Frequency Response. We now know how to analyze and design ccts via s- domain methods which yield dynamical information

Transcription

1 Frequency Repone We now now how o analyze and deign cc via - domain mehod which yield dynamical informaion Zero-ae repone Zero-inpu repone Naural repone Forced repone The repone are decribed by he exponenial mode The mode are deermined by he pole of he repone Laplace Tranform We nex will loo a decribing cc performance via frequency repone mehod Thi guide u in pecifying he cc pole and zero poiion MAE140 Linear Circui 166

2 Tranfer funcion Tranfer funcion; meaure inpu a one por, oupu a anoher I 1 V 1 - I 2 V 2 - Inpu Oupu Tranfer funcion zero - ae repone ranform inpu ignal ranform I.e., wha he circui doe o your inpu MAE140 Linear Circui 167

3 Sinuoidal Seady-Sae Repone Conider a able ranfer funcion wih a inuoidal inpu vaco A V 2 2 The Laplace Tranform of he repone ha pole Where he naural cc mode lie Thee are in he open lef half plane Re<0 A he inpu mode and - Only he repone due o he pole on he imaginary axi remain afer a ufficienly long ime Thi i he inuoidal eady-ae repone MAE140 Linear Circui 168

4 Sinuoidal Seady-Sae Repone cond Inpu Tranform x Aco" # Aco" co# $ Ain" in# X Aco" 2 # $ Ain" # 2 2 # 2 Repone Tranform Y TX " # * # " p 1 " p 2 N " p N Repone Signal y e " * e # " 1 e p 1 2 e p 2... N e p N forced repone Sinuoidal Seady Sae Repone naural repone y SS e * " e MAE140 Linear Circui 169

5 MAE140 Linear Circui 170 Sinuoidal Seady-Sae Repone cond Calculaing he SSS repone o Reidue calculaion Signal calculaion [ ] [ ] in co in co lim lim lim " " " " " " T e AT T Ae A T A T X T Y # $ $ $ % & ' * % & ' * co 2 * 1 e e e e y SS co φ T AT y SS L co φ A x

6 Sinuoidal Seady-Sae Repone cond Repone o i y SS AT co φ T Oupu frequency inpu frequency Oupu ampliude inpu ampliude T Oupu phae x Aco φ inpu phae T The Frequency Repone of he ranfer funcion T i given by i evaluaion a a funcion of a complex variable a We pea of he ampliude repone and of he phae repone They canno independenly be varied Bode relaion of analyic funcion heory MAE140 Linear Circui 171

7 Example 11-13, T&R 5h ed, p 527 Find he eady ae oupu for v 1 Acoφ Compue he -domain ranfer funcion T Volage divider V 1 Compue he frequency repone T _ T R 2 L R R L R R L 2, V 2 - T ' an ' 1 & L $ % R # " Compue he eady ae oupu AR v 2SS R 2 "L 2 co " # $ an$1 "L / R MAE140 Linear Circui [ ] 172

8 Terminology for Frequency Repone Baed on hape of gain funcion of frequency Low-pa filer:paband plu opband Paband: range of frequencie wih nearly conan gain High-pa filer: opband plu paband Sopband: range of frequency wih ignificanly reduced gain Cuoff frequency: frequency aociaed wih raniion beween band T " C 1 2 T max Bandpa filer: one paband wih wo adacen opband Bandop filer: one opband wih wo adacen paband MAE140 Linear Circui 173

9 Frequency Repone Bode Diagram Log-log plo of magt, log-linear plo argt veru Bode Diagram 0 B d Magniude db e d u i n g a M g e d Phae deg e a h P T " db 20log 10 T " paband " cuoff freq opband Frequency rad/ec MAE140 Linear Circui 174

10 Malab Command for Bode Diagram Specify componen value Se up ranfer funcion >> R1000;L0.01; >> ZfR,[L R] Tranfer funcion: >> bodez MAE140 Linear Circui 175

11 Frequency Repone Decripor Lowpa Filer [num,den]buer6,1000,''; lpafnum,den; lpa Tranfer funcion: 1e ^ ^ e06 ^ e09 ^ e12 ^ e15 1e18 bodelpa MAE140 Linear Circui 176

12 High Pa Filer [num,den]buer6,2000,'high',''; hpafnum,den Tranfer funcion: ^ ^ ^ e07 ^ e10 ^ e14 ^ e17 6.4e19 bodehpa MAE140 Linear Circui 177

13 Bandpa Filer [num,den]buer6,[ ],''; bpafnum,den Tranfer funcion: 1e18 ^ ^ ^ e07 ^ e10 ^ e14 ^ e17 ^7 3.7e20 ^ e23 ^ e26 ^ e29 ^ e32 ^ e35 6.4e37 bodebpa MAE140 Linear Circui 178

14 Bandop Filer [num,den]buer6,[ ],'op',''; bopfnum,den Tranfer funcion: ^12 1.2e07 ^10 6e13 ^8 1.6e20 ^6 2.4e26 ^4 1.92e32 ^2 6.4e ^ ^ e07 ^ e10 ^ e14 ^ e17 ^7 3.7e20 ^ e23 ^ e26 ^ e29 ^ e32 ^ e35 6.4e37 bodebop MAE140 Linear Circui 179