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EE 435 Lect 28 Spring 2010

EE 435 Lect 28 Spring 2010 - EE 435 Lecture 28 Data...

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EE 435 Lecture 28 Data Converters Spectral Performance
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Spectral Characterization .• Review from last lecture .• • •
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INL Often Not a Good Measure of Linearity X IN X OUT X REF X REF X IN X OUT X REF X REF X IN X OUT X REF X REF X IN X OUT X REF X REF Four identical INL with dramatically different linearity .• Review from last lecture .• • •
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Linearity Issues INL is often not adequate for predicting the linearity performance of a data converter Distortion (or lack thereof) is of major concern in many applications Distortion is generally characterized in terms of the harmonics that may appear in a waveform .• Review from last lecture .• • •
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Spectral Analysis T 2 π ω = ( ) = + + = 1 k k k 0 θ t k ω sin A A f(t) alternately ( ) ( ) = = + + = 1 k k 1 k k 0 t k ω cos b t k ω sin a A f(t) 2 k 2 k k b a A + = If f(t) is periodic Termed the Fourier Series Representation of f(t)
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Spectral Analysis Nonlinear System (weakly) X IN (t) X OUT (t) Often the system of interest is ideally linear but practically it is weakly nonlinear. Often the input is nearly periodic and often sinusoidal and in latter case desired output is also sinusoidal Weak nonlinearity will cause distortion of signal as is propagated through the system Spectral analysis often used to characterize effects of the weak nonlinearity
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Spectral Analysis Nonlinear System X IN (t) X OUT (t) If ( ) ( ) θ ω t sin X t X m IN + = ( ) = + + = 1 k k k 0 OUT θ t ω k sin A A (t) X All spectral performance metrics depend upon the sequence = 0 k k A Spectral performance metrics of interest: SNDR, SDR, THD, SFDR, IMOD
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Distortion Analysis = 0 k k A A 1 is termed the fundamental A k is termed the kth harmonic k k A 1 2 3 4 5 6 Often termed the DFT coefficients (will show later) Spectral lines, not a continuous function
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Distortion Analysis = 0 k k A k A Often ideal response will have only fundamental present and all remaining spectral terms will vanish
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Distortion Analysis = 0 k k A k k A 1 2 3 4 5 6 For a low distortion signal, the 2 nd and higher harmonics are generally much smaller than the fundamental The magnitude of the harmonics generally decrease rapidly with k for low distortion signals
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Distortion Analysis k A f(t) is band-limited to frequency 2 π f k if A k =0 for all k>k x
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