# Impedence calculation of colpitt oscillator circuit

#### Naveen Sankaran

Joined Nov 7, 2017
7
Hi, I built a colpitt oscillator circuit which looks like this. My aim is to find the change in the inductance coil L1. All the other values are kept constant.

I built this and got the sine wave from the collector terminal (of transistor) and the Cout terminal. With this, I can calculate the frequency.

Now, I have to arrive at a formula (with unknown variables), which can relate the frequency and the inductance. I started to break down the circuit but its a confusion for me.

Interpretation I did:

Tank circuit has C (equivalent capacitance) and L in parallel.

R1 and R2 are in series (Voltage divider). Re and Ce are in parallel. R4 and Cout are in parallel.

But I am confused as to how the combination of these circuits will happen. I require some suggestions. Thank you.

#### neonstrobe

Joined May 15, 2009
181
R4 will cause damping of the circuit at the top side of the inductor. R1 and R2 will damp the circuit at the lower end, but probably the input impedance of the transistor (hie) will be lower than R1 and R2 and will cause greater damping.
So the equivalent circuit needs to consider R4 between the top of the inductor and ground and R1, R2 and hie in parallel with the lower end and ground. There is also a base-emitter capacitance to consider but C2 should be designed to give a suitable match impedance, and collector-base capacitance but that should be small for a small signal transistor and probably C1 will be a lot larger, so don't need to be too concerned by that one.
Oscillators are a little more difficult to design than might at first seem, but almost any transistor will oscillate with a tuned circuit.

#### Naveen Sankaran

Joined Nov 7, 2017
7
R4 will cause damping of the circuit at the top side of the inductor. R1 and R2 will damp the circuit at the lower end, but probably the input impedance of the transistor (hie) will be lower than R1 and R2 and will cause greater damping.
So the equivalent circuit needs to consider R4 between the top of the inductor and ground and R1, R2 and hie in parallel with the lower end and ground. There is also a base-emitter capacitance to consider but C2 should be designed to give a suitable match impedance, and collector-base capacitance but that should be small for a small signal transistor and probably C1 will be a lot larger, so don't need to be too concerned by that one.
Oscillators are a little more difficult to design than might at first seem, but almost any transistor will oscillate with a tuned circuit.
Hi neonstrobe, thank you for your reply. I think you misinterpreted my question. The heading of the post says "impedence calculation". Even I asked some suggestions regarding impedence calculation and not in making the circuit more efficient. This is just a prototype as I just wanted to figure our the formula to find impedence, combining all the resistors, inductors and capacitors in the circuit. Thank you.

#### neonstrobe

Joined May 15, 2009
181
Well that's tricky. I can write down the impedances very simply but I'm not sure if that will help. I tend to use complex numbers because that makes things simpler, but you may need to write a program to solve your problem if you were to use them.

If I keep things simple at the moment the tuned circuit resonant frequency is 1/(2.pi. sqrt(LC)) where C is 1/(1/c1+1/c2) the series combination of C1 and C2.

For the impedances, the circuit would be solved as a network with several voltage nodes to be determined: the collector voltage, the coil voltage, the base voltage etc. So again to simplify things you could consider the input impedance of the transistor (a resistor and capacitor) in parallel with R1 and R2, and all in series with Cin, loading the coil as I mentioned, but the calculations will get more complicated.

• Naveen Sankaran