In this post we are going to understand how LC oscillator circuits functions and we will be constructing one of the popular LC based oscillator - Colpitts oscillator.

## What are Oscillators

Electronic oscillators are used in most of our daily used electronic gadgets ranging from digital clock to high end core i7 processor. Oscillators are heart of all digital circuits but, not only digital circuit employee oscillators but also analogue circuits uses oscillatory circuits.

For instant AM, FM radio, where the high frequency oscillation is used as carrier signal to transport message signal.

There are many different kinds of oscillators such as RC, LC, crystal etc. Each one of them has their own advantages and disadvantages. So there is nothing called best or ideal oscillator, we have to analyse the circumstance of our circuit and choose the best one which suit, that’s why we find wide range of oscillators in every day used gadgets.

## LC Oscillators

Let’s dive into the explanation of LC oscillator.

The LC oscillator consists of an inductor and a capacitor as shown in figure below.

The value of the capacitor and resistor determines the output oscillation. So how do they generate oscillation?

Well, we need to apply external energy between L and C i.e. voltage. When we apply the voltage, the capacitor gets charged-up. When the supply is cut-off, the stored energy from capacitor flows to inductor and inductor starts building magnetic field around it until the capacitor completely gets discharged.

When the capacitor is fully discharged, the magnetic field around inductor collapse and induces voltage and charge-up the capacitor with opposite polarity and the cycle repeats.

The charge and discharge between L and C produces oscillation and this oscillation is called resonance frequency. However the frequency generation won’t last forever due to parasitic resistance which dissipates the energy in the oscillatory circuit in the form of heat.

To maintain the oscillation and use the oscillation with reasonable output strength, we need an amplifier with zero degree phase shift and feedback.

The feedback feed small amount of output from amplifier back to LC network to compensate the loss due to parasitic resistance and maintain the oscillation. Thus we can generate steady sine wave output.

### Application circuit:

Here is a colpitts oscillator circuit which can generate around 30Mhz signal.

## Search Related Posts for Commenting

Sol says

😂 found out that 7pF = 0.000000000007 ampere second/volt.

Have no idea what that does in a self resonating coil. Will it create a standing wave?

Sol says

P.s. this is based on a one time charge of the 7 pf cap.

Sol says

I came to that conclusion imagining 409 cycles at a frequency of ca. 58 MHz how long that would take.

The 22 mA I got by using Ohms law.

9 V and the coils reactance of the coil 405.847 Ohm. => power dissipation 199.52262 mW.

But I might be far off there.

Swagatam says

A good 9V PP3 battery will be capable of powering a 22mA load for around 500 / 22 x 0.7 = 15 minutes or at the least 10 minutes.

Sol says

Sorry, maybe I’m not expressing myself clear enough. I understand that you focus on how long the battery will last. That was not my question. I wanted to find out how long a one charge of the LC tank would last.

That is, the 9V battery charges the 7pF cap before getting isolated and the tank starts it’s oscillating. So how long will the oscillating last before dies out, or needs reloading.

Swagatam says

If the 7pF is connected across the supply rail and you are asking how long the charge inside the 7pF can sustain the oscillation in the LC circuit once the battery power is cut off, then that will need some calculation?

Sol says

Indeed, and there I’m not sure I did it right.

I wrote “The coils power use, based on its resistance, would be 199.52262 mW / 22.16918 mA.

Would this give an amount of 409 oscillations before all power is used up?”

Here I was referring to the power inside the tank aka the 7pF cap.

Maybe I should have looked how much power is stored in the cap?

Something like 1 F = 1 A/sec?

Swagatam says

You mean to say the 7pF is itself the “C” in the LC circuit and you want to know how many oscillations it can complete with one full charge on the 7 pF.

That’s very complex to solve, because the oscillations will be damped oscillation which will die out slowly from t = 0 to t = infinity.

The formula will be a differential type.

Sol says

The case is, that I wish (sometimes ppl wish the imposible) to know if the charge of the 7pF could be sufficient to drive the high frequency trafo from 9 to 180 V which output would drive the next HF trafo to 960 V and from there down to 230 V AC and simultaneously to 9 V AC to drive our first coil.

Electricity travels with the speed of light, so maybe a few ms would suffice?

Sol says

Dear Sir, I am seeking your help in validating my thinking/calculations.

I have an air coil with these characteristics calculated in

Coil32 (One-layer coil calculation)

Inductance L = 1.114 µH

Number of turns N = 3.0

Reactance of the coil X = 405.969 Ohm

Self-capacitance Cs = 3.297 pF

Self-resonance frequency Fsr = 58.167 MHz

Q-factor of the coil Q = 739.0

I want to make a LC tank where this coil is the primary of an air coil trafo.

Hence I calculated that I need a 7 pf cap to resonate in the coils self resonance.

Voltage applied is 9V from a battery.

Further calculations (I use available calculators, not calculations derived from formulas) give me these values.

The coils power use, based on its resistance, would be 199.52262 mW / 22.16918 mA.

Would this give an amount of 409 oscillations before all power is used up?

Swagatam says

Dear Sol, Calculating physically can be a quite time consuming, since there are many conversions required in the process….the easiest way is to use any online resonance calculator software and confirm the results through it

Sol says

As I did explain, I do use online calculators. None of them give an indication how long the oscillation will be alive. Everybody says, if it were an idealistic case, the oscillation will go on forever, but resistance in the circuit will kill the oscillation after some time. I wanted to be able to determine how long this ” time” is. If my assumption of 409 cycles is right, it would mean some ms? That would probably to short to obtain any useful operation.

Swagatam says

OK, go it, but 22 mA is not a very high current for a 9V PP3 battery with 500 mAh capacity, it should be able to sustain it for quite sometime….from where did you get a few millisecond time?

Sol says

Low pass filter?

Sol says

I’ve been looking for a simple direct frequency changer without luck. In this case from 180v AC 1.5 MHz output to same voltage 2.17 MHz. as input for a next stage.

I was thinking using the right capacitor would do the trick.

Do you have any suggestions?

Swagatam says

Yes capacitors values can eb changed for getting the desired frequency, or you can also modify the following circuit for the same:

https://www.homemade-circuits.com/1-hz-to-1-mhz-frequency-reference-generator-circuit/

Pete says

Thanks for putting the circuit on line however I have tried to simulate this in LTSpice and I get a frequency 1.5MHz, which is the value I get using the formula f = 1/ (2*PI*SQRT(CL))

I’m looking for a simple 30MHz oscillator and was hoping this would work but I cannot get it to run at 30MHz

Swagatam says

If you are using the formula, in that case you can adjust the part values to get 30 MHz.

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