Oscillators

1
Oscillators

• Feedback amplifier but frequency dependent
  feedback
• Positive feedback, i.e. ßf (?) A (?) lt 0
• Oscillator gain defined by
• Oscillation condition at ? ?o
  (Barkhausens criterion) Af (?o) ?

2
Wien Bridge Oscillator

• Based on op amp
• Combination of Rs and Cs in feedback
  loop so feedback factor ßf has a
  frequency dependence.
• Analysis assumes op amp is ideal.
• Gain A is very large
• Input currents are negligibly small (I ? I_ ?
  0).
• Input terminals are virtually shorted (V ?
  V_ ).
• Analyze like a normal feedback amplifier.
• Determine input and output loading.
• Determine feedback factor.
• Determine gain with feedback.
• Shunt-shunt configuration.

R2
R1
V0
Vi
ZS
If
ZP
3
Wien Bridge Oscillator
Define
R1
R2
V0
ZS
Vi
If
ZP
Output Loading
Input Loading
ZS
ZS
Z1
V0 0
Z2
Vi 0
ZP
ZP
4
Wien Bridge Oscillator
I1
I2
Amplifier gain including loading effects
R2
R1
V0
Vi
IS
IS
Z2
Z1
IS
Feedback factor
ZS
If
V0
ZP
5
Wien Bridge Oscillator
Oscillation condition
Loop Gain
6
Wien Bridge Oscillator - Example
Oscillator specifications ?o1x106 rad/s
7
Wien Bridge Oscillator
Final note No input signal is needed.
Noise at the desired oscillation frequency
will likely be present at the input and
when picked up by the oscillator when the
DC power is turned on, it will start the
oscillator and the output will quickly
buildup to an acceptable level.
8
Wien Bridge Oscillator

• Once oscillations start, a limiting circuit
  is needed to prevent them from growing too
  large in amplitude

9
Phase Shift Oscillator
Rf
If
IC1
IC2
IC3
V1
V2
VX
C
C
C
V0
IR1
R
R
IR2

• Based on op amp using inverting input
• Combination of Rs and Cs in feedback
  loop so get additional phase shift. Target
  180o to get oscillation.
• Analysis assumes op amp is ideal.

10
Phase Shift Oscillator
If
Rf
IC1
IC2
IC3
V1
V2
VX
C
C
C
V0
R
R
IR1
IR2
Example
Oscillator specifications ?o1x106 rad/s
Note We get 180o phase shift from op amp
since input is to inverting terminal and
another 180o from the RC ladder.
11
Colpitts LC-Tuned Oscillator

• Feedback amplifier with inductor L and
  capacitors C1 and C2 in feedback network.
• Feedback is frequency dependent.
• Aim to adjust components to get positive
  feedback and oscillation.
• Output taken at collector Vo.
• No input needed, noise at oscillation
  frequency ?o is picked up and amplified.
• RB1 and RB2 are biasing resistors.
• RFC is RF Choke (inductor) to allow dc
  current flow for transistor biasing, but to
  block ac current flow to ac ground.
• Simplified circuit shown at midband
  frequencies where large emitter bypass
  capacitor CE and base capacitor CB are shorts
  and transistor capacitances (C? and C?) are
  opens.

CB
V0
CE
Vi
V0
Vi
12
Colpitts LC-Tuned Oscillator

• Voltage across C2 is just V?
• Neglecting input current to transistor (I? ?
  0),
• Then, output voltage Vo is
• KCL at output node (C)
• Setting s j?

AC equivalent circuit
Assuming oscillations have started, then V? ? 0
and Vo ? 0, so
sC2V?
V0
Ip 0
sC2V?
13
Colpitts LC-Tuned Oscillator

• To get oscillations, both the real and
  imaginary parts of this equation must be
  set equal to zero.
• From the imaginary part we get the
  expression for the oscillation frequency
• From the real part, we get the condition
  on the ratio of C2/C1

14
Colpitts LC-Tuned Oscillator

• Given
• Design oscillator at 150 MHz
• Transistor gm 100 mA/V, R 0.5 K
• Design
• Select L 50 nH, then calculate C2, and then
  C1

Example
15
Summary of Oscillator Design
Wien Bridge Oscillator

• Shown how feedback can be used with
  reactive components (capacitors) in the
  feedback path.
• Can be used to achieve positive feedback.
• With appropriate choice of the resistor
  sizes, can get feedback signal in phase
  with the input signal.
• Resulting circuit can produce large
  amplitude sinusoidal oscillations.
• Demonstrated three oscillator circuits
• Wien Bridge oscillator
• Phase Shift oscillator
• Colpitts LC-Tuned oscillator
• Derived equations for calculating resistor
  and capacitor sizes to produce oscillations
  at the desired oscillator frequency.
• Key result Oscillator design depends
  primarily on components in feedback network,
  i.e. not on the amplifiers characteristics.

Phase Shift Oscillator
Colpitts LC-Tuned Oscillator