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Oscillators) LC and Crystal Oscillators JBT; FET; and IC Based Oscillators the Active-Filter-Tuned Oscillator Multivibrators

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Oscillators) LC and Crystal Oscillators JBT; FET; and IC Based Oscillators the Active-Filter-Tuned Oscillator Multivibrators 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 frequency- selective 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) 1 wo 1 C1C2 wo L( ) (L1 L2)C C1 C2 (a) Colpitts and (b) Hartley. Hartley Oscillator Used in radio receivers and transmitters More stable than Armstrong oscillators Radio frequency choke (RFC) L1 L2 C 1 f0 where Leq L1 L2 2M 2 LeqC M Mutual coupling between L1 & L2 Colpitts Oscillators BJT; FET; and IC Based Rf Ri - C C1 C2 C1 2 LC network LC network 1 C1C2 f0 where Ceq 2 LCeq 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 1 wo C1C2 L( ) C1 C2 Complete Circuit for a Colpitts Oscillator Crystal Oscillators Crystal is a piezo-electric device which converts mechanical pressure to electrical voltage or vice-vasa 1 Series frequency f S 2 CS L 1 Parallel frequency f P CS CP 2 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. R crystal oscillator due to high amplifier gain f and differential input facility of the Op. R1 Amp. - Op-amp + V The two Zener diodes connected face to z face is to limit the peak to peak output voltage equal to twice of Zener voltage. Cs R2 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. VDD A FET Phase-shift Oscillator Phase-shift Oscillator b RD= ? A Vi f = 1kHz bAVi AVi C C C= ? R R R Rb R R C C C bAVi = Vi (or) Ab =1 rd= 40k gm= 5000mS Frequency of oscillation R=10k 1 f Example: 2RC 6 Determine the value of capacitance C and the value of RD of the Phase-shift oscillator Condition of oscillation shown, if the output frequency is 1 kHz. Take rd = 40k and 1 Ab 1 g =5000mS, for the FET and R = 10kW. b m 29 A 29 1 1 1 f C 6.5nF 2RC 6 2Rf 6 210k 1k 6 40 40 Ab 1 Let A 40 29 A g m RL 40 RL 8k g m 5000S 8k 40k But R R // r R // 40k 8kR 10k L D d D D 40k - 8k BJT Phase-Shift Oscillator R VDD Example: RC C= ? Determine the value of capacitance C and R 1 the value of hfe of the Phase-shift oscillator C C shown, if the output frequency is 1kHz. R R Take R=10 k. RC =1 k. R2 1 1 f 1kHz R’ 2RC 6 4RC / R 210kC 6 41k /10k 1 C 0.006F 6nF 210k 1k 6 41k /10k Frequency of oscillation 1 f 2RC 6 4R / R C R R for BJT h 23 29 4 C 1 fe Condition of oscillation b R R Ab 1A 29 29 C R R 10k 1k for BJT h 23 29 4 C 23 29 4 23 290 0.4 313.4 fe 1k 10k RC R 14 IC Phase-shift Oscillator Frequency of oscillation Rf 1 A b f 2RC 6 - C C Condition of oscillation C R + Ab 1 A 29 i R R R for IC inverting amplifier, R 1 A f 29 b Ri 29 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. 1 1 1 f C 6.5nF 2RC 6 2Rf 6 210k 1k 6 for IC inverting amplifier, R f A 29 R f 29Ri 29k Ri 15 Wien Bridge Oscillator R Frequency of oscillation 1 C1 + 1 1 if R R R f f 1 2 2 R C R C 2RC C C C - 1 1 2 2 1 2 Condition of oscillation R 2 C2 R3 R4 if R R R R3 R1 C2 R3 1 2 2 R4 R2 C1 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 2 1 f f 2 Frequency of oscillation 2 R1C1R2C2 4 R1C1R2C2 1 1 0.025ms R1C1 2 2 2 2 0.025ms C1 4 f R2C2 4 1k 10k 0.1 R1 R R C 10k R 0.1F R 0.1 3 1 2 1 1 10 - 9.996 R4 R2 C1 1k 10k 0.025ms 10k 25 R1 9.99610k 99.96k 100k 0.025ms Condition of oscillation C 0.00025 250 pF 1 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 L2 C2 Cci feedback coupling RF output Cco 1 1 tuned-input f0 C 2 L1C1 2 L2C2 1 L1 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), L+ = VZ + VD1 + VD2 and L– = –(VZ + where VD is the forward diode drop. 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.
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