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frequencyanalysis

# 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
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
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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