Thursday, August 10, 2017

Casio fx-3650p and HP 21S: Minimum Loss Matching

Casio fx-3650p and HP 21S: Minimum Loss Matching



This program takes the incoming impedances Z0 (from left) and Z1 (from right), and determines the resistance R1 and R2, with the corresponding minimum loss.  The program assumes that Z0 and Z1 are both positive and Z0 ≥ Z1. 

Formulas Used:

R1 = Z0 * √(1 – Z1/Z0)
R2 = Z1 / √(1 – Z1/Z0)
Minimum loss = 20 * log (√(Z1/Z0) + √(Z1/Z0 -1))

Casio fx-3650P

Input:  X = Z0, Y = Z1
Program (49 steps):

? → X : ? → Y : Y ÷ X → M :
X √ ( 1 – M → A
Y √ ( 1 – M → B
20 log ( √ M ^-1 + √ ( M ^-1 – 1 → C

HP 21S

Input:  Z0 gets stored in register 0, Z1 gets stored in register 1

Program (44 steps):

Step
Code
Key
Notes
01
61, 41, C
LBL C
Start the program
02
22, 1
RCL 1
Z1
03
45
÷

04
22, 0
RCL 0
Z0
05
74
=

06
21, 4
STO 4

07
33
(

08
1
1

09
65
-

10
22, 4
RCL 4

11
34
)

12
11

13
21, 5
STO 5

14
55
*

15
22, 0
RCL 0

16
74
=

17
21, 2
STO 2

18
26
R/S
Display R1
19
22, 1
RCL 1

20
45
÷

21
22, 5
RCL 5

22
74
=

23
21, 3
RCL 3

24
26
R/S
Display R2
25
33
(

26
22, 4
RCL 4

27
15
1/x

28
11

29
75
+

30
33
(

31
22, 4
RCL 4

32
15
1/x

33
65
-

34
1
1

35
34
)

36
11

37
34
)

38
51, 13
LOG

39
55
*

40
2
2

41
0
0

42
74
=

43
21, 5
STO 5
Display minimum loss (Z)
44
61, 26
RTN



Example:

Input:  Z0 = 50, Z1 = 45
Results: R1 = 15.8113883008, R2 = 142.302494708, Min Loss = 2.84419586692

Source:  Casio Scientific Formula 128 fx-1000F/fx-5000F owner’s manual, 1987

Eddie


This blog is property of Edward Shore, 2017

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