Chapter 5:Microwave Tubes

Example 1,Page No:226

In [4]:
import math

# Variable Declaration
F     =  100*10**9;   #reflex klystron operating frequency
n     =  3;         #integer corresponding to mode

#Calculations
T_c   =  (n+(3/float(4)))   #transit time in cycles
T     =  T_c/float(F);      #transit time in seconds

# Result
print'Transit Time of the electron in the repeller space is %3.1f ps'%(T/float(10**-12));

Transit Time of the electron in the repeller space is 37.5 ps

Example 2,Page No:227

In [5]:
import math

# Variable Declaration
F     =  2*10**9;#reflex klystron operating frequency
Vr    =  2000;#Repeller voltage
Va    =  500;#Accelarating voltage
n     =  1;#integer corresponding to mode
e     =  1.6*10**-19;#charge of electron
m     =  9.1*10**-31;#mass of electron in kg
s     =  2*10**-2;#space b/w exit of gap and repeller electrode
dVr1  = 2;    #(change in Vr in percentage

#Calculations
dVr   = dVr1*Vr/100;     #conversion from percentage to decimal
#dVr/df = ((2*math.pi*s)/((2*math.pi*n)-pi/2))*sqrt(8*m*Va/e));
#let df = dVr/((2*math.pi*s)/((2*math.pi*n)-pi/2))*sqrt(8*m*Va/e));

df       =  (dVr)/((2*math.pi*s)/((2*math.pi*n)-(math.pi/2))*math.sqrt(8*m*Va/e)); #change in freq as a fun of repeller voltage


# Result
print'Change in frequency is %3.0f MHz'%(df/float(10**6));

Change in frequency is  10 MHz

Example 3,Page No:228

In [1]:
import math

# Variable Declaration
# let l   = dVr/Vr ; f  = df/f ; Vr/f  = R
l     = 5;#percentage change in repeller voltage
f     = 1;#percentage change in operating frequency
R     = 1;#ratio of repeller voltage to operating frequency
NR    = 1.5;#new ratio of repeller voltage to operating frequency in volts/MHz
e     =  1.6*10**-19;#charge of electron
m     =  9.1*10**-31;#mass of electron in kg

# Calculations

#dVr/df = ((2*math.pi*s)/((2*math.pi*n)-pi/2))*math.sqrt(8*m*Va/e));
#((df/f)/(dVr/Vr)) = (Vr/f)*((2*math.pi*n)-pi/2)/(2*math.pi*s)*math.sqrt(e/(8*m*Va));
#((df/f)/(dVr/Vr)) = K*(Vr/f);
#where K = (((2*math.pi*n)-math.pi/2)/float((2*math.pi*s))*math.sqrt(e/float((8*m*Va)))
K    = (f/float(l))*(1/float(R));
PCF  = NR*K*l; #percentage change in frequency when new ratio (Vr/f)=1.5;

# Result
print'Percentage Change in frequency is %3.2f percent'%PCF;

Percentage Change in frequency is 1.50 percent

Example 4,Page No:228

In [13]:
import math

# Variable Declaration
Va    = 40*10**3;      # Anode voltage of cross field amplifier
Ia    = 15;            # Anode current in Amp
Pin   = 40*10**3;      # input power in watts
G     = 10;            # gain in dB
n     = float(40)/100;        # overall efficiency converted from percentage to decimal


# Calculations
Gain  = (1+(float(Pgen)/Pin))
Pgen  = (G-1)*Pin      # Generated power
ne    = (Pgen/float(Va*Ia)) # electronic efficiency 
nc    = n/(ne)         # circuit efficiency 
Pout  = Pin+(Pgen*nc)  # output power

# Result
print 'Electronic Efficiency is %3.2f' %ne
print 'Output power is %g KW' %(Pout/float(1000));

Electronic Efficiency is 0.60
Output power is 280 KW

Example 5,Page No:229

In [14]:
import math

# Variable Declaration
F     =  1*10**9;  #two cavity klystron operating frequency
Va    =  2500;     #Accelarating voltage in volts
e     =  1.6*10**-19;  #charge of electron
m     =  9.1*10**-31;   #mass of electron in kg
s     =  0.1*10**-2;    #input cavity space

#Calculations

u     = math.sqrt((2*e*Va)/m);   #velocity at which electron beam enters the gap
T     = s/u ;  #Time spent in the gap
f     = T*F;   #number of cycles

# result
print'Number of cycles that elase during transit of beam through input gap is %3.3f cycle'%f;

Number of cycles that elase during transit of beam through input gap is 0.034 cycle

Example 6,Page No:230

In [15]:
import math
# Given Data
N     = 8;   #no. of resonators

#Calculations
print'ϕ  = (2*π*n)/N \n';  #phase difference
print'ϕ   = (n*π)/4\n';   #phase difference
K   = N/2;                     #useful no. of nodes
# Most dominant mode is the one for which phase differnce b/w adjacent resonators is π radians
# Therefore (n*π)/4 = π
n = 4


# Output
print'Number of possible modes of Resonance is %d\n'%N;
print'Number of useful modes of Resonance is %d\n'%K;
print'value of integer n for the most dominant mode is %d'%n;

ϕ  = (2*π*n)/N 

ϕ   = (n*π)/4

Number of possible modes of Resonance is 8

Number of useful modes of Resonance is 4

value of integer n for the most dominant mode is 4

Example 7,Page No:230

In [16]:
import math

# Variable Declaration
Va    =  1200;  #Anode potential
F     =  10*10**9;  #Operating frequency in Hz 
S     =  5*10**-2;  #spacing b/w 2 cavities
GS    = 1*10**-3;   #gap spacing in either cavity
e     =  1.6*10**-19;  #charge of electron
m     =  9.1*10**-31;  #mass of electron in kg

# Calculations
# Condition of maximum output is (V1/Vo)max  =  (3.68)/((2*pi*n)-(pi/2);
# (2*pi*n)-(pi/2) = Transit angle b/w two cavities
# V1  = Peak amplitude of RF i/p
# Vo  = accelarating potential

Vo    = math.sqrt(2*e*Va/m);  #velocity of the electrons 
T     = S/Vo;            #Transit time b/w the cavities
TA    = 2*math.pi*F*T;      #transit angle in radians
V1    = (3.68*Va)/TA;

# Result
print'Required Peak Amplitude of i/p RF signal is %3.2f volts'%V1;

Required Peak Amplitude of i/p RF signal is 28.88 volts

Example 8,Page No:231

In [17]:
import math
# Given Data
R       = 10;            # circumference to pitch ratio
e       = 1.6*10**-19;   # charge of electron
m       = 9.1*10**-31;   # mass of electron in Kg
c       = 3*10**8;       # vel. of EM waves in m/s

# Calculations
Vp      = c/float(R);           # axial phase velocity = free space vel*(pitch/circumference) 
Va      = (Vp**2 * m)/float((2*e));

# Output
print'Anode Voltage = %3.2f kV' %(Va/float(1000));
print'In practice,the electron beam velocity is kept slightly greater than the axial phase velocity of RF signal';

Anode Voltage = 2.56 kV
In practice,the electron beam velocity is kept slightly greater than the axial phase velocity of RF signal