Solve system of equations

[Sancho_Pansa]

Hello Sancho,

please double check your equations. I'm looking your last code. Is it Ar = 1 - omega**2*Cs*Cl or
Ar = 1 - omega**2*Cl*L???

Hello Askic.
Here is the solution, which works fine.
Modifications that was made:

• I replaced the capacitance Cl by the resistor Rl which drastically simplifies the transfer function, which in turn simplifies the work of the fsolve function.
  
• The equations are now generated by transformations performed on the circuit, created by the Circuit function, which minimizes typos.
  

from lcapy import Circuit, j, omega
import numpy as np
from math import pi
from scipy.optimize import fsolve

def f(LCR, *args):
    omg = np.array([args[0], args[1], args[2]])
    out = np.array([args[3], args[4], args[5]])

    cct = Circuit('''
    ... Rin 1 2
    ... Cs  2 4
    ... La  2 3
    ... Rs  3 4
    ... Rl  4 0''')

    cct1 = cct.subs({'Rin': 50, 'Cs':LCR[1], 'La': LCR[0], 'Rs': LCR[2], 'Rl': 100})

    H = cct1.transfer(1,0,4,0)
    A = H(j*omega).simplify()
    Am = A.magnitude

    equ = np.zeros(3)
    
    # equation building
    for i in range(3):
        equ[i] = out[i] - Am.evaluate(omg[i])
    return equ

# Define frequencies in MHz
f1 = 130
f2 = 140
f3 = 150
omg = np.array([f1, f2, f3])*1.0e6*2*pi

# Define outputs:
out = [0.27175539, 0.24606606, 0.22193977]

# Define guesses for L [uH], Cs [pF], Rs [Ohm]
L0  = 0.3e-6
Cs0 = 1e-12
Rs0 = 1

LCR0 = np.array([L0, Cs0, Rs0])
LCR = fsolve(f, LCR0, args=tuple(np.concatenate((omg, out))), maxfev=10000)
print(LCR)

Here is output:

Output:
[3.20000543e-07 9.99996130e-13 4.99951198e+00]

Here are real values:
0.32e-6, 1.0e-12, 5.0

Sincerely,

Sancho.