Introduction to D/A and A/D conversion Professor: Dr. Miguel Alonso Jr.

Outline Analog to Digital Conversion Process Sampling – lowpass and bandpass signals Uniform and non-uniform quantization and encoding Oversampling in A/D D/A conversion: signal recovery The DAC Oversampling in D/A conversion

Analog to digital conversion process Most signals in nature are in analog form In order for transmission through a digital communication system, they must be sampled Untill now we have seen, PAM, PWM, PPM, and DM DM was the first step towards representing the amplitude of the analog signal ( the intelligence or message we are trying to send) into a binary number for transmission

Steps for A/D conversion are Bandlimit the signal: anti-aliasing low-pass filter Sample the analog signal into a discrete-time and continuous amplitude signal Convert the amplitude of each signal sample into one of 2 B levels, where B is the number of bits used to represent a sample in the ADC The discrete amplitude levels are represented or encoded into distinct binary words each of length B bits

Analog input signal – continuous in time and amplitude Sampled Signal – continuos in amplitude, but only defined at discrete points in time. Thus, the signal is zero except at time t=nT ( where T is the sampling period and n is the sample number Digital signal – signal exists only at discrete points in time and at each time point, can only have one of 2 B values. Discrete time and discrete amplitude

The discrete-time signal and the digital signal can each be represented as a sequence of numbers, x(nT), or simply x(n) where n=0,1,2,3,4…

Sampling- lowpass and bandpass The sampling theorem: if the highest frequency component in a signal is fmax, then the signal should be sampled at a rate of at least 2*fmax for the samples to describe the signal completely Fs ≥ 2*fmax

Aliasing and spectra of sampled signals Suppose a signal is sampled at a frequency of 1/T hertz There exists another frequency component with the same set of samples as the original. Thus, the frequency component can be mistaken for the lower frequency component This is aliasing

Anti-aliasing filtering To reduce the effects of aliasing, sharp cutoff anti-aliasing filters are used to bandlimit the signal Or, the sampling frequency is increased Ideally, the AA filter should remove all frequency components above the fold over frequency Practical filters: stop band attenuation is given by Amin = 20 log (sqrt(1.5) * 2 B ) Where B is the number of bits in the A/D

Key Equations for A/D Amplitude response of a butterworth filter: where N is the filter order RMS of the input: A/sqrt(2) Quantization Step Size: q = 2*A / 2 B - 1≈ 2*A / 2 B RMS quantization noise: q/(2*sqrt(3)) fs ≥ 2*fmax from computed from the minimum attenuation level Example Problem:

A to D system with 3 rd Order butterworth AA filter 12-bit ADC with sample and hold Find: the minimum stop band attenuation, Amin, for the AA filter Minimum sampling frequency Fs

Types of A/D chips