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EE 435 Lect 32 Spring 2010

EE 435 Lect 32 Spring 2010 - EE 435 Lecture 32 Quantization...

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EE 435 Lecture 32 Quantization Noise Absolute and Relative Accuracy DAC Design

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DFT Simulation from Matlab .• • • Review from last lecture .•
Summary of time and amplitude quantization assessment Time and amplitude quantization do not introduce harmonic distortion Time and amplitude quantization do increase the noise floor .• • • Review from last lecture .•

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Quantization Noise DACs and ADCs generally quantize both amplitude and time If converting a continuous-time signal (ADC) or generating a desired continuous- time signal (DAC) these quantizations cause a difference in time and amplitude from the desired signal First a few comments about Noise .• • • Review from last lecture .•
Noise We will define “Noise” to be the difference between the actual output and the desired output of a system Types of noise: Random noise due to movement of electrons in electronic circuits Interfering signals generated by other systems Interfering signals generated by a circuit or system itself Error signals associated with imperfect signal processing algorithms or circuits Quantization noise is a significant component of this noise in ADCs and DACs and is present even if the ADC or DAC is ideal .• • • Review from last lecture .•

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Quantization Noise in ADC Consider an Ideal ADC with first transition point at 0.5X LSB If the input is a low frequency sawtooth waveform of period T that goes from 0 to X REF , the error signal in the time domain will be: where T 1 =T/2 n This time-domain waveform is termed the Quantization Noise for the ADC with a sawtooth (or triangular) input (same concepts apply to DACs) .• • • Review from last lecture .•
Quantization Noise in ADC () 2 1 1 T/2 RMS 1 1 E T Q td t ε = X LSB 0.5T 1 X LSB -0.5T 1 LSB 1 X t T Q t ⎛⎞ =− ⎜⎟ ⎝⎠ 1 1 2 2 LSB RMS 11 1 E- t TT dt = X 1 1 3 RMS LSB 3 1 -T /2 1t E 3 T = X LSB RMS E 12 = X .• • • Review from last lecture .•

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Quantization Noise in ADC LSB RMS E 12 = X The signal to quantization noise ratio (SNR) can now be determined. Since the input signal is a sawtooth waveform of period T and amplitude X REF , it follows by the same analysis that it has an RMS value of REF RMS 12 = X X Thus the SNR is given by n RMS RMS RMS LSB SNR = 2 E = = XX X or, in dB, ( ) dB SNR =20 n log2 =6.02n Note: dB subscript often neglected when not concerned about confusion .• • • Review from last lecture .•
Quantization Noise in ADC ( ) SNR =20 n log2 =6.02n How does the SNR change if the input is a sinusoid that goes from 0 to X REF centered at X REF /2? .• • • Review from last lecture .•

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Quantization Noise in ADC How does the SNR change if the input is a sinusoid that goes from 0 to X REF centered at X REF /2?
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EE 435 Lect 32 Spring 2010 - EE 435 Lecture 32 Quantization...

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