Single-Transistor RLC Oscillator (Colpitts-Type Oscillator)

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Objective

This document explains a single-NPN-transistor RLC oscillator using a Colpitts-type capacitive feedback network. The animation is intended for an educational Science Viewer. It shows transistor bias, collector current, energy exchange in the resonant network, feedback, oscillation build-up, and the steady-state output waveform.

Circuit Configuration

The circuit uses one NPN transistor Q_1, a bias network R_1,R_2, emitter resistor R_E, inductor L_1, capacitors C_1,C_2, and a DC supply V_CC.

The two capacitors form an effective series capacitance C_eq=C_1C_2C_1+C_2.

The approximate resonant frequency is f_0=12L_1 C_eq.

For the demonstration values L_1=10mH, C_1=C_2=10nF, we obtain C_eq=5nF and therefore f_0 22.51kHz.

Operating Principle

When V_CC is applied, the bias network establishes the operating point of Q_1. Noise and switching transients contain small AC components. Near the resonant frequency, the LC network preferentially sustains the resonant component.

Energy alternates between the electric fields of C_1,C_2 and the magnetic field of L_1. The transistor supplies energy that compensates for resonator and load losses. The capacitive divider returns a fraction of the resonant signal to the transistor input with the phase relationship required for positive feedback.

The small oscillation therefore grows until transistor nonlinearity and circuit losses establish a stable amplitude.

A simplified build-up model used only for visualization is v_o(t)=A(t)(2 f_0 t), where A(t)=A_(1-e^-t/_g). This envelope is an educational approximation, not a transistor-level SPICE model.

Phase and Energy Exchange

For an ideal sinusoidal resonant state, the animation may represent v_C(t)=V_p(_0 t), and i_L(t)=I_p(_0t-2), with _0=2 f_0.

The current particles reverse direction every half cycle. Capacitor charge indication and inductor current indication are synchronized to the same master simulation clock.

Animation

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Interpretation of the Animated Waveform

At startup the output amplitude is very small. Positive feedback causes the resonant component to grow. As the amplitude becomes large enough for transistor nonlinearity and losses to balance the supplied energy, the envelope approaches a nearly constant value. The resulting collector output is approximately sinusoidal.

The animation should therefore show three ideas simultaneously: the direction and magnitude of current in the circuit, the exchange of energy in the resonator, and the growth and stabilization of V_out.

Practical Considerations

The calculated frequency is an ideal approximation. A real oscillator is affected by transistor junction capacitances, transistor gain, inductor series resistance, capacitor tolerance, supply impedance, temperature, and loading at the output. Accurate hardware prediction should therefore use measured component parameters or a transistor-level circuit simulator.