# Review_Ex2 - Low-Pass Circuit In frequency domain Vi 1 Vo =...

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1 Jose E. Schutt Aine ECE 442 Low-Pass Circuit In frequency domain: 1 1 i o V V j C R jC ω =⋅ + 1 11 io ov i VV VA j RC V j RC ωω =⇒ = = ++ 2 / v A jR C j f f ==

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2 Jose E. Schutt Aine ECE 442 2 11 22 f RC π πτ == 2 time constant RC τ = = Low-Pass Circuit
3 Jose E. Schutt Aine ECE 442 If f 2 = 2f 1 , then f 2 is one octave above f 1 If f 2 = 10f 1 , then f 2 is one decade above f 1 22 21 0 11 # log 3.32log ff of octaves == 2 10 1 #l o g f of decades f = 2 GHz is one octave above 1 GHz 10 GHz is one decade above 1 GHz Octave & Decade

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4 Jose E. Schutt Aine ECE 442 Model for general Amplifying Element C c1 and C c2 are coupling capacitors (large) Î μ F C in and C out are parasitic capacitors (small) Î pF
5 Jose E. Schutt Aine ECE 442 Example: R out = 3 k Ω , R g =200 Ω , R in =12 k Ω , R L =10 k Ω C in =200 pF and C out =40 pF 1 10 1 4.05 2 2 10 (12,200 200) h f MHz π == ×× × & 2 12 1 1.72 2 40 10 (10,000 3,000) h f MHz × & 6 4.05 10 log 5.52 5 12.2 ⎛⎞ × =≈ ⎜⎟ ⎝⎠ decades Summary: low-frequency <12.2 Hz, High frequency > 1.72 MHz Example

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6 Jose E. Schutt Aine ECE 442 o m gs gd gs Ig V s C V =− Unity-Gain Frequency f T f T is defined as the frequency at which the short-circuit current gain of the common source configuration becomes unity (neglect sC gd V gs since C gd is small) om g s V () i gs gs gd I V sC C = + i gs gd I s CC = + s j ω = Define:
7 Jose E. Schutt Aine ECE 442 For s=j ω , magnitude of current gain becomes unity at () 2 mm TT gs gd gs gd gg f CC ω π =⇒ = + + f T ~ 100 MHz for 5- μ m CMOS, f T ~ several GHz for 0.13 μ m CMOS Calculating f T

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8 Jose E. Schutt Aine ECE 442 () 2 m T g f CC π μ = + From which we get 2 mm TT gg f πμ ω += = , Thus C C C C μπ ωω + =⇒ =− BJT Short-Circuit Current Gain
9 Jose E. Schutt Aine ECE 442 () ' 1 Miller Capacitance =+ = eq gd m L CC g R Define C eq such that CS – Miller Effect (Textbook) ' 1 2 π == Ho in sig ff CR = + in eq gs CCC

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10 Jose E. Schutt Aine ECE 442 R sig = 100 k Ω , R G =4.7 M Ω , R D =15 k Ω , g m =1mA/V, r ds =150 k Ω , R L =10 k Ω, C gs =1 pF and C gd =0.4 pF ' 4.7 17 . 1 4 7 4.7 0.1 =− × × ++ G Mm L Gs i g R Ag R RR () ' :1 eq M m L gd Miller Cap C C g RC == + Example ' 150 15 15 7.14 =≈ = ≈≈= Ω Ld s D L Rr R R k ( ) 0.4 1 7.14 3.26 M Cp F + =
11 Jose E. Schutt Aine ECE 442 () 1 2 H in sig G f CR R π = & Upper 3 dB frequency is at: 1.0 3.26 4.26 = += in Cp F 12 6 1 3.82 2 4.26 10 0.1 4.7 10 H f kHz == ×× × × & 3.82 H fk H z = Example (cont’)

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12 Jose E. Schutt Aine ECE 442 Bipolar Miller Effect (Textbook) ' 1 2 o in sig f CR π = ' 1 2 Ho in sig ff == ( ) ' 1 in eq m L where C C C C C g R ππ μ =+ +
13 Jose E. Schutt Aine ECE 442 CS – Miller Effect – Exact Analysis

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14 Jose E. Schutt Aine ECE 442 i i 1 G R = = D D 1 G R = g g 1 G R = ds ds 1 g r ( ) ' iD m g d o '' 2 ' i i g gs gd gd D i g gd m D gd gs D GR g sC v v GG s C C s C RGG s C g Rs C C R =− ⎡⎤ ++ + + + + + ⎣⎦ CS – Miller Effect – Exact Analysis ' DD d s D ds 1 RRr Gg == + &
15 Jose E. Schutt Aine ECE 442 2' ' gd gs D gd m D gs m sC C R sC g Ro r s C g ±± We neglect the terms in s 2 since ( ) () () ' iD m g d o '' i i g gs gd m D gd D i g GR g v v GG s C C 1 g R C R =− ++ + + + + i i 1 R G = If we multiply through by CS – Miller Effect – Exact Analysis

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## This note was uploaded on 09/07/2011 for the course ECE 442 taught by Professor Schutt-aine during the Summer '08 term at University of Illinois at Urbana–Champaign.

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Review_Ex2 - Low-Pass Circuit In frequency domain Vi 1 Vo =...

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