(42S) Smith Chart Conversions
11-23-2019, 02:37 PM
Post: #1
 Eddie W. Shore Senior Member Posts: 1,234 Joined: Dec 2013
(42S) Smith Chart Conversions
Introduction

The program SMITH brings generates a custom menu that allows the user to convert between four factors:

RL: return loss
p: reflection coefficient
s: voltage standing ratio
SWR: standing wave ratio

p = 10^-(RL/20)
s = (1 + p)(1 - p)
SWR = 20 * log s

Programs here:

HP 42S/DM42 Program: SMITH

Code:
00 { 111-Byte Prgm } 01▸LBL "SMITH" 02 "RL>p" 03 KEY 1 GTO 01 04 "p>s" 05 KEY 2 GTO 02 06 "s>SWR" 07 KEY 3 GTO 03 08 "SWR>s" 09 KEY 4 GTO 04 10 "s>p" 11 KEY 5 GTO 05 12 "p>RL" 13 KEY 6 GTO 06 14 MENU 15▸LBL 07 16 STOP 17 GTO 07 18▸LBL 01 19 +/- 20▸LBL 04 21 20 22 ÷ 23 10↑X 24 RTN 25▸LBL 02 26 STO 00 27 1 28 + 29 1 30 RCL- 00 31 ÷ 32 RTN 33▸LBL 05 34 STO 00 35 1 36 - 37 1 38 RCL+ 00 39 ÷ 40 RTN 41▸LBL 06 42 1/X 43▸LBL 03 44 LOG 45 20 46 × 47 RTN 48 .END.

Example 1

Convert SWR of 12 to RL:

[XEQ] (SMITH)
12 (SWR>s) (s>p) (p>RL)

Result: 4.45901

Conversions Between Complex Reflection Coefficient and Impedance

It is recommended that you set the calculator to Degree and Polar modes. To enter complex numbers in polar mode,

Z→R: Convert from impedance to complex reflection coefficient
Stack: Z, Z0 (characteristic impedance)

Γ = (Z/Z0 - 1) / (Z/Z0 + 1)

R→Z: Convert from complex reflection coefficient to impedance
Stack: Z0, Γ

Z = Z0 * (1 + Γ) / (1 - Γ)

HP 42S/DM42 Programs: Z→R and R→Z

Code:
00 { 19-Byte Prgm } 01▸LBL "Z→R" 02 ÷ 03 ENTER 04 ENTER 05 1 06 - 07 X<>Y 08 1 09 + 10 ÷ 11 RTN 12 .END. 00 { 20-Byte Prgm } 01▸LBL "R→Z" 02 ENTER 03 ENTER 04 1 05 + 06 X<>Y 07 1 08 - 09 +/- 10 ÷ 11 × 12 RTN 13 .END.

Example 2

In a system with the resistance of 66 Ω has the impedance of 10 ∠ 15°. What is the reflection coefficient?

(Degree and Polar Mode)
10 [ENTER] 15 [(shift)] (COMPLEX) 66
[XEQ] ( Z→R )

Result: 0.40469 ∠ -163.92848

Example 3

What is the impedance of a system with a reflection coefficient of 0.86∠50° with a resistor of 125 Ω?

(Degree and Polar Mode)
125 [ENTER] 0.86 [ENTER] 50 [(shift)] (COMPLEX)
[XEQ] ( R→Z )

Result: 246.80096 ∠ 78.82055°

Source:

Step-by-Step Solutions For Your HP Calculator: Engineering Applications (HP-32S). Hewlett Packard. Edition 1. Corvallis, OR June 1988