from pylab import *

def mot(w):
    R = 1.5
    L = 5/1000
    print('tau_e = ',L/R)
    print('1/tau_e = ',R/L)

    return 1/(R+1j*w*L)

def conv(w):
    Tc = 100e-6
    tau_c = 3/2*Tc
    print('tau_c = ',tau_c)
    print('1/tau_c = ',1/tau_c)

    return 1/(1+1j*w*tau_c)

def PI(w):
    kp  = 12.78
    tau = 5/1000/1.5

    return (kp*(1+1j*w*tau)/(1j*w*tau))

def GH(w):

    return PI(w)*conv(w)*mot(w)

def W(w):

    return GH(w)/(1+GH(w))

def Wapp(w):

    return (1/(1+1j*w/2426))*conv(w)

w = logspace(-2,5)

plot(w,20*log10( abs(mot(w)) ))
plot(w,20*log10( abs(conv(w)) ))
plot(w,20*log10( abs(PI(w)) ))

plot(w,20*log10( abs(W(w)  )))
plot(w,20*log10( abs(Wapp(w)  )))


xscale('log')


from scipy import optimize

def fun(x):
    return 20*3.14/180-arctan(x*412e-6)-arctan(x*150e-6)

sol = optimize.root_scalar(fun,x0=620, method='bisect',bracket=[0, 1e5])
print(sol)

fun(883)