Oscillators

ELG4139: Oscillator Circuits Positive Feedback Amplifiers (Oscillators) LC and Crystal Oscillators JBT; FET; and IC Based Oscillators The Active-Filter-Tuned Oscillator Multivibrators

1

Introduction • There are two different approaches for the generation of sinusoids, most commonly used for the standard waveforms: – Employing a positive-feedback loop that consists an amplifier and an RC or LC frequency-selective network. It generates sine waves utilizing resonance phenomena, are known as linear oscillators (circuits that generate square, triangular, pulse waveforms are called non-linear oscillators or function generators.) – A sine wave is obtained by appropriate shaping a triangular waveform.

2

The Oscillator Feedback Loop A basic structure of a sinusoidal oscillator consists of an amplifier and a frequencyselective network connected in a positive-feedback loop.

The condition for the feedback loop to provide sinusoidal oscillations of frequency w0 is Barkhausen Criterion:  At w0 the phase of the loop gain should be zero.  At w0 the magnitude of the loop gain should be unity.

LC and Crystal Oscillators For higher frequencies (> 1MHz)

wo 

1 C1C 2 L( ) C1  C 2

wo 

1 ( L1  L2)C

(a) Colpitts and (b) Hartley.

Hartley Oscillator Used in radio receivers and transmitters More stable than Armstrong oscillators Radio frequency choke (RFC)

L2

L1 C

f0 

1 where Leq  L1  L2  2M 2 LeqC

M  Mutual coupling between L1 & L2

Colpitts Oscillators BJT; FET; and IC Based

Rf

C1

C2

LC network

f0 

1 2 LCeq

where Ceq 

-

Ri

C1

C2

LC network

C1C2 C1  C2

RFC is an impedance which is high (open) at high RF frequencies and low (short) to dc voltages

Equivalent Circuit of the Colpitts Oscillator

wo 

Complete Circuit for a Colpitts Oscillator

1 C1C 2 L( ) C1  C 2

Crystal Oscillators Crystal is a piezo-electric device which converts mechanical pressure to electrical voltage or vice-vasa

Series frequency  f S 

Parallel frequency  f P 

1 2 CS L

1  CC  2  S P  L  CS  CP 

Radio communications, broadcasting stations Piezoelectric effect Why are crystal oscillators used in many commercial transmitters?

8

An Application of Crystal Oscillator Crystals are fabricated by cutting the crude quartz in a very exacting fashion. The type of cut determines the crystal’s natural resonant frequency as well as it’s temperature coefficient.

Crystal are available at frequencies about 15kHz and up providing the best frequency stability. However above 100MHz, they become so small that handling becomes a problem.

Two crystals producing two different frequencies for measuring temperature Timing devices 9

Op-Amp Crystal Oscillator Op-amp voltage gain is controlled by the negative feedback circuit formed by Rf and R1. More NFB will damp the oscillation, critical NFB will have a sine wave output and less NFB will have a square wave output.

It is very flexible to construct the Op. Amp. crystal oscillator due to high amplifier gain and differential input facility of the Op. Amp. The two Zener diodes connected face to face is to limit the peak to peak output voltage equal to twice of Zener voltage.

Rf R1

Op-amp

+

R2

Vz

Cs

The crystal is fed in series to the positive feedback which is required for oscillation. Therefore the oscillation frequency will be crystal series resonant frequency fs.

10

Example

Crystal used instead of inductor in the tank circuit of Colpitts oscillator

11

The Phase Shifter Oscillator The phase-shifter consists of a negative gain amplifier (-K) with a third order RC ladder network in the feedback. The circuit will oscillate at the frequency for which the phase shift of the RC network is 180o. Only at the frequency will the total phase shift around the loop be 0o or 360o. The minimum number of RC sections is 3 because it is capable of producing a 180o phase shift at a finite frequency.

A

Phase-shift Oscillator

VDD

f = 1kHz

bAVi

AVi R

Rb

C

C

C

R

R

C= ?

rd= 40k  gm= 5000mS R=10k 

1 2RC 6

Example: Determine the value of capacitance C and the value of RD of the Phase-shift oscillator shown, if the output frequency is 1 kHz. Take rd = 40k and gm=5000mS, for the FET and R = 10kW.

Condition of oscillation

1 Ab  1 29  A  29

C

C

Frequency of oscillation

b

R

R

bAVi = Vi (or) Ab =1

f 

b

RD= ?

A

Vi

FET Phase-shift Oscillator

1 1 1 C    6.5nF 2RC 6 2Rf 6 2 10k  1k 6 40 40 Ab  1 Let A  40  29 A  g m RL  40  RL    8k g m 5000S f 

But RL  RD // rd  RD // 40k  8k  RD 

8k  40k  10k 40k - 8k

BJT Phase-Shift Oscillator VDD

R

Example:

RC

C= ?

Determine the value of capacitance C and the value of hfe of the Phase-shift oscillator shown, if the output frequency is 1kHz. Take R=10 k. RC =1 k.

R1 C

R

C

R

R2 R’

Frequency of oscillation

f 

1 2RC 6  4 RC / R


Ab  1  A  29

b

1 29

R R for BJT  h fe  23  29  4 C RC R

f 

1 1  1kHz  2RC 6  4 RC / R 2 10kC 6  4  1k / 10k

C

1  0.006F  6nF 2 10k  1k 6  4  1k / 10k

for BJT  h fe  23  29  23  29

R R 4 C RC R

10k 1k 4  23  290  0.4  313.4 1k 10k 14

IC Phase-shift Oscillator Frequency of oscillation

R

i Ab  1 A  29 for IC inverting amplifier , R 1 A  f  29 b  29 Ri

+


-

1 f  2RC 6

Rf

b

A

C

C R

C R

R

Example: Determine the value of capacitance C and the value of Rf of the IC Phase-shift oscillator shown, if the output frequency is 1kHz. Take R =10kW. Ri =1kW.

f 

1 1 1 C    6.5nF 2RC 6 2Rf 6 2 10k  1k 6

for IC inverting amplifier , R A  f  29  R f  29 Ri  29k Ri 15

Wien Bridge Oscillator R1

C1

+ -

Frequency of oscillation f 

1 2 R1C1 R2C2

f 

1  if R1  R2  R    2RC  C1  C2  C 

Condition of oscillation R2

C2

R4 R3

R3 R1 C2   R4 R2 C1

 if R1  R2  R  R3   2  R4  C1  C2  C 

Example: Determine the value of capacitance C1 and R1 if R2 =10kW C2 = 0.1mF R3 =10k R4 =1kW in the Wien bridge oscillator shown has an output frequency of 1kHz. 1 1 f   f2 4 2 R1C1 R2C2 Frequency of oscillation 2 R1C1 R2C2

R1C1 

1 1 0.025ms   0 . 025 ms  C  2 1 4 2 f 2 R2C2 4 2 1k  10k  0.1 R1

R3 R1 C2 10k R 0.1F R 0.1     1   1  10  9.996 R4 R2 C1 1k 10k 0.025ms 10k 25 R1  9.996  10k  99.96k  100k C1 

0.025ms  0.00025  250 pF 100k


Tuned Oscillators (Radio Frequency Oscillators) Tuned oscillator is a circuit that generates a radio frequency output by using LC tuned (resonant) circuit. Because of high frequencies, small inductance can be used for the radio frequency of oscillation. Tuned-input and tuned-output Oscillator

tuned-output

feedback coupling

L2

C2

Cci Cco

RF output

f0 

tuned-input C1

L1

1 1  2 L1C1 2 L2C2

17

The Active-Filter-Tuned Oscillator Assume the oscillations have already started. The output of the band-pass filter will be a sine wave whose frequency is equal to the center frequency of the filter. The sine-wave signal is fed to the limiter and then produces a square wave.

Practical implementation of the active-filter-tuned oscillator

Bistable Multivibrators Another type of waveform generating circuits is the nonlinear oscillators or function generators which uses multivibrators.

A bistable multivibrator has 2 stable states. The circuit can remain in either state indefinitely and changes to the other one only when triggered. Metastable state: v+=0 and vO=0. The circuit cannot exist in the mestastable state for any length of time since any disturbance causes it to switch to either stable state.

Bistable Circuit with Inverting Transfer Characteristics Assume that vO is at one of its two possible levels, say L+, and thus v+ = βL+.  As vI increases from 0 and then exceeds βL+, a negative voltage developes between input terminals of the op amp.  This voltage is amplified and vO goes negative.  The voltage divider causes v+ to go negative, increasing the net negative input and keeping the regenerative process going.  This process culminates in the op amp saturating, that is, vO = L-.

The circuit is said to be inverting

Trigger signal

Bistable Circuit with Noninverting Transfer Characteristics

Application of the Bistable Circuit as a Comparator To design a circuit that detects and counts the zero crossings of an arbitrary waveform, a comparator whose threshold is set to 0 can be used. The comparator provides a step change at its output every time zero crossing occurs.

Bistable Circuit with More Precise Output Level Limiter circuits are used to obtain more precise output levels for the bistable circuit.

L+ = VZ1 + VD and L– = –(VZ2 + VD), where VD is the forward diode drop.

L+ = VZ + VD1 + VD2 and L– = –(VZ + VD3 + VD4).

Operation of the Astable Multivibrator Connecting a bistable multivibrator with inverting transfer characteristics in a feedback loop with an RC circuit results in a square-wave generator.

Operation of the Astable Multivibrator

Generation of Triangular Waveforms Triangular waveforms can be obtained by replacing the low-pass RC circuit with an integrator. Since the integrator is inverting, the inverting characteristics of the bistable circuit is required.

Generation of a Standard Pulse In the stable state, VA=L+ (why?), VB=VD1, VC=βL+ (D2: ON and R4>>R1). When a negative-going step applies at the trigger input:  D2 conducts heavily and pulls node C down (lower than VB).  The output of the op amp switch to L- and cause VC to go toward βL-.  D2 OFF and isolates the circuit from changes at the trigger input.  D1 OFF and C1 begins to discharge toward L-.  When VB < VC, the output of the op amp switch to L+.

Generation of a Standard Pulse

The 555 Circuit Commercially available integrated-circuit package such as 555 timer exists that contain the bulk of the circuitry needed to implement monostable and astable multivibrator.

2/3 VCC 1/3 VCC