# Measuring inductance using a series resonance circuit

$$\frac{V_o}{V_i} = \frac{(\frac{1}{j \omega C} + R_l + j \omega L)}{R_s + (\frac{1}{j \omega C} + R_l + j \omega L)}$$

at resonance,
$$\left|\frac{1}{j \omega C}\right| = \left|j \omega L\right|$$$$\omega = \frac{1}{\sqrt{L C}}$$$$L = \frac{1}{\omega^2 C}, \omega = 2 \pi f$$$$L = \frac{1}{(2 \pi f)^2 C}$$


In [10]:

%matplotlib inline

from cmath import phase, pi
from math import degrees,sqrt
import matplotlib.pyplot as plt

Rs = 39000
C  = 0.1e-6
L  = 10
Rl = 384
plotpoints = 5000

def Vo(f, Vi = 1):
RLC = 1/(2*pi*f*C*1j) + Rl + (2*pi*f*L*1j)
return Vi * (RLC/(Rs+RLC))

frequencies = [ pow(10,4.0*i/plotpoints) for i in range(plotpoints)]
mags = []
phases = []

fmin = 1
magmin = 2

for f in frequencies:
vo = Vo(f)
mag = abs(vo)
mags.append(mag)
phases.append(phase(vo))
if mag < magmin:
fmin = f
magmin = mag

print "Expect  Voutmin=%0.4f at %.2fHz"%(float(Rl)/(Rl+Rs),1/(2*pi*sqrt(L*C)))
print "Calculated Vout=%0.4f at %.2fHz"%(magmin,fmin)

plt.figure()
plt.figure(figsize=(12, 6))
plt.semilogx(frequencies,mags)
plt.semilogx(frequencies,phases)
plt.grid(True)
plt.show()




Expect  Voutmin=0.0098 at 159.15Hz
Calculated Vout=0.0098 at 159.07Hz

<matplotlib.figure.Figure at 0xae4a3ccc>



with $f_{resonance}$ and C, calculate $L = \frac{1}{(2 \pi f)^2 C}$

Put your values of f and C here to calculate your L



In [19]:

f = 160.6
C = 0.1e-6

L = 1/(pow((2*pi*f),2)*C)
print "L=%0.1f"%L




L=9.8



## LTSpice Results



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