Question

Derive the RMS value of a 2Vpp a) sine wave, b) square wave, and c) sawtooth wave. Note that an RMS value can be defined for a current signal as well.

VRMs or Irms √1/T ∫ᵀ₀ x²(t)dt

Answer 1

The RMS values for a 2Vpp sine wave is 0.707V, for a square wave is 1V, and for a sawtooth wave is approximately 0.577V. These values are derived using the formula Vrms = Vpp / (2√2) for a sine wave, Vrms = Vpp / 2 for a square wave, and Vrms = Vpp / (2√3) for a sawtooth wave.

Step-by-step explanation:

The question pertains to the calculation of the root mean square (RMS) value of different waveforms. The RMS value is particularly useful in electrical engineering because it represents the effective value of a varying voltage or current, akin to the constant value in a DC circuit that would deliver the same power. Here's how to derive the RMS values for different waveforms from their peak-to-peak values (Vpp):

• For a sine wave: Vrms = Vpp / (2√2), given that the peak voltage (Vo) is Vpp/2.
• For a square wave: Since the value is constant at its peak, Vrms = Vpp / 2.
• For a sawtooth wave: The RMS value of a sawtooth wave with peak voltage Vo is Vrms = Vo / √3, and since Vo is Vpp/2, the RMS value is Vpp / (2√3).

In these formulas, T is the period of the waveform and x(t) is the instantaneous value of the voltage or current.