Positive Feedback Amplifiers (Oscillators) LC And Crystal Oscillators .

ELG4139: Oscillator CircuitsPositive Feedback Amplifiers (Oscillators)LC and Crystal OscillatorsJBT; FET; and IC Based OscillatorsThe Active-Filter-Tuned OscillatorMultivibrators1

Introduction There are two different approaches for the generation ofsinusoids, most commonly used for the standardwaveforms:– Employing a positive-feedback loop that consists anamplifier and an RC or LC frequency-selectivenetwork. It generates sine waves utilizing resonancephenomena, are known as linear oscillators (circuitsthat generate square, triangular, pulse waveforms arecalled non-linear oscillators or function generators.)– A sine wave is obtained by appropriate shaping atriangular waveform.2

The Oscillator Feedback LoopA 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 offrequency w0 isBarkhausen 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 OscillatorsFor higher frequencies ( 1MHz)wo 1C1C 2L()C1 C 2wo 1( L1 L2)C(a) Colpitts and (b) Hartley.

Hartley OscillatorUsed in radio receivers and transmitters More stable than Armstrongoscillators Radio frequency choke (RFC)L2L1Cf0 1where Leq L1 L2 2M2 LeqCM Mutual coupling between L1 & L2

Colpitts OscillatorsBJT; FET; and IC BasedRfC1C2LC networkf0 12 LCeqwhere Ceq -RiC1C2LC networkC1C2C1 C2RFC is an impedance which is high (open) at high RF frequencies and low (short)to dc voltages

Equivalent Circuit of the Colpitts Oscillatorwo Complete Circuit for a Colpitts Oscillator1C1C 2L()C1 C 2

Crystal OscillatorsCrystal is a piezo-electric device which converts mechanical pressure to electrical voltage or vice-vasaSeries frequency f S Parallel frequency f P 12 CS L1 CC 2 S P L CS CP Radio communications, broadcasting stationsPiezoelectric effectWhy are crystal oscillators used in many commercialtransmitters?8

An Application of Crystal OscillatorCrystals are fabricated by cutting the crude quartz in a very exactingfashion. The type of cut determines the crystal’s natural resonant frequencyas well as it’s temperature coefficient.Crystal are available at frequencies about 15kHz and up providing thebest frequency stability. However above 100MHz, they become so smallthat handling becomes a problem.Two crystals producing two different frequencies for measuringtemperature Timing devices9

Op-Amp Crystal OscillatorOp-amp voltage gain is controlled by the negative feedback circuit formed by Rf andR1. More NFB will damp the oscillation, critical NFB will have a sine wave output andless NFB will have a square wave output.It is very flexible to construct the Op. Amp.crystal oscillator due to high amplifier gainand differential input facility of the Op.Amp.The two Zener diodes connected face toface is to limit the peak to peak outputvoltage equal to twice of Zener voltage.RfR1Op-amp R2VzCsThe 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

ExampleCrystal used instead of inductor in the tankcircuit of Colpitts oscillator11

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

APhase-shift OscillatorVDDf 1kHzbAViAViRRbCCCRRC ?rd 40k gm 5000mSR 10k 12 RC 6Example:Determine the value of capacitance C and thevalue of RD of the Phase-shift oscillatorshown, if the output frequency is 1 kHz. Takerd 40k andgm 5000mS, for the FET and R 10kW.Condition of oscillation1 Ab 129 A 29CCFrequency of oscillationb RRbAVi Vi (or) Ab 1f bRD ?AViFET Phase-shift Oscillator111 C 6.5nF2 RC 62 Rf 6 2 10k 1k 64040Ab 1 Let A 40 29 A g m RL 40 RL 8k g m 5000 Sf But RL RD // rd RD // 40k 8k RD 8k 40k 10k 40k - 8k

BJT Phase-Shift OscillatorVDDRExample:RCC ?Determine the value of capacitance C andthe value of hfe of the Phase-shift oscillatorshown, if the output frequency is 1kHz.Take R 10 k. RC 1 k.R1CRCRR2R’Frequency of oscillationf 12 RC 6 4 RC / RCondition of oscillationAb 1 A 29b 129RRfor BJT h fe 23 29 4 CRCRf 11 1kHz 2 RC 6 4 RC / R2 10kC 6 4 1k / 10kC 1 0.006 F 6nF2 10k 1k 6 4 1k / 10kfor BJT h fe 23 29 23 29RR 4 CRCR10k1k 4 23 290 0.4 313.41k10k14

IC Phase-shift OscillatorFrequency of oscillationRiAb 1 A 29for IC inverting amplifier ,R1A f 29 b 29Ri Condition of oscillation-1f 2 RC 6RfbACCRCRRExample:Determine the value of capacitance C and the value of Rf of the IC Phase-shift oscillatorshown, if the output frequency is 1kHz. Take R 10kW. Ri 1kW.f 111 C 6.5nF2 RC 62 Rf 6 2 10k 1k 6for IC inverting amplifier ,RA f 29 R f 29 Ri 29k Ri15

Wien Bridge OscillatorR1C1 -Frequency of oscillationf 12 R1C1 R2C2f 1 if R1 R2 R 2 RC C1 C2 C Condition of oscillationR2C2R4 R3R3 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.11f f2 4 2 R1C1 R2C2 Frequency of oscillation2 R1C1 R2C2R1C1 110.025ms 0.025ms C 214 2 f 2 R2C2 4 2 1k 10k 0.1 R1R3 R1 C210kR0.1 FR0.1 1 1 10 9.996R4 R2 C11k10k 0.025ms10k25R1 9.996 10k 99.96k 100k C1 0.025ms 0.00025 250 pF100kCondition of oscillation

Tuned Oscillators (Radio Frequency Oscillators)Tuned oscillator is a circuit that generates a radio frequency output by using LCtuned (resonant) circuit. Because of high frequencies, small inductance can beused for the radio frequency of oscillation.Tuned-input and tuned-output Oscillatortuned-outputfeedback couplingL2C2CciCcoRF outputf0 tuned-inputC1L111 2 L1C1 2 L2C217

The Active-Filter-Tuned OscillatorAssume the oscillations have already started. The output of the band-pass filter will bea 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 MultivibratorsAnother type of waveform generating circuits is the nonlinear oscillatorsor function generators which uses multivibrators.A bistable multivibrator has 2 stable states. The circuit can remain ineither state indefinitely and changes to the other one only when triggered.Metastable state: v 0 and vO 0. Thecircuit cannot exist in the mestastablestate for any length of time since anydisturbance causes it to switch toeither stable state.

Bistable Circuit with Inverting Transfer CharacteristicsAssume 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 betweeninput 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 andkeeping the regenerative process going. This process culminates in the op amp saturating, that is, vO L-.The circuit is said to be invertingTrigger signal

Bistable Circuit with Noninverting Transfer Characteristics

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

Bistable Circuit with More Precise Output LevelLimiter 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 MultivibratorConnecting a bistable multivibrator with inverting transfer characteristics in afeedback loop with an RC circuit results in a square-wave generator.

Operation of the Astable Multivibrator

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

Generation of a Standard PulseIn 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 CircuitCommercially available integrated-circuit package such as 555 timer exists thatcontain the bulk of the circuitry needed to implement monostable and astablemultivibrator.2/3 VCC1/3 VCC

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