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
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! #
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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