Example: Calculating an RC Circuit¶

# Imports
%precision 2
import PhysicalQuantities as pq
import PhysicalQuantities.numpywrapper as nw
%load_ext PhysicalQuantities.ipython
from PhysicalQuantities.constants import eps0
def disp(s):
    display(HTML(s))

The PhysicalQuantities.ipython extension is already loaded. To reload it, use:
  %reload_ext PhysicalQuantities.ipython

We have a simple RC circuit, consisting of a voltage source $U_0$, a resistor with a value $R$ and a capacitor with value $C$:

Let’s start with calculating the capacitance of a simple parallel plate capacitor:

A = 1 mm * 1 mm # Plate area
d = 1 um        # Plate distance
eps_r = 3       # Permittivity of dielectric material
C  = (eps0*eps_r*A) / d
disp("Capacitor value $C$ = %s" % C.pF)

Capacitor value $C$ = 26.56 pF

The resistor is a thick film resistor:

ρ = 10 Ohm * 1 mm # Material resistivity
t = 10 um           # Sheet thickness
L = 150 um          # Structure length
W = 10 um           # Structure width
Rs = ρ / t
R = Rs * L / W
disp("Resistor value $R$ = %s" % R.kOhm)

Resistor value $R$ = 15.00 kOhm

Calculate transient response of circuit¶

u0 = 1. V
τ = 1/(R*C)
t = nw.linspace(0, 4/τ.base, 100).us

i0 = u0/R
i = (i0*e**(-t*τ)).uA
disp("Initial current is $i_0$ = %s" % i0.uA)

Initial current is $i_0$ = 66.67 uA

Plot Current and Voltage over Time¶

plot(t._,i._)
grid()
title('Circuit Current')
xlabel('Time in %s' % t.unit)
ylabel('Current in %s' % i.unit);

uc = u0 - i*R
plot(t._, uc._)
title('Capacitor Voltage')
grid()
xlabel('Time in %s' % t.unit)
ylabel('Voltage in %s' % uc.unit);