# Chapter 3

# AD/DA Conversions

The conversion of a continuous-time function *x*(*t*) (voltage, current) into a sequence of numbers *x*(*n*) is called analog-to-digital conversion (AD conversion). The reverse process is known as digital-to-analog conversion (DA conversion). The time-sampling of a function *x*(*t*) is described by *Shannon's sampling theorem*. This states that a continuous-time signal with bandwidth *f*_{B} can be sampled with a sampling rate *f*_{S} > 2*f*_{B} without changing the information content in the signal. The original analog signal is reconstructed by low-pass filtering with bandwidth *f*_{B}. Besides time-sampling, the nonlinear procedure of digitizing the continuous-valued amplitude (quantization) of the sampled signal occurs. In Section 3.1 basic concepts of Nyquist sampling, oversampling and delta-sigma modulation are presented. In Sections 3.2 and 3.3 principles of AD and DA converter circuits are discussed.

## 3.1 Methods

### 3.1.1 Nyquist Sampling

The sampling of a signal with sampling rate *f*_{S} > 2*f*_{B} is called Nyquist sampling. The schematic diagram in Fig. 3.1 shows the procedure. The band-limiting of the input at *f*_{S}/2 is carried out by an analog low-pass filter (Fig. 3.1a). The following sample-and-hold circuit samples the band-limited input at a sampling rate *f*_{S}. The constant amplitude of the time function over the sampling period *T*_{S} = 1/*f*_{S} is converted to a number sequence *x*(*n*) by a quantizer (Fig. 3.1b). This number sequence is fed to a digital signal processor (DSP) which performs signal ...