should be sufficient to overcome any positive resistance in the circuit. By inspection, oscillation is more likely for larger values of transconductance and smaller values of capacitance. A more complicated analysis of the common-base oscillator reveals that a low-frequency amplifier voltage gain must be at least 4 to achieve oscillation. The low-frequency gain is given by If the two capacitors are replaced by inductors, and magnetic coupling is ignored, the circuit becomes a Hartley oscillator. In that case, the input impedance is the sum of the two inductors and a negative resistance given by In the Hartley circuit, oscillation is more likely for larger values of transconductance and larger values of inductance. The above analysis also describes the behavior of the Pierce oscillator. The Pierce oscillator, with two capacitors and one inductor, is equivalent to the Colpitts oscillator. Equivalence can be shown by choosing the junction of the two capacitors as the ground point. An electrical dual of the standard Pierce oscillator using two inductors and one capacitor is equivalent to the Hartley oscillator. Oscillation amplitude The amplitude of oscillation is generally difficult to predict, but it can often be accurately estimated using the describing function method. For the common-base oscillator in Figure 1, this approach applied to a simplified model predicts an output (collector) voltage amplitude given by where is the bias current, and is the load resistance at the collector. This assumes that the transistor does not saturate, the collector current flows in narrow pulses, and that the output voltage is sinusoidal (low distortion). This approximate result also applies to oscillators employing different active device, such as MOSFETs and vacuum tubes. References Further reading . . Electronic oscillators Electronic design Chaotic maps