l value of the digital codeword. We may now calculate the mean square noise over the entire The circuit illustrated in Figure 19.18 is simple, but it suffers some quantiser dynamic range by averaging E over all values of i as in drawbacks. The linearity and monotonicity are both critically de- Equation 19.47, where P is probability of the signal voltage being pendent on the precision of the resistors used. Any errors in resistor in the ith interval and N is total number of quantisation intervals in value will show particularly around the transition between the lower the entire converter dynamic range. and upper halves of the converter's dynamic range. The resistor values will also almost certainly drift slowly with time and tempera- (19.47) ture. More elaborate designs based on the resistor ladder network overcome this drawback (Wallace et al., 1991). 19.4.4 Quantisation distortion The digital signal can only represent a finite number of input signal voltages. For example, a binary code of k digits can only represent For the important case of a uniform quantiser, where all intervals 2k different input voltages. When the signal is reconstructed at the have the same width (A) Equation 19.48 is obtained. receiver, it is an approximation to the original signal, since it can only change in discrete voltage steps. This signal is said to be (19.48) quantised, and a form of non-linear distortion, known as quantisa- tion distortion, has been introduced. The difference between the original signal and the reconstructed signal is the error voltage. Because the error voltage varies ran- For a sinsuoidal input signal, the maximum amplitude which can domly with time, it is often referred to colloquially as 'quantisation be handled is given by Equation 19.49, SO the signal power is given noise'. Indeed, in PCM telephony, it sounds just like noise. If the by Equation 19.50. acceptable r.m.s. noise voltage in an analogue signal is o, then a discrete representation with a voltage level spacing of the order of o will be adequate to 