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Introduction to D/A and A/D conversion

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

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Introduction to D/A and A/D conversion

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

  2. 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

  3. 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

  4. 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 2B 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

  5. 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 2B values. Discrete time and discrete amplitude

  6. 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…

  7. 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

  8. 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

  9. 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) * 2B) • Where B is the number of bits in the A/D

  10. 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 / 2B - 1≈ 2*A / 2B • RMS quantization noise: q/(2*sqrt(3)) • fs ≥ 2*fmax from computed from the minimum attenuation level • Example Problem:

  11. A to D system with • 3rd 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

  12. Types of A/D chips

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