Deriviation of RMS value of full wave and half wave rectifier signal
- Thread starter Niero
- Start date
any answers will be appreciated thankz in advance.
The traditional math approach ....
For the full-wave
\(V_{rms}=\sqr{\frac{2}{T}\int_0^{\frac{T}{2}}{(V_msin(\omega t))}^2}dt=\sqr{\frac{2}{T}\int_0^{\frac{T}{2}}{V_m}^2sin^2(\omega t)}dt\)
For the half-wave
\(V_{rms}=\sqr{\frac{1}{T}\int_0^{\frac{T}{2}}{(V_msin(\omega t))}^2}dt=\sqr{\frac{1}{T}\int_0^{\frac{T}{2}}{V_m}^2sin^2(\omega t)}dt\)
\(\omega=\frac{2\pi}{T}\)
Use
\(sin^2(\omega t)=\frac{1-cos(2\omega t)}{2}\) to do the integration.
\(\int \frac{1-cos(2\omega t)}{2}dt=\frac{t}{2}-\frac{sin(2\omega t)}{4\omega}\)
You should try to do some of the math work yourself to prove
Vrms[full-wave]=Vm/√2
Vrm[half-wave]=Vm/2
For the full-wave
\(V_{rms}=\sqr{\frac{2}{T}\int_0^{\frac{T}{2}}{(V_msin(\omega t))}^2}dt=\sqr{\frac{2}{T}\int_0^{\frac{T}{2}}{V_m}^2sin^2(\omega t)}dt\)
For the half-wave
\(V_{rms}=\sqr{\frac{1}{T}\int_0^{\frac{T}{2}}{(V_msin(\omega t))}^2}dt=\sqr{\frac{1}{T}\int_0^{\frac{T}{2}}{V_m}^2sin^2(\omega t)}dt\)
\(\omega=\frac{2\pi}{T}\)
Use
\(sin^2(\omega t)=\frac{1-cos(2\omega t)}{2}\) to do the integration.
\(\int \frac{1-cos(2\omega t)}{2}dt=\frac{t}{2}-\frac{sin(2\omega t)}{4\omega}\)
You should try to do some of the math work yourself to prove
Vrms[full-wave]=Vm/√2
Vrm[half-wave]=Vm/2
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