ECES 352 Winter 2007Ch 13 Oscillators1 Oscillators *Feedback amplifier but frequency dependent feedback *Positive feedback, i.e. β f (  ) A (  ) < 0 *Oscillator gain defined by *Oscillation condition at ω = ω o (Barkhausen’s criterion) A f (ω o ) = 

ECES 352 Winter 2007Ch 13 Oscillators2 Wien Bridge Oscillator *Based on op amp *Combination of R’s and C’s in feedback loop so feedback factor β f 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. ViVi V0V0 ZSZS ZPZP IfIf R2R2 R1R1

ECES 352 Winter 2007Ch 13 Oscillators3 Wien Bridge Oscillator V i = 0 V0V0 ZSZS ZPZP Input Loading Output Loading Z1Z1 Z2Z2 ZPZP ZPZP ZSZS ZSZS IfIf ViVi V 0 = 0 R2R2 R1R1 Define

ECES 352 Winter 2007Ch 13 Oscillators4 Wien Bridge Oscillator Z1Z1 V0V0 Z2Z2 ISIS ISIS R2R2 R1R1 ISIS Amplifier gain including loading effects Feedback factor IfIf V0V0 ZPZP ZSZS I1I1 I2I2 ViVi

ECES 352 Winter 2007Ch 13 Oscillators5 Wien Bridge Oscillator Loop Gain Oscillation condition

ECES 352 Winter 2007Ch 13 Oscillators6 Wien Bridge Oscillator - Example Oscillator specifications:  o =1x10 6 rad/s

ECES 352 Winter 2007Ch 13 Oscillators7 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.

ECES 352 Winter 2007Ch 13 Oscillators8 Wien Bridge Oscillator *Once oscillations start, a limiting circuit is needed to prevent them from growing too large in amplitude

ECES 352 Winter 2007Ch 13 Oscillators9 Phase Shift Oscillator *Based on op amp using inverting input *Combination of R’s and C’s in feedback loop so get additional phase shift. Target 180 o to get oscillation. *Analysis assumes op amp is ideal. V0V0 VXVX R I C1 R I C2 I C3 I R1 I R2 IfIf RfRf V1V1 V2V2 CC C

ECES 352 Winter 2007Ch 13 Oscillators10 Phase Shift Oscillator V0V0 VXVX R I C1 R I C2 I C3 I R1 I R2 IfIf RfRf V1V1 V2V2 Example Oscillator specifications:  o =1x10 6 rad/s Note: We get 180 o phase shift from op amp since input is to inverting terminal and another 180 o from the RC ladder. CC C

ECES 352 Winter 2007Ch 13 Oscillators11 Colpitts LC-Tuned Oscillator *Feedback amplifier with inductor L and capacitors C 1 and C 2 in feedback network. « Feedback is frequency dependent. « Aim to adjust components to get positive feedback and oscillation. « Output taken at collector V o. « No input needed, noise at oscillation frequency  o is picked up and amplified. *R B1 and R B2 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 C E and base capacitor C B are shorts and transistor capacitances (C  and C  ) are opens. CBCB CECE V0V0 ViVi V0V0 ViVi

ECES 352 Winter 2007Ch 13 Oscillators12 Colpitts LC-Tuned Oscillator *Voltage across C 2 is just V  *Neglecting input current to transistor (I   0), *Then, output voltage V o is *KCL at output node (C) *Setting s = j  AC equivalent circuit I π ≈ 0 sC 2 V  V0V0 Assuming oscillations have started, then V  ≠ 0 and V o ≠ 0, so

ECES 352 Winter 2007Ch 13 Oscillators13 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 C 2 /C 1

ECES 352 Winter 2007Ch 13 Oscillators14 Colpitts LC-Tuned Oscillator *Given: « Design oscillator at 150 MHz « Transistor g m = 100 mA/V, R = 0.5 K *Design: « Select L= 50 nH, then calculate C 2, and then C 1 Example

ECES 352 Winter 2007Ch 13 Oscillators15 Summary of Oscillator Design *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 amplifier’s characteristics. Wien Bridge Oscillator Phase Shift Oscillator Colpitts LC-Tuned Oscillator