Generate skin depths in copper and aluminum as a function of frequency

skin_depth.py

"""
Permeabilities can be found here:
https://www.engineeringtoolbox.com/permeability-d_1923.html

Resistivity can be found here:
http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/rstiv.html

"""

import numpy as np
from numpy import pi
import pandas as pd
import seaborn as sns
from matplotlib import pylab as plt
plt.ion()

# magnetic permeability of free space
mu_0 = 4*pi*1e-7 # Henry/meter

def skin_depth( resistivity, # Ohms per meter
                frequency, # Hertz
                permeability ): # Henry/meter
    delta = np.sqrt( resistivity/pi/frequency/permeability )
    return delta

class Metal(object):
    """
    abstract class to hold material properties
    """
    resistivity = None
    permeability = None

    def __init__(self):
        pass

    @classmethod
    def skin_depth(self, frequency):
        return skin_depth( self.resistivity,
                           frequency,
                           self.permeability )

class Copper(Metal):
    resistivity = 1.68e-8 # Ohm/meter
    permeability = 1.256629e-6 # Henry/meter

    def __init__(self):
        pass    
    
class Aluminum(Metal):
    resistivity = 2.65e-8 # Ohm/meter
    permeability = 1.256665e-6  # Henry/meter
            
    def __init__(self):
        pass


# generate a range of frequencies and plot the skin depth
# as a function of frequency
df = pd.DataFrame( columns = ['freq', 'Cu', 'Al' ])
df['freq'] = np.logspace(8, 12, num=100) # Hertz
df['Cu'] = Copper.skin_depth(df['freq'])
df['Al'] = Aluminum.skin_depth(df['freq'])

plt.figure(10)
plt.clf()
plt.loglog( df['freq']/1e9, df['Cu']/1e-6 )
plt.loglog( df['freq']/1e9, df['Al']/1e-6 )
plt.grid()
plt.xlabel('Freq [GHz]')
plt.ylabel('Skin depth [micron]')
plt.legend( ['Cu', 'Al'] )