# Ch-10 : Striplines & Microstrip lines¶

## Page Number: 554 Example 10.1¶

In [2]:
from __future__ import division
from math import exp, log10, pi, sqrt, log
#Given,

z0=50  #ohm
t=0.001  #mm
b=0.32  #cm
er=2.20
tandel= 0.0005
rs=0.026  #ohm
f=10e9  #Hz
c=3e8 #m/sec

p=sqrt(er)*z0
#As p<120
w=b*(((30*pi)/p)-0.441)
print 'Width %0.3f'%w,'cm'

#Attenuation
k=((2*pi*f*sqrt(er))/c)

#and
A=1+((2*w)/(b-t))+(((b+t)/((b-t)*pi))*log(((2*b)-t)/t))
#Hence
ac=(2.7e-3*rs*er*z0*A)/(30*pi*(b-t)*1e-2)
#Total attenution

#Total attenution in db
x=exp(a)
alp=20*log10(x)  #db/m

#Total attenution in db/lambda:
lam=c/(sqrt(er)*f)
lamm=lam*1e2
alph=alp/lamm
print 'Total attenution in db/lambda: %0.3f'%alph, 'db/lambda'

#Answer in book for alph is given as 0.856 but it should be 0.0856 as value of f is taken as 10e10 but it should be 10e9

Width 0.266 cm
Total attenution in db/lambda: 0.856 db/lambda


## Page Number: 555 Example 10.2¶

In [5]:

#Given,
er=9.7
h=0.25  #mm
w=0.25  #mm
f=5e9  #Hz
c=3e8  #m/s

#(i) Dielectric constant
dc=((er+1)/2)+(((er-1)/2)*(1/sqrt(1+12*h/w)))
print 'Dielectric constant: %0.3f'%dc

#(ii) Phase constant
lam0=c/f
pc=sqrt(dc)*(2*pi/lam0)

#(iii) Microstrip wavelength
lams=lam0/sqrt(dc)
print 'Microstrip wavelength: %0.3f'%(lams*100),'cm'

#(iv) Capacitance per unit length
e0=8.854e-12
cap=(2*pi*e0)/log((8*h/w)-(w/(4*h)))
print 'Capacitance per unit length: %0.3e'%cap, 'F/cm'

#(v) Characterstic Impedance
ci=(60/sqrt(dc))*log((8*h/w)+(w/(4*h)))
print 'Characterstic impedance: %0.3f'%ci, 'ohm'

Dielectric constant: 6.556
Microstrip wavelength: 2.343 cm
Capacitance per unit length: 2.717e-11 F/cm
Characterstic impedance: 49.447 ohm


## Page Number: 556 Example 10.3¶

In [6]:

#Given,
er=5.23
w=10  #mils
t=2.8  #mils
h=7  #mils

dc=((er+1)/2)+(((er-1)/2)*(1/sqrt(1+12*h/w)))
print 'Dielectric constant: %0.3f'%dc

#As w/h>1
ci=(120*pi)/(sqrt(dc)*((w/h)+1.393+0.667*log((w/h)+1.444)))
print 'Characterstic impedance: %0.3f'%ci, 'ohm'

Dielectric constant: 3.805
Characterstic impedance: 54.822 ohm


## Page Number: 556 Example 10.4¶

In [5]:

#Given,

q=2.5
dh=1.58
er=9
f=10
c=3e8

erff=((er+1)/2)+(((er-1)/2)*((1+(12/q))**(-1/2)))
vp=(c/sqrt(erff))*erff
fe1=c/(sqrt(vp)*2*dh*q)
if f<fe1:
print 'Strip supports TEM mode only'
else:
print 'Strip does not support TEM mode only'

Strip supports TEM mode only


## Page Number: 557 Example 10.5¶

In [10]:

#Given,

er=9.7
h=0.5  #mm
w=0.5  #mm
lt=2e-4
t=0.02  #mm
f=5e9  #Hz
fg=5  #HZ
c=3e8
rs=8.22e-3*sqrt(fg)

#(i) Dielectric constant
dc=((er+1)/2)+(((er-1)/2)*(1/sqrt(1+12*h/w)))
print 'Dielectric constant: %0.3f'%dc

#(ii) Characterstic Impedance
ci=(60/sqrt(dc))*log((8*h/w)+(w/(4*h)))
print 'Characterstic impedance: %0.3f'%ci,'ohm'

#(iii) Dielectric attenuation
lam0=c/f
alphd=(pi/lam0)*(er/sqrt(dc))*((dc-1)/(er-1))*lt
print 'Dielectric attenuation: %0.3f'%alphd,'Np/m'

#Conductor attenuation
r1=(0.94+(0.132*(w/h))-(0.0062*((w/h)**2)))*((1/pi)+(1/(pi**2))*log((4*pi*w)/t))*(rs/(w*1e-3))
r1m=r1*1e-2
r2=(w/h)/(((w/h)+5.8+(0.03*(h/w))))*(rs/(w*1e-3))
r2m=r2*1e-2
alphc=(r1+r2)/(2*ci)
print 'Conductor attenuation: %0.3f'%alphc,'Np/m'

#(iv) Total attenuation
A=alphc+alphd

Dielectric constant: 6.556
Characterstic impedance: 49.447 ohm
Dielectric attenuation: 0.025 Np/m
Conductor attenuation: 0.411 Np/m
Total attenuation: 0.038 db/cm


## Page Number: 558 Example 10.6¶

In [7]:

#Given

sig=5.8e7
f=10  #GHz
h=0.12e-2  #m

q=62.8*h*sqrt(f*sig)
print 'conductor Q of the stripline:' ,round(q)

conductor Q of the stripline: 1815.0


## Page Number: 558 Example 10.7¶

In [12]:

#Given
Er=6
h=4e-3  #m

#(i) W for Z0=50W
Z0=50  #W
W=(120*pi*h)/(sqrt(Er)*Z0)
print 'Required Width: %0.3f'%(W*1000), 'mm'

#(ii)Stripline capacitance
E0=8.854e-12
C=(E0*Er*W)/h
print 'Stripline capacitance: %0.3f'%(C*10**12),'pF/m'

#(iii)Stripline inductance
Mu0=4*pi*10e-7
L=(Mu0*h)/W
print 'Stripline inductance: %0.3f'%(L*10**5),' muH/m'

#(iv)Phase velocity
c=3e8
vp=c/sqrt(Er)
print 'Phase velocity',vp, 'm/s'

Required Width: 12.312 mm
Stripline capacitance: 163.522 pF/m
Stripline inductance: 0.408  muH/m
Phase velocity 122474487.139 m/s


## Page Number: 559 Example 10.8¶

In [13]:

#Given
cl=3e8  #m/s
f=5e9  #Hz
Er=9
C=-10  #db
Z0=50  #ohm
#Length
L=(cl/f)/(4*sqrt(Er))
print 'Length:' ,L*100,'cm'

#Coupling coefficient
C0=10**(C/20)
print 'Coupling coefficient: %0.3f'%C0

#Even and odd mode impedance
Z0e=(Z0*sqrt(1+C0))/sqrt(1-C0)
print 'Even mode impedance: %0.3f'%Z0e,'ohm'

Z0o=(Z0*sqrt(1-C0))/sqrt(1+C0)
print 'Odd mode impedance: %0.3f'%Z0o,'ohm'

Length: 0.5 cm
Coupling coefficient: 0.316
Even mode impedance: 69.371 ohm
Odd mode impedance: 36.038 ohm


## Page Number: 560 Example 10.9¶

In [14]:

#Given
Z0=50  #ohm
C=3  #db

#Line impedance
Z01sqr=(1-(10**(C/-10)))
Z01=sqrt(Z0*Z0*Z01sqr)
print 'Z01: %0.3f'%Z01, 'ohm'

Z02=Z01/(sqrt(1-(1/sqrt(2))**2))
print 'Z02:' ,round(Z02),'ohm'

Z01: 35.313 ohm
Z02: 50.0 ohm


## Page Number: 560 Example 10.10¶

In [16]:

#Given
W=6  #m
s=2.2  #m
b=4.8  #m
Er=2.2

#Even and odd mode impedance
Z0e=((120*pi)*(b-s))/(2*sqrt(Er)*W)
print 'Even mode impedance: %0.3f'%Z0e,'ohm'

Z0o=(Z0e*s)/b
print 'Odd mode impedance: %0.3f'%Z0o,'ohm'

#Mid band coupling
x=(Z0e-Z0o)/(Z0e+Z0o)
C=-20*log10(x)
print 'Mid band coupling: %0.3f'%C,'db'

#Answer in book for C is given as 54.2 but it should be 8.60

Even mode impedance: 55.070 ohm
Odd mode impedance: 25.240 ohm
Mid band coupling: 8.602 db


## Page Number: 562 Example 10.11¶

In [18]:

#Given
Er=6
d=3e-3  #m
Z0=50  #ohm
E0=8.854e-12  #F/m
Mu0=4*pi*10e-7  #H/m

#(i) W
W=(377*d)/(sqrt(Er)*Z0)
print 'Required Width: %0.3f'%(W*1000),'mm'

#(ii)Stripline capacitance
C=(E0*Er*W)/d
print 'Stripline capacitance: %0.3f'%(C*10**12),'pF/m'

#(iii)Stripline inductance
L=(Mu0*d)/W
print 'Stripline inductance: %0.3f'%(L*10**6), 'muH/m'

#(iv)Phase velocity
c=3e8
vp=c/sqrt(Er)
print 'Phase velocity' ,vp,'m/s'

Required Width: 9.235 mm
Stripline capacitance: 163.526 pF/m
Stripline inductance: 4.082 muH/m
Phase velocity 122474487.139 m/s


## Page Number: 562 Example 10.12¶

In [20]:

#Given
Er=2.56
w=25  #mils
t=14  #mils
d=70  #mils
E0=8.854e-12  #F/m

#(i) K factor
K=1/(1-(t/d))
print 'K factor:' ,K

#(ii) Fringe capacitance
C=((E0*Er)*(2*K*log(K+1)-(K-1)*log(K**2-1)))/pi
print 'Fringe capacitance: %0.3f'%(C*10**12), 'pF/m'

#(iii) Charecteristic Impedance
X=1/(((w*K)/d)+(C/(E0*Er)))
Z0=(94.15*X)/sqrt(Er)
print 'Charecteristic Impedance: %0.3f'%Z0,'ohm'

#Answer in book for Z0 is given as 50.29 but it should be 51.7

K factor: 1.25
Fringe capacitance: 15.665 pF/m
Charecteristic Impedance: 51.729 ohm


## Page Number: 563 Example 10.13¶

In [21]:

#Given
Z0=50  #ohm
#Sincr ratio of power is 2:3
x1=5/2
y1=5/3
#Output Impedance
Z1=x1*Z0
Z2=y1*Z0
print 'Output Impedance 1:',Z1,'ohm'
print 'Output Impedance 2: %0.3f'%Z2,'ohm'

#Input Impedance
Zin=[((Z2*2*Z2)/3)/((Z2+(2*Z2)/3))]

#Looking into Z1, Z2 is || to Z0
A1=(Z2*Z0)/(Z2+Z0)

#Looking into Z, Z2 is || to Z0
A2=(Z1*Z0)/(Z1+Z0)

#Reflection Coeffcients
R1=(A1-Z1)/(A1+Z1)
R2=(A2-Z2)/(A2+Z2)

print 'Reflection Coeffcients:\n', R1,'\n',R2,

Output Impedance 1: 125.0 ohm
Output Impedance 2: 83.333 ohm
Reflection Coeffcients:
-0.6
-0.4