This circuit is a 250 Ohm voltage source connected to a transmission of 50 Ohms characteristic impedance via an impedance matching network (a basic L-section).
The fully matched values for L and C are 159.2nH and 12.73pF, respectively. These deliver maximum power to the load resistor.
The input is a periodic sine wave with a frequency of 10 MHz. The voltage is shown at the beginning and end of the transmission line (v_in/v_out), as well as at the 250 Ohm source (v_src). If parameters are swept away from these ideal values, the voltage at v_out will decrease, since the matched parameters maximize power.
The circuit netlist is contained within the
transmission_line.spice files in this directory. To begin running the simulation harness, open the
impedance_matcher_sensitivity.jl file and begin running statements.
impedance_matcher_sensitivity.jl- simulation harness
impedance_matcher.spice- circuit netlist
transmission_line.spice- transmission line sub-circuit netlist
Before performing optimization, the example sweeps L and C values across 1nH to 200nH and 0.1pF to 20pF.
Inspecting the solution near 159.2nH and 12.73pF shows that vin and vout appear in the expected 2:1 ratio for maximal power delivery.
The script then performs a sensitivities simulation to show the relevant waveforms and intermediate derivatives. This plot shows the infinitesimal change in the transient response as the C parameter is changed.
Near the impedance matched solution, we expect this waveform to be 90 degrees out-of-phase with the transient solution. This quadrature relationship indicates that changing C would apply a phase shift to the output waveform but would not change its amplitude. Since the amplitude reaches a maximum at the impedance-matched solution, this is exactly what we'd expect.
Then, it uses standard optimization tools (specifically, L-BFGS) to optimize the parameter values. The goal for the optimization is to automatically compute the parameters for an impedance matching network for the transmission line.