chapter05:Cavity Resonators¶

Example 5.1, Page number 174¶

In [1]:
#Calculate minimum distance between two plates
import math

#Variable declaration
a = 3          #radius of circular waveguide(cm)
fo = 10*10**9  #frequency for TM011 mode(Hz)
P01 = 2.405
c = 3*10**10   #velocity of proapagation(m/s)

#Calculation
d = math.sqrt((math.pi**2)/(((4*math.pi**2)/9)-((P01/a)**2)))

#Result
print "The minimum distance between two plates is",round(d,2),"cms"

The minimum distance between two plates is 1.62 cms


Example 5.2, Page number 174¶

In [2]:
#Calculate lowest resonating frequency of a circular resonator
a = 2.
b = 1.
d = 3.
#For dominant mode TE101,
m = 1.
n = 0
p = 1.

c = 3*10**10 #velocity of propagation(m/s)

#Calculation
fo = (c/2)*(((m/a)**2+(n/b)**2+(p/d)**2))**0.5

#Result
print "The lowest resonating frequency of a rectangular cavity resonator is",round((fo/1E+9)),"Ghz"

The lowest resonating frequency of a rectangular cavity resonator is 9.0 Ghz


Example 5.3, Page number 175¶

In [3]:
#Calculate resonating frequency of a circular resonator
import math

#Variable declaration
D = 12.5     #diameter of resonator(cm)
d = 5        #length of resonator(cm)
P01 = 2.405  #dominant mode TM01
c = 3*10**10 #velocity of propagation(m/s)

#For TM012 mode,
m = 1
n = 0
p = 2

#Calculation
a = D/2
fo = (c/(2*math.pi))*((P01/a)**2+((p*math.pi)/d)**2)**0.5

#Result
print "The resonanat frequency of a circular resonator is",round((fo/1E+9),2),"GHz"

The resonanat frequency of a circular resonator is 6.27 GHz


Example 5.4, Page number 175¶

In [4]:
#Calculate lowest resonating frequency of a circular resonator
a = 3.
b = 2.
d = 4.
#For dominant mode TE101,
m = 1.
n = 0
p = 1.

c = 3*10**10 #velocity of propagation(m/s)

#Calculation
fo = (c/2)*(((m/a)**2+(n/b)**2+(p/d)**2))**0.5

#Result
print "The lowest resonating frequency of a circular resonator is",round((fo/1E+9),2),"Ghz"

The lowest resonating frequency of a circular resonator is 6.25 Ghz