Project Help Notebook by Keith Stroyan

Help NoteBook Copyright 1998 by Academic Press, Inc. - All rights reserved.
Modify this Notebook to prepare your project report.

Project 38: The Notch Filter

by A. Student and B. Pupil

with technical help from Da LabMonitor and Help Notebook

READ THE PRINT PROJECT.  This NoteBook only helps solve the technically nasty algebra associated with finding the minimum response of an electrical oscillator as a function of the frequency of the input signal.  You write the explanations.

Initialization

Needs["Graphics`Colors`"];

My Project Introduction

Write this last.  Begin with the basic question and state your main finding clearly, but with few technical details.  You might even modify the title of this section to make it more interesting.

The Laws of Kirchhoff, Ohm, and Coulomb

Transients

aX = 1/(n r c)
aY = 1/(m n r c)
bX = aX
bY = (1/(m n r c) + 1/(m r c))
mat = {{-aX, aY,-w,0},
{w,0,-aX,aY},
{bX,-bY,0,-w},
{0,w,bX,-bY}}
rhs = {0,0,0,-1/r}

TableForm[mat]

{h1,h2,k1,k2} = LinearSolve[mat,rhs]

Print["Be patient; this takes a while."];
Simplify[mat.{h1,h2,k1,k2}]

Simplify[h1]
Simplify[k1]
Simplify[h2]
Simplify[k2]

h3 = Simplify[h1/c - h2/(m c)]
k3 = Simplify[k1/c - k2/(m c) + 1]
a2 := Simplify[ (h3)^2 + (k3)^2 ]
a2

dadw = Simplify[D[a2,w]]

w02 = 1/(m n r^2 c^2)
amp := (m n (w02 - w^2)^2 + (1 + m)^2 w02 w^2)/(m n (w02 - w^2)^2 + (1 + n + m)^2 w02 w^2)
amp

h4 = Simplify[n r w k1]
k4 = Simplify[1 + n r w h1]
b2 := Simplify[(h4)^2 + (k4)^2]
b2

dbdw = Simplify[D[b2,w]]

Simplify[b2 - a2]
Simplify[a2 - amp]

r=1000
c=.000001
m= 5.
n= 1.5
1/(Sqrt[m n] r c)

Plot[Sqrt[a2],{w,0,1500},PlotRange->{0.75,1},Ticks->None,AxesLabel->{"w","eOUT"}];

Steady State Solution of the Forced Equations

Where's the Min?