF and the parallel capacitor
bypasses HF, and hence, the phase angle varies
between +90° till -90°.
• The output remains maximum in the mid-range, at the
resonant frequency, where the phase angle is 0°.
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12. When R = XC, resonance occurs, and B = 1/3.
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13. 16/10/2017
WIEN-
BRIDGE
OSCILLATOR
CIRCUIT
USING
OP-AMP
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14. • It uses both feedback types: +ve through the
lead-lag circuit, and –ve through the voltage-
divider circuit.
• At power up, there is more +ve feedback, and
AB > 1, and hence oscillations build up.
• Slowly when the Tungsten lamp heats up, its
resistance increases, and when it equals R′,
• At this point, the oscillations become stable,
and the output voltage will have a constant
peak-to-peak value.
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15. • The bridge analysis yields,
• When R1=R2 and C1=C2, then R3/R4 = 2.
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16. Exercise - 2
• Obtain the RC values for a Wien-Bridge
Oscillator with an output frequency of 20 KHz.
Solution:
Let R = 100 KΩ.
Then, C = 1/(2x3.14x100Kx20K) = 79.62 pF.
If R4 = 100 KΩ, then R3 ≥ 200 KΩ.
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17. • Different types of oscillators can be obtained by choosing the
reactance elements in feedback network.
Oscillator Type
Reactance Elements
X1 X2 X3
Colpitts C C L
Hartley L L C
Tuned input
Tuned output
LC LC ------
Fig: Basic Configuration of Tuned Oscillators
TUNED OSCILLATOR CIRCUITS
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18. Colpitts Oscillator (BJT –CE Configuration)
Fig: Colpitts oscillator using BJT CE config.
• The voltage divider
bias set up the Q-point
for biasing.
• RF CHOKE has high
inductive reactance.
• C1, C2, L provide the
feedback for
oscillations.
• The feedback voltage
is across C2 drives the
base and sustain the
oscillations.
Fig: AC equivalent Circuit
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19. Colpitts Oscillator (BJT Configuration)
Resonant Frequency:
 Exact frequency
𝑓𝑟 =
1
2∏ 𝐿𝐶𝑒𝑞
𝑄2
𝑄2 + 1
 Approximate Frequency
𝑓𝑟 =
1
2∏ 𝐿𝐶 𝑒𝑞
for Q >10
𝑄 =
𝑓𝑟
𝐵𝑊
, 𝐶𝑒𝑞 =
𝐶1 𝐶2
𝐶1 + 𝐶2
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Starting Condition for
Oscillation
• AB >1
• A>1/B
• Feedback fraction to the
oscillator ‘B’
𝐵 =
𝐶1
𝐶2
• Minimum voltage gain Av
𝐴𝑣 =
𝐶2
𝐶1
19Aravinda K., Dept. of E&C, NHCE

20. Coupling Load to Oscillator
Capacitive coupling Link coupling
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• Directly connecting load lowers Q , hence may not initiate
oscillation process.
• Coupling should not lower the Q of tank circuit.
20Aravinda K., Dept. of E&C, NHCE

21. 16/10/2017
Colpitts Oscillator (BJT –CB Configuration)
• CB Configuration oscillate at high
frequency.
• Frequency of Oscillation
• 𝑓𝑟 =
1
2∏ 𝐿𝐶 𝑒𝑞
𝑄2
𝑄2+1
𝐶𝑒𝑞=
𝐶1 𝐶2
𝐶1 + 𝐶2
• Feedback factor
• Minimum Gain
Fig:Colpitts oscillator BJT-CE confg.
21Aravinda K., Dept. of E&C, NHCE

22. Colpitts Oscillator-JFET,OPAMP
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Frequency of Oscillation 𝑓𝑟 =
1
2∏ 𝐿𝐶𝑒𝑞
Fig: Colpitts oscillator using OPAMP.Fig: Colpitts oscillator using JFET.
22Aravinda K., Dept. of E&C, NHCE

23. Problem
• What is the frequency of oscillation for Colpitts
oscillator ? What is the feedback fraction ? How
much voltage gain does circuit needs to start
oscillating ?
Given C1=0.001 uF, C2= 0.01uF, L=15 uF
Solution
fr= 1.36 MHz, B= 0.1, Av= 10
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24. 16/10/2017
Hartley Oscillator
Fig: Hartley Oscillator using BJT. Fig: Hartley Oscillator using JFET.
24Aravinda K., Dept. of E&C, NHCE

25. Crystal Oscillator
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Characteristics of Quartz crystal
• Piezoelectric effect
 R represents the internal friction.
 L represents vibrating mass.
 Cs represents crystal compliance.
 CM represents capacitance due to
mechanical mounting of crystal.
Used for accurate and stable frequency of oscillations.
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26. Characteristics of Quartz crystal
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Exhibits2 resonant frequencies
1. Series resonance frequency
-> When impedance is low (R)
2. Parallel resonance frequency
->When reactance of series
resonance equals the
reactance of CM.
26Aravinda K., Dept. of E&C, NHCE

27. 16/10/2017
Series Resonant Circuit Parallel Resonant Circuit
Crystal Oscillator
27Aravinda K., Dept. of E&C, NHCE

28. 16/10/2017
Problem
• What is the series and parallel resonant frequency of
crystal? Given L=3H, Cs=0.05 pF, R= 2KΩ, Cm=10
pF.
Solution
fs=411 KHz, Cp=0.0498 pF, fp=412 KHz.
28Aravinda K., Dept. of E&C, NHCE

29. END
OF
MODULE 4
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