Lecture 10 OSCILLATOR I Electronics Circuit design

1. 1
Oscillators

2. 2
¾Oscillators are circuits that generates a repetitive
waveform of fixed amplitude and frequency without any
external input signal.
¾The function of an oscillator is to generate alternating
current or voltage waveforms.
¾The only input to oscillator is the dc power supply
¾Oscillator are used in radio, television, computers and
communications.
¾Oscillator can be viewed as a signal generator
Introduction

3. 3
Oscillator Principles
•An oscillator is a type of f/b amp. In which part of the o/p is
f/b to the i/p via a feedback circuit.
•If the signal f/b is of proper magnitude & phase, the circuit
produces alternating currents or voltages.
•Input voltage is zero (Vin=0).
•The f/b is positive because most oscillator use positive f/b.

4. 4
Oscillator Principles
From the figure,
, ,
Hence;
but and
Therefore Expressed in polar
in
f
d v
v
v +
= 0
Bv
v f = d
vv
A
v =
0
B
A
A
v
v
v
v
in −
=
1
0 0
=
in
v 0
0 ≠
v
1
=
B
Av
o
o
360
0
1 or
B
Av ∠
=
1. The magnitude of the loop gain must be at least 1
2. The total phase shift of the loop gain must be equal to
o
o
360
0 or

5. 5
The types of Oscillator
An oscillator is a circuit that produces a repetitive signal from a dc
voltage.
The feedback type oscillator which rely on a positive feedback of
the output to maintain the oscillations.
The relaxation oscillator makes use of an RC timing circuit to
generate a non-sinusoidal signal such as square wave.

6. 6
F/b type oscillator Vs relaxation oscillator
„ Both use active (transistor, op-amp) and
passive components (R,L,C)
„ F/b type oscillator
‰ produces sine wave
‰ f/b determines the oscillation frequency
„ Relaxation oscillator
‰ produces non-sinusoidal wave (square etc)
‰ use of an RC timing circuit to generate a non-
sinusoidal signal

7. 7
Feedback Oscillator Principles
The feedback oscillator is widely used for generation of sine
wave signals. The positive (in phase) feedback arrangement
maintains the oscillations. The feedback gain must be kept to
unity to keep the output from distorting.

8. 8
Positive Feedback
„ In-phase portion of the output voltage of an amplifier is fed back to
the input with no net phase shift.
„ Vf - in-phase f/b voltage is amplified to produce the output voltage.
„ The loop –sustains the signal-produce continuous sinusoidal output
voltage. This phenomenon is called oscillation.

9. 9
Conditions for oscillation
„ 2 conditions
‰ Phase shift around the f/b loop = 0 / 360 degree
(the circuit must have a positive f/b)
‰ The loop gain, Acl must equal to 1
(this condition called the Barkhausen Criterion)
1
=
= B
A
A V
cl

10. 10
Oscillators Types
„ RC Oscillator
- generate a sinusoidal waveform at a few Hz to kHz range
- Wien-bridge, the phase-shift, and the twin-T
„ LC Oscillator
- generate a sin wave at frequencies of 100 kHz to 100 MHz
- Colpitts, Clapp, Hartley, and Armstrong
„ Crystal Oscillator
- generate a square or sin wave over a wide range,i.e. about 10
kHz to 30 MHz
- more stable than RC & LC especially at high frequency

11. 11
FEEDBACK OSCILLATORS:
RC OSCILLATOR
1. Wien-bridge
2. Phase-shift
3. Twin-T

12. 12
Oscillators With RC Feedback Circuits
ƒRC feedback oscillators are generally limited to frequencies
of 1 MHz or less.
ƒThe types of RC oscillators that we will discuss are the
Wien-bridge and the phase-shift.

13. 13
1. Wien-Bridge Oscillator

14. 14
Cont…
( )( ) 2
1
2
2
1
1
1
1
1
1
1 R
C
j
R
C
j
R
C
j
R
C
j
V
V
o ω
ω
ω
ω
+
+
+
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ +
+
+
=
2
2
2
1
1
1
2
2
2
1
1
2
2
1
1
2
1
1
1
ω
ω
ω
C
R
C
R
C
R
C
R
C
R
j
C
R
C
R
C
R
j
V
V
o
Multiply the top and bottom by jωC1,
we get
Divide the top and bottom by C1 R1 C2 R2
o
o V
V
K
V
V 1
'
1 1
=
=
Now the amp gives
Furthermore, for steady state oscillations, we want the feedback
V1 to be exactly equal to the amplifier input, V1’. Thus
K
V
V
=
'
1
0

15. 15
Cont…
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ +
+
+
=
2
2
2
1
1
1
2
2
2
1
1
2
2
1
1
2
1
1
1
ω
ω
ω
C
R
C
R
C
R
C
R
C
R
j
C
R
C
R
C
R
j
K
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ +
+
+
= 2
2
2
1
1
1
2
2
2
1
1
2
2
1
1
2
1
1
ω
ω
ω
C
R
C
R
C
R
C
R
C
R
j
C
R
C
R
C
R
K
j
0
1 2
2
2
1
1
=
−ω
C
R
C
R
Hence
Equating the real parts,
1
2
1
2
2
2
1
1
C
R
C
R
C
R
C
R
K
+
+
=
3
=
K RC
1
=
ω
If R1 = R2 = R and C1 = C2 = C
- Gain > 3 : growing oscillations
- Gain < 3 : decreasing oscillations
RC
fr
π
2
1
=

16. 16
The lead-lag circuit of a Wien-bridge oscillator reduces the input
signal by 1/3 and yields a response curve as shown. The
frequency of resonance can be determined by the formula below.
fr = 1/2πRC
Fundamental part of the Wien-Bridge Oscillator

17. 17
Basic Circuit for Wien Bridge Oscillator
The lead-lag circuit is in the
positive feedback loop of Wien-
bridge oscillator. The voltage
divider limits gain. The lead lag
circuit is basically a band-pass
with a narrow bandwidth.

18. 18
Positive Feedback Condition
Since there is a loss of about 1/3 of the signal in the positive
feedback loop, the voltage-divider ratio must be adjusted
such that a positive feedback loop gain of 1 is produced. This
requires a closed-loop gain of 3. The ratio of R1 and R2 can
be set to achieve this.
)
/(
1
1
2
1
2 R
R
R
B
Acl
+
=
=
2
2
1
R
R
R +
=
2
1 2R
R =
3
2
2
1
=
+
=
R
R
R
Acl
To achieved a Acl of 3

19. 19
Start-Up Conditions
To start the oscillations an initial gain greater than 1 must be
achieved. The back-to-back zener diode arrangement is one way
of achieving this. When dc is first applied the zeners appear as
opens. This allows the slight amount of positive feedback from turn
on noise to pass.
When dc power is first applied, the zener
diode appears as open, thus
2
1 2R
R =
1
3
2
3
2
2
3
2
1
3
3
R
R
R
R
R
R
R
R
R
Acl +
=
+
=
+
+
=

20. 20
Cont…
The lead-lag circuit narrows the feedback to allow just the
desired frequency of these turn transients to pass. The higher
gain allows reinforcement until the breakover voltage for the
zeners is reached.

21. 21
Cont…
•Zener arrangement for gain control is simple but produces
distortion because of the non-linearity of zener diodes.
•Automatic gain control (AGC) - maintain a gain of exact
unity.
•A JFET in the negative feedback loop can be used to precisely
control the gain. After the initial startup and the output signal
increases the JFET is biased such that the negative feed back
keeps the gain at precisely 1.

22. 22
2. Phase Shift Oscillator
The phase shift oscillator utilizes three RC circuits to provide
180º phase shift that when coupled with the 180º of the op-
amp itself provides the necessary feedback to sustain
oscillations. The gain must be at least 29 to maintain the
oscillations. The frequency of resonance for the this type is
similar to any RC circuit oscillator.
The feedback, B is
The frequency of oscillator,
29
1
=
B
RC
fr
6
2
1
π
=

23. 23
Cont…
The transfer function of the RC network is

24. 24
Cont…
If the gain around the loop equals 1, the circuit oscillates at this
frequency. Thus for the oscillations we want,
Putting s=jω and equating the real parts and imaginary parts,
we obtain

25. 25
Cont…
From equation (1) ;
Substituting into equation (2) ;
# The gain must be at least 29 to maintain the oscillations.

26. 26
3. Twin-T Oscillator
•The twin-T – 2 types RC filters (LPF & HPF) used in feedback loop-
utilizes a bandstop/notch arrangement of RC circuits to block all but the
frequency of operation in the negative feedback loop.
•The only frequency allowed to effectively oscillate is the frequency of
resonance, fr
•Oscillation only occur at fr where positive f/b through the voltage divider
exist. Negative f/b is negligible.