Oscillator. Introduction of Oscillator Linear Oscillator. Stability. Wien Bridge Oscillator RC Phase-Shift Oscillator LC Oscillator

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2 Oscillatr Intrductin f Oscillatr Linear Oscillatr Wien Bridge Oscillatr Phase-Shift Oscillatr L Oscillatr Stability

3 Oscillatrs Oscillatin: an effect that repeatedly and regularly fluctuates abut the mean value Oscillatr: circuit that prduces scillatin haracteristics: wave-shape, frequency, amplitude, distrtin, stability

4 Applicatin f Oscillatrs Oscillatrs are used t generate signals, e.g. Used as a lcal scillatr t transfrm the F signals t IF signals in a receiver; Used t generate F carrier in a transmitter Used t generate clcks in digital systems; Used as sweep circuits in T sets and O.

5 Linear Oscillatrs. Wien Bridge Oscillatrs. Phase-Shift Oscillatrs. L Oscillatrs 4. Stability

6 Integrant f Linear Oscillatrs s Σ ε Amplifier A Psitive Feedback f Frequency-Selective Feedback Netwrk β Fr sinusidal input is cnnected Linear because the utput is apprximately sinusidal A linear scillatr cntains: - a frequency selectin feedback netwrk - an amplifier t maintain the lp gain at unity

7 Basic Linear Oscillatr s Σ ε Af f SelectiveNetwrk β f Aε A s f and f β A s Aβ If s 0, the nly way that can be nnzer is that lp gain Aβ which implies that Aβ Aβ 0 Barkhausen riterin

8 Wien Bridge Oscillatr Frequency Selectin Netwrk Let ω and j ω j j j Therefre, the feedback factr, / / i j j j j j β j j j j β i

9 β can be rewritten as: β j Fr Barkhausen riterin, imaginary part 0, i.e., r ω / ω Suppsing, and, 0 ω Feedback factr β β / fc Phase0 β j Phase Frequency

10 By setting ω Imaginary part 0 and Example, we get β Due t Barkhausen riterin, Lp gain A v β where A v : Gain f the amplifier Av β Av Therefre, f f f Wien Bridge Oscillatr

11 Phase-Shift Oscillatr f Using an inverting amplifier The additinal 80 phase shift is prvided by an phase-shift netwrk

12 Applying KL t the phase-shift netwrk, we have I I I Slve fr I, we get 0 0 j I I I j I I I j I j j j j j I ] [ j j j I Or

13 The utput vltage, ] [ j j j I Hence the transfer functin f the phase-shift netwrk is given by, 6 5 j β Fr 80 phase shift, the imaginary part 0, i.e., ejected r 0 6 ω and, 9 β Nte: The ve sign mean the phase inversin frm the vltage

14 L Oscillatrs The frequency selectin netwrk, and prvides a phase shift f 80 The amplifier prvides an additin shift f 80 Tw well-knwn Oscillatrs: lpitts Oscillatr Harley Oscillatr Av ~ p

15 ~ Av p f // p Fr the equivalent circuit frm the utput p p v i p p i v A A r Therefre, the amplifier gain is btained, A A v i f β p Avi I

16 The lp gain, A A v β If the impedance are all pure reactances, i.e., and, j j j The lp gain becmes, j A A v β The imaginary part 0 nly when 0 It indicates that at least ne reactance must be ve capacitr and must be f same type and must be f ppsite type A A A v v β With imaginary part 0, Fr Unit Gain & 80 Phase-shift, A A v β

17 Hartley Oscillatr lpitts Oscillatr L L L ω g m L L L L ω g m L T T

18 lpitts Oscillatr Equivalent circuit L L gm π In the equivalent circuit, it is assumed that: Linear small signal mdel f transistr is used The transistr capacitances are neglected Input resistance f the transistr is large enugh

19 At nde, π i jωl where, i jω π π ω L Apply KL at nde, we have jω π gmπ jω 0 jω π gmπ π ω L jω Fr Oscillatr π must nt be zer, therefre it enfrces, L I I π gm π 0 I nde I4 g m ω L j [ ] ω ω L 0

20 g m ω L j [ ] ω ω L 0 Imaginary part 0, we have ω L T T eal part 0, yields g m

21 Frequency Stability The frequency stability f an scillatr is defined as dω ω dt ω ω ppm/ Use high stability capacitrs, e.g. silver mica, plystyrene, r tefln capacitrs and lw temperature cefficient inductrs fr high stable scillatrs.

22 Amplitude Stability In rder t start the scillatin, the lp gain is usually slightly greater than unity. L scillatrs in general d nt require amplitude stabilizatin circuits because f the selectivity f the L circuits. In scillatrs, sme nn-linear devices, e.g. NT/PT resistrs, FET r zener dides can be used t stabilized the amplitude

23 Wien-bridge scillatr with bulb stabilizatin irms Blub Operating pint rms

24 Wien-bridge scillatr with dide stabilizatin f

25 Twin-T Oscillatr lw pass filter Filter utput lw pass regin high pass regin high pass filter fr f

26 Bistable ircuit v v v v -cc th cc v v v cc cc -th v -th th v -cc -cc

27 A Square-wave Oscillatr vc vf v vf vc Ðvf vmax v Ðvmax