# Faulty Colpitts Oscillator?

#### pulkit26

Joined May 11, 2020
10
Hello Everyone,I am trying to design a colpitts oscillator on multisim which should generate a frequency of 2Mhz.I tried to take suitable values of C1 and C2 and L but i did not get the sinusoidal waveform.Then i tried to generate lower frequencies like 1Khz,then i did get a sinusoidal waveform but its frequency was around 4Khz,i am really getting confused because the frequency of the waveform was supposed to be close to 1Khz but it is nearly 4Khz.
Please tell me where i might be doing mistake.

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#### LvW

Joined Jun 13, 2013
1,226
Hard to answer because we dont know the formula you have used....perhaps you have mixed frequency f and angular frequency w ?

#### Wolframore

Joined Jan 21, 2019
2,246
Hello Everyone,I am trying to design a colpitts oscillator on multisim which should generate a frequency of 2Mhz.I tried to take suitable values of C1 and C2 and L but i did not get the sinusoidal waveform.Then i tried to generate lower frequencies like 1Khz,then i did get a sinusoidal waveform but its frequency was around 4Khz,i am really getting confused because the frequency of the waveform was supposed to be close to 1Khz but it is nearly 4Khz.
Please tell me where i might be doing mistake.
He's using the standard colpitts tank formula.

1/(2pi sqrt(L*Ct))

The problem is your XL is too high at your f0... mismatch. For tank circuits it's vital you have a Q that's high as possible. This is one of the reasons why you can't pick components arbitrarily and just guess at solutions.

is this homework?

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#### pulkit26

Joined May 11, 2020
10
He's using the standard colpitts tank formula.

1/(2pi sqrt(L*Ct))

The problem is your XL is too high at your f0... mismatch. For tank circuits it's vital you have a Q that's high as possible. This is one of the reasons why you can't pick components arbitrarily and just guess at solutions.

is this homework?
Thank you very much for your reply,yes i used the standard formula for colpitts oscillator.Yes,it is a sort of assignment and i haven't designed any oscillator circuit before this.

#### pulkit26

Joined May 11, 2020
10
Hard to answer because we dont know the formula you have used....perhaps you have mixed frequency f and angular frequency w ?
Thank you very much for your reply.I used the standard formula to calculate the frequency in colpitts oscillator.
f=1/(2pi sqrt(L*C)).

#### LvW

Joined Jun 13, 2013
1,226
Thank you very much for your reply.I used the standard formula to calculate the frequency in colpitts oscillator.
f=1/(2pi sqrt(L*C)).
In your circuit, there are TWO capacitors (C4 and C5). What is C ?

#### pulkit26

Joined May 11, 2020
10
In your circuit, there are TWO capacitors (C4 and C5). What is C ?
C=C4*C5/C4+C5

#### LvW

Joined Jun 13, 2013
1,226
pulkit26 - The formula you have used assumes that the input resistance at the base node is infinite (no loading of the feedback path). But his is not true in your case (in contrast to opamp based circuits).
You must use the proper formula, which is a third-order lowpass with a load resistance. This lowpass produces at one single frequency a phase shift of -180 deg (oscillation condition). To find the oscillation frequency, you must set the imaginary part of the lowpass denominator equal to zero. This gives a simple quadratic equation which can easily be solved.

#### pulkit26

Joined May 11, 2020
10
pulkit26 - The formula you have used assumes that the input resistance at the base node is infinite (no loading of the feedback path). But his is not true in your case (in contrast to opamp based circuits).
You must use the proper formula, which is a third-order lowpass with a load resistance. This lowpass produces at one single frequency a phase shift of -180 deg (oscillation condition). To find the oscillation frequency, you must set the imaginary part of the lowpass denominator equal to zero. This gives a simple quadratic equation which can easily be solved.
I really appreciate your explanation.But i am using RFC which blocks RF,ie it provides a very large impedance to radio frequency,that's why the formula reduced to this.

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#### MisterBill2

Joined Jan 23, 2018
8,292
On initial inspection of the circuit it seems that the emitter resistor is excessively large, being almost equal to the collector side resistor. In addition, the two capacitors coupling to the tuned circuit provide a very low impedance coupling to the low impedance points o n the transistor, lowering the effective "Q" of the tuned circuit quite a bit. So those are some of the intuitive reasons pointing towards the undesired operation.

#### LvW

Joined Jun 13, 2013
1,226
I really appreciate your explanation.But i am using RFC which blocks RF,ie it provides a very large impedance to radio frequency,that's why the formula reduced to this.
pulkit26 - I have mentioned the input resistance at the BASE TERMINAL (which you have neglected).

#### pulkit26

Joined May 11, 2020
10
pulkit26 - I have mentioned the input resistance at the BASE TERMINAL (which you have neglected).
No i did not neglect it,i am uploading the file which shows my analysis...i have used the hybrid pi model neglecting the internal capacitance...but i have taken into account the base emitter resistance.I have used the procedure which is mentioned in Microelectronic Circuits by Sedra and Smith(please see the jpeg image).

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#### pulkit26

Joined May 11, 2020
10
On initial inspection of the circuit it seems that the emitter resistor is excessively large, being almost equal to the collector side resistor. In addition, the two capacitors coupling to the tuned circuit provide a very low impedance coupling to the low impedance points o n the transistor, lowering the effective "Q" of the tuned circuit quite a bit. So those are some of the intuitive reasons pointing towards the undesired operation.
Thank you very much for your reply.I will try changing those capacitances and the emitter resistance.

#### LvW

Joined Jun 13, 2013
1,226
No i did not neglect it,i am uploading the file which shows my analysis...i have used the hybrid pi model neglecting the internal capacitance...but i have taken into account the base emitter resistance.I have used the procedure which is mentioned in Microelectronic Circuits by Sedra and Smith(please see the jpeg image).
You have taken into account the base-emitter resistance? Where ist it in your equations?
In my version of SEDRA-SMITH there is a remark: "To simplify the analysis Rπ has NOT taken into account".
More than that - what about the resistor R between collector and signal ground?
Is it contained in your circuit?
As I told you - neglecting the input resistance at the base shifts the oscillation frequency.
I recommend not to (blindly) use any formulas which can be found in textbooks.
Do your own calculations (I have mentioned the 3rd-order lowpass function in the feedback path)

#### pulkit26

Joined May 11, 2020
10
You have taken into account the base-emitter resistance? Where ist it in your equations?
In my version of SEDRA-SMITH there is a remark: "To simplify the analysis Rπ has NOT taken into account".
More than that - what about the resistor R between collector and signal ground?
Is it contained in your circuit?
As I told you - neglecting the input resistance at the base shifts the oscillation frequency.
I recommend not to (blindly) use any formulas which can be found in textbooks.
Do your own calculations (I have mentioned the 3rd-order lowpass function in the feedback path)
I have denoted the base emitter resistance by rπ and in my circuit there is no resistor between the collector and the signal ground...i have shown it in the circuit and the analysis which i done is restricted to that circuit only which is there in the pdf which i alredy uploaded,hope you have seen that pdf...and coming to sedra and smith...i have just followed the procedure and not copied any formula from anywhere...if i would have copied that formula then i would not have filled five pages....pardon me if i seem rude...maybe i am not explaining properly enough....but i have denoted the base emitter resistance by rπ and then in my equations i had the sum of inverse of RB1,RB2 and rπ which i replaced by the inverse of Rin.I hope you understand.

#### LvW

Joined Jun 13, 2013
1,226
....but i have denoted the base emitter resistance by rπ and then in my equations i had the sum of inverse of RB1,RB2 and rπ which i replaced by the inverse of Rin.I hope you understand.
For my understanding, you have R_pi NOT taken into account ......because you have cancelled its influence afterwards.
And the same applies to the relatively large but finite ouput resistance of the transistor.
I only have tried to gave you some support in finding the reason for the observed discreaoencies...

#### pulkit26

Joined May 11, 2020
10
For my understanding, you have R_pi NOT taken into account ......because you have cancelled its influence afterwards.
And the same applies to the relatively large but finite ouput resistance of the transistor.
I only have tried to gave you some support in finding the reason for the observed discreaoencies...
You are right...the influence of R_pi got cancelled when i used the RFC(radio frequency choke)....as it provides infinite impedance to the signal....and thank you very much for your support...i am sorry if anything hurt you.

#### MisterBill2

Joined Jan 23, 2018
8,292
You are right...the influence of R_pi got cancelled when i used the RFC(radio frequency choke)....as it provides infinite impedance to the signal....and thank you very much for your support...i am sorry if anything hurt you.
Unfortunately RF chokes do not offer infinite impedance at any frequency. So it seems that the simulator has an error. An RF choke has a defined inductance and a series resistance, and because of the physical construction arrangement there is also a capacitance, with the result that most real chokes have a resonant frequency as well.

#### pulkit26

Joined May 11, 2020
10
Unfortunately RF chokes do not offer infinite impedance at any frequency. So it seems that the simulator has an error. An RF choke has a defined inductance and a series resistance, and because of the physical construction arrangement there is also a capacitance, with the result that most real chokes have a resonant frequency as well.
oh..okay..I read it in the book that they offer very large impedance(tending to infinity) to Radio Frequency..that's why i considered its impedance to be infinity and hence neglected the terms in my equations containing it.Actually i tried it for the first time.
Thank You very much for your support.

#### Bordodynov

Joined May 20, 2015
2,812
Here's my oscillator pattern. It's equivalent to an Сolpitts oscillator. I've introduced inductance losses - serial and parallel resistance.

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