TI-84 Plus CE: Beam Pattern for Uniform Array

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

All original content copyright, © 2011-2026. 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.

HP 71B Programs: September 2025

HP 71B Programs: September 2025

One of my favorite calculators/pocket calculators of all time is the HP 71B.

ADDMOD: (a + b) mod n = a mod n + b mod n

10 DESTROY A, B, N

20 DISP “(A+B) MOD N” @ WAIT .5

30 INPUT “A? “; A

40 INPUT “B? “; B

50 INPUT “C? “; C

60 S = MOD(A, N) + MOD(B, N)

70 S = MOD(S, N)

80 DISP “SUM = “; S

MULTMOD: (a * b) mod n = a mod n * b mod n

10 DESTROY A, B, N

20 DISP “(A*B) MOD N” @ WAIT .5

30 INPUT “A? “; A

40 INPUT “B? “; B

50 INPUT “N? “; N

60 P = MOD(A, N) * MOD(B, N)

70 P = MOD(P, N)

80 DISP “PRODUCT = “; P

Examples:

A	630	48	15
B	320	99	47
N	700	15	7
SUM:	250	12	6
PRODUCT:	0	12	5

GABLE: Area of a Gable Roof

10 DESTROY P, S, L

20 DEGREES

30 INPUT “PITCH (IN.)? “; P

40 INPUT “SPAN (FT.)? “; S

50 INPUT “LENGTH (FT.)? “; L

60 A = 2 * S * L / COS(ATAN(P/12))

70 DISP “AREA = “; A; “ FT^2”

Input: Pitch (P)	6”	3”	4”
Input: Span (S)	110” (110/12 ft)	5’ 8” (5 + 8/12 ft)	15 ft
Input: Length (L)	100” (100/12 ft)	10’	10 ft
Output: Area (A)	170.81074828 ft^2	116.821326059 ft^2	316.227766017 ft^2

INTENSE: Light Intensity of a Spherical or a Cylindrical Light Source

intensity = power / surface area

intensity (W/m^2), power (W), surface area (m^2)

Surface area: sphere = 4 * π * r^2, cylinder = 2 * π * (r * h + r^2)

10 DESTROY P, K$, R, H

20 DISP “INTENSITY OF LIGHT!” @ WAIT .5

30 INPUT “POWER (W)? “; P

40 DISP “1. SPHERE 2. CYLINDER”

50 DELAY 0,0

60 K$ = KEY$

70 IF K$ = “1” OR K$ = “S” THEN GOTO 100

80 IF K$ = “2” OR K$ = “C” THEN GOTO 200

90 GOTO 40

100 INPUT “RADIUS (M)? “; R

110 A = 4 * PI * R^2

120 GOTO 300

200 INPUT “RADIUS (M)? “; R

210 INPUT “HEIGHT (M)? “; H

220 A = 2 * PI * (R * H + R^2)

230 GOTO 300

300 I = P / A

310 DISP I; “W/M^2”

Examples:

Sphere: r = 4 m, Power = 60 W: Intensity = .298415518297 W/M^2

Cylinder: r = 1.25 m, h = 0.75 m, Power = 70 W; Intensity = 4.45633840656 W/M^2

SIMPLE: Simple Interest – Banker’s Rule

interest = amount * rate% / 100 * #days / 360

final = principal + interest (final, maturity value)

10 DESTROY P, R, I, M

20 DISP “SIMPLE INTEREST” @ WAIT .5

30 INPUT “AMT? “; P

40 INPUT “RATE%? “; R

50 INPUT “# DAYS? “; D

60 I = P * R * D / 360 / 100

70 M = P + I

80 IMAGE K, M10D.2D

90 DISP USING 80; “INT.=”, I @ PAUSE

100 DISP USING 80; “FINAL=”, M

Notes:

* When the HP 71B is in pause, press [ f ] [ + ] to continue (CONT).

* To stop execution, press [ ON ] (ATTN).

* IMAGE K, M10D.2D: display “prompt string”, number rounded to 2 decimal places. The number is right-justified, make the prompt string 7 characters or less to fit both the string and number on the screen.

Examples

Input: Amount	1500	2000	2800
Input: Rate %	4.00%	8.00%	6.65%
Input: # Days	180	90	60
Output: Interest	30	40	31.03
Output: Final	1530	2040	2831.03

AIRSOUND: Speed of Sound in Air

S = 331.5 + .606 * T

S = speed of sound in air, m/s

T = temperature in °C

10 DESTROY K$, S, T

20 DISP “SPEED OF SOUND IN AIR” @ WAIT .5

30 DISP “SOLVE FOR…” @ WAIT .5

40 DISP “1. SPEED 2. TEMP”

60 K$ = KEY$

70 IF K$=”1” OR K$=”S” THEN GOTO 100

80 IF K$=”2” OR K$=”T” THEN GOTO 200

90 GOTO 40

100 INPUT “TEMP (°C)? “; T

110 S = 331.5 + .606 * T

120 DISP “S=”; S; “ M/S”

130 END

200 INPUT “SPEED (M/S)? “; S

210 T = (S- 331.5) / .606

220 DISP “T=”; T ; “°C”

230 END

Examples:

Input: T = 74 °F = (32 + 1/3) °C Output: S = 345.64 m/s	Input: S = 350 m/s Output: T = 30.5280528053 °C
Input: T = -8.5 °C Output: S = 326.349 m/s	Input: S = 382 m/s Output: T = 83.3333333333 °C

Eddie

All original content copyright, © 2011-2025. 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.

The author does not use AI engines and never will.