26 Chapter 1
voltage, the same power would be dissipated by a DC voltage whose value was equal
to the square root of the mean of the square of the AC voltage. Thus the volt rms was
specifi ed. An AC signal of a given number of volts rms will dissipate exactly the same
amount of power in a given resistor as the same number of volts DC.
Figure 1.21(a) shows that for a sine wave the rms voltage is obtained by dividing the
peak voltage Vpk by the square root of 2. However, for a square wave [ Figure 1.21(b) ]
the rms voltage and the peak voltage are the same. Most moving coil AC voltmeters only
read correctly on sine waves, whereas many electronic meters incorporate a true rms
calculation.
On an oscilloscope it is often easier to measure the peak-to-peak voltage, which is twice
the peak voltage. The rms voltage cannot be measured directly on an oscilloscope since it
depends on the waveform, although the calculation is simple in the case of a sine wave.
1.12 The Decibel
The fi rst audio signals to be transmitted were on telephone lines. Where the wiring is long
compared to the electrical wavelength (not to be confused with the acoustic wavelength)
of the signal, a transmission line exists in which the distributed series inductance and the
parallel capacitance interact to give the line a characteristic impedance. In telephones this
Figure 1.21 : (a) For a sine wave the conversion factor from peak to rms is^12. (b) For a
square wave the peak and rms voltage are the same.