## Saturday, November 23, 2019

### HP 42S DM42 Smith Chart Conversions

HP 42S DM42 Smith Chart Conversions

Smith 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

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
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

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

Eddie

All original content copyright, © 2011-2019.  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.