Transcript Oscillators_PartA (Chp 5)

OSCILLATORS
Oscillators
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
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.
Oscillators
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
Oscillator
V out
or
or
Oscillators
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.
Oscillators
Types of oscillators
1. RC oscilators
- Wien Bridge
- Phase Shift
2. LC oscillators
- Hartley
- Colpitts
3. Relaxation oscilators
Oscillators
Basic principles for oscillation
 An oscillator is an amplifier with positive feedback.
Ve
Vs
Ve  Vs  V f (1)
+
Vf
A
Vo
b
V f  βVo (2)
Vo  AVe  AVs  V f   AVs  βVo 
(3)
Oscillators
Vo  AVe
 AVs  V f   AVs  βVo 
Vo  AVs  AbVo
1  Ab Vo  AVs
Oscillators
The closed loop gain is;
Vo
A
Af 

Vs 1  Aβ 
Ve
Vs
+
Vf
A
b
Vo
Oscillators
In general A and b 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
Oscillators
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
Oscillators
At a specific frequency f0;
T  jω0   A jω0 β  jω0   1
At this frequency, the closed loop gain;
A jω0 
A f  jω0  
1  A jω0 β  jω0 
will be infinite, i.e. the circuit will have finite output
for zero input signal - oscillation
Oscillators
Thus, the condition for sinusoidal oscillation of
frequency f0 is;
A jω0 β  jω0   1
This is known as Barkhausen criterion.
Oscillators
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.
In phase
If the feedback circuit
returns the signal out of
phase, an inverting
amplifier produces
positive feedback.
Vf
Av
Noninverting
amplifier
Feedback
circuit
Vo
Oscillators
Design Criteria for Oscillators
1. The magnitude of the loop gain must be unity
or slightly larger i.e.
Aβ  1
– Barkhaussen criterion
2. Total phase shift, of the loop gain must be 0°
or 360°.
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.
Oscillators
1. RC Oscillators
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-bridge and the phase-shift.
Oscillator
OscillatorsThe–Wien-Bridge
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 ⅓ of the input at only
one frequency and the phase shift at this frequency will be 0o.
V in
V out
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.
1
fr 
2RC
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;
Voltagedivider
R1
–
Vout
R2
+
R3
C1
C2
R4
Lead-lag
network
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.
1
fr 
2RC
Oscillators – Wien-bridge
The loop gain for the oscillator is

R2  Z p 

T s   As β s    1 
Z Z 
R
1 
p
s 

where;
R
Zp 
1  sRC
and;
1  sRC
Zs 
sC
Oscillators – Wien-bridge
Hence;


R2 
1

T s    1 

R1  3  sRC  1 /sRC 

Substituting for s;
 R2 

1
T  j   1  

 R1  3  jRC  1/jRC 
Oscillators – Wien-bridge
For oscillation frequency f0;

 R2 
1
T  j0   1  

 R1  3  j0 RC  1/j0 RC 
Since at the frequency of oscillation, T(j) must be
real (for zero phase condition), the imaginary
component must be zero i.e.;
1
j0 RC 
0
j0 RC
Oscillators – Wien-bridge
Which gives us;
1
0 
RC
Oscillators – Wien-bridge
From the previous equation;

 R2 
1
T  j0   1  

 R1  3  j0 RC  1/j0 RC 
the magnitude condition is;
 R2  1 
1  1   
 R1  3 
or;
R2
2
R1
To ensure oscillation, the ratio R2/R1 must
be slightly greater than 2.
Oscillators – Wien-bridge
With the ratio;
R2
2
R1
then;
R2
K  1
3
R1
K = 3 ensures the loop gain of unity – oscillation.
- K > 3 : growing oscillations
- K < 3 : decreasing oscillations
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 bandpass with a narrow
bandwidth.
Oscillators – Wien-bridge
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.
Oscillators – Wien-bridge
To start the oscillations an initial loop gain
greater than 1 must be achieved.
Oscillators – Wien-bridge oscillator using back-toback zener diode
The back-to-back zener diode arrangement is
one way of achieving this.
D1
R1
D2
R3
+
V out
.

R2
f r Lead-lag
1/3
Oscillators – Wien-bridge
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.
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.
Oscillators – Wien-bridge
Oscillators – Wien-bridge
When the R’s and C’s in the feedback circuit are equal, the frequency of
the bridge is given by
1
fr 
2πRC
What is fr for the Wien bridge?
Rf
C1
10 kW
4.7 nF
R1
–
Vout
680 W
+
1
fr 
2πRC
1

2π  680 W  4.7 nF 
= 48.9 kHz
D1
Q1
R2
680 W
C2
4.7 nF
R3
1.0 kW
R4
10 kW
C3
1.0 mF
Oscillators – Phase-shift
The three RC circuits combine to produce a phase shift of 180o.
Rf
0V
R

C
C
C
Vo
.
+
R
R
Fig. 3 shows a circuit containing three RC circuits in its
feedback network called the phase-shift oscillator.
Oscillators – Phase-shift
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.
1
fr 
2 6 RC
Oscillators – Phase-shift
Phase-shift network
C V1 C
I1
Vi
I2
V2
C
I5
R
I3
R
I4
R Vo
I6
The transfer function of the RC network is



Vo 
1


1
5
6
Vi 
 2 2 2
 1
3 3 3
sC R
sCR 
s C R
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
or;
1
5
6



1

K

0
3 3 3
2 2 2
sC R
sC R
sCR
Oscillators – Phase-shift
Putting s = j and equating the real parts and
imaginary parts to zero at  = o, we obtain;
Imaginary part:
1
6


0
3 3 3
 j o C R
joCR
1
o 
6CR
(1)
Oscillators – Phase-shift
Real part:
5
 2 2 2 1 K  0
o C R
(2)
K  29
1
o 
6CR
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 Rf /R3 ≥ 29.
Oscillators – Phase-shift
Rf
0V
R

C
C
C
Vo
.
+
R
Even with identical R’s and C’s,
the phase shift in each RC circuit
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.
R
The last R has been
incorporated into the
summing resistors at the
input of the inverting opamp.
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:
R
1
1

 8.12 kW (Use 8.2 kW.)
2π 6 f r C 2π 6 800 Hz 10 nF 
Calculate the feedback
resistor needed:
Rf = 29R = 238 kW.
Rf
238 kW
–
C1
C2
C3
Vout
+
10
nF
10
nF
8.2 kW
R1
10
nF
8.2 kW
R2
R3
8.2 kW