Section 3.2 Characterizing Signal Size
With AC signals, there are multiple ways to represent amplitude. Here, we will examine methods of characterizing voltage amplitudes, but all methods discussed apply equally well to any other sinusoidally-varying quantity.
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Peak voltage \(V_p\) corresponds to the traditional definition of amplitude for a sinusoidal waveform where \(V_p = V_\text{max}\text{.}\)
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Peak-to-Peak voltage \(V_{pp}=V_\text{max}-V_\text{min} = 2V_p\text{.}\)
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Root-mean-square (RMS) amplitude is calculated by examining a single cycle of data \(\left(V(t_i)\right)\) containing \(n\) measurements where \(t_i\) \(\left(i=1..(n-1)\right)\) are the discrete values of time for which measurements were recorded. Then,\begin{equation*} V_\text{rms}=\sqrt{\frac{\sum\limits_{i=1}^{n} V_i^2}{n}} \end{equation*}which is \(V_p/\sqrt{2}\) for sinusoidal waves.
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The average power \(P_\text{avg}\) dissipated in a resistor \(R\) due to a sinusoidal signal is\begin{equation*} P_\text{avg}=I_\text{rms}^2 R = \frac{V_\text{rms}^2}{R}\text{.} \end{equation*}
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Power in a signal \(P_2\) (with amplitude \(A_2\)) relative to the power in some other signal \(P_1\) (with amplitude \(A_1\)) can be represented using a logarithmic scale called decibels, where\begin{align*} P_\text{dB} \amp =10\log_{10}\left(\frac{P_2}{P_1}\right)\\ \amp = 20\log_{10}\left(\frac{A_2}{A_1}\right) \text{.} \end{align*}
