Chapter 5:Resonant Circuits

Example 5.1, Page 158

In [1]:
import math

#Variable declaration
f2=9      #MHz
f1=11        #MHz
R=50.          #ohm
W1=2*math.pi*11*10**6      #rad/s
W2=2*math.pi*9*10**6         #rad/s

#Calculations&Results
Wo=math.sqrt(W1*W2)
fo=math.sqrt(f1*f2)
print "fo = %.6f MHz"%fo
L=R/(W1-W2)
print "L = %.f uH"%(L*10**6)
C=1./(L*Wo**2)
print "C = %.1f pF"%(C*10**12)

fo = 9.949874 MHz
L = 4 uH
C = 64.3 pF

Example 5.2, Page 163

In [2]:
import math

#Variable declaration
Lp=10**(-5)    #H
Cp=10**(-11)   #F
Rp=10**5       #ohm
RL=10**5       #ohm

#Calculations&Results
Wo=1/math.sqrt(Lp*Cp)
print "Wo=%.0e rad/s"%Wo
Q=Rp/(Wo*Lp)
print "Q=%.0f"%Q
Qe=RL/(Wo*Lp)
print "Qe=%.0f"%Qe
QL=Q*Qe/(Q+Qe)
print "QL=%.0f"%QL

Wo=1e+08 rad/s
Q=100
Qe=100
QL=50

Example 5.3, Page 166

In [7]:
import math

#Variable declaration
R2=62.5*10**3    #ohm
E=1.
L1=320.*10**(-9)    #H
L2=20.*10**(-9)        #H

#Calculations&Results
n=math.sqrt(E*L1/L2)
print "n=%.0f"%n
R1=n**(2)*R2
print "Z1=%.0e ohm\n"%R1
C1=(6+1./4**2*30.7)*10**-12
print "C1=%.2e F\n"%C1
Wo=1./math.sqrt(L1*C1)
print "Wo=%.4e rad/s\n"%Wo
fo=Wo/(2*math.pi)
print "fo=%.2e Hz\n"%fo
Q=R1/(Wo*L1)
print "Q=%.4f"%Q

n=4
Z1=1e+06 ohm

C1=7.92e-12 F

Wo=6.2820e+08 rad/s

fo=1.00e+08 Hz

Q=4974.5446

Example 5.5, Page 175

In [9]:
import math

#Variable declaration
a=0.455*10**-3    #m
b=1.499*10**-3    #m
W=2*math.pi*5*10**9    #rad/s
uo=4*math.pi*10**-7    
q=5.813*10**7
Eo=8.854*10**-12
Er=2.08
d=0.0004

#Calculations&Results
Rs=math.sqrt(W*uo/2/q)
print "Rs=%f ohm"%Rs
ac=Rs*(1/a+1/b)/(2*math.log(b/a)*math.sqrt(uo/Eo))
print "ac=%f Np/m"%ac
ac=ac*math.sqrt(Er)
ad=W/2*math.sqrt(uo*Eo*Er)*(d)
Bo=2*math.pi*5*10**9/(3*10**8)
Bd=2*math.pi*5*10**9*math.sqrt(2.08)/(3*10**8)
a=0.058768
Qair=Bo/(2*a)
a=0.114963
Qteflon=Bd/(2*a)
print "\nwith teflon\n ac=%f Np/m\nad=%f Np/m\nBo=%f rad/m\nBd=%f rad/m,\nQair=%f,\nQteflon=%f"%(ac,ad,Bo,Bd,Qair,Qteflon)

Rs=0.018427 ohm
ac=0.058768 Np/m

with teflon
 ac=0.084757 Np/m
ad=0.030226 Np/m
Bo=104.719755 rad/m
Bd=151.028979 rad/m,
Qair=890.958984,
Qteflon=656.859071

Example 5.6, Page 175

In [13]:
import math

#Variable declaration
Zo=50.    #ohms
Er=2.08
B=60*math.pi**2/Zo/math.sqrt(Er)
c=3.*10**8
f=2.*10**9  #Hz
Ee=1.7875
t=0.159*10**-6
a=5.813*10**7
fGHz=2.    #Hz

#Calculations&Results
A=Zo/60*((Er+1)/2)**(1./2)+(Er-1)/(Er+1)*(0.23+0.11/Er)
print "A=%.4f\nB=%.4f"%(A,B)
h=1.59*10**-3
if A>1.52:
    W=h*(8*math.exp(A)/(math.exp(2*A)-2))
else:
    W=h*(2/math.pi*(B-1-math.log(2*B-1)+(Er-1)/2/Er*(math.log(B-1)+0.39-0.61/Er)))
print "W=%.6f cm"%W

Ere=0.5*(2.08+1+(2.08-1)/math.sqrt(1+12/3.192094))-(2.08-1)*0.0001/4.6/math.sqrt(3.1921)
print "Ere=%.4f"%Ere
l=c/(2*f*math.sqrt(Ee))
print "l=%.6f m"%l
We=W/h+0.3979*t/h*(1+math.log(2*h/t))
print "We/h=%.4f"%We
F=1+1/We*(1-1.25*t/(math.pi*h)+1.25/math.pi*math.log(2*h/t))
ac=44.1255*10**-5*F*Zo*Ere/h*math.sqrt(fGHz/a)*(We+0.667*We/(We+1.444))
print "ac=%.4f Np/m"%ac
deln=0.00040
ad=10.4766*Er/(Er-1)*(Ere-1)/math.sqrt(Ere)*fGHz*math.tan(deln)
print "ad=%.4f Np/m"%ad
B=2*math.pi/(2*l)
print "B=%.4f rad/m"%B
Q=B/(2*(ac+ad))
print "Q=%.1f"%Q

A=1.1333
B=8.2120
W=0.005075 cm
Ere=1.7875
l=0.056097 m
We/h=3.1925
ac=0.0428 Np/m
ad=0.0095 Np/m
B=56.0030 rad/m
Q=535.3

Example 5.7, Page 179

In [15]:
import math

#Variable declaration
a=2.286*10**-2
b=1.016*10**-2
f=9.379*10**9

#Calculations
c=1./2/math.sqrt((9379./300)**2-(1./2/a)**2)

print "c=%.5f m = %.4f cm"%(c,c*100)

c=0.02238 m = 2.2383 cm

Example 5.8, Page 179

In [16]:
import math

#Variable declaration
Er=2.05
ur=1
a=.016 #m
b=.0071   #m
c=.0156   #m
m=1  
p=1 

#Calculations
fr=(300/math.sqrt(ur*Er))*math.sqrt((m/(2*a))**2+(p/(2*c))**2) 

#Result
print "fr = %.3e MHz"%fr

fr = 9.379e+03 MHz

Example 5.9, Page 181

In [17]:
import math

#Variable declaration
w=2*math.pi*5*10**9
u=4*math.pi*10**-7
a=5.8*10**7

#Calculations&Results
r=math.sqrt((3.832**2+(math.pi/2)**2)/(5000*2*math.pi/300)**2)
h=2*r
deln=math.sqrt(2/(w*u*a))
print "del=%.4e m"%deln
Qc=47.7465*10**6/(9.3459*10**-7*5*10**9)*(3.832**2+(math.pi/2)**2)**1.5/((3.832**2+(math.pi/2)**2)+1)
print "Qc=%.2f"%Qc

del=9.3459e-07 m
Qc=39984.60

Example 5.10, Page 183

In [18]:
import math

#Variable declaration
fr=35*10**9
w=2*math.pi*fr
Es=9.9
Er=36
uo=4*math.pi*10**-7
Eo=8.8154*10**-12

#Calculations&Results
z1=1.2892*10**8/(fr*math.sqrt(Es))
z2=1.2892*10**8/(fr*math.sqrt(Er))
r=0.835*10**-3
ko=w*math.sqrt(uo*Eo)
y=math.sqrt((ko*r)**2*(Er-1)-5.784)
print "y=%.3f"%y
k_=2.405/r+y/(2.405*r*(1+2.43/y+0.291*y))
print "k_=%.3e"%k_
a1=math.sqrt(k_**2-ko**2*Es)
a2=math.sqrt(k_**2-ko**2)
B=math.sqrt(ko**2*Er-k_**2)
print "a1=%.3e\na2=%.3e\nB=%.3e"%(a1,a2,B)
d=10**-3
t=.25*10**-3
h=1/B*(math.atan(a1/(B*math.tanh(a1*t)))+math.atan(a2/(B*math.tanh(a2*d))))
print "h=%.3e m"%h

y=2.700
k_=3.381e+03
a1=2.475e+03
a2=3.301e+03
B=2.803e+03
h=6.713e-04 m