## 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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