TI-84 Plus CE: Beam Pattern for Uniform Array
Introduction
The following formula calculates an antenna’s normalized beam response in decibels given the following:
* the number of sensors of an antenna
* the wavelength of the beam pattern
* the angle incident of the wavelength from the ground, in degrees.
* the steering angle of the array, in degrees; which is measured from the zenith, starting directly upwards with the angle going downwards.
The program calculates the response in from a range of incident angles.
R(ΘI) = [ sin(180 * n * d * (sin(ΘI) – sin(ΘS) ÷ λ ] ÷ [ n * sin(180 * d * (sin(ΘI) – sin(ΘS) ÷ λ ]
If the denominator is 0, then the response is 0 dB.
Variables:
n = number of sensors
d = spacing between sensors
λ = wavelength
ΘI = incident angle
ΘS = steering angle
TI-84 Plus CE Code: BEAMPTN
ClrHome
Degree
Disp “BEAM PATTERN”, “BY STEPHEN A HERTZ”, “(HP 67 ANTENNAS)”
Input “NO. SENSORS? “, N
Input “INTERIOR SPACING? “, D
Input “WAVELENGTH? “, L
Input “STEERING Θ°? “, S
Input “STARTING ΘI? “, I
Input “NO. PTS? “, K
Input “CHG Θ°? “, J
For(Θ, I, I+K*J, J)
180 * D / L → A
sin(Θ) – sin(S) → B
N * sin(A * B) → R
If R=0
0 → R
Else
sin(N * A * B) / R → R
20 * log(abs(R)) → R
End
ClrHome
Disp “ΘI=”, Θ, “R (DB)=”, R
Pause
End
Example
Input:
n = 6
d = 36 ft
λ = 100 ft
ΘS = 0° (steering angle)
Range: ΘI = starting at 0°, 5 calculations, in increments of 5°
Results:
K = |
ΘI = |
R(ΘI) = |
0 |
0 |
0 |
1 |
5 |
-0.4983317822 |
2 |
10 |
-2.056358346 |
3 |
15 |
-4.9617921711 |
4 |
20 |
-9.809670689 |
The negative response signifies that there is a reduction of signal strength.
Source
Hertz, Stephen A. “Beam Pattern for Uniform Array” HP-67/HP-97: Users’ Library Solutions: Antennas. Hewlett Packard. Corvallis, OR. Rev. D. April 1979. pp. 24-27
Eddie
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