A Colpitts oscillator, named after its inventor Edwin H. Colpitts, is one of a number of designs for electronic oscillator circuits. One of the key features of this type of oscillator is its simplicity and robustness. It is not difficult to achieve satisfactory results with little effort. Western Electric research branch chief in early 1900s. ... An electronic oscillator is an electronic circuit that produces a repetitive electronic signal, often a sine wave or a square wave. ...

A Colpitts oscillator is the electrical dual of a Hartley oscillator. In the Colpitts circuit, two capacitors and one inductor determine the frequency of oscillation. The Hartley circuit uses two inductors (or a tapped single inductor) and one capacitor. (Note: the capacitor can be a variable device by using a varactor). Schematic Diagram The Hartley oscillator is an LC electronic oscillator that derives its feedback from a tapped coil in parallel with a capacitor (the tank circuit). ...

The following schematic is an example using an NPN transistor in the common-base configuration. Frequency of oscillation is roughly 50 MHz:

Image File history File links Colpitts oscillator schematic of working circuit Source of image Created by Madhu as a screenshot. ...

The following schematic is a common-collector version of the same oscillator:

Image File history File links Colpitts oscillator schematic of working circuit, coil connected to base Source of image Created by Madhu as a screenshot. ...

The bipolar transistor could be replaced with a JFET or other active device capable of producing gain at the oscillation frequency.

The ideal frequency of oscillation is given by this equation:

A simplified version of the formula is this:

In this simplified version, remember that L is in uH (micro Henrys), C is in uF (micro Farads), and f is in MHz.

Given the values in the circuit above, the equation predicts a frequency of roughly 58 MHz. The real circuit will oscillate at a slightly lower frequency due to junction capacitances of the transistor and possibly other stray capacitances.

Analysis

Colpitts oscillator model

One method of oscillator analysis is to determine the input impedance of an input port neglecting any reactive components. If the impedance yields a negative resistance term, oscillation is possible. This method will be used here to determine conditions of oscillation and the frequency of oscillation. Image File history File links Colpitts oscillator ideal analysis model Screen shot created by Madhu 20:10, 5 Mar 2005 (UTC) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... In electrical circuits, static resistance is the ratio of the voltage across a circuit element to the current through it. ...

An ideal model is shown to the right. This configuration models the common collector circuit in the section above. For initial analysis, parasitic elements and device non-linearities will be ignored. These terms can be included later in a more rigorous analysis. Even with these approximations, acceptable comparison with experimental results is possible. A parasite is an organism that lives in or on the living tissue of a host organism at the expense of it. ...

Ignoring the inductor, the input impedance can be written as In electrical engineering, Impedance is a measure of opposition to a sinusoidal electric current. ...

Where v₁ is the input voltage and i₁ is the input current. The voltage v₂ is given by

v₂ = i₂Z₂

Where Z₂ is the impedance of C₂. The current flowing into C₂ is i₂, which is the sum of two currents:

i₂ = i₁ + i_s

Where i_s is the current supplied by the transistor. i_s is a dependent current source given by

Where g_m is the transconductance of the transistor. The input current i₁ is given by Transconductance, also known as mutual conductance, is a property of certain electronic components. ...

Where Z₁ is the impedance of C₁. Solving for v₂ and substituting above yields

Z_in = Z₁ + Z₂ + g_mZ₁Z₂

The input impedance appears as the two capacitors in series with an interesting term, R_in which is proportional to the product of the two impedances:

R_in = g_mZ₁Z₂

If Z₁ and Z₂ are complex and of the same sign, R_in will be a negative resistance. If the impedances for Z₁ and Z₂ are substituted, R_in is In electrical circuits, static resistance is the ratio of the voltage across a circuit element to the current through it. ...

If an inductor is connected to the input, the circuit will oscillate if the magnitude of the negative resistance is greater than the resistance of the inductor and any stray elements. The frequency of oscillation is as given in the prevous section.

For the example oscillator above, the emitter current is roughly 1 mA. The transconductance is roughly 40 mS. Given all other values, the input resistance is roughly The ampere (symbol: A) is the SI base unit of electrical current equal to one coulomb per second. ... The siemens (symbol: S) is an SI derived unit of measurement for electric conductance, being the inverse of the ohm (Ω), named after Werner von Siemens. ...

R_in = − 30Ω

This value should be sufficient to overcome any positive resistance in the circuit. By inspection, oscillation is more likely for larger values of transconductance and/or smaller values of capacitance.

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: Schematic Diagram The Hartley oscillator is an LC electronic oscillator that derives its feedback from a tapped coil in parallel with a capacitor (the tank circuit). ...

R_in = − g_mω²L₁L₂

In the Hartley circuit, oscillation is more likely for larger values of transconductance and/or larger values of inductance.