oscillators introduction abcdefghijklmno

oscillators

1. OSCILLATORS

2. Objectives

+ 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

3. 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. 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 sawtooth wave.

dc supply

voltage NSVVY

Oscillator

5. An oscillator is a circuit that produces a repetitive
signal from a dc voltage.

The feedback oscillator relies on a positive
feedback of the output to maintain the
oscillations.

The relaxation oscillator makes use of an RC
timing circuit to generate a nonsinusoidal signal
such as square wave.

6. Types of oscillators

1. RC oscilators
- Wien Bridge
- Phase Shift

2. LC oscillators
- Hartley
- Colpitts

3. Relaxation oscilators

7. Basic principles for oscillation

> An oscillator is an amplifier with positive feedback.

y, PE (1)
V,=PV, (2)
V,= AV, =A(V, +V,)=A(V, + PV,) (3)

8. V, = AV

oO e

= AV, +V,)= AV, + BV.)
V, = AV, + ABV,

(1- AP), = AV,

9. The closed loop gain is;

10. In general A and fare functions of frequency and
thus may be written as;

4,(s)="2(s)= _

v,* 2 1-Als)p(s)

A(s)p(s) is known as loop gain

11. Writing T(s)= A(s)ß (s) the loop gain becomes;

As)
AS

Replacing s with ja;

A(jo)
1-T(jo)

A,(jo)=
and

T(jo)= A(jo)B( jo)

12. Ata specific frequency fi;
T(jo,)= A(jo,)Pljo,)=1
At this frequency, the closed loop gain;

A(jo,)
I- A(jo, io)

will be infinite, i.e. the circuit will have finite output
for zero input signal - oscillation

A, (jo, ) =

13. Thus, the condition for sinusoidal oscillation of
frequency fy is;

A(jo, Pio, ) =i

This is known as Barkhausen criterion.

14. 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.

Os

Noninverting
amplifier |

ja
«circuit \/

15. Design Criteria for Oscillators

1. The magnitude of the loop gain must be unity
or slightly larger i.e.

[AP =1 — Barkhaussen criterion

2. Total phase shift, $ of the loop gain must be 0°
or 360°.

16. 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
ata 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

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-bridge and the phase-shift.

18. Oscillators — Wein-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 % of the input at only
one frequency and the phase shift at this frequency will be 0°.

19. Oscillators - Wien-bridge

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.

20. 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;

R
AWW
Ri
AWN —o— =
UN 40 Vo 1
+ v, SR
~ E Voltage-
Sao divider
I
(o) ——— Hum
ss ne *: z,
¡ canes
i+ a
ape E » 2% = Lead-lag
asie sis eel network

21. Oscillators - Wien-bridge

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.

22. Oscillators - Wien-bridge

The loop gain for the oscillator is

| Ze |

À Z,+Z,
where;
Z= fi
P 1+sRC
and;
z _1+sRO

à sC

23. Oscillators - Wien-bridge

Hence;

rt

Substituting for s;

R, 1
T(jo)=| 142
Ge) | TR, co

24. Oscillators - Wien-bridge

For oscillation frequency fj;

R |
T{ ja, )=| 1+
Go.) | R Emo]

Since at the frequency of oscillation, T(j@) must be
real (for zero phase condition), the imaginary
component must be zero i.e.;

J@,RC +— -=0
JO RC

25. Oscillators - Wien-bridge

Which gives us;

a, = —

26. Oscillators - Wien-bridge

From the previous equation;

R |
modal El 1
(jo) | TR Ex m.

the magnitude condition is;

[= 14% 8 or; dls y
E R,

To ensure oscillation, the ratio R,/R, must
be slightly greater than 2.

27. Oscillators - Wien-bridge

With the ratio;

then;

K =3 ensures the loop gain of unity — oscillation.

- K > 3: growing oscillations
- K <3: decreasing oscillations

28. Oscillators - Wien-bridge

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.

29. 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 R, and R, can be set to achieve this.

Positive

feedback loop = Loop gain =

Phase shift = 0°

Lead-lag d-lag

(a) The phase shift around the loop is 0°. (b) The voltage gain around the loop is 1.

30. Oscillators - Wien-bridge

To start the oscillations an initial loop gain
greater than 1 must be achieved.

31. Oscillators — Wien-bridge oscillator using back-to-

back zener diode

The back-to-back zener diode arrangement is
one way of achieving this.

32. Oscillators - Wien-bridge

3 When dc is first applied the zeners appear
as opens. This allows the slight amount of
positive feedback from turn on noise to pass.

>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.

33. Oscillators — Wien-bridge oscillator using a JFET
negative feedback loop

Automatic gain control is 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.

34. Oscillators - Wien-bridge

35. Oscillators - Wien-bridge

When the R’s and C's in the feedback circuit are equal, the frequency of
the bridge is given by

example:
What is f, for the Wien bridge?

Solution:

1
2nRC

f=

1
21680 Q)(4.7 nF)

= 48.9 kHz

36. Oscillators - Phase-shift

The three RC circuits combine to produce a phase shift of 180°.

Fig. 3 shows a circuit containing three RC circuits in its
feedback network called the phase-shift oscillator.

37. Oscillators - Phase-shift

The phase shift oscillator utilizes three RC
circuits to provide 180° phase shift that when
coupled with the 180° 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.

1
27 V6RC

NA

38. Oscillators - Phase-shift

Phase-shift network
ee ¢ Fm €

3773 D3 + 2772 p2 + = +1
sCR s CR sCR

39. Oscillators - Phase-shift

If the gain around the loop equals 1, the circuit
oscillates at this frequency. Thus for the
oscillations we want,

K(TF)=1
OF,
1 5 6

—— toma + +l-K=0
SE A FOR stk

40. Oscillators - Phase-shift

Putting s = jo and equating the real parts and
imaginary parts to zero at w= @,, we obtain;

Imaginary part:

1 6
— + ———=0
—jaR jo CR

L, .-.
O, ===
° J6CR

(1)

41. Oscillators - Phase-shift

Real part:
5
CR

+1-K=0 (2)

by .-

1
o J6CR

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 R,/R,2 29.

42. Oscillators - Phase-shift

Even with identical R's and C's, The last R has been
ig eae oe RC incorporated into the
is slightly different because o R i

loading effects. When all R's and summing resistors at the
C's are equal, the feedback input of the inverting op-
attenuates the signal by a factor amp.

of 29.

43. Oscillators - Phase-shift

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:
1 1
R= = =
me mel) 224 (Use8.2 ka)

Calculate the feedback
8

resistor needed:
R,= 29R = 238 ka. a
— à a a a
| ram ! HH
E 10