# Lect_01 - ECE 442 ECE 442 1 Networks& Systems Jose E...

This preview shows pages 1–14. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE 442 ECE 442 1. Networks & Systems Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois [email protected] 1 Jose E. Schutt " Aine " ECE 442 1 2 3 What is Capacitance? 1 2 3 Voltage=0 No Charge Voltage build up Charge build up Voltage = 6V Charge=Q N C 2 Jose E. Schutt " Aine " ECE 442 No Current Transient Current No Current 4 5 6 What is Capacitance? 4 5 6 Voltage=6V Charge=Q Voltage decaying Charge decaying Voltage=0 No Charge No Curren 3 Jose E. Schutt " Aine " ECE 442 No Current Transient Current 4 5 6 What is Capacitance? 4 5 6 Voltage=6V Charge=Q Voltage decaying Charge decaying Voltage=0 No Charge No Curren 3 Jose E. Schutt " Aine " ECE 442 No Current Transient Current No Current Capacitance Relation: Q = Cv Q : charge stored by capacito Q : charge stored by capacitor C : capacitance : voltage across capacito v : voltage across capacitor i : current into capacitor ( ) dv dQ i t C dt dt ! ! dt dt 1 ( ) ( ) t v t i d " " ! # 4 Jose E. Schutt " Aine " ECE 442 C # What is Inductance? z- Current in wire produces magnetic field- Flux is magnetic field integrated over area r H Total Flux Linked Idl R Inductance Total Flux Linked Current ! 5 Jose E. Schutt " Aine " ECE 442 Inductance d \$ d L N di \$ ! \$ L I \$ ! ! ! 2 v B Hdv L I % ! # 6 Jose E. Schutt " Aine " ECE 442 Inductance Relation: \$ = Li \$ : flux stored by inducto \$ : flux stored by inductor L : inductance : current through inducto i : current through inductor v : voltage across inductor ( ) di d v t L dt dt \$ ! ! dt dt 1 ( ) ( ) t i t v d " " ! # 7 Jose E. Schutt " Aine " ECE 442 L # Low-Pass Circuit ( ) ( o dv i t C i t ( ) ( ) o R C i t C i t dt ! ! ( ) ( ) ( ) i R o v t Ri t v t ! & ( ) ( ) o i o dv v t RC v t dt ! & Need to solve for v o (t) 8 Jose E. Schutt " Aine " ECE 442 Reactive Circuit ( ) ( ) ( ) C R L i t i t i t ! & Need to solve for v x (t) L x di v L dt ! ’ ( i x C d v v i C ) ! 9 Jose E. Schutt " Aine " ECE 442 dt C dt Laplace Transforms The Laplace transform F(s) of a function f(t) is defined as: * + ( ) ( ) ( ) st L f t f t e dt F s , ) ! ! # To a mathematician, this is very meaningful; however circuit engineers seldom use that however circuit engineers seldom use that integral The Laplace transform provides a conversion from the time domain into a new domain, the s domain 10 Jose E. Schutt " Aine " ECE 442 Laplace Transforms The Laplace transform of the derivative of a function f(t) is given by ( ) ( ) st df t d f t , )- . ( ) st L e d t s F s dt dt )- . ! ! / 1 2 # Differentiation in the time domain becomes a multiplication in the s domain. That is why Laplace transforms are useful to circuit engineers s = 3 11 Jose E. Schutt " Aine " ECE 442 s = j 3 Low-Pass Circuit Time s ( ) ( ) o o v t V s 4 domain domain ( ) ( ) o o dv t sV s dt 4 Time domain ( ) ( ) o i o dv v t RC v t dt ! & ( ) ( ) ( ) i o o V s sRCV s V s ! & Time domain s domain 12 Jose E. Schutt " Aine " ECE 442 dt Low-Pass Circuit - Solution ( ) ( ) 1 ( ) 1 ( ) 1 i o o i V s V s...
View Full Document

{[ snackBarMessage ]}

### Page1 / 55

Lect_01 - ECE 442 ECE 442 1 Networks& Systems Jose E...

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online