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Electronics · Ch 6 — Oscillators

Chapter Summary

Chapter Summary

  • An oscillator converts DC energy into AC energy of a desired frequency (a few Hz to several GHz) with no AC input, using an amplifier with positive feedback.
  • Oscillators are classified by waveform into sinusoidal and non-sinusoidal, and sinusoidal ones by feedback components into LC, RC and crystal oscillators. Damped oscillations decay in amplitude, un-damped (sustained) oscillations stay constant.
  • Feedback theory gives the gain with positive feedback Af=A1−AβA_f = \dfrac{A}{1 - A\beta}. When Aβ=1A\beta = 1 the amplifier becomes an oscillator. Oscillations start from circuit noise; at switch-on Aβ>1A\beta > 1 so they build up, then settle at Aβ=1A\beta = 1.
  • Barkhausen criterion: the loop phase shift is 0 degrees (or 360 degrees) and ∣Aβ∣=1|A\beta| = 1. Aβ<1A\beta < 1 gives damped, Aβ>1A\beta > 1 growing, and Aβ=1A\beta = 1 sustained oscillations.
  • A tank (oscillatory) circuit is an L-C combination that exchanges energy between the capacitor's electric field and the coil's magnetic field, giving f=12πLCf = \dfrac{1}{2\pi\sqrt{LC}}; real losses make it damped, so an amplifier restores the energy.
  • Hartley oscillator (inductive feedback): f=12πLCf = \dfrac{1}{2\pi\sqrt{LC}}, L=L1+L2L = L_1 + L_2, β=L2L1\beta = \dfrac{L_2}{L_1}. Colpitts oscillator (capacitive feedback): f=12πL Ceqf = \dfrac{1}{2\pi\sqrt{L\,C_{eq}}}, Ceq=C1C2C1+C2C_{eq} = \dfrac{C_1 C_2}{C_1 + C_2}, β=C1C2\beta = \dfrac{C_1}{C_2}.
  • RC oscillators generate low frequencies without inductors. The phase-shift oscillator uses three 60-degree RC sections plus an inverting op-amp: f=12π6 RCf = \dfrac{1}{2\pi\sqrt{6}\,RC}, A=29A = 29, β=129\beta = \dfrac{1}{29}. The Wein bridge oscillator uses a lead-lag network: f=12πRCf = \dfrac{1}{2\pi RC}, gain A=3A = 3, β=13\beta = \dfrac{1}{3}.
  • A crystal oscillator uses the piezoelectric effect of quartz for very high frequency stability, with a series resonant frequency fs=12πLCsf_s = \dfrac{1}{2\pi\sqrt{L C_s}} and a slightly higher parallel resonant frequency fpf_p; the oscillation lies between them and is set by the crystal, independent of supply and transistor changes. …
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← Previous · 6.5Non sinusoidal OscillatorNext →Example 1 — A Hartley Oscillator has \(L₁ = 2mH\), \(L₂ = 4mH\) and \(C = 10nF\). …