oscillator_frequency_derive.pdf

12 - 1 Electronics(3), 2013Prof. Tai-Haur Kuo Basic Principles of Sinusoidal Oscillators Linear oscillator ?Linear region of circuit : linear oscillation ?Nonlinear region of circuit : amplitudes stabilization Barkhausen criterion ? loop gain L(s) = β (s)A(s) ? characteristic equation 1-L(s) = 0 ?oscillation criterion L(jw0) = A(jw0) β(jw0) = 1 Amplifier A?SX OX fX ? ? Frequency-selective network ? 12 - 2 Electronics(3), 2013Prof. Tai-Haur Kuo Basic Principles of Sinusoidal Oscillators (Cont.) at w0, the phase of the loop should be zero and the magnitude of the loop gain should be unity. Oscillation frequency w0 is determined solely by A steep phase response results in a small for a given change in phase 0w? ?? dωdφ Δφ Δω0 ? Δφ 0 φ 0ω ω 12 - 3 Electronics(3), 2013Prof. Tai-Haur Kuo Nonlinear Amplitude Control To sustain oscillation : βA1 a.overdesign for βA variations b.oscillation will grow in amplitude ?poles are in the right half of the s-plane c.Nonlinear network reduces βA to 1 when the desired amplitude is reached ?poles will be pulled to jw-axis 12 - 4 Electronics(3), 2013Prof. Tai-Haur Kuo Nonlinear Amplitude Control (Cont.) Limiter circuit for amplitude control ? linear region 54 5 O 54 4 B 32 2 O 32 3 A i 1 f O RR R V RR R VV RR R V RR R VV )V R R (V ? ? ? ?? ? ? ? ? ?? 2D 1D R1 ? ? OV IV Rf R2 R3 R4 R5 A B V -V 12 - 5 Electronics(3), 2013Prof. Tai-Haur Kuo Nonlinear Amplitude Control (Cont.) ?nonlinear region ) R R (1V R R VL similarly, ) R R (1V R R V )V RR R V( R RR L V 5 4 D 5 4 2 3 D 2 3 D 32 3 2 32 -VVO DA ??? ???? ? ? ? ? ?? ? ?? 1 3f R )R(R Slope ?? ?L ?L 0 1 4f R )R(R Slope ?? OV IV 1 f R R Slope ?? 12 - 6 Electronics(3), 2013Prof. Tai-Haur Kuo OPAMP-RC Oscillator Circuits Wien-bridge oscillator ? _ C R C R 1R 2R SZ PZ OV dV ? ) ? ) ? ) 2 R R 1sL RC 1 ω RCω 1 RCω 0. phase For ωRC 1 ωRCj3 R R 1 jωL SCR 1 SCR3 R R 1 ZZ Z R R 1sL 1 2 0 0 0 1 2 1 2 sp p 1 2 ???????? ?? ??????? ? ? ? ? ? ? ?? ? ? ?? ? ?