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1. OSCILLATORS

2. Oscillators
Describe the basic concept of an oscillator
Discuss the basic principles of operation of an
oscillator
Analyze the operation of RC, LC and crystal
oscillators
Describe the operation of the basic relaxation
oscillator circuits
Objectives

3. Oscillators
Introduction
Oscillators are circuits that produce a continuous
signal of some type without the need of an input.
These signals serve a variety of purposes.
Communications systems, digital systems
(including computers), and test equipment make
use of oscillators.

4. Oscillatorsdc supply
voltage
V
out
or
or
Oscillator
Oscillator is an electronic circuit that generates a periodic
waveform on its output without an external signal source.
It is used to convert dc to ac.
The waveform can be sine wave, square wave, triangular wave,
and sawtoothwave.

5. Oscillators
An oscillator is a circuit that produces a repetitive
signal from a dc voltage.
The feedback oscillatorrelies on a positive
feedback of the output to maintain the
oscillations.
The relaxation oscillatormakes use of an RC
timing circuit to generate a nonsinusoidal signal
such as square wave.

6. Oscillators
Types of oscillators
1. RC oscilators
-Wien Bridge
-Phase Shift
2. LC oscillators
-Hartley
-Colpitts
3. Relaxation oscilators

7. Oscillators
Basic principles for oscillation
An oscillator is an amplifier with positive feedback.(1)
fse
VVV  (2)
of
βVV   (3)
osfseo
βVVAVVAAVV  A
b
V
e
V
f
V
s
V
o
+

8. Oscillators  
osfs
eo
βVVAVVA
AVV


oso VAAVV b  
soAVVA b1

9. Oscillators Aβ
A
V
V
A
s
o
f


1
The closed loop gain is;A
b
V
e
V
f
V
s
V
o
+

10. Oscillators
In general Aand bare functions of frequency and
thus may be written as; 

sβsA1
sA
s
V
V
sA
s
o
f

 sβsA
is known as loop gain

11. Oscillators
WritingssβAsT the loop gain becomes;

sT1
sA
sA
f


Replacing swith j;

jωT1
jωA
jωA
f


andjωβjωAjωT 

12. Oscillators
At a specific frequency f
0;1
000  jωβjωAjωT
At this frequency, the closed loop gain;


00
0
0
jωβjωA1
jωA
jωA
f


will be infinite, i.e. the circuit will have finite output
for zero input signal -oscillation

13. Oscillators
Thus, the condition for sinusoidal oscillation of
frequency f
0
is;1
00 jωβjωA
This is known as Barkhausen criterion.

14. Oscillators
Thefeedbackoscillatoriswidelyusedforgenerationof
sinewavesignals.Thepositive(inphase)feedback
arrangementmaintainstheoscillations.Thefeedback
gainmustbekepttounitytokeeptheoutputfrom
distorting.In phase
Noninverting
amplifier
V
f V
o
A
v
Feedback
circuit
If the feedback circuit
returns the signal out of
phase, an inverting
amplifier produces
positive feedback.

15. Oscillators
Design Criteria for Oscillators
1. The magnitude of the loop gain must be unity
or slightly larger i.e.1Aβ
–Barkhaussen criterion
2. Total phase shift,of the loop gain must be 0°
or 360°.

16. Oscillators
Factors determining the frequency of
oscillation
Oscillators can be classified into many types
depending on the feedback components,
amplifiers and circuit topologies used.
RC components generate a sinusoidal waveform
at a few Hz to kHz range.
LC components generate a sine wave at
frequencies of 100 kHz to 100 MHz.
Crystals generate a square or sine wave over a
wide range,i.e. about 10 kHz to 30 MHz.

17. 1. RC Oscillators
Oscillators

18. Oscillators
1. RC Oscillators
RC feedback oscillators are generally limited to
frequencies of 1 MHz or less.
The types of RC oscillators that we will discuss are
the Wien-bridgeand the phase-shift.

19. The Wien-Bridge Oscillator
RCfeedback 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 ⅓of the input at only
one frequency and the phase shift at this frequency will be 0
o
.
Oscillators –Wein–bridge oscillatorV
in V
out

20. The lead-lag circuit of a Wien-bridge oscillator
reducesthe input signal by 1/3 and yields a
response curve as shown. The frequency of
resonance can be determined by the formula
below.RC
f
r
2
1

Oscillators –Wien-bridge

21. Oscillators –Wien-bridge
It is a low frequency oscillator which ranges from a few
kHz to 1 MHz.
Structure of this oscillator is shown below;V
out
–
+
R
4
R
3
R
2
R
1
C
1
C
2
Lead-lag
network
Voltage-
divider

22. The lead-lag circuit of a Wien-bridge oscillator
reducesthe input signal by 1/3 and yields a
response curve as shown. The frequency of
resonance can be determined by the formula
below.RC
f
r
2
1

Oscillators –Wien-bridge

23. 


















sp
p
ZZ
Z
R
R
sβsAsT
1
2
1 The loop gain for the oscillator is
where;sRC
R
Z
p


1
and;sC
sRC
Z
s


1
Oscillators –Wien-bridge

24. 
 
















/sRCsRCR
R
sT
13
1
1
1
2 Hence;
Substituting for s;
 
















RC/jRCjR
R
jT


13
1
1
1
2
Oscillators –Wien-bridge

25. For oscillation frequency f
0;
 
















RC/jRCjR
R
jT
001
2
0
13
1
1


Since at the frequency of oscillation, T(j) must be
real (for zero phase condition), the imaginary
component must be zero i.e.;0
1
0
0 
RCj
RCj


Oscillators –Wien-bridge

26. Which gives us;RC
1
0
Oscillators –Wien-bridge

27. From the previous equation;














3
1
11
1
2
R
R 
 
















RC/jRCjR
R
jT
001
2
0
13
1
1


the magnitude condition is;
or;2
1
2

R
R
To ensure oscillation, the ratio R
2/R
1must
be slightly greater than 2.
Oscillators –Wien-bridge

28. With the ratio;2
1
2

R
R 31
1
2

R
R
K
then;
K= 3 ensures the loop gain of unity –oscillation.
-K> 3 : growing oscillations
-K< 3 : decreasing oscillations
Oscillators –Wien-bridge

29. The lead-lag circuit
is in the positive
feedback loop of
Wien-bridge
oscillator. The
voltage divider
limits the gain.
The lead lag circuit
is basically a band-
pass with a narrow
bandwidth.
Oscillators –Wien-bridge

30. Sincethereisalossofabout1/3ofthesignalinthe
positivefeedbackloop,thevoltage-dividerratiomust
beadjustedsuchthatapositivefeedbackloopgainof1
isproduced.Thisrequiresaclosed-loopgainof3.The
ratioofR
1andR
2canbesettoachievethis.
Oscillators –Wien-bridge

31. To start the oscillations an initial loop gain
greater than 1 must be achieved.
Oscillators –Wien-bridge

32. The back-to-back zener diode arrangement is
one way of achieving this.
Oscillators –Wien-bridge oscillator using back-to-
back zener diode. R
1
R
2
R
3
D
1D
2
+

V
out
Lead-lag
1/3
f
r

33. When dc is first applied the zeners appear
as opens. This allows the slight amount of
positive feedback from turn on noise to pass.
Oscillators –Wien-bridge
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.

34. Automatic gain controlis necessary to maintain
a gain of exact unity.
The zener arrangement for gain control is simple
but produces distortion because of the nonlinearity
of zener diodes.
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 feedback keeps the gain at precisely 1.
Oscillators –Wien-bridge oscillator using a JFET
negative feedback loop

35. Oscillators –Wien-bridge

36. Oscillators –Wien-bridge
When the R’s and C’s in the feedback circuit are equal, the frequency of
the bridge is given byR
f
R
3
R
1
R
2
C
1
Q
1
C
2
–
+
V
out
C
3R
4
D
1 1
2π
r
f
RC

10 kW
1.0 kW 10 kW
680 W
680 W
4.7 nF
4.7 nF
1.0 mF
What is f
rfor the Wien bridge?  
1
2π
1
2π 680 4.7 nF
r
f
RC


W
= 48.9 kHz

37. Oscillators –Phase-shift. C C C
R R
R
R
f
+

V
o0 V
The three RC circuits combine to produce a phase shift of 180
o
.
Fig. 3 shows a circuit containing three RC circuits in its
feedback network called the phase-shift oscillator.

38. Oscillators –Phase-shift
The phase shift oscillator utilizes three RC
circuitsto 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.RC
f
r
62
1



39. Oscillators –Phase-shift
The transfer function of the RC network is 











1
651
1
222333
sCRRCsRCs
V
V
i
o
Phase-shift network V
i V
o
V
1 V
2
I
1
I
2
I
3
I
4
I
5
C
R R R
C C
I
6

40. Oscillators –Phase-shift
If the gain around the loop equals 1, the circuit
oscillates at this frequency. Thus for the
oscillations we want,1TFK
or;01
651
222333
 K
sCRRCsRCs

41. Oscillators –Phase-shift
Putting s= jand equating the real parts and
imaginary parts to zero at = 
o, we obtain;)1(0
61
333

 CRjRCj
oo 
Imaginary part:CR
o
6
1


42. Oscillators –Phase-shift)2(01
5
222
 K
RC
o
Real part:29K CR
o
6
1

Conditionsforoscillationwith
thephase-shiftoscillatoris
thatifallR’sandC’sare
equal,theamplifiermusthave
againofatleast29tomake
upfortheattenuationofthe
feedbackcircuit.Thismeans
thatR
f/R
3≥29.

43. Oscillators –Phase-shift. C C C
R R
R
R
f
+

V
o0 V
ThelastRhasbeen
incorporatedintothe
summingresistorsatthe
inputoftheinvertingop-
amp.
Even with identical R’s and C’s,
the phase shift in each RCcircuit
is slightly different because of
loading effects. When all R’s and
C’s are equal, the feedback
attenuates the signal by a factor
of 29.

44. Design a phase-shift oscillator for a frequency of 800 Hz. The
capacitors are to be 10 nF.
Start by solving for the resistors needed in the feedback
circuit:  
11
2π 6 2π 6 800 Hz 10 nF
r
R
fC
  
8.12 kW(Use 8.2 kW.)
R
f= 29R= 238 kW. –
+
V
out
R
2
R
f
R
1 R
3
C
3C
2C
1
Calculate the feedback
resistor needed:
10
nF
10
nF
10
nF
8.2 kW8.2 kW
8.2 kW
238 kW
Oscillators –Phase-shift