public override void stamp(Circuit sim)
{
// equations for transformer:
// v1 = L1 di1/dt + M di2/dt
// v2 = M di1/dt + L2 di2/dt
// we invert that to get:
// di1/dt = a1 v1 + a2 v2
// di2/dt = a3 v1 + a4 v2
// integrate di1/dt using trapezoidal approx and we get:
// i1(t2) = i1(t1) + dt/2 (i1(t1) + i1(t2))
// = i1(t1) + a1 dt/2 v1(t1) + a2 dt/2 v2(t1) +
// a1 dt/2 v1(t2) + a2 dt/2 v2(t2)
// the norton equivalent of this for i1 is:
// a. current source, I = i1(t1) + a1 dt/2 v1(t1) + a2 dt/2 v2(t1)
// b. resistor, G = a1 dt/2
// c. current source controlled by voltage v2, G = a2 dt/2
// and for i2:
// a. current source, I = i2(t1) + a3 dt/2 v1(t1) + a4 dt/2 v2(t1)
// b. resistor, G = a3 dt/2
// c. current source controlled by voltage v2, G = a4 dt/2
//
// For backward euler,
//
// i1(t2) = i1(t1) + a1 dt v1(t2) + a2 dt v2(t2)
//
// So the current source value is just i1(t1) and we use
// dt instead of dt/2 for the resistor and VCCS.
//
// first winding goes from node 0 to 2, second is from 1 to 3
double l1 = inductance;
double l2 = inductance * ratio * ratio;
double m = couplingCoef * Math.Sqrt(l1 * l2);
// build inverted matrix
double deti = 1 / (l1 * l2 - m * m);
double ts = isTrapezoidal ? sim.timeStep / 2 : sim.timeStep;
a1 = l2 * deti * ts; // we multiply dt/2 into a1..a4 here
a2 = -m * deti * ts;
a3 = -m * deti * ts;
a4 = l1 * deti * ts;
sim.stampConductance(lead_node[0], lead_node[2], a1);
sim.stampVCCS(lead_node[0], lead_node[2], lead_node[1], lead_node[3], a2);
sim.stampVCCS(lead_node[1], lead_node[3], lead_node[0], lead_node[2], a3);
sim.stampConductance(lead_node[1], lead_node[3], a4);
sim.stampRightSide(lead_node[0]);
sim.stampRightSide(lead_node[1]);
sim.stampRightSide(lead_node[2]);
sim.stampRightSide(lead_node[3]);
}
public override void stamp(Circuit sim)
{
nodes[0] = lead_node[0];
nodes[1] = lead_node[1];
if (isTrapezoidal)
{
compResistance = 2 * inductance / sim.timeStep;
}
else
{
compResistance = inductance / sim.timeStep; // backward euler
}
sim.stampResistor(nodes[0], nodes[1], compResistance);
sim.stampRightSide(nodes[0]);
sim.stampRightSide(nodes[1]);
}
public override void stamp(Circuit sim)
{
// equations for transformer:
// v1 = L1 di1/dt + M1 di2/dt + M1 di3/dt
// v2 = M1 di1/dt + L2 di2/dt + M2 di3/dt
// v3 = M1 di1/dt + M2 di2/dt + L2 di3/dt
// we invert that to get:
// di1/dt = a1 v1 + a2 v2 + a3 v3
// di2/dt = a4 v1 + a5 v2 + a6 v3
// di3/dt = a7 v1 + a8 v2 + a9 v3
// integrate di1/dt using trapezoidal approx and we get:
// i1(t2) = i1(t1) + dt/2 (i1(t1) + i1(t2))
// = i1(t1) + a1 dt/2 v1(t1)+a2 dt/2 v2(t1)+a3 dt/2 v3(t3) +
// a1 dt/2 v1(t2)+a2 dt/2 v2(t2)+a3 dt/2 v3(t3)
// the norton equivalent of this for i1 is:
// a. current source, I = i1(t1) + a1 dt/2 v1(t1) + a2 dt/2 v2(t1)
// + a3 dt/2 v3(t1)
// b. resistor, G = a1 dt/2
// c. current source controlled by voltage v2, G = a2 dt/2
// d. current source controlled by voltage v3, G = a3 dt/2
// and similarly for i2
//
// first winding goes from node 0 to 1, second is from 2 to 3 to 4
double l1 = inductance;
double cc = .99;
// double m1 = .999*Math.sqrt(l1*l2);
// mutual inductance between two halves of the second winding
// is equal to self-inductance of either half (slightly less
// because the coupling is not perfect)
// double m2 = .999*l2;
// load pre-inverted matrix
a[0] = (1 + cc) / (l1 * (1 + cc - 2 * cc * cc));
a[1] = a[2] = a[3] = a[6] = 2 * cc / ((2 * cc * cc - cc - 1) * inductance * ratio);
a[4] = a[8] = -4 * (1 + cc) / ((2 * cc * cc - cc - 1) * l1 * ratio * ratio);
a[5] = a[7] = 4 * cc / ((2 * cc * cc - cc - 1) * l1 * ratio * ratio);
int i;
for (i = 0; i != 9; i++)
{
a[i] *= sim.timeStep / 2;
}
sim.stampConductance(lead_node[0], lead_node[1], a[0]);
sim.stampVCCS(lead_node[0], lead_node[1], lead_node[2], lead_node[3], a[1]);
sim.stampVCCS(lead_node[0], lead_node[1], lead_node[3], lead_node[4], a[2]);
sim.stampVCCS(lead_node[2], lead_node[3], lead_node[0], lead_node[1], a[3]);
sim.stampConductance(lead_node[2], lead_node[3], a[4]);
sim.stampVCCS(lead_node[2], lead_node[3], lead_node[3], lead_node[4], a[5]);
sim.stampVCCS(lead_node[3], lead_node[4], lead_node[0], lead_node[1], a[6]);
sim.stampVCCS(lead_node[3], lead_node[4], lead_node[2], lead_node[3], a[7]);
sim.stampConductance(lead_node[3], lead_node[4], a[8]);
for (i = 0; i != 5; i++)
{
sim.stampRightSide(lead_node[i]);
}
}
public override void stamp(Circuit sim)
{
// Capacitor companion model using trapezoidal approximation
// (Norton equivalent) consists of a current source in
// parallel with a resistor. Trapezoidal is more accurate
// than backward euler but can cause oscillatory behavior
// if RC is small relative to the timestep.
if (isTrapezoidal)
{
compResistance = sim.timeStep / (2 * capacitance);
}
else
{
compResistance = sim.timeStep / capacitance;
}
sim.stampResistor(lead_node[0], lead_node[1], compResistance);
sim.stampRightSide(lead_node[0]);
sim.stampRightSide(lead_node[1]);
}
public void stamp(Circuit sim, double deltaTime, int n0, int n1)
{
// inductor companion model using trapezoidal or backward euler
// approximations (Norton equivalent) consists of a current
// source in parallel with a resistor. Trapezoidal is more
// accurate than backward euler but can cause oscillatory behavior.
// The oscillation is a real problem in circuits with switches.
nodes[0] = n0;
nodes[1] = n1;
if (isTrapezoidal)
{
compResistance = 2 * inductance / deltaTime;
}
else
{
compResistance = inductance / deltaTime; // backward euler
}
sim.stampResistor(nodes[0], nodes[1], compResistance);
sim.stampRightSide(nodes[0]);
sim.stampRightSide(nodes[1]);
}
public override void step(Circuit sim)
{
double vd = lead_volt[1] - lead_volt[0];
if (Math.Abs(lastvd - vd) > 0.1)
{
sim.converged = false;
}
else if (lead_volt[2] > maxOut + 0.1 || lead_volt[2] < minOut - 0.1)
{
sim.converged = false;
}
double x = 0;
int vn = sim.nodeCount + voltSource;
double dx = 0;
if (vd >= maxOut / gain && (lastvd >= 0 || getRand(4) == 1))
{
dx = 1E-4;
x = maxOut - dx * maxOut / gain;
}
else if (vd <= minOut / gain && (lastvd <= 0 || getRand(4) == 1))
{
dx = 1E-4;
x = minOut - dx * minOut / gain;
}
else
{
dx = gain;
}
// newton-raphson
sim.stampMatrix(vn, lead_node[0], dx);
sim.stampMatrix(vn, lead_node[1], -dx);
sim.stampMatrix(vn, lead_node[2], 1);
sim.stampRightSide(vn, x);
lastvd = vd;
}
public override void step(Circuit sim)
{
double vbc = lead_volt[0] - lead_volt[1]; // typically negative
double vbe = lead_volt[0] - lead_volt[2]; // typically positive
if (Math.Abs(vbc - lastvbc) > 0.01 || Math.Abs(vbe - lastvbe) > 0.01)
{
sim.converged = false;
}
gmin = 0;
if (sim.subIterations > 100)
{
// if we have trouble converging, put a conductance in parallel with
// all P-N junctions. Gradually increase the conductance value for each iteration.
gmin = Math.Exp(-9 * Math.Log(10) * (1 - sim.subIterations / 3000.0));
if (gmin > .1)
{
gmin = .1;
}
}
vbc = pnp * limitStep(sim, pnp * vbc, pnp * lastvbc);
vbe = pnp * limitStep(sim, pnp * vbe, pnp * lastvbe);
lastvbc = vbc;
lastvbe = vbe;
double pcoef = vdcoef * pnp;
double expbc = Math.Exp(vbc * pcoef);
double expbe = Math.Exp(vbe * pcoef);
if (expbe < 1)
{
expbe = 1;
}
ie = pnp * leakage * (-(expbe - 1) + rgain * (expbc - 1));
ic = pnp * leakage * (fgain * (expbe - 1) - (expbc - 1));
ib = -(ie + ic);
double gee = -leakage * vdcoef * expbe;
double gec = rgain * leakage * vdcoef * expbc;
double gce = -gee * fgain;
double gcc = -gec * (1 / rgain);
// stamps from page 302 of Pillage. Node 0 is the base,
// node 1 the collector, node 2 the emitter. Also stamp
// minimum conductance (gmin) between b,e and b,c
sim.stampMatrix(lead_node[0], lead_node[0], -gee - gec - gce - gcc + gmin * 2);
sim.stampMatrix(lead_node[0], lead_node[1], gec + gcc - gmin);
sim.stampMatrix(lead_node[0], lead_node[2], gee + gce - gmin);
sim.stampMatrix(lead_node[1], lead_node[0], gce + gcc - gmin);
sim.stampMatrix(lead_node[1], lead_node[1], -gcc + gmin);
sim.stampMatrix(lead_node[1], lead_node[2], -gce);
sim.stampMatrix(lead_node[2], lead_node[0], gee + gec - gmin);
sim.stampMatrix(lead_node[2], lead_node[1], -gec);
sim.stampMatrix(lead_node[2], lead_node[2], -gee + gmin);
// we are solving for v(k+1), not delta v, so we use formula
// 10.5.13, multiplying J by v(k)
sim.stampRightSide(lead_node[0], -ib - (gec + gcc) * vbc - (gee + gce) * vbe);
sim.stampRightSide(lead_node[1], -ic + gce * vbe + gcc * vbc);
sim.stampRightSide(lead_node[2], -ie + gee * vbe + gec * vbc);
}
public override void step(Circuit sim)
{
double[] vs = new double[3];
vs[0] = lead_volt[0];
vs[1] = lead_volt[1];
vs[2] = lead_volt[2];
if (vs[1] > lastv1 + .5)
{
vs[1] = lastv1 + .5;
}
if (vs[1] < lastv1 - .5)
{
vs[1] = lastv1 - .5;
}
if (vs[2] > lastv2 + .5)
{
vs[2] = lastv2 + .5;
}
if (vs[2] < lastv2 - .5)
{
vs[2] = lastv2 - .5;
}
int source = 1;
int drain = 2;
if ((pnp ? -1 : 1) * vs[1] > (pnp ? -1 : 1) * vs[2])
{
source = 2;
drain = 1;
}
int gate = 0;
double vgs = vs[gate] - vs[source];
double vds = vs[drain] - vs[source];
if (Math.Abs(lastv1 - vs[1]) > .01 || Math.Abs(lastv2 - vs[2]) > .01)
{
sim.converged = false;
}
lastv1 = vs[1];
lastv2 = vs[2];
double realvgs = vgs;
double realvds = vds;
vgs *= (pnp ? -1 : 1);
vds *= (pnp ? -1 : 1);
ids = 0;
gm = 0;
double Gds = 0;
double beta = getBeta();
if (vgs > .5 && this is JfetElm)
{
sim.panic("JFET is reverse biased!", this);
return;
}
if (vgs < _threshold)
{
// should be all zero, but that causes a singular matrix,
// so instead we treat it as a large resistor
Gds = 1e-8;
ids = vds * Gds;
mode = 0;
}
else if (vds < vgs - _threshold)
{
// linear
ids = beta * ((vgs - _threshold) * vds - vds * vds * .5);
gm = beta * vds;
Gds = beta * (vgs - vds - _threshold);
mode = 1;
}
else
{
// saturation; Gds = 0
gm = beta * (vgs - _threshold);
// use very small Gds to avoid nonconvergence
Gds = 1e-8;
ids = 0.5 * beta * (vgs - _threshold) * (vgs - _threshold) + (vds - (vgs - _threshold)) * Gds;
mode = 2;
}
double rs = -(pnp ? -1 : 1) * ids + Gds * realvds + gm * realvgs;
sim.stampMatrix(lead_node[drain], lead_node[drain], Gds);
sim.stampMatrix(lead_node[drain], lead_node[source], -Gds - gm);
sim.stampMatrix(lead_node[drain], lead_node[gate], gm);
sim.stampMatrix(lead_node[source], lead_node[drain], -Gds);
sim.stampMatrix(lead_node[source], lead_node[source], Gds + gm);
sim.stampMatrix(lead_node[source], lead_node[gate], -gm);
sim.stampRightSide(lead_node[drain], rs);
sim.stampRightSide(lead_node[source], -rs);
if (source == 2 && (pnp ? -1 : 1) == 1 || source == 1 && (pnp ? -1 : 1) == -1)
{
ids = -ids;
}
}
/*public override double getPower() {
* return (lead_volt[0] - lead_volt[2]) * current;
* }*/
public override void step(Circuit sim)
{
double[] vs = new double[3];
vs[0] = lead_volt[0];
vs[1] = lead_volt[1];
vs[2] = lead_volt[2];
if (vs[1] > lastv1 + 0.5)
{
vs[1] = lastv1 + 0.5;
}
if (vs[1] < lastv1 - 0.5)
{
vs[1] = lastv1 - 0.5;
}
if (vs[2] > lastv2 + 0.5)
{
vs[2] = lastv2 + 0.5;
}
if (vs[2] < lastv2 - 0.5)
{
vs[2] = lastv2 - 0.5;
}
int grid = 1;
int cath = 2;
int plate = 0;
double vgk = vs[grid] - vs[cath];
double vpk = vs[plate] - vs[cath];
if (Math.Abs(lastv0 - vs[0]) > 0.01 || Math.Abs(lastv1 - vs[1]) > 0.01 || Math.Abs(lastv2 - vs[2]) > 0.01)
{
sim.converged = false;
}
lastv0 = vs[0];
lastv1 = vs[1];
lastv2 = vs[2];
double ids = 0;
double gm = 0;
double Gds = 0;
double ival = vgk + vpk / mu;
currentg = 0;
if (vgk > .01)
{
sim.stampResistor(lead_node[grid], lead_node[cath], gridCurrentR);
currentg = vgk / gridCurrentR;
}
if (ival < 0)
{
// should be all zero, but that causes a singular matrix,
// so instead we treat it as a large resistor
Gds = 1E-8;
ids = vpk * Gds;
}
else
{
ids = Math.Pow(ival, 1.5) / kg1;
double q = 1.5 * Math.Sqrt(ival) / kg1;
// gm = dids/dgk;
// Gds = dids/dpk;
Gds = q;
gm = q / mu;
}
currentp = ids;
currentc = ids + currentg;
double rs = -ids + Gds * vpk + gm * vgk;
sim.stampMatrix(lead_node[plate], lead_node[plate], Gds);
sim.stampMatrix(lead_node[plate], lead_node[cath], -Gds - gm);
sim.stampMatrix(lead_node[plate], lead_node[grid], gm);
sim.stampMatrix(lead_node[cath], lead_node[plate], -Gds);
sim.stampMatrix(lead_node[cath], lead_node[cath], Gds + gm);
sim.stampMatrix(lead_node[cath], lead_node[grid], -gm);
sim.stampRightSide(lead_node[plate], rs);
sim.stampRightSide(lead_node[cath], -rs);
}
