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M2-3 Oscillators
1. Wein-Bridge Oscillator
2. Active-filter Tuned Oscillator
1
The basic structure of a sinusoidal oscillator.
- A positive-feedback loop is formed by an amplifier A and a
frequency-selective network β.
- In an actual oscillator circuit, no input signal will be present;
here an input signal xs is employed to help explain the principle
of operation.
2
Dependence of the oscillator-frequency stability on the slope of the
phase response. A steep phase response (i.e., large df/dw) results in a
small Dw0 for a given change in phase Df (resulting from a change (due,
for example, to temperature) in a circuit component).
3
Barkhausen stability criterion
1. The loop gain is equal to unity in absolute magnitude,
2. The phase shift around the loop is zero or an integer
multiple of 2π:
4
1. Wien-bridge oscillator without
amplitude stabilization
5
A Wien-bridge oscillator with a limiter used for
amplitude control
6
A Wien-bridge oscillator with an alternative method for
amplitude stabilization.
7
- A Wien-bridge oscillator uses two RC networks
connected to the positive terminal to form a frequency
selective feedback network
- Causes Oscillations to Occur
8
-Amplifies the signal with the two negative feedback
resistors
9
Analysis
-The loop gain can be found by doing a voltage division
V o( s )
V 1( s ) 
Z 2( s )
Z 1( s )  Z 2( s )
10
Analysis
Z 1( s )
R
R
Z 2( s )
R
1
sC
1
sC
1
sC
-The two RC Networks must have equal resistors and capacitors
11
Analysis
Need to find the Gain over the whole Circuit: Vo/Vs
Operational amplifier gain
G
V1( s )
Vs( s )
V o( s )
1
R2
R1
V 1( s ) 
Z 2( s )
Z 1( s )  Z 2( s )
- Solve G equation for V1 and substitute in for above equ.
V o( s )
G  V s( s ) 
sRC
2
2
2
s  R  C  3 s  R  C  1
12
Analysis
An equation for the overall circuit gain
T( s )
V o( s )
s  R  C G
V s( s )
s  R  C  3 s  R  C  1
2
2
2
Simplifying and substituting jω for s
T jw
j w  R  C G
1  w2  R2  C2  3  j  w  R  C
13
Analysis
In order to have a phase shift of zero,
2
2
2
1w R C
0
This happens at wRC
T jw
When wRC, T(jw) simplifies to:
G
3
- If G = 3, oscillations occur
- If G < 3, oscillations attenuate
- If G > 3, oscillation amplify
14
Capture schematic of a Wien-bridge oscillator.
15
Start-up transient behavior of the Wien-bridge oscillator
for various values of loop gain.
16
(Continued)
17
(Continued)
18
2. Active-filter-tuned oscillator
19
A practical implementation of the active-filter-tuned
oscillator.
20
Capture schematic of an active-filter-tuned oscillator for
which the Q of the filter is adjustable by changing R1.
21
Output waveforms of the active-filter-tuned
oscillator for Q = 5 (R1 = 50 kW).
22
Conclusion
• No Input Signal yet Produces Output
Oscillations
• Can Output a Large Range of Frequencies
• With Proper Configuration, Oscillations can
go on indefinitely
23
Memo
24