Editing Colpitts oscillator (section)

=== Working Principle ===
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.<ref>{{Cite web |last=Ayushi |date=2023-10-04 |title=Colpitts Oscillator - Principle, Working, Circuit Diagram |url=https://www.electricalvolt.com/colpitts-oscillator/ |access-date=2023-12-27 |website=Electrical Volt |language=en-us}}</ref>

The working principle of a Colpitts oscillator can be explained as follows:

* When the power supply is switched on, the capacitors <math>C_1</math> and <math>C_2</math> start charging through the resistor <math>R_1</math> and <math>R_2</math>. The voltage across <math>C_2</math> is coupled to the base of the transistor through the capacitor <math>C_\text{in}</math>.
* The transistor amplifies the input signal and produces an inverted output signal at the collector. The output signal is coupled to the tank circuit through the capacitor <math>C_\text{out}</math>.
* The tank circuit resonates at its natural frequency, which is given by:

:<math>f = \frac{1}{2 \pi \sqrt{LC_t}}</math>

Where:

* f = frequency of oscillation
* L = inductance of the inductor
* <math>C_t</math> = total capacitance of the series combination of <math>C_1</math> and <math>C_2</math>, given by:

:<math>C_t = \frac{C_1 C_2}{C_1 + C_2}</math>

* The resonant frequency is independent of the values of <math>C_1</math> and <math>C_2</math>, but depends on their ratio. The ratio of <math>C_1</math> and <math>C_2</math> also affects the feedback gain and the stability of the oscillator.
* The voltage across the inductor L is in phase with the voltage across <math>C_2</math>, and 180 degrees out of phase with the voltage across <math>C_1</math>. Therefore, the voltage at the junction of <math>C_1</math> and <math>C_2</math> is 180 degrees out of phase with the voltage at the collector of the transistor. This voltage is fed back to the base of the transistor through <math>C_\text{in}</math>, providing another 180 degrees phase shift. Thus, the total phase shift around the loop is 360 degrees, which is equivalent to zero degrees. This satisfies the Barkhausen criterion for oscillation.
* The amplitude of the oscillation depends on the feedback gain and the losses in the tank circuit. The feedback gain should be equal to or slightly greater than the losses for sustained oscillation. The feedback gain can be adjusted by varying the values of <math>R_1</math> and <math>R_2</math>, or by using a variable capacitor in place of <math>C_1</math> or <math>C_2</math>.<ref>{{Cite web |last=Ayushi |date=2023-10-04 |title=Colpitts Oscillator - Principle, Working, Circuit Diagram |url=https://www.electricalvolt.com/colpitts-oscillator/ |access-date=2023-12-27 |website=Electrical Volt |language=en-us}}</ref>

The Colpitts oscillator is widely used in various applications, such as RF communication systems, signal generators, and electronic testing equipment. It has better frequency stability than the Hartley oscillator, which uses a tapped inductor instead of a tapped capacitor in the tank circuit.<ref>{{Cite web |date=2009-10-12 |title=Colpitts Oscillator Circuit diagram & working. Frequency equation. Colpitts oscillator using opamp |url=https://www.circuitstoday.com/colpitts-oscillator |access-date=2023-12-27 |website=Electronic Circuits and Diagrams-Electronic Projects and Design |language=en-US}}</ref> However, the Colpitts oscillator may require a higher supply voltage and a larger coupling capacitor than the Hartley oscillator.<ref>{{Cite web |date=2023-10-26 |title=Colpitts Oscillators {{!}} How it works, Application & Advantages |url=https://www.electricity-magnetism.org/colpitts-oscillators/ |access-date=2023-12-27 |website=Electricity - Magnetism |language=en-us}}</ref>