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 .•
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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 .•
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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 .•
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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 .•
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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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This note was uploaded on 01/31/2012 for the course EE 345 taught by Professor Geiger during the Fall '11 term at Iowa State.

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

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