OSCILLATOR

Objectives

 Describe the basic concept of an oscillator

 Discuss the basic principles of operation of an
oscillator
 Describe the operation of Phase-Shift Oscillator, Wien
Bridge Oscillator, Crystal Oscillator and
Relaxation Oscillator
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
such as communications systems, digital
systems (including computers), and test
equipment
The Oscillator

 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 non-sinusoidal signal
such as square wave.
The Oscillator
Types of Oscillator
1. RC Oscillator - Wien Bridge Oscillator
- Phase-Shift Oscillator
2. LC Oscillator - Crystal Oscillator
3. Relaxation Oscillator
 Feedback Oscillator Principles

Positive feedback circuit used as an

oscillator
 When switch at the amplifier input is open, no oscillation
occurs.
 Consider Vi,, results in Vo=AVi (after amplifier stage) and Vf =
(AVi) (after feedback stage)
 Feedback voltage Vf = (AVi) where A is called the loop gain.
 In order to maintain Vf = Vi , A must be in the correct
Feedback Oscillator Principles

Positive feedback circuit used as an

oscillator
 When the switch is closed and Vi is removed, the circuit will
continue operating since the feedback voltage is sufficient
to drive the amplifier and feedback circuit, resulting in proper
input voltage to sustain the loop operation.
Feedback Oscillator Principles
 An oscillator is an amplifier with positive
feedback.

Ve = Vi + Vf (1)
Vo = AVe (2)
Vf = (AVe)=Vo (3)

From (1), (2) and (3), we get

Vo A
Af  
Vs 1  Aβ  where A is loop gain
Feedback Oscillator Principles
In general A and  are functions of frequency and thus
may be written as;

Vo As 
A f s   s  
Vs 1  As β s 

As β s  is known as loop gain

Feedback Oscillator Principles
Writing T s   As β s  the loop gain becomes;

As 
A f s  
1  T s 
Replacing s with j;
A jω
A f  jω 
1  T  jω

and T  jω  A jωβ  jω

Feedback Oscillator Principles
At a specific frequency f0;

T  jω0   A jω0 β  jω0  1

At this frequency, the closed loop gain;

A jω0  A jω0 
A f  jω0    
1  A jω0 β  jω0  (1  1)

will be infinite, i.e. the circuit will have finite output

for zero input signal – thus we have oscillation
 Design Criteria for oscillators

1) |A| equal to unity or slightly larger at the

desired oscillation frequency.
- Barkhaussen criterion, |A|=1

2) Total phase shift, of the loop gain must be

0° or 360°.
 Build-up of steady- state oscillations

 The unity gain condition

must be met for oscillation
to be sustained
 In practice, for
oscillation to begin, the
voltage gain around the
positive feedback loop
must be greater than 1
so that the amplitude of
the output can build up to
the desired value.
Build-up of steady-state  If the overall gain is
oscillations
greater than 1, the
Build-up of steady- state oscillations

Then voltage gain

decreases to 1 and
maintains the desired
amplitude of waveforms.
 The resulting
waveforms are never
exactly sinusoidal.
 However, the closer
the value A to 1, the more
nearly sinusoidal is the
waveform.
Buildup of steady-state
oscillations
Factors that determine 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.
1. RC Oscillators
1. RC Oscillators

 RC feedback oscillators are generally limited to

frequencies of 1MHz or less
 The types of RC oscillators that we will discuss are
the Wien-Bridge and the Phase Shift
Wien-Bridge Oscillator

 Itis a low frequency oscillator which ranges

from a few kHz to 1 MHz.
 Structure of this oscillator is
 Wien-Bridge Oscillator
 Based on op amp
 Combination of R’s and C’s in
feedback loop so feedback factor
βf has a frequency dependence.
 Analysis assumes op amp is ideal.
 Gain A is very large

 Input currents are negligibly

R2
small (I+  I_  0).
R1  Input terminals are virtually
shorted (V+  V_ ).
V0
 Analyze like a normal feedback
Vi
ZS amplifier.
If
 Determine input and output

loading.
ZP  Determine feedback factor.

 Determine gain with feedback.

 Shunt-shunt configuration.
Wien Bridge Oscillator

Define
R1 R2 1 1  sRC
Z S R  Z C R  
V0 sC sC
1 1
Vi ZS 1 1  1 
If Z P  R Z C      sC 
 R Z C  R 
ZP
R

1  sCR
Wien-Bridge Oscillator
Oscillation condition
Phase of  f Ar equal to 180o. It already is since  f Ar  0.
 R  sCR
Then need only  f Ar  1  2  1
 R1  sCR  (1  sCR ) 2
Rewriting
 R2  sCR
 f Ar  1  
 R1  sCR  (1  sCR ) 2
 R  sCR
 1  2 
 
R1  sCR  1  2 sCR  s 2C 2 R 2 
 R  sCR  R  1
 1  2   1  2 

2 2 2
R1  1  3sCR  s C R  R1  3  1  sCR
sCR
 R  1
 1  2 
 R1   1 
3  j  CR  
 CR 
Then imaginary term 0 at the oscillatio n frequency
1
 o 
RC
Then, we can get  f Ar 1 by selecting the resistors R1 and R2
appropriately using
 R 1 R
 1  2  1 or 2 2
 R1  3 R1
 Wien-Bridge Oscillator

Multiply the top and bottom by jωC1, we get

V1 jC1 R2

Vo 1  jC1 R1 1  jC2 R2  jC1 R2

Divide the top and bottom by C1 R1

C2 R2
V1 j

Vo  1  R1C1  R2C2  R2C1  

R1C2   j     
2

 R1C1 R2C2  R1C1 R2C2  
 Wien-Bridge Oscillator

Now the amp

gives
V0
'
K
V1
Furthermore, for steady state oscillations, we want the
feedback
V1 to be exactly equal to the amplifier input, V 1’. Thus
'
V1 1 V
  1
Vo K Vo
 Wien-Bridge Oscillator
Hence 1 j

K  1  R C  R2C2  R2C1  
R1C2   j  1 1    2 

 R1C1 R2C2  R1C1 R2C2  

jK  1  R1C1  R2C2  R2C1  

  j 
 
   
2

R1C2  R1C1 R2C2  R1C1 R2C2  

Equating the real parts,

1 R1C1  R2C2  R2C1

  2 0 K
R1C1 R2C2 R2C1
 Wien-Bridge Oscillator
If R1 = R2 = R and C1 = C2
=C

Acl
K 3

1 1
 fr 
RC 2RC
- Gain > 3 : growing oscillations
- Gain < 3 : decreasing oscillations

K = 3 ensured the loop gain of unity - oscillation

Wien-Bridge Oscillator
V in V out

A lead-lag circuit

 The fundamental part of the Wien-Bridge

oscillator is a lead-lag circuit.
 It is comprise of R1 and C1 is the lag portion of
the circuit, R2 and C2 form the lead portion
Wien-Bridge Oscillator
 The lead-lag circuit of a
Wien-bridge oscillator
reduces the input signal by
1/3 and yields a response
curve as shown.
The response curve indicate
that the output voltage peaks
at a frequency is called
frequency resonant.

Response Curve The frequency of resonance

can be determined by the
formula below. 1
fr 
2RC
Wien-Bridge Oscillator
 The lead-lag circuit is in
the positive feedback loop
of Wien-bridge oscillator.
 The voltage divider
limits gain (determines
the closed-loop gain).
The lead lag circuit is
basically a band-pass with
a narrow bandwidth.
The Wien-bridge oscillator
circuit can be viewed as a
noninverting amplifier
Basic circuit configuration with the input
signal fed back from the
output through the lead-lag
 Wien-Bridge Oscillator

Conditions for sustained oscillation

 The 0o phase-shift condition is met when the frequency is f r
because the phase-shift through the lead lag circuit is 0 o
 The unity gain condition in the feedback loop is met when A cl = 3
 Wien-Bridge Oscillator
 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. In
order to achieve a closed loop gain of 3, R1 = 2R2

R1
2
R2

To ensure oscillation, the ratio R1/R2 must be

slightly greater than 2.
 Wien-Bridge Oscillator
 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 with
additional resistor R3 in
parallel.
 When dc is first applied the
zeners appear as opens. This
places R3 in series with R1,
thus increasing the closed
loop gain of the amplifier.
Self-starting Wien-bridge oscillator using back-to-back Zener diodes
 Wien-Bridge Oscillator
 The lead-lag circuit permits only a signal with a
frequency equal to fr to appear in phase on the
noninverting input. The feedback signal is amplified and
continually reinforced, resulting in a buildup of the
output voltage.
 When the output signal reaches the zener breakdown
voltage, the zener conduct and short R3. The amplifier’s
closed loop gain lowers to 3. At this point, the total loop
gain is 1 and the oscillation is sustained.
Phase-Shift Oscillator
Rf

-
0V C C C Vo
.
R
+
R R

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.
Phase-Shift Oscillator

The transfer function of the RC network is

 The frequency for this type is similar to any RC circuit oscillator :

1
f 
2RC 6
where  = 1/29 and the phase-shift is 180o

 For the loop gain A to be greater than unity, the gain of the amplifier
stage must be greater than 29.
 If we measure the phase-shift per RC section, each section would not
provide the same phase shift (although the overall phase shift is 180 o).

 In order to obtain exactly 60o phase shift for each of three stages,
emitter follower stages would be needed for each RC section.
The gain must be at least 29 to maintain the oscillation
Phase-Shift Oscillator

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
 Phase-Shift Oscillator

From equation (1) ;

Substituting into equation (2) ;

# The gain must be at least 29 to maintain the oscillations.

Phase Shift Oscillator – Practical

The last R has been incorporated into the summing resistors

at the input of the inverting op-amp.

1  Rf
fr  K  29
2 6 RC R3
2. LC Oscillators
Oscillators With LC Feedback
Circuits

 For frequencies above 1 MHz, LC feedback

oscillators are used.
 We will discuss the crystal-controlled
oscillators.
 Transistors are used as the active device in
these types.
Crystal Oscillator

The crystal-controlled oscillator is the most stable

and accurate of all oscillators. A crystal has a
natural frequency of resonance. Quartz material can
be cut or shaped to have a certain frequency. We
can better understand the use of a crystal in the
operation of an oscillator by viewing its electrical
equivalent.
 Crystal Oscillator
The crystal appears as a resonant
circuit (tuned circuit oscillator).

The crystal has two resonant

frequencies:

Series resonant condition

• RLC determine the resonant
frequency
• The crystal has a low impedance

Parallel resonant condition

• RLC and CM determine the
resonant frequency
• The crystal has a high impedance
Series-Resonant Crystal
Oscillator
 RLCdetermine the resonant
frequency

 The crystal has a low impedance

at the series resonant frequency
 Parallel - Resonant Crystal
Oscillator
 RLC and CM
determine the
resonant
frequency

 The crystal has a

high impedance
at parallel
resonance
3. Relaxation
Oscillators
Relaxation Oscillator

Relaxation oscillators make use of an RC timing and a

device that changes states to generate a periodic
waveform (non-sinusoidal) such as:

1. Triangular-wave
2. Square-wave
3. Sawtooth
 Triangular-wave Oscillator

Triangular-wave oscillator circuit is a combination of a

comparator and integrator circuit.

1  R2   R3   R3 
fr    VUTP Vmax   VLTP  Vmax  
4CR1  R3   R2   R2 
Square-wave Oscillator
 A square wave relaxation oscillator is like the
Schmitt trigger or Comparator circuit.
 The charging and discharging of the capacitor cause
the op-amp to switch states rapidly and produce a
square wave.
 The RC time constant determines the frequency.
Sawtooth Voltage-Controlled
Oscillator (VCO)
Sawtooth VCO circuit is a combination of a
Programmable Unijunction Transistor (PUT) and
integrator circuit.
 Sawtooth Voltage-Controlled
Oscillator (VCO)
Operation
Initially, dc input = -VIN

• Volt = 0V, Vanode < VG

• The circuit is like an
integrator.
• Capacitor is charging.
• Output is increasing
positive going ramp.
Sawtooth Voltage-Controlled
Oscillator (VCO)
Operation
When Vout = VP

• Vanode > VG , PUT turn

‘ON’
• The capacitor rapidly
discharges.
• Vout drop until Vout = VF.

• Vanode < VG , PUT turn

‘OFF’ peak value
VP-maximum
VF-minimum peak value
Sawtooth Voltage-Controlled
Oscillator (VCO)
Oscillation frequency is

VIN  1 
f   
Ri C  VP  VF 
Summary
 Sinusoidal oscillators operate with positive
feedback.
 Two conditions for oscillation are 0º feedback
phase shift and feedback loop gain of 1.
 The initial startup requires the gain to be
momentarily greater than 1.
 RC oscillators include the Wien-bridge and phase
shift.
 LC oscillators include the Crystal Oscillator.
Summary
 The crystal actually uses a crystal as the LC
tank circuit and is very stable and accurate.
 A voltage controlled oscillator’s (VCO)
frequency is controlled by a dc control voltage.