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.

+ Vi Vs Σ A( f) Vo +

Vf SelectiveNetwork β(f) V A o = V = AV = A(V +V ) and V f = βVo o i s f 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 = If βA=1 then V o = ∞ ; Very high output with zero input. Vs 1− Aβ

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 −1 X C Vo = ( )Vin and φ = tan ( ) R − jX c R

o o  Φ =0 if Xc=0 and Φ =90 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 ≤ 90 o 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 an inverting Rf amplifier. R1  The additional 180 o − CCC phase shift is provided + by an RC ladder network. RRR  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 1 f = 2πCR 6 v 1 o = − At this frequency the gain of the network is v i 29 6 RC Oscillators: Phase shift Oscillator

At node V 2 I V = V + I X = V + 3 2 o 3 c o jwC V But I = o 3 R 1 V = V 1( + ) 2 o jωCR

V 1 V2 Vo Vo 1 o I = I + = + 1( + ) I2 = 2( + ) 2 3 R R R jωCR R jωCR

At node V 1 I 3 1 V = V + 2 = V 1( + − ) 1 2 jωC o jωcR ω 2C 2 R 2 7 RC Oscillators: Phase shift Oscillator

I 3 1 V = V + 2 = V 1( + − ) 1 2 jωC o jωcR ω 2C 2 R 2 V V 4 1 I = I + 1 = 0 3( + − ) 1 2 R R jωcR ω 2C 2R 2

I 6 5 1 V = V + 1 = V 1( + − − ) i 1 jωC o jωcR ω 2C 2 R 2 jω 3C 3R3

Output voltage should be real hence imaginary part equal to zero. 6 1 2 2 2 1 − 3 3 3 = 0 6ω C R = 1 ω = jωcR jω C R RC 6

At this frequency: V i =-29 Vo therefore, A v = -29 8 RC Oscillators: Wien Bridge Oscillator

Rf

Z1 R1 − R1 C1 Z2 + Vi C2 R2 Vo C R Vo

R Z1 C Z2 Feedback Network

 Feedback network is a lead-lag circuit where R 1, C 1 form the lag portion and R 2, C 2 form the lead portion. Thus feedback network provides 0o phase shift.

9 RC Oscillators: Wien Bridge Oscillator 1 1 Z1 Let and X C1 = X C 2 = ωC1 ωC2 R1 C1 Z2

Z1 = R1 − jX C1  −1 Vi C2 R2 Vo 1 1 − jR 2 X C 2 Z2 =  +  =  R2 − jX C 2  R2 − jX C 2 Therefore, the feedback factor, V Z (− jR X / R − jX ) β = o = 2 = 2 C 2 2 C 2 Vi Z1 + Z2 (R1 − jX C1) + (− jR 2 X C 2 / R2 − jX C 2 )

− jR X β = 2 C 2 (R1 − jX C1)( R2 − jX C 2 ) − jR 2 X C 2

R X β = 2 C 2 R1 X C 2 + R2 X C1 + R2 X C 2 + j(R1R2 − X C1 X C 2 ) 10 RC Oscillators: Wien Bridge Oscillator For Barkhausen Criterion , imaginary part = 0, R1R2 − X C1 X C 2 = 0 1 1 R R = 1 2 ω = /1 R1R2C1C2 0.34 ωC1 ωC2

β 0.32 0.3 Supposing, R =R =R and X = X =X , 1 2 C1 C2 C 0.28 β=1/3 0.26 RX C 0.24 β = 2 2

3RX C + j(R − X C ) factorfactor FeedbackFeedback 0.22 0.2 At this frequency: β = 1 / 3 and phase shift = 0o f(R=Xc) 1 Due to Barkhausen Criterion , gain A β=1 v Phase=0 A 0.5 Where v : Gain of the amplifier R 0 R f Phase f = 2 Avβ =1⇒ Av = 3 =1+ R1 -0.5 R1

-1 Frequency 11 Stabilization method for Wien Bridge Oscillator

Rf R C

R1 R − 3 + Vo + R C − C R R2

R C Blub

When dc power is first applied, both zener diode is off. R + R R f 3 R3 Because f Av =1+ = 3+ = 2 R1 R1 R1 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