# Ch-9 : Microwave Solid State Generators & Amplifiers¶

## Page Number: 448 Example 9.2¶

In [2]:
from __future__ import division
from math import pi
#Given
fc=5e9  #Hz
Em=2e7  #V/m
vs=4e3  #ms/s
Xc=1  #ohm

#Maximum allowable power
Pm=((Em*vs)**2)/(((2*pi*fc)**2)*Xc)
print 'Maximum allowable power: %0.3f'%Pm, 'W'

Maximum allowable power: 6.485 W


## Page Number: 451 Example 9.3¶

In [3]:

#Given
XeGe=4.0  #eV
XeGaAs=4.1  #eV
delEgGe=0.78  #eV
delEgGaAs=1.42  #eV

#Conduction band differential
delEc=XeGe-XeGaAs
print 'Conduction band differential:' ,delEc,'eV'

#Valence band differential
delEv=delEgGaAs-delEgGe-delEc
print 'Valence band differential:' ,delEv,'eV'

Conduction band differential: -0.1 eV
Valence band differential: 0.74 eV


## Page Number: 454 Example 9.4¶

In [4]:

#Given
S11=0.89
S12=0.02
S21=3.1
S22=0.78

Del=(S11*S22)-(S12*S21)
K=(1-(S11)**2-(S22)**2+(Del)**2 )/(2*S12*S21)
if(K<1):
print 'Amplifier is potentially unstable'
else:
print 'Amplifier is potentially stable'


Amplifier is potentially unstable


## Page Number: 454 Example 9.5¶

In [25]:

#Given
S11=0.40
S12=0.01
S21=2.00
S22=0.35

ZL=20  #ohm
ZS=30  #ohm
Z0=ZL+ZS  #ohm

#Reflection coefficients of source and load
TL=(ZL-Z0)/(ZL+Z0)
TLm=-TL
TS=(ZS-Z0)/(ZS+Z0)
TSm=-TS

#Reflection coefficients of input and output
Tin=S11+((S12*S21*TL)/(1-(S22*TL)))
Tout=S22+((S12*S21*TS)/(1-(S22*TS)))

#Transducer Gain
x=(1-(TSm)**2)/((1-(S11*TSm))**2)  #Value of should be 1.145
y=(S21*S21)
z=(1-(TLm)**2)/((1-(Tout*TLm))**2)
GT=x*y*z
print 'Transducer Gain: %0.3f'%GT

#Available Power Gain
z1=1-(Tout)**2
GA=(x*y)/z1
print 'Available power Gain: %0.3f'%GA

#Power Gain
z2=1-(Tin)**2
GP=(x*y)/z2
print 'Power Gain: %0.3f'%GP

#All the end calculations of finding gain are not accurate in the book, hence the answers dont match

Transducer Gain: 5.207
Available power Gain: 5.257
Power Gain: 5.473


## Page Number: 455 Example 9.6¶

In [26]:
from math import sqrt
#Given
S11=0.60
S12=0.045
S21=2.50
S22=0.50
TS=0.5
TL=0.4
Vrms=10  #V
Z0=50  #ohm

#(i)Reflection coefficients of input and output
Tin=S11+((S12*S21*TL)/(1-(S22*TL)))
Tout=S22+((S12*S21*TS)/(1-(S22*TS)))
print 'Reflection coefficients of input: %0.3f'%Tin
print 'Reflection coefficients of output:' ,Tout

#(ii) Gains
#Transducer Gain
x=(1-(TS)**2)/((1-(S11*TS))**2)
y=(S21*S21)
z=(1-(TL)**2)/((1-(Tout*TL))**2)
GT=x*y*z
print 'Transducer Gain: %0.3f'%GT

#Available Power Gain
z1=1-(Tout)**2
GA=(x*y)/z1
print 'Available power Gain: %0.3f'%GA

#Power Gain
z2=1-(Tin)**2
GP=(x*y)/z2
print 'Power Gain: %0.3f'%GP

#Calculation for Tout and Gains are wrong in the book, hence the answers dont match

#(iii) Power available
Gt=9.4
Pas=(sqrt(2)*Vrms)**2/(8*Z0)
Pal=Gt*Pas
print 'Power available at source:' ,Pas,'W'
print 'Power available at load:',Pal, 'W'

Reflection coefficients of input: 0.656
Reflection coefficients of output: 0.575
Transducer Gain: 13.553
Available power Gain: 14.291
Power Gain: 16.803
Power available at source: 0.5 W
Power available at load: 4.7 W


## Page Number: 457 Example 9.7¶

In [27]:
from math import log10
#Given
S11=0.90
S12=0
S21=2.40
S22=0.80

Gmax=(S21*S21)/((1-(S11)**2)*(1-(S22)**2))
Gdb=10*log10(Gmax)
print 'Maximum gain: %0.3f'%Gdb

Maximum gain: 19.254


## Page Number: 468 Example 9.8¶

In [29]:

#Given
e=1.6e-19
Nd=1.1e23  #m-3
a=0.2e-6  #m
er=11.8
e0=8.854e-12
mue=800e-4  #m2/Vs
Z=50e-6
L=8.5e-6  #m
W0=1  #V
Vd=12  #V
Vg=1.5  #V

#(i) Pinch off voltage and pinch off current
Vp=(e*Nd*a*a)/(2*er*e0)
print 'Pinch off voltage: %0.3f'%Vp,'V'

Ip=(mue*e*e*Nd*Nd*Z*a*a)/(e0*er*L)
print 'Pinch off current: %0.3f'%Ip,'A'
#Answer for Ip is 55809 A but it is given as 0.00558 A

#(ii) Drain and maximum drain current
#Taking Ip=5.58mA as given in book
Ip1=0.00558  #A
x=(2/3)*(((Vd+Vg+W0)/Vp)**(3/2))
y=(2/3)*(((Vg+W0)/Vp)**(3/2))
Id=Ip1*((Vd/Vp)-x+y)
print 'Drain current: %0.3f'%-Id,'A'

#Saturation Current
Is=Ip1*((1/3)-((Vg+W0)/Vp)+((2/3)*(((Vg+W0)/Vp)**(3/2))))
print 'Drain saturation current: %0.3e'%Is, 'A'

#(iii) Cut off frequency
f=(2*mue*e*Nd*a*a)/(pi*er*e0*L*L)
print 'Cutt off freqency: %0.3f'%(f/10**9),'GHz'

Pinch off voltage: 3.369 V
Pinch off current: 55809.081 A
Drain current: 0.011 A
Drain saturation current: 9.728e-05 A
Cutt off freqency: 4.750 GHz


## Page Number: 469 Example 9.9¶

In [9]:

#Given
e=1.6e-19
Nd=8e23  #m-3
a=0.12e-6  #m
er=13.2
e0=8.854e-12

#Pinch off voltage
Vp=(e*Nd*a*a)/(2*er*e0)
print 'Pinch off voltage:' ,Vp,'V'

Pinch off voltage: 7.88549602645 V


## Page Number: 486 Example 9.10¶

In [31]:

#Given
vd=2e5  #m/s
L=10e-6  #m
Ec=3.2e5  #V/m

#Natural frequency
f=vd/L
print 'Natural frequency:' ,f/10**9,'GHz'

#Critical voltage
Vc=Ec*L
print 'Critical voltage:',Vc, 'V'

Natural frequency: 20.0 GHz
Critical voltage: 3.2 V


## Page Number: 487 Example 9.11¶

In [11]:

#Given
n=0.08
A=3e-8  #m2
n0=1e21  #m-3
e=1.6e-19
vd=1.5e5  #m/s
M=3.2
E=350e3  #V
L=12e-6  #m

#Power output
Pout=n*A*n0*e*vd*M*L*E
print 'Power output:' ,Pout*1000,'mW'

Power output: 774.144 mW


## Page Number: 487 Example 9.12¶

In [32]:

#Given
G=15.85
Rn=75  #ohm

Rl=Rn-(Rn/G)
C=Rl+(10*1J)
print 'Cavity impedance: {:.3f}'.format(C), 'ohms'

Cavity impedance: 70.268+10.000j ohms


## Page Number: 487 Example 9.13¶

In [33]:

#Given
e=1.6e-19
n1=1e16  #m-3
mu1=8000e-4  #m2/Vs
nu=1e14  #m-3
muu=180e-4  #m2/Vs

#/Conductivity
C=e*((n1*mu1)+(nu*muu))
print 'Conductivity: %0.3f'%(C*1000),'m mho'

Conductivity: 1.280 m mho


## Page Number: 488 Example 9.14¶

In [34]:

#Given
e0=8.854e-12
er=13.1
vd=2.5e5  #m/s
e=1.6e-19
mu=0.015  #m2/Vs

#Criteria
n0L=(e0*er*vd)/(e*mu)
print 'n0L should be greater than  %0.3e'%n0L,'m**-3'

n0L should be greater than  1.208e+16 m**-3


## Page Number: 488 Example 9.15¶

In [15]:

#Given
L=10e-6  #m
f=10e9  #Hz
e=1.6e-19
n0=2e20  #m3
E=3200e2  #V/m

#Current density
vd=L*f
J=n0*e*vd
print 'Current density:' ,J,'A/m sqr'

#Negative electron mobility
mu=-vd/E
print 'Negative electron mobility:' ,mu*10000,'cm sqr/Vs'

#Answer for Negative electron mobility is 3125 but it is given as 3100

Current density: 3200000.0 A/m sqr
Negative electron mobility: -3125.0 cm sqr/Vs


## Page Number: 497 Example 9.17¶

In [35]:

#Given
n=0.15
Vdc=100  #V
Idc=200e-3  #A
vd=2e5  #m/s
L=6e-6  #m

#(i) Maximum CW output power
Pdc=Vdc*Idc
Pout=n*Pdc
print 'Maximum CW power output:' ,Pout,'W'

#(ii) Resonant frequency
f=vd/(2*L)
print 'Resonant frequency:  %0.3f'%(f/10**9),'GHz'

Maximum CW power output: 3.0 W
Resonant frequency:  16.667 GHz


## Page Number: 497 Example 9.18¶

In [36]:

#Given
n=0.1
Vdc=100  #V
Idc=100e-3  #A
vd=2e5  #m/s
L=5e-6  #m
V0=90  #V
k=3

#(i) Maximum CW output power
Pdc=Vdc*Idc
Pout=n*Pdc
print 'Maximum CW power output:' ,Pout,'W'

#(ii) Resonant frequency
f=vd/(2*L)
print 'Resonant frequency:' ,f,'Hz'

#(iii)Transit time
T=L/vd
print 'Transit time:' ,T,'s'

#(iv) Avalanche multiplication factor
M=1/(1-((Vdc/V0)**k))
print 'Avalanche multiplication factor:  %0.3f'%-M

Maximum CW power output: 1.0 W
Resonant frequency: 20000000000.0 Hz
Transit time: 2.5e-11 s
Avalanche multiplication factor:  2.690


## Page Number: 498 Example 9.19¶

In [18]:

#Given
n=0.1
Vdc=100  #V
Idc=0.9  #A
t=0.01e-9  #s
f=16e9  #Hz

#(i)Power output
Pdc=Vdc*Idc
Pout=n*Pdc
print 'Power output:' ,Pout,'W'

#(ii)Duty cycle
D=(t/2)+(1/(2*f))
print 'Duty cycle:',D, 's'

Power output: 9.0 W
Duty cycle: 3.625e-11 s


## Page Number: 498 Example 9.20¶

In [38]:

#Given
Cj=0.5e-12  #F
Lp=0.5e-9  #H
Irf=0.65  #A
Rl=2  #ohms
Vbd=80  #V
Idc=0.08  #A

#Resonant frequency
f=1/(2*pi*sqrt(Cj*Lp))
print 'Resonant frequency:  %0.3f'%f,'Hz'

#Efficiency
Pout=(Irf*Irf*Rl)/2
Pin=Vbd*Idc
n=(Pout*100)/Pin
print 'Efficiency:  %0.3f'%n, '%'

Resonant frequency:  10065842420.897 Hz
Efficiency:  6.602 %


## Page Number: 501 Example 9.21¶

In [20]:

#Given
J=25e7  #A/m
Na=2.5e21  #m3
e=1.6e-19

#Avlance zone velocity
vz=J/(Na*e)
print 'Avlanche zone velocity:' ,vz,'m/s'

Avlanche zone velocity: 625000.0 m/s


## Page Number: 503 Example 9.22¶

In [39]:

#Given
e=1.6e-19
N=4e21  #m
L=10e-6  #m
e0=8.854e-12
er=11

#Breakdown voltage
Vbd=(e*N*L*L)/(e0*er)
print 'Breakdown voltage:' ,round(Vbd),'V'

#Breakdown electric field
E=Vbd/L
print 'Breakdown electric field: %0.3f'%E, 'V/m'

Breakdown voltage: 657.0 V
Breakdown electric field: 65712466.887 V/m


## Page Number: 515 Example 9.23¶

In [41]:

#Given
lam=8000e-10  #m
a=0.5e-2  #m
D=4e8  #m

t=(1.22*lam)/a

A=pi*((D*t)**2)

#Answer for A is given as 193 m sqr but it is 1.915e10 m sqr

Angular spread: 0.0001952 rad


## Page Number: 515 Example 9.24¶

In [42]:

#Given
E=10  #W
T=1e-9  #s
c=3e8  #m/s
lam=650e-9  #m

#Pulse Power
P=E/T
print 'Pulse Power:' ,P,'W'

#Q value
Q=(c*T)/lam
print 'Q value: %0.3f'%Q

Pulse Power: 10000000000.0 W
Q value: 461538.462


## Page Number: 515 Example 9.25¶

In [43]:

#Given
h=6.626e-34
c=3e8  #m/s
e=1.6e-19
Eg=1.85  #eV

#Wavelenght emitted
lam=(h*c)/(Eg*e)
lamarm=lam*1e10
print 'Wavelenght emitted:' ,round(lamarm),'A'

Wavelenght emitted: 6716.0 A