Analog & Digital Electronics
Course No: PH-218
Lec-16: Oscillator
Course Instructors:
Dr. A. P. VAJPEYI
Department of Physics,
Indian Institute of Technology Guwahati, India
1
Positive Feedback
When input and feedback signal both are in same phase, It is
called a positive feedback.
Positive feedback is used in analog and digital systems.
A primary use of +ve feedback is in the production of oscillators.
Vs
+
Σ
+
Vi
Vf
A(f)
Vo
SelectiveNetwork
β(f)
Vo = AVi = A(Vs + V f ) and V f = βVo
Vo
A
=
Vs 1 − Aβ
Barkhausen Criterion: for oscillator βA=1 and +ve feedback
2
Oscillator Circuit
Oscillator is an electronic circuit which converts dc signal into ac
signal.
Oscillator is basically a positive feedback amplifier with unity loop
gain.
For an inverting amplifier- feedback network provides a phase shift
of 180°° while for non-inverting amplifier- feedback network provides
a phase shift of 0°° to get positive feedback .
Vo
A
=
Vs 1 − Aβ
If βA=1 then Vo = ∞ ;
Very high output with zero input.
Use positive feedback through frequency-selective feedback network to ensure sustained oscillation at ω0
Use of Oscillator Circuits
Clock input for CPU, DSP chips …
Local oscillator for radio receivers, mobile receivers, etc
As a signal generators in the lab
Clock input for analog-digital and digital-analog converters
3
Oscillators
If the feedback signal is not
positive and gain is less than
unity, oscillations dampen out.
If the gain is higher than unity
then oscillation saturates.
Type of Oscillators
Oscillators can be categorized according to the types of feedback
network used:
RC Oscillators: Phase shift and Wien Bridge Oscillators
LC Oscillators: Colpitt and Hartley Oscillators
Crystal Oscillators
4
RC Oscillators
R
Vo = (
)Vin
R − jX c
and
XC
φ = tan ( )
R
−1
Φ =0o if Xc=0 and Φ =90o if R=0
However adjusting R to zero is impractical because it would lead
to no voltage across R, thus in a RC circuit, phase shift is always
≤ 90o and it is a function of frequency.
Hence to get 180o phase shift from the feedback network, we
need 3 RC circuits.
RC oscillators build by using inverting amplifier and 3 RC
circuits is known as phase shift oscillator.
5
RC Oscillators: Phase shift Oscillator
Use of
amplifier.
an
Rf
inverting
R1
−
The
additional
180o
phase shift is provided
by an RC ladder network.
C
+
C
R
C
R
R
It can be used for very
low
frequencies
and
provides good frequency
stability.
A phase shift of 180°° is obtained at a frequency f, given by
f =
1
2πCR 6
At this frequency the gain of the network is
vo
1
=−
vi
29
6
RC Oscillators: Phase shift Oscillator
At node V2
I3
V2 = Vo + I 3 X c = Vo +
jwC
V
But I 3 = o
R
1
)
V2 = Vo (1 +
jω CR
1
V V V
)
I 2 = I 3 + 2 = o + o (1 +
R R R
jωCR
At node V1
1
Vo
)
I 2 = (2 +
R
jωCR
3
1
I2
= Vo (1 +
− 2 2 2)
V1 = V2 +
jω C
jωcR ω C R
7
RC Oscillators: Phase shift Oscillator
I2
3
1
V1 = V2 +
= Vo (1 +
− 2 2 2)
jω C
jωcR ω C R
V1 V0
4
1
I1 = I 2 + = ( 3 +
− 2 2 2)
R R
jωcR ω C R
I1
6
5
1
Vi = V1 +
= Vo (1 +
− 2 2 2−
)
3 3 3
jω C
jωcR ω C R
jω C R
Output voltage should be real hence imaginary part equal to zero.
6
1
−
=0
3 3 3
jωcR jω C R
6ω 2C 2 R 2 = 1
At this frequency: Vi =-29 Vo therefore, Av = -29
1
ω=
RC 6
8
RC Oscillators: Wien Bridge Oscillator
Rf
Z1
R1
−
R1
+
C
Vi
R
Z2
C1
C2
R2
Vo
Vo
Z1
R
C
Z2
Feedback Network
Feedback network is a lead-lag circuit where R1, C1 form the lag
portion and R2, C2 form the lead portion. Thus feedback network
provides 0o phase shift.
9
RC Oscillators: Wien Bridge Oscillator
1
X C1 =
ωC1
Z1 = R1 − jX C1
Let
X C2
Z1
1
and
=
ωC2
−1
1
− jR2 X C 2
1 
Z2 =  +
 =
R2 − jX C 2
 R2 − jX C 2 
R1
Z2
C1
Vi
C2
R2
Vo
Therefore, the feedback factor,
Vo
Z2
(− jR2 X C 2 / R2 − jX C 2 )
β= =
=
Vi Z1 + Z 2 ( R1 − jX C1 ) + (− jR2 X C 2 / R2 − jX C 2 )
β=
− jR2 X C 2
( R1 − jX C1 )( R2 − jX C 2 ) − jR2 X C 2
R2 X C 2
β=
R1 X C 2 + R2 X C1 + R2 X C 2 + j ( R1 R2 − X C1 X C 2 )
10
RC Oscillators: Wien Bridge Oscillator
R1 R2 − X C1 X C 2 = 0
For Barkhausen Criterion, imaginary part = 0,
1 1
ω
=
1
/
R
R
C
C
1
2
1
2
ωC1 ωC2
Supposing, R1=R2=R and XC1= XC2=XC,
RX C
β=
3RX C + j ( R 2 − X C2 )
At this frequency: β = 1 / 3 and phase shift = 0o
0.34
Feedback factor β
R1R2 =
0.32
0.3
0.28
β=1/3
0.26
0.24
0.22
0.2
f(R=Xc)
1
Av β = 1 ⇒ Av = 3 = 1 +
Rf
Rf
R1
R1
=2
0.5
Phase
Due to Barkhausen Criterion, gain Avβ=1
Where Av : Gain of the amplifier
Phase=0
0
-0.5
-1
Frequency 11
Stabilization method for Wien Bridge Oscillator
Rf
R1
R
R3
−
R
C
C
+
Vo
+
C
C
−
R
R2
R
Blub
When dc power is first applied, both zener diode is off.
Av = 1 +
R f + R3
R1
R3
= 3+
R1
Because
Rf
R1
=2
Initially, a small +ve feedback signal develops from noise or turn-on transients. This
feedback signal is amplified and continually reinforced , resulting in a buildup of the output
voltage. When the output voltage reaches the zener breakdown voltage , zener diode
conducts and effective short out R3 and thus lowers the close loop voltage gain to 3.
12