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Question about Nodal Analysis of non-linear component

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genxium

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When I'm reading a tutorial about Harmonic Balance algorithm (this is a link to the tutorial website), I'm quite confused by the concept it mentions about the nodal analysis of non-linear components, especially for:


The non-linear circuit is modeled by its current function i(t) = i(v[1], ..., v[P]) and by the charge of its capacitances q(t) = q(v[1], ..., v[Q]) . These functions must be Fourier-transformed to give the frequency-domain vectors Q and I , respectively.

Say for a simple BJT with 3 nodes b,c,e, as conventional notations, I can understand how i_c=f(v_b,v_c,v_e) coming from Early Effect, and i_b=(i_c)/(β•[1+(V_CB/V_A)]) or anything similar, to indicate "non-linearity", but what's the parameters involved with charge of capacitances?

I really have no idea how Charge of Capacitances is playing a role in nodal analysis, any suggestion is appreciated ^_^
 
Hi,

Sometimes the caps are modeled as charge devices rather than just capacitors with current and voltage. That sometimes simplifies the analysis.
To find out more about this, look up the relationships between caps and charge, how a cap is defined basically by charge rather than current or voltage.
 
Hi,

Sometimes the caps are modeled as charge devices rather than just capacitors with current and voltage. That sometimes simplifies the analysis.
To find out more about this, look up the relationships between caps and charge, how a cap is defined basically by charge rather than current or voltage.

Thank you for your reply, but I'm still confused for 1 issue, I think capacitors, are often regarded as linear components , but in that tutorial, http://qucs.sourceforge.net/tech/node31.html , it's said that non-linear circuits are measured by (1) current function and (2) charges of capacitance, does the word "capacitance" here refer to only the parasitic capacitance of the non-linear components , but not all capacitors?
 
Hi again,


That linked site looks very interesting, i'll have to spend a bit more time reading there i think.

I havent used that particular kind of analysis, but generally defining the capacitor a bit different than usual sometimes leads to an immediate simplification in the equations, so for that method they may want to base that part of the analysis on charge rather than current or voltage directly. This is usually achieved by using:
i=dq/dt

What this does is an expression defined in terms of current of the form:
v=i*R

turns into;
v=R*dq/dt

and for an inductor instead of:
v=L*di/dt

we have:
v=L*d^2q/dt^2 (now a second derivative)

so an integrodifferential equation like this:
V=R*i+L*di/dt+(1/C)*Integral(i) dt

turns into:
V=R*dq/dt+L*d^2q/dt^2+q/C

So we got to a pure differential equation simply by swapping out all i=dq/dt, and the capacitance now enters as a constant.

Also, starting with:
dv/dt=i/C

we get:
dv/dt=(dq/dt)/C

or:
dv/dt=dq/(C*dt)

or:
dv=dq/C

or:
dv/dq=1/C

so we end up with the capacitance defined in terms of charge and voltage.

This i believe would help with a general non linearity of the capacitor, but to get the full explanation i think maybe you should contact:
jens.flucke@gmail.com

If you can get one complete full analysis example from him (or someone else at that site) we could follow it through from start to finish and see how it goes.
 
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I just can't think of a word to convey how I'm grateful for your reply~! It's really helpful for me and explains lots of confusing issues for me!

I will contact jens asap when I fully digest your explanation and get a good sample to ask, thank you again for the helpful reply ^_^ !!
 
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