part3 - Part 3: System Modeling and Analysis Circuit Theory...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Part 3: System Modeling and Analysis Circuit Theory z Voltage-Current Relationship z Resistor z Capacitor z Inductor R i v R R = C C i dt dv C = L L v dt di L = Kirchhoff’s voltage law (KVL) z Conservation of electrostatic field z Apply to a loop – a closed path z The algebraic sum of the voltage dropped in a closed path circuit is equal to the algebraic sum of the source voltage applied. 3 2 1 v v v v S + + = Kirchhoff’s current law (KCL) z Conservation of charge z Apply to a junction or a node in a circuit - a point in the circuit where charge has several possible paths to travel z The sum of the currents flowing into a junction is equal to the sum of the currents flowing out of that same point. 3 2 1 i i i i R + + = Something you should know z Mathematics ¡ Complex Number ¡ Exponential Functions L + + + + = ! 3 ! 2 1 3 2 x x x e x x x e dx de = 1 − = j 1 2 − = j ( ) ( ) t j t e t j ω ω ω sin cos + = t j t j e j dt de ω ω ω = c e j dt e t j t j + = ∫ ω ω ω 1 ( ) ( ) 2 2 1 b a jb a jb a jb a jb a jb a + − = − + − = + ( ) a b j e b a jb a 1 tan 2 2 − + = + System Modeling - Ordinary Differential Equation z A linear time-invariant system is usually modeled as an ordinary differential equation: where x(t) and y(t) are the input and output of the system, respectively; all the coefficients are constant. z Let p be the differentiation operation z ( ♦ ) can be rewritten as or where D(p) and N(p) are polynomials of p; ( ) ( ) ( ) ( ) t x p N t y p D = x b dt x d b y a dt dy a dt y d a dt y d a o m m m n n n n n n + + = + + + + − − − L L 1 1 1 1 dt d p = ( ) ( ) ( ) ( ) t x b p b p b t y a p a p a p a m m n n n n 1 1 1 1 + + + = + + + + − − L L ( ) k k k dt y d t y p = ( ♦ ) How to find the system output if the input is a trigonometric function? Approach 1. Assume a complex exponential input. Eg. 2. Refer to ( ♦ ), the frequency remains unchanged for an ODE. Assume the output function as 3. Replace x and y in ( ♦ ) with the corresponding exponential functions....
View Full Document

Page1 / 13

part3 - Part 3: System Modeling and Analysis Circuit Theory...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online