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)
{
// 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]);
}
}
