Sinusoidal Oscillators

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Justin Wade
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1 Sinusoidal Oscillatos Signal geneatos: sinusoidal, ectangula, tiangula, TLV, etc. Obtaining a sine wave: tiangle functional tansfome sine sine wave geneation: fequency selective netwok in a feedback loop of a PF amplifie: sinusoidal oscillato -Oscillation fequency: f -Oscillation amplitude: Vˆo - Oscillation citeion - Fequency stability - Amplitude stability - Distotion coefficient

2 Oscillato feedback loop PF amplifie: If x i But if x s x a A a xo Ax s a ; A ; x s xo ; x finite

3 Oscillato feedback loop In the complex domain x s a A a fo a unique f a Fequency dependent components, L Zc Z L L f fl

4 Oscillation citeion Bakhausen s citeion a f fo a unique Signal econstuction on the feedback loop a a e a e a a a e module condition: phase condition: Who sets Vˆ? o a a k Nonlineaity of the gain gives a gives f

5 Oscillatos Basic amplifie fequency independent o inveting a 8 noninveting a Fequency selective feedback netwok To fulfil the phase condition, thee must be a unique fequency, f whee the phase shift is: 8, if a, if a 8

6 v v o v v o v v o Z Z Z Z Z WIEN Bidge Fequency selective netwok out in Tansfe function complex numbe voltage tansfe

7 WIEN Bidge e actg out in module phase

8 WIEN Bidge o The maximum value as a function of ω: asymptote asymptote The module

9 The phase actg WIEN Bidge 9 asymptote 9 asymptote o intemediate value

10 WIEN Bidge Fequency esponse out in Fo only one unique fequency, f we have Fo the phase condition: noninveting amplifie a f

11 v v o f f 3 out in If WIEN Bidge Summay

12 Op amp and WIEN bidge oscillato t f V t v o o sin ˆ f

13 Op amp and WIEN bidge oscillato f Fo a f 3 a Vˆ o? Nonlineaity on the gain, close to satuation

14 Automatic gain contol AG a oscillations ae attenuated - zeo a oscillations ae amplified - satuation a oscillations ae maintained - oscillate Stability of the oscillation amplitude Automatic gain contol - depending on the output voltage magnitude Vˆo ˆ V o v Vˆ sin f o o cst, a, Vˆ t

15 AG fo WIEN bidge oscillato a 4 3 How an AG can be implemented, so that a will depend on v o value? 4 - dependent on v o o 3 - dependent on v o

16 Diode evisited - as vaiable esisto Static esistance of a diode in the opeating point Q 4 D V I D D Q Q Q 3 D D3 V I V I D D D3 D3.495V.79 ma.6v.79ma 4.4k.63k D D4 V I V I D D D4 D4.555V.96 ma.645v 5.64 ma.599k.5k If the voltage dop V D inceases, the equivalent static esistance D deceases

17 AG using Diodes - how? V D I D D If the voltage dop V D inceases, the equivalent static esistance 4 D a deceases dependent on v o o 3 - dependent on v o

18 . AG using diodes 4,ech fo a off a v o t small, D, D off ' 4 4, ech 3 3 '' 4 a off a on ' '' D a on Vˆ o v o t is given by the value of D inceases, D on on the positive half-cycle D on on the negative half-cycle to maintain oscillations

19 . AG using n-channel depletion-type MOSFET 4 a ' DS 3 DS v V GS Th v GS < v, GS DS

20 Poblem a How does the voltages v o t and v + t look like in the steadystate egime? What is the oscillation fequency? b Size 4 so that the cicuit will maintain the oscillation. Fo the maximum value magnitude of the sinusoidal output, conside D = D =.5 kω. Veify if the oscillation can stat. c What is the magnitude of v o t in the conditions of question b, if the voltage dop acoss one diode is v D =.58 V fo the equivalent esistance D =.5 kω d How does the voltage v o t look like in the steady-state egime if D diode is missing?

21 Op amp and ladde netwok oscillato High pass band Low pass band the phase-shift is in the ange of [ o ; -9 o ] inveting basic amplifie how many identical cells ae necessay to build an oscillato?

22 5 6 3 Low pass ladde with 3 cells 6 3 f 6 9

23 The cicuit of ladde netwok oscillato

Discussion #7 Example Problem This problem illustrates how Fourier series are helpful tools for analyzing electronic circuits. Often in electronic

Discussion #7 Example Problem This problem illustrates how Fourier series are helpful tools for analyzing electronic circuits. Often in electronic Discussion #7 Example Poblem This poblem illustates how Fouie seies ae helpful tools fo analyzing electonic cicuits. Often in electonic cicuits we need sinusoids of vaious fequencies But we may aleady