#### Question 7.3

## Dynamic range

The ability of an A/D converter to cope with both large and small signals is an important factor in waveform encoding, and the ratio of Vmax to Vmin over which a converter will operate is called the dynamic range. This parameter depends heavily on the resolution of the A/D, that is, the number of bits available to represent any given sample. The more bits in the converter, the more quantization levels the converter is using to match to any given waveform sample. It is not difficult to see that an n-bit converter can differentiate between 2n = M discrete signal levels and that the minimum signal variation that it can detect and represent is Vmax / M volts. This is often called the quantization step size. |

#### The dynamic range for an A/D converter is thus given by: #### Dynamic range = Vmax / Vmin = Vmax / (Vmax / M) = M or 2n #### Expressed in dBs, this gives us the well known formula: the dynamic range of a linear A/D is n x 6.02 dB.

An 8-bit converter thus has a dynamic range of approximately 48 dB.