ShuntResistor

class pmrf.models.components.lumped.ShuntResistor(R: Any, *, name: str | None = None, metadata: Any = None)

Bases: Model

A 2-port model of a shunt resistor shunting to ground.

Mathematical Formulation

With port reference impedances \(Z_1\) and \(Z_2\), and \(R = a / b\), the power-wave S-parameters are

\[S_{11} = \frac{a (Z_2 - Z_1^*) - b Z_1^* Z_2}{a (Z_1 + Z_2) + b Z_1 Z_2}, \qquad S_{21} = S_{12} = \frac{2 a \sqrt{\mathrm{Re}\,Z_1 \, \mathrm{Re}\,Z_2}}{a (Z_1 + Z_2) + b Z_1 Z_2}\]

and \(S_{22}\) is \(S_{11}\) with the ports swapped. Taking \((a, b) = (R, 1)\), or \((1, 0)\) for an infinite \(R\), makes them exact at R = 0, where the node is shorted to ground (ADR-0007), and at R = ∞, where the resistor is absent.

Parameters:

R (Param) – The resistance in Ohms.

References

K. Kurokawa, “Power waves and the scattering matrix,” IEEE Trans. Microw. Theory Techn., vol. 13, no. 2, pp. 194-202, 1965.

R: Param

Resistance in Ohms