TI-84 Plus CE: Rectangular Waveguide - Cutoff Frequency
Introduction
The program WAVEGDE computes the cutoff frequency of a rectangular guide. The waveguide has energy propagating in the TE_m,n mode with dimensions a x b (in meters) with relative permittivity E. The cutoff frequencies is calculated as:
V = speed of light / √E
where speed of light = 299,792,458 m/s
Cutoff frequency (in Hz):
f_c = V/2 * √( (m/a)^2 + (n/b)^2 )
The second part of the calculation will depend on the target frequency, either the attenuation or phase and group velocities will be calculated:
If f < f_c, attenuation (in nerpers) is calculated:
attenuation = (2 π f_c)/V * √( 1 - (f/f_c)^2 )
If f > f_c, the phase and group velocities are calculated:
phase velocity = V / √( 1 - (f_c/f)^2 )
group velocity = V * √(1 - (f_c/f)^2 )
TI-84 Plus CE Program WAVEGDE
"EWS 2019-07-14"
Disp "RECTANGULAR WAVEGUIDE"
Input "WIDE (M): ",A
Input "NARROW (M): ",B
Input "PERMITTIVITY: ",E
Disp "HALF-WAVE VARIATIONS", "T-M,N"
Input "M: ",M
Input "N: ",N
Input "FREQUENCY (HZ):",F
299792458/√(E)→V
V/2*√((M/A)²+(N/B)²)→C
Disp "CUTOFF FREQ: (HZ)",C
Pause
If F
Then
(2πC)/V*√(1-(F/C)²)→U
Disp "ATTENUATION:",U,"NEPERS"
Else
V/√(1-(C/F)²)→P
V*√(1-(C/F)²)→G
Disp "PHASE VELOCITY: M/S",P
Disp "GROUP VELOCITY: M/S",G
End
Examples
Example 1:
A rectangular waveguide has the dimensions 2.7 cm x 1.09 cm with permittivity of 1. (a = 2.7/100, b = 1.09/100, E = 1). The waves propagate in the TE_2,1 mode (m = 2, n = 1). The target frequency is 10 GHZ (10E9 Hz).
Results:
Cutoff Frequency = 1.767490017E10 Hz
Attenuation = 305.4488993 nepers
Example 2:
Same as Example 1, but set target frequency as 20 GHZ.
Results:
Cutoff Frequency = 1.767490017E10 Hz
Phase Velocity = 640,624,938.6 m/s
Group Velocity = 140,293,504.8 m/s
Source:
"Rectangular Waveguide Calculations" HP-65 E.E. Pac 2 Hewlett Packard Cupertino, CA 1977
Eddie
All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
Introduction
The program WAVEGDE computes the cutoff frequency of a rectangular guide. The waveguide has energy propagating in the TE_m,n mode with dimensions a x b (in meters) with relative permittivity E. The cutoff frequencies is calculated as:
V = speed of light / √E
where speed of light = 299,792,458 m/s
Cutoff frequency (in Hz):
f_c = V/2 * √( (m/a)^2 + (n/b)^2 )
The second part of the calculation will depend on the target frequency, either the attenuation or phase and group velocities will be calculated:
If f < f_c, attenuation (in nerpers) is calculated:
attenuation = (2 π f_c)/V * √( 1 - (f/f_c)^2 )
If f > f_c, the phase and group velocities are calculated:
phase velocity = V / √( 1 - (f_c/f)^2 )
group velocity = V * √(1 - (f_c/f)^2 )
TI-84 Plus CE Program WAVEGDE
"EWS 2019-07-14"
Disp "RECTANGULAR WAVEGUIDE"
Input "WIDE (M): ",A
Input "NARROW (M): ",B
Input "PERMITTIVITY: ",E
Disp "HALF-WAVE VARIATIONS", "T-M,N"
Input "M: ",M
Input "N: ",N
Input "FREQUENCY (HZ):",F
299792458/√(E)→V
V/2*√((M/A)²+(N/B)²)→C
Disp "CUTOFF FREQ: (HZ)",C
Pause
If F
Then
(2πC)/V*√(1-(F/C)²)→U
Disp "ATTENUATION:",U,"NEPERS"
Else
V/√(1-(C/F)²)→P
V*√(1-(C/F)²)→G
Disp "PHASE VELOCITY: M/S",P
Disp "GROUP VELOCITY: M/S",G
End
Examples
Example 1:
A rectangular waveguide has the dimensions 2.7 cm x 1.09 cm with permittivity of 1. (a = 2.7/100, b = 1.09/100, E = 1). The waves propagate in the TE_2,1 mode (m = 2, n = 1). The target frequency is 10 GHZ (10E9 Hz).
Results:
Cutoff Frequency = 1.767490017E10 Hz
Attenuation = 305.4488993 nepers
Example 2:
Same as Example 1, but set target frequency as 20 GHZ.
Results:
Cutoff Frequency = 1.767490017E10 Hz
Phase Velocity = 640,624,938.6 m/s
Group Velocity = 140,293,504.8 m/s
Source:
"Rectangular Waveguide Calculations" HP-65 E.E. Pac 2 Hewlett Packard Cupertino, CA 1977
Eddie
All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.