Ch-12 : Microwave Measurements

Page Number: 649 Example 12.1

In [1]:
from __future__ import division
#Given
Is=0.1*(10**-6)  #A
Pi=0  #dBm
Cs=0.1*(10**-12)  #F
Ls=2*(10**-9) 
Cj=0.15*(10**-12)  #F
Rs=10  #ohm
T=293  #K
nktbye=25*(10**-3)  #V

#Rj
Rj=(nktbye/Is) 
print 'Rj:' ,Rj/1000,'Kohm'

#Bi
Bi=nktbye/2 
Bii=Bi*1000 
print 'Bi:' ,Bii,'A/W'

#Bv
Bv=Rj*Bii 
print 'Bv:',Bv, 'V/W'

Rj: 250.0 Kohm
Bi: 12.5 A/W
Bv: 3125000.0 V/W

Page Number: 650 Example 12.2

In [3]:
from math import log10 
#Given
vswr=4 

modT=(vswr-1)/(vswr+1) 
Lm=-10*log10(1-(modT*modT))  #dB
print 'Mismatch Loss:' ,Lm,'dB'

#Sensitivity reduces by a factor
Bvd=(1-(modT*modT)) 
Bvdp=Bvd*100 
print 'Voltge sensitivity reduces by:' ,Bvdp,'%'

Mismatch Loss: -0.0 dB
Voltge sensitivity reduces by: 100 %

Page Number: 650 Example 12.3

In [4]:
from math import sqrt , pi
#Given
f=10e9  #Hz
c=3e10  #cm/s
a=4  #cm
s=0.1  #cm
lmb=c/f  #cm
lmbg=lmb/(sqrt(1-((lmb/(2*a))**2))) 
vswr=lmbg/(pi*s) 
print 'VSWR: %0.3f'%vswr

#Answer in book for lmbg is given as 3.49 but it should be 3.23 and hence the answer will be 10.3

VSWR: 10.301

Page Number: 651 Example 12.4

In [5]:
 
#Given
delx=3.5  #cm
s=0.25  #cm

lmbg=2*delx 
vswr=lmbg/(pi*s) 
print 'VSWR: %0.3f'%vswr

VSWR: 8.913

Page Number: 651 Example 12.5

In [5]:
 
#Given
vswr=2 
Pin=4.5e-3  #W

modT=(vswr-1)/(vswr+1) 
#Power reflected,
Pr=(modT**2)*Pin 
#As coupler samples only 1/1000th power
Prr=Pr*1000 
print 'Reflected Power:' ,Prr,'W'

Reflected Power: 0.5 W

Page Number: 652 Example 12.6

In [6]:
from math import tan
#Given
Z0=50  #ohm
p=2.4 
L=0.313 
x=2*pi*L 
y=tan(x) 

Zl=(Z0*(1+(p*p*1J)))/(p+(p*1J)) 
T=(Zl-Z0)/(Zl+Z0) 
p=sqrt(((T.real))**2+((T.imag))**2) 
print 'Reflection coefficient: %0.3f'%p

Reflection coefficient: 0.412

Page Number: 652 Example 12.7

In [8]:
 
#Given
Zl=25+25*1J  #ohm
Z0=50  #ohm

T=(Zl-Z0)/(Zl+Z0) 
p=sqrt(((T.real))**2+((T.imag))**2) 
print 'Reflection coefficient: %0.3f'%p

vswrr=(1+p)/(1-p) 
print 'VSWR: %0.3f'%vswrr

#Fraction of power delivered
Pd=1-(p**2) 
Pdp=Pd*100 

print 'Fraction of power delivered:',Pdp, '%'

Reflection coefficient: 0.447
VSWR: 2.618
Fraction of power delivered: 80.0 %

Page Number: 653 Example 12.8

In [9]:
 
#Given
d=2.4 #cm
lmbc=1.8 
c=3*10**10  #cm/s

lmbg=2*d 
lmb=(lmbg*lmbc)/(sqrt(lmbg**2+lmbc**2)) 
#Operating frequency
f=c/lmb 
print 'Operating frequency: %0.3f'%(f/10**9),'GHz'

Operating frequency: 17.800 GHz

Page Number: 653 Example 12.9

In [10]:
from numpy import mat
#Given
p=1.5 
IsL=1  #dB
InL=30  #dB

S21=10**(-IsL/20) 

#Assuming tgree ports to be identical
S32=S21 
S13=S21 

#Isolations are also the same
S31=10**(-InL/20) 
S23=S31 
S12=S31 

#Refelction coefficients are also the same
T=(p-1)/(p+1) 
S11=T 
S22=T 
S33=T 

S=mat([[S11, S12, S13], [S21, S22, S23], [S31, S32, S33] ])
print 'Matrix is:\n' ,S

Matrix is:
[[ 0.2         0.03162278  0.89125094]
 [ 0.89125094  0.2         0.03162278]
 [ 0.03162278  0.89125094  0.2       ]]

Page Number: 654 Example 12.10

In [13]:
 
#Given
R1=10.6  #GHz
R2=8.30  #GHz
Q0=8200 
Q0d=890 

Er=(R1/R2)**2 
print 'Dielectric constant %0.3f'%Er

Qd=(Q0-Q0d)/(Q0*Q0d) 
print 'Loss tangent of dielectric' ,Qd

Dielectric constant 1.631
Loss tangent of dielectric 0

Page Number: 654 Example 12.11

In [14]:
 
#Given
l0=0.15  #cm
lmbg=2*2.24  #cm
le=1.14  #cm
a=2.286  #cm
d=2 

B0=(2*pi)/lmbg 
x=tan(B0*l0)/(B0*l0) 
#Also
x1=(l0*x)/le 
#Correct value seems to be
Bele=2.786 
e1=((((a/pi)**2)*(Bele/le)**2)+1) 
e2=(((2*a)/lmbg)**2)+1 
Er=e1/e2 
print 'Er: %0.3f'%Er


#Answer in book for Er is given as 2.062 but it should be 2.038

Er: 2.039