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frequencyanalysis - (Chapter3 section3.1 ECE412 (Fall2007...

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Adaptive Integrated Microsystems Basics of frequency analysis (Chapter 3:  section 3.1) ECE 412 Introduction to mixed-signal circuits (Fall 2007) Class website: http://www.egr.msu.edu/classes/ece412/shantanu
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Adaptive Integrated Microsystems DC gain versus High-frequency gain Gain ) || ( 2 1 1 ds ds m in in out v r r g V V V A - = - = - + 1 Q 2 Q - in V + in V b I 2 s V dd V dd V 3 Q 4 Q out V dd V 5 Q 6 Q Till now we calculated small signal DC gain: When the input signal changes by an increment, by how much does the output voltage change. Not concerned about speed, bandwidth and settling behavior of the amplifier. in V out V t
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Adaptive Integrated Microsystems DC gain versus AC gain Gain | ) ( | | ) ( | ) ( f V f V f A in out v = 1 Q 2 Q - in V + in V b I 2 s V dd V dd V 3 Q 4 Q out V dd V 5 Q 6 Q AC gain of the amplifier is defined as a small signal gain at a particular frequency. AC gain is defined as the ratio of the amplitude of the output sinusoid versus the amplitude of the input sinusoid. For a small signal model, if the input of the amplifier is a sinusoid, is the output a sinusoid ?
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Adaptive Integrated Microsystems Gain and Phase response (Bode-plots) Gain plot ) ( ) ( ) ( f V f V f A in out v = | ) ( | log 20 f A v in V out V ) ( f ∆Φ f 0 0 ) ( f ∆Φ ) ( dB (deg) f Phase plot Phase difference DC gain AC gain
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Adaptive Integrated Microsystems Fundamental rules of frequency analysis The relationship is independent of time. When the input voltage changes instantaneously, the current through a resistor changes instantaneously (without any delay). R in V R V I in in = in I dt dV C I in in = Voltage across a capacitor can NOT change instantaneously. DC current through a capacitor =0 C in V in I We will not consider inductors in this course. (But is important for radio-frequency integrated circuits).
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Adaptive Integrated Microsystems Analysis using Laplace transforms dt dv C R v v out out in = - C R in V out V ) ( ) ( ) ( t v t v dt t dv RC in out out = + How to solve the differential equation for a general class of input.
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