Design of a vertical broadcasting tower
Description
For the design of a vertical broadcasting tower, radio engineer Ann Tenor wants to find the angle from the tower at which the relative field intensity is most negative. The relative intensity created by the tower is given by:
cos(2πhθ) - cos(2πh)
E = ————————————————————
(1 - cos(2πh)sinθ
Where E is the relative field intensity, h is the antenna height in wavelengths, and θ is the angle from vertical in radians. The height is 0.6 wavelengths for her design. The desired angle is one at which the derivative of the intensity with respect to θ is zero.
To save program memory space and execution time, store the following constants in registers and recall them as needed:
r0 = 2πh and is stored in register R0 ,
r1 = cos(2πh) and is stored in register R1 ,
r2 = 1/(1 − cos(2πh)) and is stored in register R2,
The derivative of the intensity E with respect to the angle θ is given by
dE cos(r0 cosθ)-r1
—— = r2[r0 sin(r0 cosθ) - ———————————————]
dθ sinθ tanθ
In Radians mode, calculate and store the three constants.
g RAD
2 g π ×
.6 × STO 0
COS STO 1
CHS 1 +
1/x STO 2
The relative field intensity is maximum at an angle of 90° (perpendicular to the tower). To find the minimum, use angles closer to zero as initial estimates, such as the radian equivalents of 10° and 60°.
10 f →RAD
60 f →RAD
f SOLVE 0
R↓ R↓
g R↑ g R↑
g →DEG
The relative field intensity is most negative at an angle of 28.0680° from vertical.
Program Resources
Labels
Name |
Description |
|
0 |
Main program |
|
Storage Registers
Name |
Description |
|
0 |
2πh |
|
1 |
cos(2πh) |
|
2 |
1/[1 − cos(2πh)] |
|
Program
Line |
Display |
Key Sequence |
|
Line |
Display |
Key Sequence |
|
000 |
|
|
|
013 |
10 |
÷ |
|
001 |
42,21, 0 |
f LBL 0 |
|
014 |
16 |
CHS |
|
002 |
24 |
COS |
|
015 |
34 |
x↔y |
|
003 |
45 0 |
RCL 0 |
|
016 |
24 |
COS |
|
004 |
20 |
× |
|
017 |
45 0 |
RCL 0 |
|
005 |
24 |
COS |
|
018 |
20 |
× |
|
006 |
45 1 |
RCL 1 |
|
019 |
23 |
SIN |
|
007 |
30 |
− |
|
020 |
45 0 |
RCL 0 |
|
008 |
34 |
x↔y |
|
021 |
20 |
× |
|
009 |
23 |
SIN |
|
022 |
40 |
+ |
|
010 |
10 |
÷ |
|
023 |
45 2 |
RCL 2 |
|
011 |
34 |
x↔y |
|
024 |
20 |
× |
|
012 |
25 |
TAN |
|
025 |
43 32 |
g RTN |
|