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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) ?

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

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

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

Wien Bridge Oscillator

Oscillation condition

Loop Gain

Wien Bridge Oscillator - Example

Oscillator specifications ?o1x106 rad/s

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.

Wien Bridge Oscillator

- Once oscillations start, a limiting circuit

is needed to prevent them from growing too

large in amplitude

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.

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.

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

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?

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

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

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

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