OSCILLATORS AND WAVEFORM-SHAPING CIRCUITS

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1 OSILLATORS AND WAVEFORM-SHAPING IRUITS Signals having prescribed standard waveforms (e.g., sinusoidal, square, triangle, pulse, etc). To generate sinusoidal waveforms: o Positive feedback loop with non-linear gain limiting. o Appropriately shaping other waveforms such as a triangle waves. I. SINUSOIDAL OSILLATORS: Linear sine-wave oscillators (some forms of non-linearity employed to limit the output amplitude). More difficult to analyze using s-plane (non-linear). Basic structure: an amplifier and a frequency selective network connected in a positive feedback loop. EE33 - Oscillators

2 x S + Σ + x f Amplifier A Freq. Selective network β x O No input will be present (Xs 0). Feedback signal X F is summed with a positive sign: Af (s) A(s) A(s)(s) Loop gain: L (s) A(s)(s) haracteristic equation: - L(s) 0 At a specific frequency f 0, the loop gain A(s)β(s) is equal to unity and A f (s) will be infinite (a definition of an oscillator). For the sinusoidal oscillator at ω 0 : L 0 (j0 ) A(j0 ) (j ) EE33 - Oscillators

3 This condition is called Barkhausen riteria for oscillation: UNITY GAIN, ZERO PHASE SHIFT The frequency of oscillation ω 0 is determined by the phase characteristics of the feedback loop. The loop oscillates at the frequency for which the phase is ZERO. The steeper the phase shift as a function of frequency φ(ω), the more stable the frequency of oscillation. EE33 - Oscillators 3

4 Another approach to examine oscillator is to analyze the circuit poles (i.e., roots of the haracteristic Equation): - L(s) 0 To produce sustained oscillation at frequency ω 0, the E must have roots at s±jω 0 (i.e., -A(s)β(s) should have a factor of the from s +ω 0 ) Example. EE33 - Oscillators 4

5 NON-LINEAR AMPLITUDE ONTROL: Difficult to design circuits with Aβ (circuit parameters vary with temperature, time, and component values). If Aβ < oscillator ceases If Aβ > oscillation grows until the circuit saturates. Needs a mechanism to force Aβ Accomplished by a non-linear circuit for gain control. Two ways:. Design circuit Aβ > as voltage of oscillation increases, gain control mechanism kicks in and reduces gain to.. Design circuit with right half plane poles. The gain control pulls the poles back to the imaginary axis. EE33 - Oscillators 5

6 Two approaches:. Use limiter circuit: oscillations are allowed to grow until the level reaches the limiter set value. Once the limiter comes into operation, the amplitude remains constant. The limiter should be designed to minimize non-linear distortion.. Use a resistive element in the feedback loop: whose resistance can be controlled by the sinusoidal output amplitude. Diodes or JFETs (operating in triode region) are commonly used. EE33 - Oscillators 6

7 A popular limiter circuit: EE33 - Oscillators 7

8 II. OP-AMP- R OSILLATORS:. WIEN-BRIDGE OSILLATOR Loop gain: A(s) β(s) L(s) [ + R R Z ] Z + P P Z S EE33 - Oscillators 8

9 R + R L( j ) 3 + j(r R ) The loop gain will be a real number (i.e., the phase will be zero when imaginary part 0) at one frequency: 0 0 R R 0 R To sustain oscillation at this frequency, the magnitude of the loop gain should be unity by setting R R To ensure oscillation start, choose R/R slightly greater than. The amplitude of the oscillation can be controlled using a non-linear limiter. EE33 - Oscillators 9

10 EE33 - Oscillators 0

11 . PHASE SHIFT OSILLATOR onsists of a negative gain amplifier (-K) with a three-section (3 rd order) R ladder network in the feedback. The circuit will oscillate at the frequency when the phase shift of the R network is 80 O. Only at this frequency the phase shift around the loop be 0 O (360 O ). Three R sections are required to produce a 80 O phase shift at a finite frequency. EE33 - Oscillators

12 The value of K is chosen to be slightly higher than the inverse of the magnitude of the R network transfer function at the frequency of oscillation. EE33 - Oscillators

13 3. ATIVE FILTER TUNED OSILLATOR EE33 - Oscillators 3

14 III. L AND RYSTAL OSILLATORS: Useful for operation in the range from 00KHz to 500MHz. They exhibit higher Q than R types (more stable). L oscillators are difficult to tune over wide ranges. rystal oscillators operate at a single frequency (extremely stable response). L TUNED OSILLATORS EE33 - Oscillators 4

15 Frequency of oscillation is determined by the resonant frequency of the parallel tuned circuit (i.e., tank circuit). 0 For olpitts oscillator: L( ) + For Hartley oscillator: 0 (L + L) EE33 - Oscillators 5

The ratio L /L or / determines the feedback factor and must be adjusted in conjunction with the transistor gain to ensure that oscillations will start.

16 The ratio L /L or / determines the feedback factor and must be adjusted in conjunction with the transistor gain to ensure that oscillations will start. Node equation at the transistor collector: s Vπ gmvπ + ( + s)( + s L)V R + π 0 V π 0 (oscillations have started), it can be eliminated (i.e., the other terms are zero). s 3 L + s (L R ) + s( + ) + (g m + ) 0 R EE33 - Oscillators 6

17 ( L g 3 m + ) + j[( + ) L ] R R 0 For oscillations to start, both real and imaginary parts must be 0. Setting the imaginary part to zero: L( which is the resonant frequency of the tank circuit. 0 + ) Setting the real part to zero: g m R To sustain oscillation, the magnitude of the gain from the base to collector (g m R) must be equal to the inverse of the voltage ratio provided by the capacitive divider. v v be ce EE33 - Oscillators 7

18 To start oscillation, the loop gain must be greater than unity: g R > m As oscillation grows in amplitude, the transistors non-linear characteristics reduce the loop gain to unity, thus sustaining oscillations. EE33 - Oscillators 8

19 L tuned oscillators utilize the non-linear i c -v be characteristics of the BJT (or i d versus v gs for FET) for amplitude control. As the oscillations grow, the effective gain of the transistor is reduced below its small signal value. The L tuned oscillators are known as self-limiting oscillators. Reliance on the non-linear characteristics of the BJT (or the FET) implies that the collector (drain) current waveform will be nonlinearity distorted. Nevertheless, sinusoidal of high purity because of the filtering action of the L tuned circuit. EE33 - Oscillators 9

20 RYSTAL OSILLATORS Electro-mechanical resonance Very stable (with time and temperature) Very high selectivity (having very high Q factor). EE33 - Oscillators 0

21 Large inductance L (as high as hundreds of Henrys), A very small series capacitance s (as small as pF), A parallel capacitance p (a few picofarad), represents the electrostatic capacitance between the two parallel plates of the crystal ( p >> s ), A small series resistance r, A high Q factor (ω 0 L/r): as high as few hundred thousand. Neglect the resistance r (high Q) and express the crystal impedance as: or Z(s) Z(s) s p s + p sl + / s s s s + Ls p + + L( p s s ) EE33 - Oscillators

22 Two resonant frequencies (series and parallel): s L s and p L s s p + p ω p >ω s and p >> s, the two resonant frequencies are very close. s dominates (much smaller than the other capacitances): For sjω ω 0 L Z(j) j s ω p s ( s p ) EE33 - Oscillators

23 rystal reactance is inductive over a narrow frequency band between ω p and ω s. Use the crystal to replace the inductor in a olpitts oscillator. ircuit will oscillate at the resonant frequency of the crystal inductance L with the series equivalent of s and ( p + + ). EE33 - Oscillators 3

24 IV. MULTIVIBRATORS:. Bistable Multivibrator: Two stable states. ircuit has stable states: positive saturation and negative saturation. ircuit can remain in either stable state indefinitely. Moves to the other stable state only when triggered. Obtained by connecting an amplifier in a positive feedback loop having loop gain greater than unity. EE33 - Oscillators 4

25 Triggering the bistable circuit: Trigger signal EE33 - Oscillators 5

26 v I initiates or triggers regeneration (can be removed with no effect on the regeneration process). v I can simply be a pulse (i.e., trigger signal). The circuit is known as the Schmitt trigger. A simple change in the input converts the circuit into a non-inverting bistable circuit. EE33 - Oscillators 6

27 The output levels of the bistable circuit adjusted by cascading the op-amp with a limiter circuit. EE33 - Oscillators 7

28 . Astable Multivibrator: No stable state (astable). A square waveform can be generated by making a bistable multivibrator switch state periodically. onnecting a bistable mutivibrator with an R circuit in the feedback loop. EE33 - Oscillators 8

29 EE33 - Oscillators 9

30 harging: v - βl + at tt v L T + (L + ln( L )e L L t + ) where R Similarly for the discharge cycle, T L + L ln( ) If L + L - and TT +T then T Adjusting and/or R varies frequency. ln Waveform across can be made almost triangular by using a small value for the parameter β. EE33 - Oscillators 30 +

31 Generation of triangle waveforms: The exponential waveform generated in the astable circuit can be changed to triangular by replacing the low pass R circuit with an integrator. The integrator causes linear charging and discharging of the capacitor. The integrator is inverting, it is necessary to use the non-inverting bistable circuit. EE33 - Oscillators 3

32 V TH V T TL L+ R T R V TH V L + TL V TH V T TL L R T R V TH V L TL IF L + L - then symmetrical waveforms are obtained EE33 - Oscillators 3

33 3. Monostable Multivibrator: Need a pulse of known height and width generated in response to a trigger signal. The width of the pulse is predictable, its trailing edge used for timing purposes. Generated by a monostable multivibrator. Has one stable state which can remain indefinitely. Has a quasi-stable state (remains for a predetermined interval equal to the desired width of the output pulse). Once the interval expires, returns to the stable state and remains there awaiting another triggering signal. The circuit is commonly called a one shot. Is an augmented form of the astable circuit. EE33 - Oscillators 33

34 v B (t) L (L V D ) e t R 3 EE33 - Oscillators 34

35 Substitute v B (T)βL -, L L (L V D )e T R 3 T R 3 V ln( L D L L ) For V D << L -, T R 3 ln( ) Note: should not be re-triggered again until has been recharged to V D (recovery period). EE33 - Oscillators 35

36 INTEGRATED IRUIT TIMERS To implement monostable and astable multivibrators having precise characteristics. Most popular is the 555 timer. EE33 - Oscillators 36

37 Monostable circuit v V ( e v V TH 3 t R V ) t T T R ln(3).r EE33 - Oscillators 37

38 Astable circuit: EE33 - Oscillators 38

39 v V (V V TL )e (R A t + R B ) Rise in v : v V TH 3 V t T H V TL 3 V T H (R A + R B )ln() 0.69(R A + R B ) v V TH e t R B Fall in v : v V TL 3 V t T L V TH 3 V T L R B ln() 0.69R B Total period : T TH + TL 0.69(R A + R B ) EE33 - Oscillators 39

CHAPTER 3: OSCILLATORS AND WAVEFORM-SHAPING CIRCUITS

CHAPTER 3: OSCILLATORS AND WAVEFORM-SHAPING CIRCUITS In the design of electronic systems, the need frequently arises for signals having prescribed standard waveforms (e.g., sinusoidal, square, triangle,