**Procedure**
- First I calculated the transfer function for the ideal condition of the bias tee having one capacitor and one inductor with 50-ohm impedances on each output.
- Using this function I used both scipy.optimize.curve_fit and scipy.optimize.least_squares to try and pull out approximate values for C and L, as well as their parasitic resistances.
- The data was taken from S31 and S32, where the S31 fit should tell us more about the capacitors value, while the S32 fit tells more about the inductor value. This is more relevant for the curve_fit function as it acts on the S31 data and S32 data separately. The least_squares used a cost function that attempts to fit both curves simultaneously, so it should give us good information on both components.
- While curve_fit outputs the covariance matrix, the least_squares does not. For least_squares I used its Jacobian to estimate the Hessian and from there calculated the covariance matrix.
- In order to calculate the strength of randomness in residuals, I used the procedure defined on slides 26-29 from http://www2.compute.dtu.dk/~pcha/LSDF/LinDataFit.pdf. These were implemented as functions within the code "RandomSignTest" and "AutoCorrelationTest".
**Conclusions**
- Our best value for C is from the S31 fit and LSQ fits, which both fall within the range of 211nF.
- The value for L taken from the LSQ fit, which should be better correlated than the S31 fit and has a smaller error bar than the S32 fit, is around 694 uH.
- The parasitic resistance of the inductor given by the LSQ fit is around 3 ohms, while S31 fit yields 530 ohms. In this case, because the LSQ fit uses data from both and is more reasonable, we will take the value from the LSQ fit.
- It is important to note here that the test to determine the strength of randomness in the residuals failed for all fits used. This indicates we may be oversimplifying the electrical schematic of the bias tee.
- The values for the parasitic resistance of the capacitor vary wildly and seems to make little difference in the fitting.
**Next Step**
I will add the simplified model of the bias tee into the EOM driver Circuit simulation within LTspice. I will include the parasitic resistance of the inductor, but due to the reason mentioned above will not include the parasitic resistance of the capacitor. Then I will see if it is possible to maintain the impedance peak at 37MHz by using the tuning inductor within the circuit. |