HP 20S: Triac Waveforms

HP 20S:   Triac Waveforms

Introduction

The following calculations involve triode AC switches, better known as triacs.  A triac is generally used as a bidirectional power switch device.  James J. Davidson, the original author of the HP 25 programs states "these programs are for use with mean-absolute (also called average) responding voltmeters which are calibrated to read the rms value of a sine wave"  (Davidson, 38).

The variables used in Davidson's programs are: 

Vs = root mean square from source

VLMS = root mean square voltage

VLMA = average load voltage

θ = firing angle of triac in degrees (Davidson, 38)

These programs have been translated to for the use of the HP 20S calculator.  

HP 20S Program:  Triac Waveforms

(59 steps)

Given:  Vs and θ°, calculate VLMA and VLMS

Store Vs in R0

Store θ° in R1 (degrees)

Press [ XEQ ] [ A ]

VLMA is displayed

Press [ R/S ], VLMA is displayed

Given:  Vs and VLMA, calculate θ° and VLMS

Store Vs in R0

Store VLMA in R4

Press [ XEQ ] [ B ]

θ° is displayed

Press [ R/S ], VLMA is displayed

Variables:

R0 = Vs

R1 = θ in degrees

R2 = θ in radians

R3 = VLMA 

R4 = VLMS

Program Code

Key Code:  { Key }

61, 41, A:  { LBL A }

61, 24:  { RAD }

22, 1:  { RCL 1 }

61, 55:  { →RAD }

21, 2:  { STO 2 }

24:  { COS }

75:  { + }

1:  { 1 }

74:  { = }

55: { × }

22, 0:  { RCL 0 }

45:  { ÷ }

2:  { 2 }

74:  { = }

21, 3:  { RCL 3 }

26:  { R/S }

51, 41, 1:  { GTO 1 }

61, 26:  { RTN }

61, 41, b:  { LBL B }

61, 24:  { RAD }

33:  { ( }

2:  { 2 }

55:  { × }

22, 3:  { RCL 3 }

45:  { ÷ }

22, 0:  { RCL 0 }

65:  { - }

1:  { 1 }

34:  { ) }

51, 24:  { ACOS }

21, 2:  { STO 2 }

51, 55:  { →DEG }

21, 1:  { STO 1 }

26:  { R/S }

51, 41, 1:  { GTO 1 }

61, 26:  { RTN }

61, 41, 1:  { LBL 1 }

61, 22:  { π }

65:  { - }

22, 2:  { RCL 2 }

75:  { + }

33:  { ( }

2:  { 2 }

55:  { ÷ }

22, 2:  { RCL 2 }

34:  { ) }

23:  { SIN }

45:  { ÷ }

2:  { 2 }

74:  { = }

11:  { √ }

55:  { × }

22, 0:  { RCL 0 }

45:  { ÷ }

61, 22:  { π }

11:  { √ }

74:  { = }

21, 4:  { STO 4 }

61, 26:  { RTN }

Example

Example 1:

Inputs:  θ  = 75° (stored in R1), Vs = 160 (stored in R0)

Results:

VLMA ≈ 100.70552

VLMS ≈ 130.27094

Example 2:

Inputs:  VLMA = 130 (stored in R3), Vs = 160 (stored in R0)

Results:

θ ≈ 51.31781°

VLMS ≈ 149.25534

Source

Davidson, James J.  "Triac Waveforms #1" and "Traic Waveforms #2" 65 Notes V3N10 December 1976.  pg. 38.  

All original content copyright, © 2011-2022.  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 and any authors of original programs and scripts.  

HP 11C (and Emulators): The Four Means

HP 11C (and Emulators):  The Four Means

Introduction

The following program uses the statistical registers to calculate four types of mean:

Arithmetic Mean:  μ = Σx / n

Harmonic Mean:  HM = n / Σ(1/x)

Geometric Mean:  GM = (Πx) ^ (1/n)

Root Mean Square:  RMS = √(Σx^2 / n)


The HP 11C uses the following registers in statistical analysis.  Be sure to clear registers by pressing [ f ] [ x<>y ] (CLEAR REG) before beginning.  Also, after clearing the registers, store 1 in register 7 (R7).  

R0 = n
R1 = Σx
R2 = Σx^2
R3 = Σy
R4 = Σy^2
R5 = Σxy

LBL A:  Enter data
LBL B:  Analysis: μ [R/S], HM [R/S], GM [R/S], RMS

HP 11C Program: The Four Means

Don't forget to store 1 in R7 prior to running the program. 

001 42, 21, 11 LBL A
002 49 Σ+
003 43, 36 LAST x
004 44, 20, 7 STO× 7
005 15 1/x
006 44, 40, 6 STO+ 6
007 43, 32 RTN

008 42, 21, 12 LBL B
009 43, 0         x-bar 
010 32 R/S
011 45, 6         RCL 6
012 15 1/x
013 45, 0 RCL 0
014 20 *
015 31 R/S
016 45, 7         RCL 7
017 45, 0         RCL 0
018 15 1/x
019 14 y^x
020 31 R/S
021 45, 2         RCL 2
022 45, 0         RCL 0
023 10 ÷
024 11 √
025 43, 32 RTN

Example:
Sample set:  4.25, 4.08, 5.63, 6.13, 4.48, 7.02 ( 6 data points )

Keystrokes:

4.25 [ f ] [ √ ] (A)
4.08 [ f ] [ √ ] (A)
5.63 [ f ] [ √ ] (A)
6.13 [ f ] [ √ ] (A)
4.48 [ f ] [ √ ] (A)
7.02 [ f ] [ √ ] (A)

[ f ] [e^x] (B)   5.2650 (arithmetic mean, μ)
[R/S] 5.0556 (harmonic mean, HM)
[R/S] 5.1575 (geometric mean, GM)
[R/S] 5.3748 (root mean square, RMS)


Eddie
All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions.