In one line
An oscillator is an amplifier (BJT or FET) with positive feedback through a frequency-selective network; it produces a sustained sine wave at the frequency where the loop gain is one and the total phase shift is 0° or 360° (Barkhausen criterion).
Explained simply
Hold a microphone near its own speaker and you hear a loud whistle: the sound is amplified, fed back, amplified again, and locks onto one tone. An oscillator does this deliberately and in a controlled way, using a tuning network so that only one chosen frequency survives. No input signal is needed; it starts from tiny electrical noise.
Technically, if the amplifier gain is \( A \) and the feedback fraction is \( \beta \), oscillations are sustained when \( A\beta = 1 \) in magnitude and the total phase shift around the loop is 0° (or 360°). At switch-on, \( |A\beta| \) is kept slightly greater than 1 so oscillations grow, and then circuit non-linearity limits the amplitude.
How it works
- The transistor (CE or CS stage) amplifies and gives 180° phase shift.
- The feedback network gives another 180° at one particular frequency, making 360° in total.
- RC phase-shift oscillator: three RC sections, about 60° each, give 180°. For the basic ladder, \( f = \dfrac{1}{2\pi RC\sqrt6} \), and the network attenuates by 1/29, so the amplifier gain must be at least 29. Used for audio frequencies.
- LC oscillators (Hartley, Colpitts): a tank circuit sets the frequency. Hartley uses a tapped inductor (\( L_1 + L_2 \)) with one capacitor; Colpitts uses split capacitors (\( C_1, C_2 \)) with one inductor. Used for radio frequencies.
- Crystal oscillator: a quartz crystal replaces the tank; very stable frequency. Used in clocks, watches and microcontrollers.
- FETs are often used in oscillators for their high input impedance, which loads the tank circuit less.
Key formula
Barkhausen: \( |A\beta| = 1,\; \angle A\beta = 0^\circ \text{ or } 360^\circ \). LC: \( f = \dfrac{1}{2\pi\sqrt{L_{eq}C_{eq}}} \), Hartley \( L_{eq} = L_1 + L_2 \) (+2M if coupled), Colpitts \( C_{eq} = \dfrac{C_1C_2}{C_1+C_2} \).
\( A \) = amplifier gain, \( \beta \) = feedback factor (no units), \( f \) = frequency (Hz), \( R \) in \( \Omega \), \( C \) in F, \( L \) in H, \( M \) = mutual inductance (H).
Quick example
An RC phase-shift oscillator with \( R = 10 \) kΩ and \( C = 10 \) nF gives \( f = 1/(2\pi\times10^4\times10^{-8}\times2.449) \approx 650 \) Hz, an audible tone. A quartz-watch crystal oscillates at 32 768 Hz, which divides down neatly to 1 pulse per second.
Common mistakes
- Using negative feedback for an oscillator; it must be positive (regenerative) feedback.
- Saying \( A\beta \) must be exactly 1 at start-up; it is slightly greater than 1 at start, settling to 1.
- Forgetting that the amplifier's own 180° shift is part of the 360° total.
How MU asks it
Numericals are not expected in this module (MU syllabus), so questions are theory with diagrams. Typical: "Explain the application of BJT/FET as an oscillator" or "State the Barkhausen criterion" (5 marks). For full marks draw the block diagram (amplifier + feedback network), state both Barkhausen conditions, draw one circuit (RC phase-shift or Colpitts) with the transistor, write its frequency formula, and give uses.