Lect.6.Intrinsic.Cap

# Lect.6.Intrinsic.Cap - L e c tu r e 6 In t r in s ic C a p...

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R. Dutton, B. Murmann 1 Lecture 6 Intrinsic Capacitance Bandwidth-Supply Current Tradeoff R. Dutton, B. Murmann Stanford University EE114/214A

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R. Dutton, B. Murmann 2 Common Source Amplifier Revisited Interesting question How fast can this circuit go? R i models finite resistance in the driving circuit Needed for a realistic discussion v i V I R i “Transducer” V o V B R I B EE114/214A
R. Dutton, B. Murmann 3 Circuit Speed There are two perspectives on “how fast” a circuit can go Somewhat dependent on the application which one of the two matters more Time domain Apply a transient at the input (e.g. a voltage step), measure how fast the output settles Frequency domain Apply a sinusoid at the input, measure the gain and phase of the circuit transfer function across frequency Knowing the time domain response, we can estimate the frequency domain response, and vice versa In EE114/214A we will mostly work with frequency domain analyses to argue about the useful frequency range of a circuit EE114/214A

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R. Dutton, B. Murmann 4 Application Perspective Frequency ranges for various applications Audio ~20Hz to 20kHz Video signals ~50MHz Cable TV ~100-800MHz – Radios AM ~500kHz–1700kHz FM ~100MHz Wireless LAN ~2.4GHz or 5GHz Cellular phones ~1GHz GPS ~1227 and 1575 MHz – … EE114/214A
R. Dutton, B. Murmann 5 The Culprit In practical circuits, the presence of capacitance prevents us from building circuits that can run “infinitely” fast Sometimes inductors can be used improve the situation See EE314 i C + v C - dt dv C i C C = Intuition High frequency results in large dv C /dt and large i C Capacitor becomes a “short” for high frequencies EE114/214A

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R. Dutton, B. Murmann 6 RC Low-pass i C + v C =v o - + v i - R dt dv C i C C = ) s ( sCv ) s ( i C C = Laplace domain (ignoring initial condition) H ( s ) = v o ( s ) v i ( s ) = 1 sC 1 sC + R = 1 1 + sRC = 1 1 " s p sC Z ) s ( i ) s ( v C C C 1 = = RC p 1 ! = “Pole” ! + " = j s EE114/214A
R. Dutton, B. Murmann 7 0 1 2 3 0 1 2 3 0 1 2 3 ! - " | H ( s ) | Pole RC=1 -1/RC j ! " s EE114/214A

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R. Dutton, B. Murmann 8 Magnitude and Phase Evaluate H(s) for s=j ω Steady-state phasor analysis ( ) ( ) RC tan ) j ( H RC RC j ) j ( H ! " = ! # ! + = ! + = ! " 1 2 1 1 1 1 Magnitude and phase of the transfer function are commonly illustrated using Bode plots Simply a log-log plot of the magnitude along with a log-angle plot for the phase (note red dashed curve on Slide 7) EE114/214A
R. Dutton, B. Murmann 9 Bode Plot 10 -2 10 -1 10 0 10 1 10 2 -40 -20 0 | H ( j ! ) | [ d B ] 10 -2 10 -1 10 0 10 1 10 2 -100 -50 0 ! *RC A n g l e [ H ( j ! ) ] [ d e g ] At ω = 1/RC = |p|: ( ) ( ) ° ! = ! = " # ! \$ % & ( ) * + = + = " ! 45 1 [dB] 3 2 1 20 2 1 1 1 1 1 2 tan ) j ( H log ) j ( H EE114/214A

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R. Dutton, B. Murmann 10 Zeros Many circuit transfer functions also contain zeros In most cases that we are interested in, zeros occur beyond the dominant pole frequencies and can intuitively be related to “some” mechanism preventing further transfer function roll-off A simple example + v o - + v i - R C R p s z s RC s sRC R R sC R sC )
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