EE 230 Lecture 24 Spring 2010

EE 230 Lecture 24 Spring 2010 - EE 230 Lecture 24 Waveform...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
EE 230 Lecture 24 Waveform Generators - Sinusoidal Oscillators
Background image of page 1

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

View Full DocumentRight Arrow Icon
Quiz 18 Determine the characteristic equation for the following network without adding an excitation. C R L
Background image of page 2
And the number is ? 1 3 8 4 6 7 5 2 9 ?
Background image of page 3

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

View Full DocumentRight Arrow Icon
Quiz 18 Determine the characteristic equation for the following network without adding an excitation. C R L V X Solution: 0 X 1 V G+sC+ sL 2 X 11 V s +s + = 0 CR LC 2 D s = s +s + CR LC
Background image of page 4
Theorem: The poles of any transfer function of a linear system are independent of where the excitation is applied and where the response is taken provided the “dead network” for the systems are the same. Linear Network X OUT X IN Ns T s = Ds Theorem: The characteristic equation D(s) of a linear system are independent of where the excitation is applied and where the response is taken provided the “dead network” for the systems are the same. Or, equivalently, Review from Last Lecture
Background image of page 5

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

View Full DocumentRight Arrow Icon
Linear Network X OUT X IN =0 Dead Network Linear Network X OUT X IN Ns T s = Ds Poles of a Network Review from Last Lecture
Background image of page 6
Theorem: The characteristic polynomial D(s) of a system can be obtained by assigning an output variable to the “dead network” of the system and using circuit analysis techniques to obtain an expression that involves only the output variable expressed as X 0 F(s)=0 where F(s) is a polynomial. When expressed in this form, the characteristic polynomial of the system is D(s)=F(s) Review from Last Lecture
Background image of page 7

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

View Full DocumentRight Arrow Icon
Review from Last Time: V OUT2 R C Inverting Integrator V OUT1 R 2 R 1 Noninverting Comparator with Hysteresis V OUT2 R 2 R 1 R C V OUT1 Pole Locations of Waveform Generators Re Im Both have a single pole on the positive real axis 2 1 R 1 p = R RC 1- θ1 p = θ RC 1 12 R θ = RR
Background image of page 8
Sinusoidal Oscillators • The previous two circuits provided square wave and triangular (“triangularish”) outputs - previous two circuits had a RHP pole on positive real axis • What properties of a circuit are needed to provide a sinusoidal output • What circuits have these properties
Background image of page 9

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

View Full DocumentRight Arrow Icon
What properties of a circuit are needed to provide a sinusoidal output? Insight into how a sinusoidal oscillator works Characteristic Equation Requirements for Sinusoidal Oscillation (Sec 13.1) Barkhausen Criterion (Sec 13.1)
Background image of page 10
Insight into how a sinusoidal oscillator works Linear Network X OUT X IN Ns T s = Ds 1 2 n {p , p , . .. p } If e(t) is any excitation, no matter how small, can be expressed as E E E s = E 1 2 m = s-x s-x . .. s-x E E N s N s R s =E s T s = D s D s Then the output can be expressed, in the s-domain, as
Background image of page 11

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

View Full DocumentRight Arrow Icon
Insight into how a sinusoidal oscillator works Linear Network X OUT X IN Ns T s = Ds 1 2 n {p , p , . .. p } Using a partial fraction expansion for R(s) obtain E E N s N s R s = D s D s Then the output can be expressed, in the time domain, as ... ... 1 2 n 1 2 m 1 2 n 1 2 m a a a b b b s-p s-p s-p s-x s-x s-x -1 r t = R s L 1 2 n 1 2 m p t p t p t x t x t x t 1 2 n 1 2 m r t a e + a e +. ..+ a e + b e + b e +.
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/01/2012 for the course EE 230 taught by Professor Mina during the Fall '08 term at Iowa State.

Page1 / 57

EE 230 Lecture 24 Spring 2010 - EE 230 Lecture 24 Waveform...

This preview shows document pages 1 - 13. Sign up to view the full document.

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