Non-Linear Dependant Sources

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Non-Linear Dependant Sources

General form:

BXXXXXXX N+ N- <I=EXPR> <V=EXPR>

Examples:

B1 0 1 I=cos(v(1))+sin(v(2)) B1 0 1 V=ln(cos(log(v(1,2)^2)))-v(3)^4+v(2)^v(1) B1 3 4 I=17 B1 3 4 V=exp(pi^i(vdd))

N+ is the positive node, and N- is the negative node. The values of the V and I parameters determine the voltages and currents across and through the device, respectively. If I is given then the device is a current source, and if V is given the device is a voltage source. One and only one of these parameters must be given.

The small-signal AC behavior of the nonlinear source is a linear dependent source (or sources) with a proportionality constant equal to the derivative (or derivatives) of the source at the DC operating point.

The expressions given for V and I may be any function of voltages and currents through voltage sources in the system. The following functions of real variables are defined:

abs

asinh

cosh

sin

acos

atan

exp

sinh

acosh

atanh

ln

sqrt

asin

cos

log

tan

The function "u" is the unit step function, with a value of one for arguments greater than one and a value of zero for arguments less than zero. The function "uramp" is the integral of the unit step: for an input x, the value is zero if x is less than zero, or if x is greater than zero the value is x. These two functions are useful in sythesizing piece-wise non-linear functions, though convergence may be adversely affected.

The following standard operators are defined:

+ - * / ^ unary -

If the argument of log, ln, or sqrt becomes less than zero, the absolute value of the argument is used. If a divisor becomes zero or the argument of log or ln becomes zero, an error will result. Other problems may occur when the argument for a function in a partial derivative enters a region where that function is undefined.

To get time into the expression you can integrate the current from a constant current source with a capacitor and use the resulting voltage (don't forget to set the initial voltage across the capacitor). Non-linear resistors, capacitors, and inductors may be synthesized with the nonlinear dependent source. Non-linear resistors are obvious. Non-linear capacitors and inductors are implemented with their linear counterparts by a change of variables implemented with the nonlinear dependent source. The following subcircuit will implement a nonlinear capacitor:

.Subckt nlcap pos neg

* Bx: calculate f(input voltage)

Bx 1 0 v = f(v(pos,neg))

* Cx: linear capacitance

Cx 2 0 1

* Vx: Ammeter to measure current into the capacitor

Vx 2 1 DC 0Volts

* Drive the current through Cx back into the circuit

Fx pos neg Vx 1

.ends

Non-linear inductors are similar.