lecture_10_low_freq_distortion

# lecture_10_low_freq_distortion - Handout#10 EE 214 Winter...

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Handout #10 EE 214 Winter 2009 Low Frequency Distortion Analysis B. Murmann and B. A. Wooley Stanford University Corrections: 2/02/09: Added gain compression term in HD 2 expression on slide 13 2/02/09: Added I s term in derivation of a 1 on slide 19 2/02/09: Replaced v be /2V T with “x” in Taylor series for tanh() on slide 24 2/04/09: Added missing “3/4” in IM3 expression 2/06/09: Added “-” in a 3 expression and | | in sqrt() expression on slides 24, 26 Overview ± All electronic circuits exhibit some level of nonlinear behavior – The resulting waveform distortion is not captured in linearized small- signal models ± In this lecture, we will look at the basic tools needed to analyze “memoryless” nonlinearities, i.e. nonlinearities that can be represented by a frequency independent model Such models are valid in a frequency range where all capacitances – Such models are valid in a frequency range where all capacitances and inductances in the circuit of interest can be ignored ± As a driving example, we will analyze the nonlinearity in the V-I transduction of BJTs and MOSFETs ± The general approach taken is to model the nonlinearities via a power series that links the input and output of the circuit This approach is useful and accurate for the case of “small distortion” – This approach is useful and accurate for the case of small distortion and cannot be used to predict the effect of gross distortion, e.g. due to signal clipping B. A. Wooley, B. Murmann EE214 Winter 2008-09 2

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Small-Signal AC Model I o = I OQ + i o i o + V i = V IQ + v i o dI g + v i - g m v i - I o = f(V i ) iI Q m i VV IQ dV f'(V ) = = = i o v g m g m V V i i B. A. Wooley, B. Murmann EE214 Winter 2008-09 3 IQ Taylor Series Model 3 23 12 3 () IQ IQ IQ Q i I Q i I Q i I Q f '(V ) f ''(V ) f (V ) f(V ) f(V ) (V V ) (V V ) (V V ) ... !! ! =+ + + + (V f 2 (V i ) f(V i ) f 3 i ) f 2 (V i ) V IQ V i B. A. Wooley, B. Murmann EE214 Winter 2008-09 4 f 3 (V i )
Relationship Between Incremental Variables ± Using and iiI Q vV V =− ooO Q i I Q i I I f(V ) f(V ) =− = we obtain 23 12 3 oii i ia v a v a v . . . = +++ (m) f( V ) where ± Note tha IQ m a m! = ag Note that ± In practice, it is often sufficient to work with a truncated n th order power 1 m series 2 n n i v a v. . . a v ≅+ + + B. A. Wooley, B. Murmann EE214 Winter 2008-09 5 Graphical Illustration i o n=2 v i n →∞ ± A model that relates the incremental signal components (v i , i o ) though a n=3 nonlinear expression is sometimes called “large-signal AC model” ± The accuracy of a truncated power series model depends on the signal range and the curvature of the actual transfer function – Using a higher order series generally helps, but also makes the analysis more complex – As we will see, using a third order series is often sufficient to model B. A. Wooley, B. Murmann EE214 Winter 2008-09 6 the relevant distortion effects in practical, weakly nonlinear circuits

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Harmonic Distortion Analysis ± Apply a sinusoidal signal and collect harmonic terms in the output signal () ii ˆ vv c o s t = ⋅ω 23 11 21 33 cos cos cos cos cos ⎡⎤ α= α+ α () () () 12 3 oi i i ˆˆ ˆ i avcos t a vco s t a vcos t . . . = ω +
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lecture_10_low_freq_distortion - Handout#10 EE 214 Winter...

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