Continue to Site

Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

How to compute the amplitude of Colpitt's Oscillator

Status
Not open for further replies.

Niki112

Newbie level 3
Joined
Oct 21, 2017
Messages
4
Helped
0
Reputation
0
Reaction score
0
Trophy points
1
Activity points
38
Hello,
I came up with problem of calculating Colpitt's oscillator amplitude. I was looking on the internet for some resources but I haven't found anything. However, after deep search, I only found that I should use Van der Pol equation for describing such non-linear system. I'm asking for help because I have stucked on this equation and I'dont know how to connect this equation with that circuit diagram.
Thank you
schemat_colpitts.JPG
equvan.JPG
 

you need d2x/dt2 --- not d2x/dt.

You need to use graphical solutions. Use matlab or octave.
 

Yeah, but what about parameters (micro and A). I only know that micro is damping factor and A is amplitude of AC source. So at the beginning I should do transient analysis to find A and damping factor from RLC circuit(transient analysis)? Something like that https://en.wikipedia.org/wiki/RLC_circuit?
 

Have you ever read Ulrich Rohde's textbook ?? It's been well explained the nonlinear phenomena of the oscillator with integrate-differential equations.
 

Hi Niki,

The colpitts oscillator you are trying to figure it out is nothing but a CE amplifier coupled with a LC tank circuit.
Replace the inductance value by its relative impedance.
You can trim the emitter resistance value to improve its amplitude.
You can simply try transient analysis as you mentioned and figure it out too

Congrats!!!!
 
No I haven't. I will check that book.

HI bala0x007,
So If that way is ok, I will try it :)
 
Last edited:

Niki112 - itis really a challenging task to get - by calculation - a rough information for the amplitude of an oscillating system if a sinusoidal form is desired.
This applies to all oscillators.
The reason is: Each oscillator requires a certain amount of non-linearity for limiting the loop gain LG for rising amplitudes to LG=1.
Such a non-linearity is necessary because for a safe start-up of oscillations we need LG>1 for small amplitudes .
Hence, an exact calculation requires a system of non-linear diff. equations.
Therefore, you only cann make an assessment for the amplitude - based on loop gain information: (1) amount of excess gain LG>1 and (2) degree and form of non-linearity.
 
You need stepwise approach to see the solution. I suggest the following:

1. First determine omega; that is the steady state osc freq.

2. Put mu equal to zero and see the solution. (what is that?)

3. Use steady state results to estimate mu (this is nothing but dissipation). We assume there is no loss in the transistor

4. In the steady state A will be a const and in the transient analysis you will see change in the amplitude.

5. Study the case of the vibration of a spring with some friction and try to get the ideas in similar cases.
 
Hello after a long time ;),
Yesterday I was playing with harmonic oscillations (RLC circuit). I solved second order differential equation. It was the simplest case of underdamped oscillations. It seems that I know how it works. I saw which parameters are important for the maximum amplitude. Today I formed equation which allows me to model for example ideal op amp sinusoidal oscillator.(for example with wien bridge - i have chosen ideal op amp beacuse i think it will simplify equations, what is more I found that this equation was used for modelling oscillator with vacuum tubes). I based on the forced van der pol oscillator. I put it to wolframalpha
Here is the link with diagrams. It seems that amplitude strictly depends on the micro parameter(nonlinearity and damping facotr of opamp)
https://www.wolframalpha.com/input/?i=y%27%27(t)+-+0.04*(1-y%5E2)*y%27(t)%2By(t)+%3D+20sin+t
 

Status
Not open for further replies.

Similar threads

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Back
Top