Ch-7 : Cross Field Microwave tube M Type

Page Number: 369 Example 7.1

In [4]:
from __future__ import division 
from math import pi
#Given
f=10e9  #Hz
C=2.5e-12  #F
Gr=2e-4  #mho
Ge=0.025e-3  #mho
Ploss=18.5e3  #W
V0=5.5e3  #V
I0=4.5  #A

w=2*pi*f 

#(i) Unloaded Q
Qun=(w*C)/Gr 
print 'Unloaded quality factor: %0.3f'%Qun

#External Q
Qe=(w*C)/Ge 
print 'External quality factor: %0.3f'%Qe

#(ii) Circuit effciency
n=1/(1+(Qe/Qun)) 
print 'Circuit effciency: %0.3f'%(n*100), '%'

#Electronic effciency
ne=1-(Ploss/(V0*I0)) 
print 'Electronic effciency: %0.3f'%(ne*100), '%'

#Answer for Qe is given as 6285.6 but it should be 6283.1 

Unloaded quality factor: 785.398
External quality factor: 6283.185
Circuit effciency: 11.111 %
Electronic effciency: 25.253 %

Page Number: 370 Example 7.2

In [6]:
from math import sqrt 
#Given
V0=25e3  #V
ebym=1.76e11 
B0=0.0336  #T
a=5e-2  #m
b=10e-2  #m

#(i) Cut off voltage
x=(b/((b*b)-(a*a)))**2 
V=(ebym*B0*B0)/(8*x) 
print 'Cut off voltage: %0.3f'%(V/1000),'KV'

#(ii) Cut off magnetic field
y=((8*V0*x)/ebym) 
B=sqrt(y) 
print 'Cut off magnetic field: %0.3f'%(B*1000),'mT'

Cut off voltage: 139.709 KV
Cut off magnetic field: 14.213 mT

Page Number: 371 Example 7.3

In [8]:
 
#Given
Pout=250e3  #W
V0=25e3  #V
I0=25  #A
ebym=1.76e11 
B0=0.035  #T
a=4e-2  #m
b=8e-2  #m


#(i) Efficiency
n=Pout/(V0*I0) 
print 'Efficiency:' ,n*100,'%'

#(ii) Cyclotron frequency
f=(ebym*B0)/(2*pi) 
print 'Cyclotron frequency: %0.3f'%(f/10**9),'Ghz'

#(iii) Cut off magnetic field
x=(b/((b*b)-(a*a)))**2 
y=((8*V0*x)/ebym) 
B=sqrt(y) 
print 'Cut off magnetic field: %0.3f'%(B*1000),'mT'

#(iv) Cut off voltage
V=(ebym*B0*B0)/(8*x) 
print 'Cut off voltage:' ,round(V/1000),'KV'

#Answer for Cyclotron frequency is is given as 9.8GHz but it should be 0.98 GHz as value of B0=0.035 not 0.35 as taken in part 2

Efficiency: 40.0 %
Cyclotron frequency: 0.980 Ghz
Cut off magnetic field: 17.767 mT
Cut off voltage: 97.0 KV

Page Number: 372 Example 7.4

In [9]:
 
#Given
Gr=3e-4  #mho
Ge=3e-5  #mho
Ploss=200e3  #W
V0=22e3  #V
I0=28  #A

#(i) Circuit effciency
n=1/(1+(Gr/Ge)) 
print 'Circuit effciency: %0.3f'%(n*100), '%'

#(ii) Electronic effciency
ne=1-(Ploss/(V0*I0)) 
print 'Electronic effciency: %0.3f'%(ne*100),'%'

Circuit effciency: 9.091 %
Electronic effciency: 67.532 %

Page Number: 372 Example 7.5

In [11]:
 
#Given
f=9e9  #Hz
C=2.5e-12  #F
Gr=2e-4  #mho
Ge=2.5e-5  #mho
Ploss=18.5e3  #W
V0=5.5e3  #V
I0=4.5  #A

#(i) Angular resonant frequency
w=2*pi*f 
print 'Angular resonant frequency: %0.3f'%w, 'rad/s'

#(ii) Unloaded Q
Qun=round((w*C)/Gr) 
print 'Unloaded quality factor:' ,Qun

#(iii) Loaded Q
Ql=round((w*C)/(Gr+Ge)) 
print 'Loaded quality factor:' ,Ql

#(iv) External Q
Qe=(w*C)/Ge 
print 'External quality factor: %0.3f'%Qe

#(v) Circuit effciency
n=1/(1+(Qe/Qun)) 
print 'Circuit effciency: %0.3f'%(n*100),'%'

#(vi) Electronic effciency
ne=1-(Ploss/(V0*I0)) 
print 'Electronic effciency: %0.3f'%(ne*100), '%'

#Answer for external Q is given as 56.57 but it should be 5654.8

Angular resonant frequency: 56548667764.616 rad/s
Unloaded quality factor: 707.0
Loaded quality factor: 628.0
External quality factor: 5654.867
Circuit effciency: 11.113 %
Electronic effciency: 25.253 %

Page Number: 373 Example 7.6

In [14]:
 
#Given
f=4e9  #Hz
V0=25e3  #V
I0=3  #A
B0=0.3  #T
D=0.8 
Z0=50  #ohm
ebym=1.76e11 

#(i) Electron beam phase constant
be=(2*pi*f)/sqrt(2*ebym*V0) 
print 'Electron beam phase constant: %0.3f'%be,'rad/s'

#(ii) Gain Parameter
C=((I0*Z0)/(4*V0))**(1/3) 
print 'Gain Parameter: %0.3f'%C

#(iii) Length for oscillation condition
N=1.25/D 
l=(2*pi*N)/be 
print 'Length for oscillation condition: %0.3f'%l,'m'

Electron beam phase constant: 267.916 rad/s
Gain Parameter: 0.114
Length for oscillation condition: 0.037 m

Page Number: 374 Example 7.7

In [15]:
 
#Given
N=20 
t=0.2e-6  #s
DC=0.001  #Duty cycle

#(i) Agile excursion
A=N/t 
print 'Agile excursion:' ,A/10**6,'MHz'

#(ii) Signal frequency
f=DC/t 
print 'Signal frequency:',f/1000, 'Khz'

#(iii) Agile rate
R=f/(2*N) 
print 'Agile Rate:',R, 'Hz'

Agile excursion: 100.0 MHz
Signal frequency: 5.0 Khz
Agile Rate: 125.0 Hz

Page Number: 375 Example 7.8

In [16]:
from math import log10 
#Given
V0=1.8e3  #V
I0=1.3  #A
Pin=70  #W
n=0.22 

#(i) Power generated
Pgen=n*I0*V0 
print 'Power generated:' ,Pgen,'W'

#(ii) Total RF power generated
Pt=Pin+Pgen 
print 'Total RF power generated:' ,Pt,'W'

#(iii) Power gain
G=Pt/Pin 
Gdb=10*log10(G) 
print 'Power Gain: %0.3f'%Gdb,'dB'

Power generated: 514.8 W
Total RF power generated: 584.8 W
Power Gain: 9.219 dB

Page Number: 375 Example 7.9

In [18]:
 
#Given
V0=10e3  #V
I0=2  #A
b=4e-2  #m
a=3e-2  #m
B0=0.01  #Wb/m2
ebym=1.759e11 

#Cut off voltage
x=1-((b*b)/(a*a)) 
V=(ebym*(B0**2)*(a**2)*(x**2))/8 
KV=V/1000  #Kilovolts
print 'Cut off voltage: %0.3f'%KV, 'KV'

#Magnetic flux density
y=-sqrt((8*V0)/ebym) 
B=y/(a*x) 
print 'Magnetic flux density: %0.3f'%B, 'T'

Cut off voltage: 1.197 KV
Magnetic flux density: 0.029 T

Page Number: 376 Example 7.10

In [20]:
 
#Given
V0=10e3  #V
I0=2  #A
b=4e-2  #m
a=3e-2  #m
B0=0.01  #Wb/m2
ebym=1.759e11 

#Cut off voltage
x=1-((b*b)/(a*a)) 
V=(ebym*(B0**2)*(a**2)*(x**2))/8 
print 'Cut off voltage: %0.3f'%(V/1000), 'KV'

#Magnetic flux density
y=-sqrt((8*V0)/ebym) 
B=y/(a*x) 
print 'Magnetic flux density: %0.3f'%B, 'T'

Cut off voltage: 1.197 KV
Magnetic flux density: 0.029 T

Page Number: 376 Example 7.11

In [21]:
 
#Given
e=1.6e-19  #J
B0=0.01  #Wb/m2
d=6e-2  #m
V0=20e3  #V
ebym=1.759e11 

#(i) Hull cut off voltage
Voc=(B0*B0*d*d*ebym)/2 
print 'Hull cut off voltage:' ,Voc/1000,'KV'

#(ii) Hull magnetic field
Boc=sqrt((2*V0)/ebym)/d 
print 'Hull magnetic field: %0.3f'%(Boc*1000),'mT'

Hull cut off voltage: 31.662 KV
Hull magnetic field: 7.948 mT

Page Number: 377 Example 7.12

In [23]:
 
#Given
V0=10e3  #V
V01=5e3  #V
I0=2  #A
b=3e-2  #m
a=2e-2  #m
B0=0.01  #Wb/m2
ebym=1.759e11 

#Cut off voltage
x=1-((b*b)/(a*a)) 
V=(ebym*(B0**2)*(a**2)*(x**2))/8 
KV=V/1000  #Kilovolts
print 'Cut off voltage: %0.3f'%KV,'KV'

#Magnetic flux density
y=-sqrt((8*V01)/ebym) 
B=y/(a*x) 
print 'Magnetic flux density: %0.3f'%B, 'Wb/m2'

#Answer in book is wrong for Magnetic flux density as a*a ,where a=2, is taken as 5, which should be 4

Cut off voltage: 1.374 KV
Magnetic flux density: 0.019 Wb/m2

Page Number: 377 Example 7.13

In [26]:
#Given
N=15 
t=0.3e-6  #s
DC=0.0011  #Duty cycle

#(i) Agile excursion
A=N/t 
print 'Agile excursion:',A/10**6, 'MHz'

#(ii) Pulse to pulse frequency seperation
fp=1/t 
print 'Pulse to pulse frequency seperation: %0.3f'%(fp/10**6),'Mhz'

#(iii) Signal frequency
f=DC/t 
print 'Signal frequency: %0.3f'%(f/1000), 'Khz'

#(iv) Agile rate
Tp=N/f 
R=1/(2*Tp) 
print 'Agile Rate: %0.3f'%R,'ps'

Agile excursion: 50.0 MHz
Pulse to pulse frequency seperation: 3.333 Mhz
Signal frequency: 3.667 Khz
Agile Rate: 122.222 ps