RMS value of a triangular pulse

Calculator and formulas for calculating the RMS and mean value of a triangular pulse

Triangular Pulse Calculator

Triangular Pulse

This function calculates the RMS and mean value of a triangular pulse. Enter the value of the peak voltage for the calculation.

V
Results
RMS voltage:
Mean voltage:

Triangular Pulse & Parameters

Triangular pulse
Parameters
\(\displaystyle U_s\) = Peak voltage [V]
\(\displaystyle U_{eff}\) = RMS voltage [V]
\(\displaystyle U_m\) = Mean voltage [V]
Basic formulas
\[U_{eff} = \frac{U_s}{\sqrt{3}}\]
\[U_m = \frac{U_s}{2}\]

Example calculations

Practical calculation examples

Example 1: Standard triangular pulse

Given: Us = 10V

\[U_{eff} = \frac{10V}{\sqrt{3}} = \frac{10V}{1{,}732} = 5{,}77V\]
\[U_m = \frac{10V}{2} = 5{,}0V\]
The RMS value is about 57.7% of the peak value
Example 2: Audio application

Given: Us = 3V (typical audio level)

\[U_{eff} = \frac{3V}{\sqrt{3}} = 1{,}73V\]
\[U_m = \frac{3V}{2} = 1{,}5V\]
Typical values for audio signals
Example 3: High voltage

Given: Us = 100V

\[U_{eff} = \frac{100V}{\sqrt{3}} = 57{,}7V\]
\[U_m = \frac{100V}{2} = 50{,}0V\]
Application in power electronics
Ratios for triangular pulse
RMS ratio:
Ueff / Us: 1/√3 ≈ 0.577
Percent: ≈ 57.7%
Factor: 0.577
Mean value ratio:
Um / Us: 1/2 = 0.5
Percent: 50%
Factor: 0.5

Formula for triangular pulse

What is a triangular pulse?

The RMS value of a triangular pulse (usually referred to as a triangular voltage with periodic pulses) can be calculated in a similar way as the RMS value of a classic triangular wave. It is important that the triangular voltage has a symmetrical shape, where the voltage alternates between positive and negative peak values.

Definition of RMS value

The RMS value is defined as the DC value with the same thermal effect as the considered AC value. For triangular pulses, it is calculated using the following formula:

RMS value
\[U_{eff} = \frac{U_s}{\sqrt{3}}\]

The RMS value is about 57.7% of the peak voltage.

Mean value
\[U_m = \frac{U_s}{2}\]

The mean value is 50% of the peak voltage.

Mathematical derivation

Calculation

For a symmetrical triangular pulse with period T and peak voltage Us:

\[U_{eff} = \sqrt{\frac{1}{T} \int_0^T u^2(t) \, dt}\]
For triangular function: \[U_{eff} = \frac{U_s}{\sqrt{3}}\]

Practical applications

Signal generation
  • Function generators
  • Modulation methods
  • Test signals
  • Sweep generators
Measurement technology
  • Oscilloscopes
  • Spectrum analyzers
  • RMS measurement
  • Calibration
Power electronics
  • PWM signals
  • Triangle comparators
  • Switching regulators
  • Motor control

Comparison with other signal forms

RMS factors
Sine voltage:
Ueff = Us/√2 ≈ 0,707
Triangular voltage:
Ueff = Us/√3 ≈ 0,577
Square voltage:
Ueff = Us = 1,0
Sawtooth voltage:
Ueff = Us/√3 ≈ 0,577

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AC functions

Alternating voltage values  •  Alternating voltage and time  •  Frequency and wavelength  •  Alternating voltage value and angle  •  Frequency and periodic time  •  RMS value of a sinusoidal oscillation  •  RMS value of a sinusoidal oscillation with offset  •  RMS value of a sine pulse (half-wave rectification)  •  RMS value of a sine pulse (full-wave rectification)  •  RMS value of a square wave voltage  •  RMS value of a square pulse  •  RMS value of a triangle voltage  •  RMS value of a triangular pulse  •  RMS value of a sawtooth voltage  •  RMS value of a sawtooth pulse  •