In [1]:

    

from lcapy import Circuit, j, omega, s
cct = Circuit("""
Vi 1 0_1 step; down
C 1 2; right, size=1.5
R 2 0; down
W 0_1 0; right
W 0 0_2; right, size=0.5
P1 2_2 0_2; down
W 2 2_2;right, size=0.5""")


    

In [2]:

    

cct.draw()


    

In [3]:

    

H = (cct.R.V(s) / cct.Vi.V(s)).simplify(); H


    

    
Out[3]:





$$\frac{C R s}{C R s + 1}$$

In [4]:

    

H(j * omega)


    

    
Out[4]:





$$\frac{\mathrm{j} C R \omega}{\mathrm{j} C R \omega + 1}$$

In [5]:

    

H(j * omega).rationalize_denominator()


    

    
Out[5]:





$$\frac{C^{2} R^{2} \omega^{2} + \mathrm{j} C R \omega}{C^{2} R^{2} \omega^{2} + 1}$$

In [6]:

    

H(j * omega).real_imag


    

    
Out[6]:





$$\frac{C^{2} R^{2} \omega^{2}}{C^{2} R^{2} \omega^{2} + 1} + \frac{\mathrm{j} C R \omega}{C^{2} R^{2} \omega^{2} + 1}$$

In [7]:

    

H(j * omega).magnitude


    

    
Out[7]:





$$\frac{\sqrt{C^{4} R^{4} \omega^{4} + C^{2} R^{2} \omega^{2}}}{C^{2} R^{2} \omega^{2} + 1}$$

In [8]:

    

H(j * omega).phase_degrees


    

    
Out[8]:





$$\frac{180 \operatorname{atan_{2}}{\left(1,C R \omega \right)}}{\pi}$$

In [9]:

    

H1 = H.subs('C', 1e-6).subs('R', 1e3)
H1(j * omega)


    

    
Out[9]:





$$\frac{\mathrm{j} \omega}{1000 \left(\frac{\mathrm{j} \omega}{1000} + 1\right)}$$

In [10]:

    

from numpy import logspace
w = logspace(1, 6, 500)
%matplotlib inline
ax = H1(j * omega).dB.plot(w, log_frequency=True)


    

In [11]:

    

ax = H1(j * omega).phase_degrees.plot(w, log_frequency=True)


    

In [12]:

    

H1


    

    
Out[12]:





$$\frac{s}{1000 \left(\frac{s}{1000} + 1\right)}$$