Solnf99

Solnf99 - EE 4605 Homework/Solutions Homework 1: 1. (1.2-1)...

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1 SOLN.WXP EE 4605 Homework/Solutions Homework 1: 1. (1.2-1) Solutions 1: 1. 1e3 -24 -18 -12 -6 100 10e3 -30 0 Frequency (Hz) db(uv21) 100 -72 -54 -36 -18 80 160 240 320 10 1e3 -90 0 0 400 Frequency (MHz) DB(S21) ang(s21) 0.2 0.5 1 2 5 10 0.2 0.5 1 2 5 10 0 -0.2 -0.5 -1 -2 -5 -10 Sweeping C2:C (pF) @ 100 MHz s11 1 1: 15 pF 109.5, -66.81 <Rs, Xs> RC Filter 5-pole Filter with Angle 5-pole Filter with Autolines
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2 SOLN.WXP Homework 2: 2. (1.3-1) 3. the impedance formula for the parallel combination of , , and in terms of , , and Develop VP G V = 9 U . Solutions 2: 2. a. "!! œ Ê Z œ #!! Z œ "!! #‚&! W (1/2 used for peak to RMS conversion) V or V Š‹ Z # # Wß:/+5 69+.ß :/+5 Wß:/+5 b. Z œ "!! ‚ œ !Þ**!" "5 "5  "!!5 7 V ] œ "!  4'Þ#)$ ‚ "! Ê ^ œ  4 "5 "5 $ % 717.0 450.5 H H ] œ "!  4'Þ#)$ ‚ "! Ê ^ œ #&Þ$#  4"&*" "!!5 "!!5 & % then Z œ "!! ‚ œ "!! ‚ ^] ^ ^ ]  ] œ "!! ‚ œ "!! ‚ œ $)Þ*)Z "Þ!" ‚ "Þ'"# ‚ "! 'Þ#)% ‚ "! 7 "5 "!!5 "5 "!!5 "!!5 "5 % $ ºº º º "!  4'Þ#)$ ‚ "! "!  4# ‚ 'Þ#)$ ‚ "! & % $ % d. We would like to maintain 0.9901V vs f. Thus ] œ "!!] œ "!  4'Þ#)$ ‚ "! "5ß-9<</->/. "!!5 $ # 4F œ ]  ] œ 4'Þ#)$ "!  "! œ 4'Þ##! ‚ "! - "5ß-9<</->/. "5 # % $ ˆ‰ or Gœ ** pF across the 1k H pF total ab "!! [Note: the RC time constant for the 100k and the 1k are identical now (10 s ] ( Ñ e. The total impedance across the 50 H load is given by ^ œ ^ "  Þ!" œ #&Þ&(  4"'!( œ "Þ!" ‚ "! ²  4"'!( œ "'!( n  )*Þ" "!!5 & HH H ° The magnitude of this impedance is , giving a small error in the load kk ^ œ "'!( œ $#Þ"$ ‚ &! impedance. 3. Consider the parallel connection of , , and which has an impedance of G ^4 œ œ œ œ "V V  4 G "4 VG "4 VG ˆ = = == "" V4 P V P 9 V "4U = = = = 9 9 9 9 = = where = 99 9 œU œ V G œ PG P È and
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3 SOLN.WXP Homework 3: 4. 2.2-1 5. 2.3-1 Solutions 3: 4. a. H 1 pF 10 ; œ  " œ $ Ê P œ œ %(Þ(& Ð$ ‚ !! Ñ $ ‚ "!! #‚ " ! G œ œ %((Þ& Ð Ñ $ ‚ "! !! # ‚ "! $ É "!!! "!! ' $ ' 1 .H 1 H b. r P> 9 > + 6 $!! $! œ œ "! V œ ""! HH ab d. H pF ; ¸  " œ $Þ")! Ê P œ œ %&Þ&& Ð#)'Þ# Ñ $Þ") ‚ *! " ! G œ œ &!'Þ" Ð$"%Þ& Ñ $Þ") ‚ "! " ! É "!!! "!!"! ' $ ' 1 1 H Exact solution with H, , , < œ \ Î$! À U œ $!ß P œ %&Þ'" U œ $Þ"(" < œ *Þ&' PP 3 8 . ? - > 9 < P G œ &!%Þ) pF 5. a. pF H ; œ  " œ %Þ$&)* Ê \ œ  œ  &!; œ  #"(Þ*%& Ê G œ ($Þ!$ " G \ œ P œ œ ##*Þ% Á  \ Ê P œ $Þ'&" "!!! ; É "!!! &! G 9 P9 G = H =H . b. U œ œ œ #Þ*!' Ê F œ œ $Þ%% V²V \U "0 ##*Þ% => P "" #!!! "!!! 9 ˆ‰ MHz
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4 SOLN.WXP Homework 4: 6. 2.4-1 7. 2.4-2 8. 2.5-1 Solution 4: 6. a. V œ V Ê ; œ  " œ 'Þ#%& #!!! &! >= Ê \ œ V ‚ ; œ &! ‚ 'Þ#%& œ $"#Þ#& PP H. Ê P œ œ %*Þ(! $"#Þ#& 'Þ#)$ ‚ "! ' H \ œ  œ  $#!Þ#' V ; G"!:J > H Ê G œ  "! œ %)(Þ! " $#!Þ#' ‚ 'Þ#)$ ‚ "! ' pF pF b. U œ œ œ $Þ"## Ê F œ œ $#!Þ$ V²V \ $#!Þ#' $Þ"## "!!! "! => G"!:J ' kk kHz 7. "œ$ "!!! "!! Ê \ œ  œ  $$$Þ$ V ; \  \ œ ; ‚ V œ $!! G > PG # " # H H ÊG œ$! " pF U œ "! œ œ Ê \ œ #!!! V  V # ‚ "!! \ \ P #= = P P H (a bit large!) Pœ#! . H \ œ $!!  #!!! œ  "(!! œ  Ê G œ &Þ)) " G# # = 9# G pF (a bit small!) 8. U œ œ œ "! Ê ; œ #! Ê P œ #! ‚ "!! œ #!!! Ê P œ #! ;; " # ## V V #9 = > =H . H > V œ "!!! œ V Ê ;  " œ ;  " Ê ; œ 'Þ#&$ Ê G œ œ "Þ&** ;" ;  " "! 'Þ#&$ ‚ "! ‚ "!!! "" ># > " # # > # ) H ˆ‰ pF a bit small! #
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5 SOLN.WXP V œ #!  " "!! œ %!"!! \ œ œ œ #!!& œ VV V \ #!!! ; %!"!! ‚ "!! #: P: # #: # #: P# ˆ‰ HH \ œ œ œ '%"#Þ* V ; 'Þ#&$ %!"!! >: #: > H 4 G  œ Ê G œ œ $Þ%#) "" 4\ 4\  = = 9# # P: >: 9 '%"#Þ* #!!& pF Comment on Q: Odd Element Pi Tee \U œ U œ œ U œ œ U œ " ;; " " # " " $ ;; " " >> > V => = V ## > V = V ># > V = V How: (pi example used) " œ œ V²V \\ V V ; " = > >= > V V kk a b > = $ œ œ œ ¸ ;ß; ¦" \ VV ;; V V ab $ == #= # = V V ;" V #= V V V " " V >" = > " # " # # > = V > \ " # V= \ " # > = Œ Š‹ for # œ œ œ ¸ ;ß; ß;ß; ¦" \V V V ; ; "V #= > > # V \ => > # # V ;"
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Solnf99 - EE 4605 Homework/Solutions Homework 1: 1. (1.2-1)...

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