An oscillator is a circuit that generates a periodic, oscillating signal without any external input. One type of oscillator is the transistor oscillator, which uses a transistor to generate the oscillating signal. The 2N5550 is a specific type of transistor that can be used in a transistor oscillator circuit.

The 2N5550 is a NPN bipolar junction transistor (BJT) with a maximum collector-emitter voltage of 60V, a maximum collector current of 1A, and a maximum power dissipation of 625mW. These specifications make it suitable for a wide range of applications, including oscillator circuits.

When used in an oscillator circuit, the 2N5550 acts as an amplifier. In the amplifier mode, the transistor amplifies the input signal. Usually an LC feedback circuit is connected from 2N5550 amplifier output back to the transistor and this generate the oscillating signal. The frequency of the oscillating signal is determined by the values of the feedback components in the feedback circuit.

One popular circuit for using 2N5550 as an oscillator is the Colpitts oscillator which is as shown below.

In this circuit, the two capacitor and inductor in the circuit form a feedback circuit which feedback partial signal from the output to the input of the amplifier. The two capacitor and the inductors determines the frequency of oscillation which can be determined using online Colpitts oscillator calculator. The frequency can be adjusted by changing the values of the capacitors and the inductor.Here C1=40nF, C2=40nF and L=150uF which gives the calculated frequency of oscillation of 91.89KHz.

The frequency of oscillation in a Colpitts oscillator circuit can be calculated using the following formula:

Frequency of oscillation = 1 / (2 * pi * √(L * C))

Where L is the value of the inductor in Henry, and C is the value of the capacitor in farads.

And the capacitor C series combination of C1 and C2 given by,

\(C = \frac{C_1 C_2}{C_1+C_2}\)

Where Ctotal is the total capacitance of the circuit, C1 is the capacitance of the first capacitor, and C2 is the capacitance of the second capacitor.

This formula is based on the fact that the two capacitors are connected in series. In a series connection, the total capacitance is,

\(\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}\)

This is because the voltage across each capacitor is the same and the charge stored on each capacitor is inversely proportional to its capacitance.

It's important to note that when selecting the value of C1 and C2 for a Colpitts oscillator circuit, the values should be chosen carefully to achieve the desired frequency of oscillation. By adjusting the values of C1 and C2, the frequency of oscillation can be fine-tuned to the desired value.

Additionally, the value of C1 and C2 also affect the Q factor and stability of the oscillator. The Q factor is the measure of how "sharp" the resonance is, and a high Q factor means that the oscillator is more stable and less prone to drifting over time.

It's always recommended to consult the datasheet of the oscillator circuit and consult with the manufacturer for the recommended values of the components based on the desired frequency and stability of the oscillator.

Similarly, the value of L and C can be adjusted to change the frequency of oscillation. In general, a larger value of L and C will result in a lower frequency.

It's worth mentioning that the frequency of oscillation is also affected by the transistor's gain and the value of the resistors in the circuit, but the above formula gives a rough estimate of the oscillation frequency.

It's also important to note that the Colpitts oscillator is a type of LC oscillator, which means that it is based on the resonant frequency of an LC circuit. The LC circuit is formed by the series combination of an inductor and a capacitor. The oscillation frequency is determined by the natural resonant frequency of this LC circuit.

Additionally, the Colpitts oscillator is known for its high frequency stability, and it can generate a sine wave output. It's a popular choice in RF circuit designs such as RF transmitters and local oscillator circuits.

The output of the oscillator circuit can be used for a variety of purposes, such as generating a radio frequency (RF) signal for communication, generating a clock signal for digital logic circuits, or driving a piezoelectric transducer for sound generation.

A Colpitts oscillator circuit using a 2N5550 transistor can be constructed on a breadboard or PCB. The 2N5550 Colpitts Oscillator circuit implemented on breardboard in this tutorial is shown below.

To demonstrate the circuit, you will need a power supply, an oscilloscope or a frequency counter to measure the frequency of oscillation and some resistors, wires and tools to build the circuit. The following video demonstrates how the above build 2N5550 Colpitts oscillator works.Another popular oscillator circuit using 2N5550 is the Hartley oscillator. It is similar to the Colpitts oscillator, but with a tapped
inductor and a capacitor instead of two capacitors. The tapped inductor
allows for a more stable frequency and a larger frequency range.