rizer.electrical_model.circuit.rc_source_circuit#

Classes#

RC_Source_Circuit

Capacitor C_s driven by two independent current branches through R_g and Z_c.

Module Contents#

class rizer.electrical_model.circuit.rc_source_circuit.RC_Source_Circuit(R_g: float, Z_c: float, C_s: float, drive: Callable[[float], float], u_s_0: float = 0.0)#

Bases: rizer.electrical_model.circuit.base_circuit.BaseCircuit

Capacitor C_s driven by two independent current branches through R_g and Z_c.

Unlike RC_Rp_Circuit (one drive branch through R_par, one load branch R_p(t)), this node has two independent drive branches – one through R_g, one through Z_c – and no third (load) resistor at all: the plasma resistance does not sit at this node. drive is the caller-supplied combined current injection into the node, so Kirchhoff’s current law gives:

\[\frac{du_s}{dt} = \frac{\text{drive}(t) - u_s\left(\dfrac{1}{R_g}+\dfrac{1}{Z_c}\right)}{C_s}\]

where u_s is the voltage across C_s. What R_g, Z_c, and drive represent physically – and whether u_s is a node-to-ground voltage or a voltage across some other element as well – depends on the topology the caller derived drive from: see TransmissionLineCapacitiveSourceResistiveLoadCircuit (C_s shunting the node to ground, u_s a node voltage) and TransmissionLineParallelCapacitiveSourceResistiveLoadCircuit (C_s bridging R_g, u_s the voltage across the R_g/C_s pair) for the two derivations that instantiate this same ODE.

This circuit only supports externally-driven mode – it has no self-contained solve. R_p is accepted (to match compute_derivatives_driven()’s signature) but unused: the plasma resistance does not appear in this node’s own KCL at all.

Parameters:

  • R_g (float) – Source resistance, one drive branch [Ohm].

  • Z_c (float) – Cable characteristic impedance, the other drive branch [Ohm].

  • C_s (float) – Capacitance whose voltage is this circuit’s own state [F].

  • drive (Callable) – Combined current injection into the node, as a function of time [A].

  • u_s_0 (float, optional) – Initial voltage across C_s at t=0 [V]. Default 0 V.

R_g#

Source resistance, generator branch.

Z_c#

Cable characteristic impedance, returning-wave branch.

C_s#

Capacitance at the source’s own output node.

drive#

Combined current injection at node A, as a function of time.

u_s_0 = 0.0#

Initial voltage across C_s at time t=0.

initial_state() → numpy.ndarray#

Return the initial circuit state [u_s_0], for externally-driven mode.

compute_derivatives_driven(t: float, y: numpy.ndarray, R_p: float) → numpy.ndarray#

Time-derivative of the circuit state [u_s].

Parameters:

  • t (float) – Time at which the circuit is solved.

  • y (numpy.ndarray of float) – Array containing the present value of the system: y[0]=u_s, the voltage across C_s (see class docstring for what that voltage represents in the caller’s own topology).

  • R_p (float) – Unused – the plasma resistance does not appear in this node’s own KCL (see class docstring). Accepted only to match compute_derivatives_driven()’s signature.

Returns:

Array containing the derivative dy[0]=du_s/dt.

Return type:

numpy.ndarray of float