AC Voltage at a Given Angle
Calculation of the voltage of a sine wave at a given angle
Calculate Voltage at Angle
Angle-Voltage Calculator
On this page you can calculate the instantaneous value of a sine wave at a certain angle position. The voltage can be entered as RMS or peak value.
Sine Wave Angle Values
Unit circle - angles and corresponding sine values
Characteristic Angles
| 0° | sin(0°) = 0 | u = 0V |
| 30° | sin(30°) = 0.5 | u = 0.5·û |
| 45° | sin(45°) = 0.707 | u = 0.707·û |
| 60° | sin(60°) = 0.866 | u = 0.866·û |
| 90° | sin(90°) = 1 | u = û (Maximum) |
| 180° | sin(180°) = 0 | u = 0V |
Parameters
Calculation of Voltage at Angle
Basic Formula for Sine Waves
With uniform rotation of a rotor in a homogeneous magnetic field, the induced voltage changes sinusoidally. If the peak value û is known, the instantaneous value can be determined from the angle.
Basic formula
The instantaneous voltage is the product of the peak voltage and the sine of the angle.
Important Properties
- Periodicity: sin(φ + 360°) = sin(φ)
- Symmetry: sin(-φ) = -sin(φ)
- Value range: -1 ≤ sin(φ) ≤ 1
- Zeros: sin(φ) = 0 at φ = 0°, 180°, 360°, ...
- Extrema: sin(φ) = ±1 at φ = 90°, 270°, ...
Example calculations
Practical calculation examples
Example 1: Maximum of the sine wave
Given: û = 10V, φ = 90°
Example 2: Zero crossing
Given: û = 10V, φ = 180°
Example 3: Arbitrary angle
Given: û = 10V, φ = 34°
Important angles and their sine values
First quadrant (0° - 90°):
Second quadrant (90° - 180°):
Other quadrants:
Theory of the Angle-Voltage Relationship
Physical principles
To calculate the voltage with respect to an angle for a sinusoidal AC voltage, the voltage is described by the sine function. The general form of a sinusoidal voltage is:
Basic formula
Where û is the peak voltage, u the instantaneous voltage, and φ the angle.
Angle dependence
The voltage u is determined by the sine function and depends on the angle φ, which is often expressed as a function of time. By inserting the corresponding angle and amplitude into the formula, you get the voltage at a certain angle or time.
Degree calculation
Direct input in degrees (0° to 360°).
Radian calculation
Input in radians (0 to 2π).
Practical applications
Electrical engineering
- Generator voltages
- Transformer analysis
- Phase relationships
- Load distribution
Simulation
- SPICE models
- Signal generation
- Harmonic analysis
- Frequency response analysis
Measurement technology
- Oscilloscope trigger
- Phase measurements
- Harmonic analysis
- Distortion measurement
Conversion between units
Degree ↔ Radian conversion
\[\text{rad} = \text{degree} \times \frac{\pi}{180°}\]
\[\text{degree} = \text{rad} \times \frac{180°}{\pi}\]
Design notes
Practical considerations
- Phase shift: Note angle differences between current and voltage
- Harmonics: Real signals often contain harmonics at multiples of the fundamental frequency
- Symmetry: Three-phase systems have 120° phase shift
- Measurement: Trigger points for stable oscilloscope display
- Reference point: Clear definition of the 0° reference point required
- Quadrants: Note the sign of the voltage depending on the angle range
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