# Colpitts Oscillator: Working, Circuit, frequency derivation

Colpitts Oscillator – hey friends welcome to the Kohiki all about electronics in this article we will learn about the Colpitts oscillator now this Colpitts oscillator is one kind of LC oscillator and it is used for the generation of a high-frequency signal typically in the range of Heredia frequencies.

so in this oscillator, the LC circuit is used in the feedback path of the oscillator, and as we know this LC circuit oscillates at the resonant frequency.

## Introduction to LC Oscillator and working of LC tank circuit

### What is meant by the Colpitts oscillator?

so in a way this LC tank circuit provides a frequency selectivity for this oscillator now in the previous article on resonance we have already talked about this LC circuit but here let us briefly understand the working of this LC circuit and let us see how this LC circuit provides the frequency selectivity Colpitts Oscillator.

so here we have an LC tank circuit and here let us assume that the capacitor is initially charged to some finite voltage or we can say that initially some finite voltage is applied to this LC tank circuit.

so whenever some finite voltage is applied then the capacitor starts charging towards this supply voltage and as soon as this capacitor fully gets charged and let’s say we have disconnected this voltage supply.

so as soon as we disconnect this word is supply then this capacitor starts discharging through this inductor or we can say that the electrostatic energy of the capacitor will get stored across the inductor and the inductor will store this energy in the form of magnetic field Colpitts Oscillator.

so what is the period of time the voltage across the capacitor will reduce and at one point of time the voltage across the capacitor will become zero.

so at that point, there should not be any flow of the current through the inductor but as we know the inductor opposes the instantaneous change in the current so according to the Lenz law it produces a back EMF.

so that the same amount of current can continuously flow through the inductor so because of this back EMF the same amount of current will flow through the inductor and because of that now the capsule starts charging in the reverse direction.

so gradually the energy which is stored across the inductor will get converted into the electrostatic energy of the capacitor and once this capacitor gets fully charged then this capacitor once again discharges through the inductor in the reverse direction.

## What is the LC circuit called tank circuit of an oscillator?

so in this way in this LC tank circuit the energy gets transferred between the inductor and the capacitor and because of that we are getting oscillations in the output and the frequency of the oscillation can be given by the expression 1 divided by 2 pi times under root LC now.

so far in this discussion, we have assumed that in this tank circuit this inductor and the capacitor are ideal but in reality, this inductor has some finite ohmic contacts as well as this capacitor has some finite leakage current and because of that over the period of time and these oscillations will die out

so to get the sustained oscillations we need to provide the external energy to this LC tank circuit and in case of the LC oscillators this energy is provided through the amplifier circuit now in general if we talk about the LC oscillator then this LC circuit used to have a three elements and depending upon the type of the elements this LC oscillator can be classified in the different categories

so in the feedback circuit if Z 1 and Z 2 are capacitors and z3 is inductor then this configuration is known as the culprit’s oscillator on the other end of this devil and z2 are inductor and z3 is capacitor then this type of configuration is known as the Hartley oscillator so in this article we will focus on the culprit’s oscillator.

so this is a basic block diagram of the culprit’s oscillator so in this culprits oscillator either a transistor or the op-amp can be used as an amplifier on the feedback path seems to have this LC tank circuit.

so it consists of two capacitors and one inductor now in general if we talk about any LC oscillator circuit then the feedback circuit is used to provide a 180 degree of phase shift and the remaining 180 degrees of phase shift is provided by the amplifier circuit.

so that the old phase shift of the circuit will become zero degrees and the gain of the amplifier and the feedback circuit is set in such a way that the in loop gain of the circuit will become unity and by satisfying these two criteria we can get the sustained oscillations so like I said in these oscillators we can use in the transistor or as an amplifier

### What is a tank circuit

An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. For a circuit model incorporating resistance, see the RLC circuit.

### HOW DOES tank circuit work

Tank Circuit Working In a tank circuit, the resonance can be formed through the movement of electrical charge among the inductor and capacitor. … When electrical charge flows from the capacitor to the coil then the capacitor drops electromagnetic energy so the inductor turns into electromagnetically charged.

### Which feedback is used in the Colpitts oscillator

The Colpitts oscillator uses positive feedback for oscillation. The feedback is provided through a capacitor voltage divider tank circuit to the amplifying element.

## Colpitts Oscillator using the transistor (BJT) and op-amp

so first of all let us see how this Colpitts oscillator can be designed using the transistor so here this transistor is configured as an amplifier while this LC tank circuit is connected in the feedback path.

so whenever the circuit is just turned on at that time this LC tank circuit starts resonating at the resonating frequency but the amplitude of this frequency will be very low.

so here through this capacitor C 2, the fraction of this generated signal is given as feedback to this amplifier circuit and this amplifier circuit amplifies the feedback signal and the amplified signal is once again fed to this feedback circuit.

so here by adjusting the loop gain of this amplifier in the feedback circuit we can get the sustained oscillations at the resonating frequency and here the frequency of the oscillation F can be given by the expression 1 divided by 2 pi times under root LC where C is equal to C 1 C 2 divided by C 1 plus C 2 now these same cockpit oscillator circuit can also be designed using the open.

so here this transistor is replaced by this Oh Pam and here the open is configured in the inverting configuration but if you see the feedback circuit remains the same so here the output is measured across this capacitor c2 while the feedback circuit is provided where this capacitor c1.

so here the ratio of this C 2 by C 1 is also known as the feedback fraction that is the amount of signal which is being fed back to the amplifier circuit and we will talk more about it whenever we derived an expression for the frequency.

### Which transistor used the Colpitts oscillator

The common emitter transistor produces an 1800 phase shift between the input and output voltage. Thus, from the Barkhausen criterion, we can get undamped continuous oscillations.

### Which configuration of a

transistor amplifier is used for Colpitts oscillator: Which configuration of a transistor amplifier is used for Colpitts oscillator? Explanation: Common emitter configuration is used for amplifying the distorted oscillatory signals to a perfect oscillation. The transistor provides a 180° phase shift and tank circuit another 180°, a total of 0 phase shift.

## Derivation of frequency for Colpitts Oscillator

so now let us derive the expression of the frequency for the Colpitts oscillator so for the derivation we will assume that the gain that is corroborated by the amplifier is equal to AV and the amplifier has a finite output impedance all are not apart from that we will also assume that the input impedance of the amplifier is very high meaning that no current is flowing into the input terminals and for the simplification, we will consider this capacitor c1 c2 and inductor LS z1 z2 and z3.

so under this assumption has no current is flowing into the input terminals this impedance Z 1 and Z 3 will be in a series and the equivalent circuit in the feedback can be represented like this.

so at one end we have an output voltage V out and the other end is connected to the ground and through this impedance Z 1 the feedback signal is given to this amplifier circuit.

so here this feedback voltage VF will be equal to Z 1 divided by Z 1 plus Z 3 times V naught or we can say that the feedback fraction beta that is VF by V naught is equal to Z 1 divided by Z 1 plus Z 3 now if we see the circuit from the output side then the entire feedback network will appear as a load to this output terminal and let’s say the equivalent impedance of this feedback network is equal to Z P.

so we can say that the era P will be equal to Z 2 in parallel with there 1 plus Z 3 so this impedance will appear as a load across this output terminal and the equivalent circuit will look like this

## Colpitts oscillator equivalent circuit

so here the input signal is amplified by the voltage gain of a V and the amplifier also provides a one-day degree of phase shift C if we consider the output impedance of the amplifier then the output which is appearing across this load Z P will be equal to Z P divided by Z P plus R naught times – any times.

V in or we can say that V naught by V n will be equal to minus AV times share P divided by Z P plus R naught nowhere let’s say the ratio of this output voltage by input voltage is equal to a which is the overall gain of the amplifier now if this output impedance.

R naught is 0 in that case this a and AV both are equal but because of some finite output impedance this overall voltage gain will be slightly less than the AV so this voltage gain a can be written as minus ami times Z P bigger it away Z P plus R naught so here.

let’s put the value of Z P in this expression and we know that Z P is equal to Z 2 parallel red one plus Z 3 so if you put the value of this Z 2 P and if you simplify the expression then the overall voltage gain a will be equal to minus AV times.

Z 2 into Z 1 plus Z 3 divided by said 2 into Z 1 plus Z 3 plus ro times Z 1 plus Z 2 plus Z 3 now earlier like we have discussed the feedback fraction for this oscillator will be equal to Z 1 divided by Z 1 plus Z 3 see if you multiply this feedback fraction beta by this.

overvoltage gain then we get the loop gain so the loop gains a beta will become minus AV times Z 2 into Z 1 plus Z 3 times 0 1 divided by third 1 plus Z 3 so here this term is nothing but the feedback friction and in the denominator, we will have say 2 times Z 1 plus Z 3 plus R naught times AR 1 plus Z 2 plus Z 3 see.

if we simplify that expression then the loop gains a beta can be represented like this so for the called Pizza oscillator now let us put the value of this Z 1 Z 2 n Z 3 so here for the pulpits oscillator, this said 1 is equal to 1 by J Omega C 1 while Z 2 is equal to 1 by omega c 2 and z 3 is the reactance of this inductor which is equal to J Omega L.

so if you put the value of this Z 1 Z 2 and Z 3 then the loop gain a beta can be represented like this and if we simplify this expression and the beta can be represented like this so here to get a 0 degree of phase shift the imaginary term in the denominator should be equal to 0.

what we can say is that C 1 plus C 2 should be equal to Omega square n times C 1 times C 2 what we can say that Omega square should be equal to C 1 plus C 2 divided by L times C 1 times C 2 that means Omega will be equal to 1 by under root L times C equivalent where C equivalent is equal to C 1 C 2 divided by C 1 plus C 2

so in this way, we got the expression of the frequency for the Colpitts oscillator now let us put this value of Omega in this expression so under this condition a beta will be equal to this ami divided by minus one plus Omega squares head times c1.

and if you put the value of this Omega that is Omega is equal to 1 by under root L times sequent then this loop gain a beta will be equal to AV times c2 divided by c1 now for the sustained oscillations the loop gain betas should be equal to one and under that condition, this voltage gain AV will become c1 divided by c2.

now like I said earlier this overall voltage gain a is slightly less than this AV but if we assume that the output impedance R naught is much less than the foreign impedance z DP, in that case, this gain a is approximately equal to AV and under this condition, the feedback fraction beta will be equal to C 2 divided by c1.

so this is the expression of the feedback fraction so using this expression of Omega we can find the frequency of oscillation for the culprit’s oscillator and using this feedback fraction beta we can set the gain of the amplifier such that we can get the sustained oscillations so to understand that let us take one example

## Example on Colpitts Oscillator

so here we have given this cockpit oscillator circuit and in this circuit we have been asked to find the frequency as well as the gain which is required for the sustained oscillation.

so here as we have given the value of C 1 C 2 and L so it is easy to find the frequency and as we know the frequency F can be given by the expression 1 you get rid of Y 2 pi times under root L times C equivalent where C equivalent is equal to C 1 C 2 divided by C 1 plus C 2 C.

if we put the value of the C 1 and C 2 in the C equivalent will be equal to one point six six nano farad and if we put the value of this equivalent and this inductor L in this expression in the value of frequency F will roughly come around s twenty-seven point five kiloHertz.

so this is the oscillation frequency for the Colpitts oscillator now let us find the value of the gain for the sustained oscillations.

so if you observe here the feedback fraction beta is equal to C two numerator by Cone and in this case, it is equal to 1 by 5.

so the gain of the amplifier should be more than five nowhere the op-amp is configured in the inverting configuration

and as we know in the inverting configuration the gain of the op-amp can be given as minus RF divided by R 1 nowhere.

if you only consider the magnitude of the gain then the gain of this amplifier should be more than 5.

so here let us assume that R 1 is equal to 1 kilo-ohm and to get a gain of more than 5 the value of this RF should be more than five kilos.

so in this way by using this expression we can design a culprits oscillator of the desired frequency and by using this feedback fraction beta.

## Applications of Colpitts Oscillator

we can set the gain of the amplifier to get the sustained oscillations so like I said earlier this culprit oscillator is used for the

• generation of very high frequencies typically in the range of RF frequencies
• it is very useful in mobile and communication systems
• apart from that this complete oscillator is also used for the generation of the surface acoustic waves.

### What is the major advantage of the Colpitts oscillator

The Colpitts oscillator can generate sinusoidal signals of very high frequencies. It can withstand high and low temperatures. The frequency stability is high. Frequency can be varied by using both the variable capacitors.

The Colpitts Oscillator can be used in high frequency to produce pure sinusoidal waveform because of the low impedance paths of the capacitors at high frequencies. It has a wide operation range from 1 to 60 MHz. Disadvantages: It is difficult to design.

## FAQ’s

1. ### What is meant by the Colpitts oscillator?

Colpitts oscillator is the electrical dual of a Hartley oscillator, where the feedback signal is taken from an “inductive” voltage divider consisting of two coils in series

2. ### What is the use of the Colpitts oscillator?

It is used for the generation of sinusoidal output signals with very high frequencies. The Colpitts oscillator using the SAW device can be used as a different type of sensor such as a temperature sensor.

3. ### What is the difference between Hartley and Colpitts oscillator?

The frequency of the oscillations is determined by the value of the capacitors and inductors in the tank circuit. Thus the main difference between a Colpitts Oscillator and a Hartley Oscillator is that the former uses tapped capacitance, while the latter uses tapped inductance.

The Colpitts Oscillator can be used in high frequency to produce pure sinusoidal waveform because of the low impedance paths of the capacitors at high frequencies. It has a wide operation range from 1 to 60 MHz. Disadvantages: It is difficult to design.

5. ### What is the basic principle of an oscillator?

There are many types of electronic oscillators, but they all operate according to the same basic principle: an oscillator always employs a sensitive amplifier whose output is fed back to the input in phase. Thus, the signal regenerates and sustains itself. This is known as positive feedback.

So here are a you tube video based on Colpitts oscillator, Which was uploaded by Ekeeda

## Last Word / Summary

so these are the few applications of this computer oscillator. so I hope in this article you understood how we can design the cockpit oscillator

how it can be used for the generation of the high frequencies.

so if you have an equation or sedation do let me hear in the comment section below.

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