# Characteristics of a Quantization

In A/D converters the original analog signal has essentially an infinite resolution, as the signal is continuous. The digital representation of this signal would of course reduce the resolution, as digital quantities are discrete and vary in equal steps.

Consider analog voltage in the range of 0 to V and a 3-bit digital output for any voltage in this range. Let us divide the whole range of analog voltage into 8 intervals of the size S V/8, Each interval is assigned a unique digital value. This process is referred to as quantization. In order to convert an analog quantity to a digital number involves quantization. The characteristics of a quantizer are shown in Fig 1.2 (a).

This quantizer is used for conversion of the analog voltage of 0-7 V Now in Binary code, decimal number 7-binary 111 Therefore the digital number has 3 bits. The analog input is shown in Fig 1.2 (a) on the horizontal axis and the discrete output voltage level on the vertical axis. The basic operation of A/D conversion two processes, viz.,

• quantization
• coding. The decision levels of the A/D converting are at 0.5,1.5,2.5,3.5, etc. Thus the design levels are spaced 1 V apart. Analog values between two decision levels cannot values between l+0,5 are read as digital value 001. The distance between decision levels is Q, the quantization size. In a bit A/D converter has 2n discrete levels with resolution=1/2 n or 1 part in 2n analog decision levels=2n-1.

If the input to the quantizer is moved through its full range and subtracted from the discrete output levels. The error signal is shown in Fig 1.2 (b). This is called quantization error. The quantization error is dependent on the number of quantization levels. The quantization levels are an index of the resolution of the instrument. The quantization error is of a sawtooth waveform as shown in fig 1.2 (b). The peak to peak-to-peak value is Q. The output of the quantizer can be can consider as a noise signal with a value of Eq Q/2 Square root 3.