Lighting systems, and systems for determining periodic values of a phase angle of a waveform power input
System for determining periodic values of phase angle Φ of waveform power input including voltage detector for detecting periodic values of average voltage of waveform power input and detecting corresponding periodic values of peak voltage of waveform power input. System also includes phase angle Φ detector in signal communication for receiving periodic values of average voltage and peak voltage from voltage detector. Phase angle Φ detector also detects periodic values each being ratio of one of periodic values of average voltage divided by corresponding periodic value of peak voltage, or being ratio of peak voltage divided by average voltage; and determines periodic values of phase angle Φ of waveform power input corresponding to periodic values of ratio. Lighting systems.
1. A system for determining periodic values of a phase angle (Φ) of a waveform power input, comprising:
a voltage detector for receiving a waveform power input including a sinusoidal portion, the voltage detector being configured for generating a plurality of periodic values of an average voltage (“V-ave”) of the waveform power input and for generating a corresponding plurality of periodic values of a peak voltage “(V-peak)” of the waveform power input;
a phase angle (Φ) detector being in signal communication for receiving the periodic values of the average voltage (V-ave) and the peak voltage (V-peak) from the voltage detector and being configured for: generating a plurality of periodic values each being a ratio (“V-ap”) of Hall one of the plurality of periodic values of the average voltage (V-ave) divided by the corresponding one of the plurality of periodic values of the peak voltage (V-peak); and determining a plurality of periodic values of a phase angle (Φ) of the waveform power input each corresponding to one of the plurality of periodic values of the ratio (V-ap);
a power transmission circuit being configured for being placed in electrical communication with a light emitter, the power transmission circuit being configured for receiving a power control signal for controlled transmission of the waveform power input to the light emitter; and
a power control circuit being configured to: for utilizing the plurality of periodic values of the phase angle (Φ) of the waveform power input in generating the power control signal; and for sending the power control signal to the power transmission circuit.
2. The system of claim 1 , wherein the voltage detector is configured for generating the plurality of periodic values of the average voltage (V-ave) and the corresponding plurality of periodic values of the peak voltage (V-peak) with the waveform power input as being a phase-cut waveform power input.
3. The system of claim 2 , wherein the voltage detector is configured for generating the plurality of periodic values of the average voltage (V-ave) and the corresponding plurality of periodic values of the peak voltage (V-peak) with the waveform power input as being a leading edge phase-cut waveform power input or a trailing edge phase-cut waveform power input.
4. The system of claim 2 , wherein the voltage detector is configured for generating the plurality of periodic values of the average voltage (V-ave) the corresponding plurality of periodic values of the peak voltage (V-peak) with the waveform power input as a half-waveform pulsating direct power input being rectified from a full-waveform sinusoidal alternating power input.
5. The system of claim 4 , wherein the phase angle (Φ) detector is configured for determining the plurality of periodic values of the phase angle (Φ) of the waveform power input by pairing each one of the plurality of generated periodic values of the ratio (V-ap) with a closely-matching one of a plurality of calculated periodic values for the ratio (V-ap) being determined for a plurality of corresponding periodic values of the phase angle (Φ) according to the following formulas:
for the plurality of periodic values of the phase angle (Φ)
as being
<
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
π
(
sine
Φ
)
Formula
1
for the plurality of periodic values of the phase angle (Φ)
as being
≥
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
[
[
π
]
]
π
.
Formula
2
6. The system of claim 5 , wherein the phase angle (Φ) detector is configured for pairing each one of the plurality of generated periodic values of the ratio (V-ap) with the closely-matching one of the plurality of calculated periodic values for the ratio (V-ap) by using a lookup table of the plurality of calculated periodic values for the ratio (V-ap) being determined for the plurality of corresponding periodic values of the phase angle (Φ) according to Formulas 1 and 2.
7. The system of claim 4 , wherein the phase angle (Φ) detector is configured for determining the plurality of periodic values of the phase angle (Φ) of the waveform power input by: iteratively determining a plurality of calculated periodic values for the ratio (V-ap) according to the following Formulas 1 and 2 for a plurality of corresponding periodic values of the phase angle (Φ); and pairing each one of the plurality of generated periodic values of the ratio (V-ap) with a closely-matching one of the plurality of calculated periodic values for the ratio (V-ap):
for the plurality of periodic values of the phase angle (Φ)
as being
<
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
π
(
sine
Φ
)
Formula
1
for the plurality of periodic values of the phase angle (Φ)
as being
≥
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
[
[
π
]
]
π
.
Formula
2
8. A lighting system, comprising:
a dimmer being configured for performing a phase-cutting operation on a waveform power input including a sinusoidal portion, forming a phase-cut waveform power input;
a power transmission circuit being in electrical communication with the dimmer and configured for being placed in electrical communication with a light emitter, the power transmission circuit being configured for receiving a power control signal for controlled transmission of the phase-cut waveform power input to the light emitter;
a voltage detector for receiving the phase-cut waveform power input, the voltage detector being configured for generating a plurality of periodic values of an average voltage (“V-ave”) of the phase-cut waveform power input and for generating a corresponding plurality of periodic values of a peak voltage “(V-peak)” of the phase-cut waveform power input; and
a phase angle (Φ) detector being in signal communication for receiving the periodic values of the average voltage (V-ave) and the peak voltage (V-peak) from the voltage detector, and being configured for: generating a plurality of periodic values each being a ratio (“V-ap”) of Hall one of the plurality of periodic values of the average voltage (V-ave) divided by the corresponding one of the plurality of periodic values of the peak voltage (V-peak); and determining a plurality of periodic values of a phase angle (Φ) of the phase-cut waveform power input each corresponding to one of the plurality of periodic values of the ratio (V-ap); and
a power control circuit being configured: for utilizing the plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input in generating the power control signal; and for sending the power control signal to the power transmission circuit.
9. The system of claim 8 , wherein the dimmer is configured for performing either a leading edge phase cut operation or a trailing edge phase cut operation on the waveform power input; and wherein the voltage detector is configured for generating the plurality of periodic values of the average voltage (V-ave) and the corresponding plurality of periodic values of the peak voltage (V-peak) with the phase-cut waveform power input as respectively being either a leading edge phase-cut waveform power input or a trailing edge phase-cut waveform power input.
10. The system of claim 8 , wherein the voltage detector is configured for generating the plurality of periodic values of the average voltage (V-ave) the corresponding plurality of periodic values of the peak voltage (V-peak) with the phase-cut waveform power input as a half-waveform pulsating direct power input being rectified from a full-waveform sinusoidal alternating power input.
11. The system of claim 10 , wherein the phase angle (Φ) detector is configured for determining the plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input by pairing each one of the plurality of generated periodic values of the ratio (V-ap) with a closely-matching one of a plurality of calculated periodic values for the ratio (V-ap) being determined for a plurality of corresponding periodic values of the phase angle (Φ) according to the following formulas:
for the plurality of periodic values of the phase angle (Φ)
as being
<
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
π
(
sine
Φ
)
Formula
1
for the plurality of periodic values of the phase angle (Φ)
as being
≥
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
[
[
π
]
]
π
.
Formula
2
12. The system of claim 11 , wherein the phase angle (Φ) detector is configured for pairing each one of the plurality of generated periodic values of the ratio (V-ap) with the closely-matching one of the plurality of calculated periodic values for the ratio (V-ap) by using a lookup table of the plurality of calculated periodic values for the ratio (V-ap) being determined for the plurality of corresponding periodic values of the phase angle (Φ) according to Formulas 1 and 2.
13. The system of claim 10 , wherein the phase angle (Φ) detector is configured for determining the plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input by: iteratively determining a plurality of calculated periodic values for the ratio (V-ap) according to the following Formulas 1 and 2 for a plurality of corresponding periodic values of the phase angle (Φ); and pairing each one of the plurality of generated periodic values of the ratio (V-ap) with a closely-matching one of the plurality of calculated periodic values for the ratio (V-ap):
for the plurality of periodic values of the phase angle (Φ)
as being
<
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
π
(
sine
Φ
)
Formula
1
for the plurality of periodic values of the phase angle (Φ)
as being
≥
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
[
[
π
]
]
π
.
Formula
2
14. A system for determining periodic values of a phase angle (Φ) of a waveform power input, comprising:
a voltage detector for receiving a waveform power input including a sinusoidal portion, the voltage detector being configured for generating a plurality of periodic values of a peak voltage “(V-peak)” of the waveform power input and for generating a corresponding plurality of periodic values of an average voltage (“V-ave”) of the waveform power input;
a phase angle (Φ) detector being in signal communication for receiving the periodic values of the average voltage (V-ave) and the peak voltage (V-peak) from the voltage detector, and being configured for: generating a plurality of periodic values each being a ratio (“V-pa”) of Hall one of the plurality of periodic values of the peak voltage (V-peak) divided by the corresponding one of the plurality of periodic values of the average voltage (V-ave); and determining a plurality of periodic values of a phase angle (Φ) of the waveform power input each corresponding to one of the plurality of periodic values of the ratio (V-pa);
a power transmission circuit being configured for being placed in electrical communication with a light emitter, the power transmission circuit being configured for receiving a power control signal for controlled transmission of the waveform power input to the light emitter; and
a power control circuit being configured: for utilizing the plurality of periodic values of the phase angle (Φ) of the waveform power input in generating the power control signal; and for sending the power control signal to the power transmission circuit.
15. The system of claim 14 , wherein the voltage detector is configured for generating the plurality of periodic values of the average voltage (V-ave) and the corresponding plurality of periodic values of the peak voltage (V-peak) with the waveform power input as being a phase-cut waveform power input.
16. The system of claim 15 , wherein the voltage detector is configured for generating the plurality of periodic values of the average voltage (V-ave) the corresponding plurality of periodic values of the peak voltage (V-peak) with the waveform power input as being a leading edge phase-cut waveform power input or a trailing edge phase-cut waveform power input.
17. The system of claim 15 , wherein the voltage detector is configured for generating the plurality of periodic values of the average voltage (V-ave) the corresponding plurality of periodic values of the peak voltage (V-peak) with the waveform power input as a half-waveform pulsating direct power input being rectified from a full-waveform sinusoidal alternating power input.
18. The system of claim 17 , wherein the phase angle (Φ) detector is configured for determining the plurality of periodic values of the phase angle (Φ) of the waveform power input by pairing each one of the plurality of generated periodic values of the ratio (V-pa) with a closely-matching one of a plurality of calculated periodic values for the ratio (V-pa) being determined for a plurality of corresponding periodic values of the phase angle (Φ) according to the following formulas:
for the plurality of periodic values of the phase angle (Φ)
as being > 0
and < 90°,
(
V
-
pa
)
=
π
(
sine
Φ
)
1
-
(
cosine
Φ
)
Formula
3
for the plurality of periodic values of the phase angle (Φ)
as being ≥ 90°, (
V
-
pa
)
=
π
1
-
(
cosine
Φ
)
.
Formula
4
19. The system of claim 18 , wherein the phase angle (Φ) detector is configured for pairing each one of the plurality of generated periodic values of the ratio (V-pa) with the closely-matching one of the plurality of calculated periodic values for the ratio (V-pa) by using a lookup table of the plurality of calculated periodic values for the ratio (V-pa) being determined for the plurality of corresponding periodic values of the phase angle (Φ) according to Formulas 3 and 4.
20. The system of claim 17 , wherein the phase angle (Φ) detector is configured for determining the plurality of periodic values of the phase angle (Φ) of the waveform power input by: iteratively determining a plurality of calculated periodic values for the ratio (V-pa) according to the following Formulas 3 and 4 for a plurality of corresponding periodic values of the phase angle (Φ); and pairing each one of the plurality of generated periodic values of the ratio (V-pa) with a closely-matching one of the plurality of calculated periodic values for the ratio (V-pa):
for the plurality of periodic values of the phase angle (Φ)
as being > 0 and < 90°,(
V
-
pa
)
=
π
(
sine
Φ
)
1
-
(
cosine
Φ
)
Formula
3
for the plurality of periodic values of the phase angle (Φ)
as being ≥ 90°, (
V
-
pa
)
=
π
1
-
(
cosine
Φ
)
.
Formula
4
21. A lighting system, comprising:
a dimmer being configured for performing a phase-cutting operation on a waveform power input including a sinusoidal portion, forming a phase-cut waveform power input;
a power transmission circuit being in electrical communication with the dimmer and configured for being placed in electrical communication with a light emitter, the power transmission circuit being configured for receiving a power control signal for controlled transmission of the phase-cut waveform power input to the light emitter;
a voltage detector for receiving the phase-cut waveform power input, the voltage detector being configured for generating a plurality of periodic values of a peak voltage “(V-peak)” of the phase-cut waveform power input and for generating a corresponding plurality of periodic values of an average voltage (“V-ave”) of the phase-cut waveform power input; and
a phase angle (Φ) detector being in signal communication for receiving the periodic values of the average voltage (V-ave) and the peak voltage (V-peak) from the voltage detector, and being configured for: generating a plurality of periodic values each being a ratio (“V-pa”) of one of the plurality of periodic values of the peak voltage (V-peak) divided by the corresponding one of the plurality of periodic values of the average voltage (V-ave); and determining a plurality of periodic values of a phase angle (Φ) of the phase-cut waveform power input each corresponding to one of the plurality of periodic values of the ratio (V-pa); and
a power control circuit being configured: for utilizing the plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input in generating the power control signal; and for sending the power control signal to the power transmission circuit.
22. The system of claim 21 , wherein the dimmer is configured for performing either a leading edge phase cut operation or a trailing edge phase cut operation on the waveform power input; and wherein the voltage detector is configured for generating the plurality of periodic values of the average voltage (V-ave) and the corresponding plurality of periodic values of the peak voltage (V-peak) with the phase-cut waveform power input as respectively being either a leading edge phase-cut waveform power input or a trailing edge phase-cut waveform power input.
23. The system of claim 21 , wherein the voltage detector is configured for generating the plurality of periodic values of the average voltage (V-ave) the corresponding plurality of periodic values of the peak voltage (V-peak) with the phase-cut waveform power input as a half-waveform pulsating direct power input being rectified from a full-waveform sinusoidal alternating power input.
24. The system of claim 23 , wherein the phase angle (Φ) detector is configured for determining the plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input by pairing each one of the plurality of generated periodic values of the ratio (V-pa) with a closely-matching one of a plurality of calculated periodic values for the ratio (V-pa) being determined for a plurality of corresponding periodic values of the phase angle (Φ) according to the following formulas:
for the plurality of periodic values of the phase angle (Φ)
as being > 0 and < 90°, (
V
-
pa
)
=
π
(
sine
Φ
)
1
-
(
cosine
Φ
)
Formula
3
for the plurality of periodic values of the phase angle (Φ)
as being ≥ 90°, (
V
-
pa
)
=
π
1
-
(
cosine
Φ
)
.
Formula
4
25. The system of claim 24 , wherein the phase angle (Φ) detector is configured for pairing each one of the plurality of generated periodic values of the ratio (V-pa) with the closely-matching one of the plurality of calculated periodic values for the ratio (V-pa) by using a lookup table of the plurality of calculated periodic values for the ratio (V-pa) being determined for the plurality of corresponding periodic values of the phase angle (Φ) according to Formulas 3 and 4.
26. The system of claim 23 , wherein the phase angle (Φ) detector is configured for determining the plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input by: iteratively determining a plurality of calculated periodic values for the ratio (V-pa) according to the following Formulas 3 and 4 for a plurality of corresponding periodic values of the phase angle (Φ); and pairing each one of the plurality of generated periodic values of the ratio (V-pa) with a closely-matching one of the plurality of calculated periodic values for the ratio (V-pa):
for the plurality of periodic values of the phase angle (Φ)
as being > 0 and < 90°, (
V
-
pa
)
=
π
(
sine
Φ
)
1
-
(
cosine
Φ
)
Formula
3
for the plurality of periodic values of the phase angle (Φ)
as being ≥ 90°, (
V
-
pa
)
=
π
1
-
(
cosine
Φ
)
.
Formula
4
27. A process for determining periodic values of a phase angle (Φ) of a waveform power input, comprising:
providing a waveform power input including a sinusoidal portion, and providing a power transmission circuit being in electrical communication with a light emitter, the power transmission circuit being configured for receiving a power control signal for controlled transmission of the waveform power input to the light emitter;
generating a plurality of periodic values of an average voltage (“V-ave”) of the waveform power input, and generating a corresponding plurality of periodic values of a peak voltage “(V-peak)” of the waveform power input;
generating a plurality of periodic values each being a ratio (“V-ap”) of one of the plurality of periodic values of the average voltage (V-ave) divided by the corresponding one of the plurality of periodic values of the peak voltage (V-peak);
determining a plurality of periodic values of the phase angle (Φ) of the waveform power input each corresponding to flail one of the plurality of periodic values of the ratio (V-ap);
utilizing the plurality of periodic values of the phase angle (Φ) of the waveform power input in generating the power control signal; and
sending the power control signal to the power transmission circuit.
28. The process of claim 27 , wherein the providing the waveform power input includes providing the waveform power input as being a phase-cut waveform power input.
29. The process of claim 28 , wherein the providing the waveform power input includes providing the waveform power input as being a leading edge phase-cut waveform power input or a trailing edge phase-cut waveform power input.
30. The process of claim 28 , wherein the providing the waveform power input includes providing the waveform power input as a half-waveform pulsating direct power input being rectified from a full-waveform sinusoidal alternating power input.
31. The process of claim 30 , wherein the determining the plurality of periodic values of the phase angle (Φ) of the waveform power input includes pairing each one of the plurality of generated periodic values of the ratio (V-ap) with a closely-matching one of a plurality of calculated periodic values for the ratio (V-ap) being determined for a plurality of corresponding periodic values of the phase angle (Φ) according to the following formulas:
for the plurality of periodic values of the phase angle (Φ)
as being
<
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
π
(
sine
Φ
)
Formula
1
for the plurality of periodic values of the phase angle (Φ)
as being
≥
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
[
[
π
]
]
π
.
Formula
2
32. The process of claim 31 , wherein the pairing each one of the plurality of generated periodic values of the ratio (V-ap) with the closely-matching one of the plurality of calculated periodic values for the ratio (V-ap) includes using a lookup table of the plurality of calculated periodic values for the ratio (V-ap) being determined for the plurality of corresponding periodic values of the phase angle (Φ) according to Formulas 1 and 2.
33. The process of claim 30 , wherein the determining the plurality of periodic values of the phase angle (Φ) of the waveform power input includes: iteratively determining a plurality of calculated periodic values for the ratio (V-ap) according to the following Formulas 1 and 2 for a plurality of corresponding periodic values of the phase angle (Φ); and pairing each one of the plurality of generated periodic values of the ratio (V-ap) with a closely-matching one of the plurality of calculated periodic values for the ratio (V-ap):
for the plurality of periodic values of the phase angle (Φ)
as being
<
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
π
(
sine
Φ
)
Formula
1
for the plurality of periodic values of the phase angle (Φ)
as being
≥
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
[
[
π
]
]
π
.
Formula
2
34. A lighting process, comprising:
providing a waveform power input including a sinusoidal portion;
providing a dimmer being configured for performing a phase-cutting operation on the waveform power input to form a phase-cut waveform power input, and providing a power transmission circuit being in electrical communication with the dimmer and with a light emitter, the power transmission circuit being configured for receiving a power control signal for controlled transmission of the phase-cut waveform power input to the light emitter;
generating a plurality of periodic values of an average voltage (“V-ave”) of the phase-cut waveform power input and generating a corresponding plurality of periodic values of a peak voltage “(V-peak)” of the phase-cut waveform power input;
generating a plurality of periodic values each being a ratio (“V-ap”) of one of the plurality of periodic values of the average voltage (V-ave) divided by the corresponding one of the plurality of periodic values of the peak voltage (V-peak);
determining a plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input each corresponding to one of the plurality of periodic values of the ratio (V-ap);
utilizing the plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input in generating the power control signal; and
sending the power control signal to the power transmission circuit.
35. The process of claim 34 , wherein the providing the dimmer includes providing the dimmer as being configured for performing either a leading edge phase cut operation or a trailing edge phase cut operation on the waveform power input; and wherein the providing the phase-cut waveform power input includes providing the phase-cut waveform power input as respectively being either a leading edge phase-cut waveform power input or a trailing edge phase-cut waveform power input.
36. The process of claim 34 , wherein the providing the phase-cut waveform power input includes providing the phase-cut waveform power input as a half-waveform pulsating direct power input being rectified from a full-waveform sinusoidal alternating power input.
37. The process of claim 36 , wherein the determining the plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input includes pairing each one of the plurality of generated periodic values of the ratio (V-ap) with a closely-matching one of a plurality of calculated periodic values for the ratio (V-ap) being determined for a plurality of corresponding periodic values of the phase angle (Φ) according to the following formulas:
for the plurality of periodic values of the phase angle (Φ)
as being
<
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
π
(
sine
Φ
)
Formula
1
for the plurality of periodic values of the phase angle (Φ)
as being
≥
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
[
[
π
]
]
π
.
Formula
2
38. The process of claim 37 , wherein the pairing each one of the plurality of generated periodic values of the ratio (V-ap) with the closely-matching one of the plurality of calculated periodic values for the ratio (V-ap) includes using a lookup table of the plurality of calculated periodic values for the ratio (V-ap) being determined for the plurality of corresponding periodic values of the phase angle (Φ) according to Formulas 1 and 2.
39. The process of claim 36 , wherein the determining the plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input includes: iteratively determining a plurality of calculated periodic values for the ratio (V-ap) according to the following Formulas 1 and 2 for a plurality of corresponding periodic values of the phase angle (Φ); and pairing each one of the plurality of generated periodic values of the ratio (V-ap) with a closely-matching one of the plurality of calculated periodic values for the ratio (V-ap):
for the plurality of periodic values of the phase angle (Φ)
as being
<
90
°
,
(
V
-
ap
)
=
1
-
(
cosine
Φ
)
π
(
sine
Φ
)
Formula
1
for the plurality of periodic values of the phase angle (Φ)
as being
≥
90
°
,
(
V-ap
)
=
1
-
(
cosine
Φ
)
[
[
π
]
]
π
.
Formula
2
40. A process for determining periodic values of a phase angle (Φ) of a waveform power input, comprising:
providing a waveform power input including a sinusoidal portion, and providing a power transmission circuit being in electrical communication with a light emitter, the power transmission circuit being configured for receiving a power control signal for controlled transmission of the waveform power input to the light emitter;
generating a plurality of periodic values of a peak voltage “(V-peak)” of the waveform power input, and generating a corresponding plurality of periodic values of an average voltage (“V-ave”) of the waveform power input;
generating a plurality of periodic values each being a ratio (“V-pa”) of one of the plurality of periodic values of the peak voltage (V-peak) divided by the corresponding one of the plurality of periodic values of the average voltage (V-ave);
determining a plurality of periodic values of the phase angle (Φ) of the waveform power input each corresponding to one of the plurality of periodic values of the ratio (V-pa);
utilizing the plurality of periodic values of the phase angle (Φ) of the waveform power input in generating the power control signal; and
sending the power control signal to the power transmission circuit.
41. The process of claim 40 , wherein the providing the waveform power input includes providing the waveform power input as being a phase-cut waveform power input.
42. The process of claim 41 , wherein the providing the waveform power input includes providing the waveform power input as being a leading edge phase-cut waveform power input or a trailing edge phase-cut waveform power input.
43. The process of claim 41 , wherein the providing the waveform power input includes providing the waveform power input as a half-waveform pulsating direct power input being rectified from a full-waveform sinusoidal alternating power input.
44. The process of claim 43 , wherein the determining the plurality of periodic values of the phase angle (Φ) of the waveform power input includes pairing each one of the plurality of generated periodic values of the ratio (V-pa) with a closely-matching one of a plurality of calculated periodic values for the ratio (V-pa) being determined for a plurality of corresponding periodic values of the phase angle (Φ) according to the following formulas:
for the plurality of periodic values of the phase angle (Φ)
as being > 0 and < 90°, (
V
-
pa
)
=
π
(
sine
Φ
)
1
-
(
cosine
Φ
)
Formula
3
for the plurality of periodic values of the phase angle (Φ)
as being ≥ 90°, (
V
-
pa)
=
π
1
-
(
cosine
Φ
)
.
Formula
4
45. The process of claim 44 , wherein the pairing each one of the plurality of generated periodic values of the ratio (V-pa) with the closely-matching one of the plurality of calculated periodic values for the ratio (V-pa) includes using a lookup table of the plurality of calculated periodic values for the ratio (V-pa) being determined for the plurality of corresponding periodic values of the phase angle (Φ) according to Formulas 3 and 4.
46. The process of claim 43 , wherein the determining the plurality of periodic values of the phase angle (Φ) of the waveform power input includes: iteratively determining a plurality of calculated periodic values for the ratio (V-pa) according to the following Formulas 3 and 4 for a plurality of corresponding periodic values of the phase angle (Φ); and pairing each one of the plurality of generated periodic values of the ratio (V-pa) with a closely-matching one of the plurality of calculated periodic values for the ratio (V-pa):
for the plurality of periodic values of the phase angle (Φ)
as being > 0 and < 90°, (
V
-
pa
)
=
π
(
sine
Φ
)
1
-
(
cosine
Φ
)
Formula
3
for the plurality of periodic values of the phase angle (Φ)
as being ≥ 90°, (
V
-
pa
)
=
π
1
-
(
cosine
Φ
)
.
Formula
4
47. A lighting process, comprising:
providing a waveform power input including a sinusoidal portion;
providing a dimmer being configured for performing a phase-cutting operation on the waveform power input to form a phase-cut waveform power input, and providing a power transmission circuit being in electrical communication with the dimmer and with a light emitter, the power transmission circuit being configured for receiving a power control signal for controlled transmission of the phase-cut waveform power input to the light emitter;
generating a plurality of periodic values of a peak voltage “(V-peak)” of the phase-cut waveform power input and generating a corresponding plurality of periodic values of an average voltage (“V-ave”) of the phase-cut waveform power input;
generating a plurality of periodic values each being a ratio (“V-pa”) of one of the plurality of periodic values of the peak voltage (V-peak) divided by the corresponding one of the plurality of periodic values of the average voltage (V-ave);
determining a plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input each corresponding to one of the plurality of periodic values of the ratio (V-pa);
utilizing the plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input in generating the power control signal; and
sending the power control signal to the power transmission circuit.
48. The process of claim 47 , wherein the providing the dimmer includes providing the dimmer as being configured for performing either a leading edge phase cut operation or a trailing edge phase cut operation on the waveform power input; and wherein the providing the phase-cut waveform power input includes providing the phase-cut waveform power input as respectively being either a leading edge phase-cut waveform power input or a trailing edge phase-cut waveform power input.
49. The process of claim 47 , wherein the providing the phase-cut waveform power input includes providing the phase-cut waveform power input as a half-waveform pulsating direct power input being rectified from a full-waveform sinusoidal alternating power input.
50. The process of claim 49 , wherein the determining the plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input includes pairing each one of the plurality of generated periodic values of the ratio (V-pa) with a closely-matching one of a plurality of calculated periodic values for the ratio (V-pa) being determined for a plurality of corresponding periodic values of the phase angle (Φ) according to the following formulas:
for the plurality of periodic values of the phase angle (Φ)
as being > 0 and < 90°, (
V
-
pa
)
=
π
(
sine
Φ
)
1
-
(
cosine
Φ
)
Formula
3
for the plurality of periodic values of the phase angle (Φ)
as being ≥ 90°, (
V
-
pa
)
=
π
1
-
(
cosine
Φ
)
.
Formula
4
51. The process of claim 50 , wherein the pairing each one of the plurality of generated periodic values of the ratio (V-pa) with the closely-matching one of the plurality of calculated periodic values for the ratio (V-pa) includes using a lookup table of the plurality of calculated periodic values for the ratio (V-pa) being determined for the plurality of corresponding periodic values of the phase angle (Φ) according to Formulas 3 and 4.
52. The process of claim 49 , wherein the determining the plurality of periodic values of the phase angle (Φ) of the phase-cut waveform power input includes: iteratively determining a plurality of calculated periodic values for the ratio (V-pa) according to the following Formulas 3 and 4 for a plurality of corresponding periodic values of the phase angle (Φ); and pairing each one of the plurality of generated periodic values of the ratio (V-pa) with a closely-matching one of the plurality of calculated periodic values for the ratio (V-pa):
for the plurality of periodic values of the phase angle (Φ)
as being > 0 and < 90°, (
V
-
pa
)
=
π
(
sine
Φ
)
1
-
(
cosine
Φ
)
Formula
3
for the plurality of periodic values of the phase angle (Φ)
as being ≥ 90°, (
V
-
pa
)
=
π
1
-
(
cosine
Φ
)
.
Formula
4