Colpitts oscillator
The distinguishing feature of the Colpitts oscillator is that the feedback for the active device is taken from a voltage divider made of two capacitors in series across the inductor.
[2][3][4][5] The Colpitts circuit, like other LC oscillators, consists of a gain device (such as a bipolar junction transistor, field-effect transistor, operational amplifier, or vacuum tube) with its output connected to its input in a feedback loop containing a parallel LC circuit (tuned circuit), which functions as a bandpass filter to set the frequency of oscillation.
The amplifier will have differing input and output impedances, and these need to be coupled into the LC circuit without overly damping it.
A Colpitts oscillator uses a pair of capacitors to provide voltage division to couple the energy in and out of the tuned circuit.
(It can be considered as the electrical dual of a Hartley oscillator, where the feedback signal is taken from an "inductive" voltage divider consisting of two coils in series (or a tapped coil).)
The inductor L and the series combination of C1 and C2 form the resonant tank circuit, which determines the frequency of the oscillator.
The voltage across C2 is applied to the base-emitter junction of the transistor, as feedback to create oscillations.
As with any oscillator, the amplification of the active component should be marginally larger than the attenuation of the resonator losses and its voltage division, to obtain stable operation.
Therefore the amplifier input, the source, is connected to the low impedance tap of the LC circuit L1, C1, C2, C3 and the amplifier output, the drain, is connected to the high impedance top of the LC circuit.
The resistor R1 sets the operating point to 0.5mA drain current with no oscillating.
An additional variable capacitor between drain of J1 and ground allows to change the frequency of the circuit.
If the impedance yields a negative resistance term, oscillation is possible.
This configuration models the common collector circuit in the section above.
For initial analysis, parasitic elements and device non-linearities will be ignored.
Ignoring the inductor, the input impedance at the base can be written as where
and substituting above yields The input impedance appears as the two capacitors in series with the term
[7] 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.
[8] Equivalence can be shown by choosing the junction of the two capacitors as the ground point.
A Colpitts oscillator is an electronic circuit that generates a sinusoidal waveform, typically in the radio frequency range.
It uses an inductor and two capacitors in parallel to form a resonant tank circuit, which determines the oscillation frequency.
The output signal from the tank circuit is fed back into the input of an amplifier, where it is amplified and fed back into the tank circuit.
The feedback signal provides the necessary phase shift for sustained oscillation.
[9] The working principle of a Colpitts oscillator can be explained as follows: Where: The Colpitts oscillator is widely used in various applications, such as RF communication systems, signal generators, and electronic testing equipment.
[12] 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[13] where
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.
