ho9_l06_intrinsic_cap

ho9_l06_intrinsic_cap - Lecture 6 Intrinsic Capacitance...

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1 Lecture 6 Intrinsic Capacitance Bandwidth-Supply Current Tradeoff R. Dutton, B. Murmann R. Dutton, B. Murmann 1 EE114 (HO #9) Stanford University Common Source Amplifier Revisited Interesting question – How fast can this circuit go? R models finite resistance in the driving circui R i models finite resistance in the driving circuit – Needed for a realistic discussion “Transducer” V o V B R I B R. Dutton, B. Murmann 2 EE114 (HO #9) v i V I R i
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2 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 R. Dutton, B. Murmann 3 Knowing the time domain response, we can estimate the frequency domain response, and vice versa In EE114 we will mostly work with frequency domain analyses to argue about the useful frequency range of a circuit EE114 (HO #9) 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 R. Dutton, B. Murmann 4 GPS 1227 and 1575 MHz –… EE114 (HO #9)
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3 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 dt dv C i C C = R. Dutton, B. Murmann 5 EE114 (HO #9) Intuition – High frequency results in large dv C /dt and large i C – Capacitor becomes a “short” for high frequencies RC Low-pass R Laplace domain (ignoring initial condition) ω + σ = j s i C + v C =v o - + v i - dt dv C i C C = ) s ( sCv ) s ( i C C = 1 sC Z ) s ( i ) s ( v C C C 1 = = R. Dutton, B. Murmann 6 EE114 (HO #9) p s sRC R sC sC ) s ( v ) s ( v ) s ( H o o = + = + = = 1 1 1 1 1 RC p 1 = “Pole”
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4 Pole 3 0 1 2 3 |H(s)| RC=1 R. Dutton, B. Murmann 7 0 1 2 3 0 1 2 ω - σ EE114 (HO #9) Magnitude and Phase Evaluate H(s) for s=j ω – Steady-state phasor analysis () RC tan ) j ( H RC RC j ) j ( H ω = ω ω + = ω + = ω 1 2 1 1 1 1 Magnitude and phase of the transfer function are commonly R. Dutton, B. Murmann 8 EE114 (HO #9) 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
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5 Bode Plot 0 B] At ω = 1/RC = |p|: 10 -2 10 -1 10 0 10 1 10 2 -40 -20 |H(j ω )| [d -50 0 (j )] [deg] () = + = ω [dB] 3 2 1 20 2 1 1 1 1 2 log ) j ( H R. Dutton, B. Murmann 9 EE114 (HO #9) 10 -2 10 -1 10 0 10 1 10 2 -100 50 ω *RC Angle[H( ° = = ω 45 1 1 tan ) j ( H 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
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ho9_l06_intrinsic_cap - Lecture 6 Intrinsic Capacitance...

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