[SOLVED] Polynomial Capacitor and Non Linear Capacitor

[Krishnendu]

Can a polynomial capacitor be considered as a non-linear capacitor?

 

[BigBoss]

What are the coefficients ?? If the coefficients are applied voltage/current to the capacitor, yes it may be considered as nonlinear.For instance..

C=Co(*a1*Vcap+a2*Vcap^2+a3*Vcap^3+.... ) or similar one.

Co=Initial value
Vcap=Applied cap. Voltage
an=coefficients..

 

[Krishnendu]

Thank you very much BigBoss. Yes the capacitor equation which I am using is dependent on the applied voltage.

 

[BigBoss]

Thank you very much BigBoss. Yes the capacitor equation which I am using is dependent on the applied voltage.

But this dependency may be linear like...

C=k*Vcap

So C value is not nonlinear, it's linear.Nonlinearity should have nth order dependencies ( n>2)

 

[D.A.(Tony)Stewart]

Similarly, all Diodes , and in particular, Varicap diodes are binned voltage controlled capacitors when reverse biased.

As such the exponents are 0, -1, -2 .. On a log scale a good varicap is linear and gives linear V vs f VCO characteristics but over a limited range, so the non-linearity is the 2nd order effects.

Polynomial Caps can have both negative and positive powers, when expressed as |integers| in a power series must be > 1

So think of it ;
Fixed, linear and nonlinear
as ; fixed, linear and Poly.

where linear is a 1st order

I think....

 

[FvM]

Re: "Polynomial" Capacitor and Non Linear Capacitor

The initial question creates the impression that "Polynomial Capacitor" is a known technical term. Is it so?

Obviously it refers to a capacitor that can be described somehow with polynomial equations. But "Polynomial Capacitor" is a neologism which doesn't make much sense in my view, as long as it doesn't describe a particularly component type.

I would by the way also rate a capacitor with linear voltage dependant capacitance as nonlinear component, because it creates a nonlinear dependency between voltage and current and generates waveform distortions.

 

[D.A.(Tony)Stewart]

Re: "Polynomial" Capacitor and Non Linear Capacitor

I think Polynomial Capacitor is used recently to emulate optimal switch Cap. PFC distributed on power grid and many other things and not the RF or distortion behaviors we are familiar with.

e.g. MOSFET junction capacitors are very nonlinear, but I haven't seen a Polynomial for it yet, but it probably exists.

Then there are the Ic=C * ΔV/Δt + V*ΔC/Δt non-linear effects,

I dont know how that fits with Poly Caps

 

[Krishnendu]

Actually, I want to implement a non-linear capacitor where the capacitance depends on the applied voltage and follows a specific equation, in Tanner EDA. Now Tanner EDA provides capacitor to be either Linear or Polynomial, and here is my query that what is the difference between a non-linear capacitor and polynomial capacitor and are they synonymous to each other?

And I have not much idea what precisely does a polynomial capacitor mean.

 

[D.A.(Tony)Stewart]

Tanner supports any number of polynominal exponents if that is what you have.

However your choices are Linear or Polynomial"
Polynomial does NOT describe all "Non-linear" behaviors.

For example Radiant Tech. at www.ferrodevices.com describe their nonlinear dielectrics as ones with ferroeletric memory or hysteresis. So Q=CV does not apply at all times.

 

[crutschow]

I would think that a "linear" capacitor would be one that stores a charge that is directly proportional to voltage (a fixed capacitance value).
So a capacitor that has a linear change in capacitance with voltage (or any capacitor whose capacitance is a polynomial function of voltage) would be non-linear from a stored charged basis.

 

[BigBoss]

Actually, I want to implement a non-linear capacitor where the capacitance depends on the applied voltage and follows a specific equation, in Tanner EDA. Now Tanner EDA provides capacitor to be either Linear or Polynomial, and here is my query that what is the difference between a non-linear capacitor and polynomial capacitor and are they synonymous to each other?

And I have not much idea what precisely does a polynomial capacitor mean.

Simulators use always this technical definition.. " Polynominal ...caps,res,inds etc"
It means that any electrical component's value depends on something ( it may be a voltage,currnet or anything else ).It doesn't have to be voltage that is applied to the component.It can also be any electrical or non-electrical variable..

For instance..a Resistor value can be

R=Ro(a1*Tamb+a2*Tamb^gamma1+a3*T^gamma2)
It's also polynominal definition.

 

[Krishnendu]

So can it be concluded that depending on the coefficients and equation, the Polynomial capacitor available in Tanner EDA can be made to behave as a Non-Linear capacitor?

 

[FvM]

You can conclude that any capacitor described by a polynomial is nonlinear. And there are other ways to describe a nonlinear capacitor than a polynomial.

 

[Krishnendu]

Thank you everybody for helping me out. Much appreciated.

 

[D.A.(Tony)Stewart]

You may find however in different versions of TANNER EDA that the Linear Capacitor is in itself a linear algorithm and an Option for TANNER EDA, separate from the POLY CAP. ;|

Apparently this is useful for defining the voltage controlled junctions I suspected all along need to be defined for many designs.