ELG4139: Oscillator Circuits
Positive Feedback Amplifiers (Oscillators)
LC and Crystal Oscillators
JBT; FET; and IC Based Oscillators
The Active-Filter-Tuned Oscillator
Multivibrators
1
Introduction
• There are two different approaches for the generation of
sinusoids, most commonly used for the standard
waveforms:
– Employing a positive-feedback loop that consists an
amplifier and an RC or LC frequency-selective
network. It generates sine waves utilizing resonance
phenomena, are known as linear oscillators (circuits
that generate square, triangular, pulse waveforms are
called non-linear oscillators or function generators.)
– A sine wave is obtained by appropriate shaping a
triangular waveform.
2
The Oscillator Feedback Loop
A basic structure of a sinusoidal oscillator consists of an amplifier and a frequencyselective network connected in a positive-feedback loop.
The condition for the feedback loop to provide sinusoidal oscillations of
frequency w0 is
Barkhausen Criterion:
 At w0 the phase of the loop gain should be zero.
 At w0 the magnitude of the loop gain should be unity.
LC and Crystal Oscillators
For higher frequencies (> 1MHz)
wo 
1
C1C 2
L(
)
C1  C 2
wo 
1
( L1  L2)C
(a) Colpitts and (b) Hartley.
Hartley Oscillator
Used in radio receivers and transmitters More stable than Armstrong
oscillators Radio frequency choke (RFC)
L2
L1
C
f0 
1
where Leq  L1  L2  2M
2 LeqC
M  Mutual coupling between L1 & L2
Colpitts Oscillators
BJT; FET; and IC Based
Rf
C1
C2
LC network
f0 
1
2 LCeq
where Ceq 
-
Ri
C1
C2
LC network
C1C2
C1  C2
RFC is an impedance which is high (open) at high RF frequencies and low (short)
to dc voltages
Equivalent Circuit of the Colpitts Oscillator
wo 
Complete Circuit for a Colpitts Oscillator
1
C1C 2
L(
)
C1  C 2
Crystal Oscillators
Crystal is a piezo-electric device which converts mechanical pressure to electrical voltage or vice-vasa
Series frequency  f S 
Parallel frequency  f P 
1
2 CS L
1
 CC 
2  S P  L
 CS  CP 
Radio communications, broadcasting stations
Piezoelectric effect
Why are crystal oscillators used in many commercial
transmitters?
8
An Application of Crystal Oscillator
Crystals are fabricated by cutting the crude quartz in a very exacting
fashion. The type of cut determines the crystal’s natural resonant frequency
as well as it’s temperature coefficient.
Crystal are available at frequencies about 15kHz and up providing the
best frequency stability. However above 100MHz, they become so small
that handling becomes a problem.
Two crystals producing two different frequencies for measuring
temperature Timing devices
9
Op-Amp Crystal Oscillator
Op-amp voltage gain is controlled by the negative feedback circuit formed by Rf and
R1. More NFB will damp the oscillation, critical NFB will have a sine wave output and
less NFB will have a square wave output.
It is very flexible to construct the Op. Amp.
crystal oscillator due to high amplifier gain
and differential input facility of the Op.
Amp.
The two Zener diodes connected face to
face is to limit the peak to peak output
voltage equal to twice of Zener voltage.
Rf
R1
Op-amp
+
R2
Vz
Cs
The crystal is fed in series to the positive feedback which is required for oscillation.
Therefore the oscillation frequency will be crystal series resonant frequency fs.
10
Example
Crystal used instead of inductor in the tank
circuit of Colpitts oscillator
11
The Phase Shifter Oscillator
The phase-shifter consists of a negative gain amplifier (-K) with a third
order RC ladder network in the feedback.
The circuit will oscillate at the frequency for which the phase shift of the
RC network is 180o. Only at the frequency will the total phase shift around
the loop be 0o or 360o.
The minimum number of RC sections is 3 because it is capable of
producing a 180o phase shift at a finite frequency.
A
Phase-shift Oscillator
VDD
f = 1kHz
bAVi
AVi
R
Rb
C
C
C
R
R
C= ?
rd= 40k 
gm= 5000mS
R=10k 
1
2RC 6
Example:
Determine the value of capacitance C and the
value of RD of the Phase-shift oscillator
shown, if the output frequency is 1 kHz. Take
rd = 40k and
gm=5000mS, for the FET and R = 10kW.
Condition of oscillation
1 Ab  1
29  A  29
C
C
Frequency of oscillation
b
R
R
bAVi = Vi (or) Ab =1
f 
b
RD= ?
A
Vi
FET Phase-shift Oscillator
1
1
1
C 

 6.5nF
2RC 6
2Rf 6 2 10k  1k 6
40
40
Ab  1 Let A  40  29 A  g m RL  40  RL 

 8k
g m 5000S
f 
But RL  RD // rd  RD // 40k  8k  RD 
8k  40k
 10k
40k - 8k
BJT Phase-Shift Oscillator
VDD
R
Example:
RC
C= ?
Determine the value of capacitance C and
the value of hfe of the Phase-shift oscillator
shown, if the output frequency is 1kHz.
Take R=10 k. RC =1 k.
R1
C
R
C
R
R2
R’
Frequency of oscillation
f 
1
2RC 6  4 RC / R
Condition of oscillation
Ab  1  A  29
b
1
29
R
R
for BJT  h fe  23  29  4 C
RC
R
f 
1
1
 1kHz 
2RC 6  4 RC / R
2 10kC 6  4  1k / 10k
C
1
 0.006F  6nF
2 10k  1k 6  4  1k / 10k
for BJT  h fe  23  29
 23  29
R
R
4 C
RC
R
10k
1k
4
 23  290  0.4  313.4
1k
10k
14
IC Phase-shift Oscillator
Frequency of oscillation
R
i
Ab  1 A  29
for IC inverting amplifier ,
R
1
A  f  29 b 
29
Ri
+
Condition of oscillation
-
1
f 
2RC 6
Rf
b
A
C
C
R
C
R
R
Example:
Determine the value of capacitance C and the value of Rf of the IC Phase-shift oscillator
shown, if the output frequency is 1kHz. Take R =10kW. Ri =1kW.
f 
1
1
1
C 

 6.5nF
2RC 6
2Rf 6 2 10k  1k 6
for IC inverting amplifier ,
R
A  f  29  R f  29 Ri  29k
Ri
15
Wien Bridge Oscillator
R1
C1
+
-
Frequency of oscillation
f 
1
2 R1C1 R2C2
f 
1  if R1  R2  R 


2RC  C1  C2  C 
Condition of oscillation
R2
C2
R4 R3
R3 R1 C2
 
R4 R2 C1
 if R1  R2  R 
R3

 2 
R4
 C1  C2  C 
Example: Determine the value of capacitance C1 and R1 if R2 =10kW C2 = 0.1mF R3 =10k R4
=1kW in the Wien bridge oscillator shown has an output frequency of 1kHz.
1
1
f 
 f2
4 2 R1C1 R2C2 Frequency of oscillation
2 R1C1 R2C2
R1C1 
1
1
0.025ms


0
.
025
ms

C

2
1
4 2 f 2 R2C2 4 2 1k  10k  0.1
R1
R3 R1 C2
10k
R
0.1F
R
0.1



 1 
 1  10  9.996
R4 R2 C1
1k
10k 0.025ms
10k
25
R1  9.996  10k  99.96k  100k
C1 
0.025ms
 0.00025  250 pF
100k
Condition of oscillation
Tuned Oscillators (Radio Frequency Oscillators)
Tuned oscillator is a circuit that generates a radio frequency output by using LC
tuned (resonant) circuit. Because of high frequencies, small inductance can be
used for the radio frequency of oscillation.
Tuned-input and tuned-output Oscillator
tuned-output
feedback coupling
L2
C2
Cci
Cco
RF output
f0 
tuned-input
C1
L1
1
1

2 L1C1 2 L2C2
17
The Active-Filter-Tuned Oscillator
Assume the oscillations have already started. The output of the band-pass filter will be
a sine wave whose frequency is equal to the center frequency of the filter.
The sine-wave signal is fed to the limiter and then produces a square wave.
Practical implementation of the active-filter-tuned oscillator
Bistable Multivibrators
Another type of waveform generating circuits is the nonlinear oscillators
or function generators which uses multivibrators.
A bistable multivibrator has 2 stable states. The circuit can remain in
either state indefinitely and changes to the other one only when triggered.
Metastable state: v+=0 and vO=0. The
circuit cannot exist in the mestastable
state for any length of time since any
disturbance causes it to switch to
either stable state.
Bistable Circuit with Inverting Transfer Characteristics
Assume that vO is at one of its two possible levels, say L+, and thus v+ = βL+.
 As vI increases from 0 and then exceeds βL+, a negative voltage developes between
input terminals of the op amp.
 This voltage is amplified and vO goes negative.
 The voltage divider causes v+ to go negative, increasing the net negative input and
keeping the regenerative process going.
 This process culminates in the op amp saturating, that is, vO = L-.
The circuit is said to be inverting
Trigger signal
Bistable Circuit with Noninverting Transfer Characteristics
Application of the Bistable Circuit as a Comparator
To design a circuit that detects and counts the zero crossings of an arbitrary
waveform, a comparator whose threshold is set to 0 can be used. The comparator
provides a step change at its output every time zero crossing occurs.
Bistable Circuit with More Precise Output Level
Limiter circuits are used to obtain more precise output levels for the bistable circuit.
L+ = VZ1 + VD and L– = –(VZ2 + VD),
where VD is the forward diode drop.
L+ = VZ + VD1 + VD2 and L– = –(VZ +
VD3 + VD4).
Operation of the Astable Multivibrator
Connecting a bistable multivibrator with inverting transfer characteristics in a
feedback loop with an RC circuit results in a square-wave generator.
Operation of the Astable Multivibrator
Generation of Triangular Waveforms
Triangular waveforms can be obtained by replacing the low-pass RC circuit
with an integrator. Since the integrator is inverting, the inverting characteristics
of the bistable circuit is required.
Generation of a Standard Pulse
In the stable state, VA=L+ (why?), VB=VD1, VC=βL+ (D2: ON and R4>>R1).
When a negative-going step applies at the trigger input:
 D2 conducts heavily and pulls node C down (lower than VB).
 The output of the op amp switch to L- and cause VC to go toward βL-.
 D2 OFF and isolates the circuit from changes at the trigger input.
 D1 OFF and C1 begins to discharge toward L-.
 When VB < VC, the output of the op amp switch to L+.
Generation of a Standard Pulse
The 555 Circuit
Commercially available integrated-circuit package such as 555 timer exists that
contain the bulk of the circuitry needed to implement monostable and astable
multivibrator.
2/3 VCC
1/3 VCC