10-25-2022, 01:25 PM
The following calculations involve troide 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 }
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.
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 }
Code:
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.