The first part of designing the matching crictuit was choosing a frequency range to match over. We chose 100 MHz to 1000 MHz.

The geometric mean of this range in 316.227 MHz, which is the ideal frequeny to match to.

Then, we need the impedance of the antenna we are matching to.

The data for the best antenna is found in 

/fs/project/PAS0654/BiconeEvolutionOSC/BiconeEvolution/current_antenna_evo_build/XF_Loop/Evolutionary_Loop/Run_Outputs/AraSim_Polarity_Fix_2021_03_19/AraSim_Polarity_Fix_2021_03_19.xf/Simulations/001108/Run0001/output/SteadyStateOutput

The files begin at 83.33 MHz and increment by 16.66 MHz, so file 14 (316.57 MHz) is the best choice for matching.

This antenna has Impedance Z = 229.839 -i151.515 ohms

From here, we need to decide a design architecture for the matching circuit. Since the real component of the impedance is greater than the source's (50 ohms, the standard for electrical sources), a natural design is a lowpass downward circuit. 

Next, we decide on a number of L networks to cascade in the circuit design, or how many 'rungs' in the ladder.

The purpose of these rungs is to artificially lower the ratio between the source impedance and the load impedance, as the closer these values, the broader the range of frequencies we can match.

The formula to calculate this is 

N = ln(Rl/Rs)/ln(1+Q^2)

where 

Q = ((Rl/Rs)-1)^½

Rs = real source impedance

Rl = real load impedance

For the given values, N is 14.

From here, we have all the information to find the capacitances and impedances for each L network in the ladder circuit.

The proccess of calciulating these values starts with finding the desired ratio between the impedances. 

ratio = Q^2+1

Which we can use to create a list of 13 impedances between the source and load (corresponding to 14 rungs), each Q^2+1 times larger than the last. Then we can use the formula for a single lowpass downward match between the impedances of each rung. 

All of this process is described in /users/PAS1960/dylanwells1629/improved_match_maker.py

The key functions PCSL, calcN, and broadbandMatchLP