The maximum Transmisison factor achieved with this circuit was 0.86 or 86%. I can calculate what is roughly the maximum voltage I provided.
Vpi = 306.26V from elog 3750
Vpi * asin(sqrt(0.86)) / 1.5 = 284 V at resonant freq of 189.13 kHz.
Considering the length of transmission line I have as l = 35cm, of R0=50 ohm, I can compute the stray capacitance of the EOM due to the tranmission line as follows:
f = np.arange(1E5, 1E6, 1E4)
lam = 3E8/f #lambda
omega = 2 * np.pi * f
C_eom = 12E-12 #12pF, capacitance of eom from thorlabs datasheet
Z_eom = 1/(1j*omega*C_eom)
Beta = 2*np.pi/lam
l = 35E-2 #length of cable
R0 = 50 #ohm, impedance of cable
The resultant input impedance then becomes,
Z_in_eom = R0 * (Z_eom * np.cos(Beta * l) + 1j*R0*np.sin(Beta*l)) / (R0*np.cos(Beta*l) + 1j*Z_eom*np.sin(Beta*l))
We can then evlauate roughly the stray capapcitance as:
C_reality_eom = np.real( 1/ ((1j*omega*Z_in_eom))) #F
This leads to the EOM becoming a 35pF capacitor. This is the reason of my reduction in gain of LC series circuit. This is also the reason of shift resonant frequency of the circuit. If the cable is longer, the stray capacitance will increase further more. In short, you should either take into account the length of your cable between your circuit and EOM or reduce the length of transmisison line as much as possible. If I take into account this 35pF into my simulation with Opamp, the maxmium voltage at my eom is 280V, and the reosnant freq is around 230Khz.
It is quite interesting because the total capacitance looking from the input of the cable becomes a little bit larger depending on the length of the cable. In order to decrease the amount of the stay capacitance, one has to reduce the length of the transmission line.
f = np.arange(1E5, 1E6, 1E4)
# f_res = 189.128E3 #Khz
# omega_res = 2*np.pi*f_res
lam = 3E8/f
omega = 2 * np.pi * f
C_eom = 12E-12 #14pF
ind = 6.8*2*1E-3 #mH
Z_eom = 1/(1j*omega*C_eom)
Z_ind = 1j*omega*ind
Beta = 2*np.pi/lam
l = 90E-2 #length of cable
R0 = 50 #ohm
Z_in_eom = R0 * (Z_eom * np.cos(Beta * l) + 1j*R0*np.sin(Beta*l)) / (R0*np.cos(Beta*l) + 1j*Z_eom*np.sin(Beta*l))
Z_in_ind = R0 * (Z_ind * np.cos(Beta * l) + 1j*R0*np.sin(Beta*l)) / (R0*np.cos(Beta*l) + 1j*Z_ind*np.sin(Beta*l))
C_reality_eom = np.real( 1/ ((1j*omega*Z_in_eom))) #F
L_reality_ind = np.real(Z_in_ind/(1j*omega))