Exercises 39 & 40

As with all of the exercises you will complete in this course, you will be expected to turn your *.nb file in to the course TA before the next lecture.  Please do so by e-mailing your completed exercise file to Lan Yu (lanyu2@illinois.edu), make sure you name the file using the following notation: “Exn_Last_First.nb”, where n is the Exercise number (in this case, 39), and First and Last would be your first and last name.  So my submission to Lan for this exercise would be titled “Ex39_Wasserman_Dan.nb”.  You will receive full credit for your exercise if it turned in before the next lecture (Lecture n+1).  No late submissions will be accepted.

Objective/Overview:

Over the last few weeks we have spent a lot of time studying transmission lines.  At this point you should be fairly well up to speed on how to model them and how to calculate their properties.  In today’s exercise, you will solve a problem on your own!  Because there will be no ‘baby steps’ in this exercise, I am giving you until Wednesday to turn this in, and it will count for 2 assignments.

Problem

The circuit depicted below consists of a transmission line with characteriztic impedance (Subscript[Z, o]) and length “ℓ”.  Let’s assume that (Subscript[Z, o])=50Ω and ℓ=2.65λ.  A shunt resistor ((Subscript[Z, s])=(Subscript[R, s])=100Ω) is placed at a position d1 on the TL, and a shorted stub of length (Subscript[ℓ, s]) and characteristic impedance (Subscript[Z, o])=50Ω is placed at the input of the TL.  If the TL is driven by a voltage generator with (Subscript[V, g])=100∠0V, over a source resistor (Subscript[R, g])=50Ω.

Use your Mathematica skills to write a Manipulate program that calculates the power dropped over the shunt resistor and the power dropped over the load, with user inputs of:  (Subscript[ℓ, s]), (Subscript[Z, L]), and d1.  Assume that (Subscript[Z, L]) can be complex, so the user should enter both real and imaginary components

p1=Graphics[Table[Circle[{r/(r+1),0},(1/(r+1))],{r,{0,.25,.5,1,2,5}}]];
p2=Graphics[Table[Circle[{1,1/x},Abs[1/x]],{x,{5,2,1,.5,.25,.01,-5,-2,-1,-.5,-.25,-.01}}]];
smith1=Show[p1,p2, Axes->True ,AxesLabel-> {(Subscript[Γ, r]),(Subscript[Γ, i])},PlotRange->{{-1,1},{-1,1}}]

ex39[zo_,zLre_,zLim_,d1_,ls1_]:=(

Show[p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,PlotRange->{{-1,1},{-1,1}}])

Manipulate[ex39[zo,zLre,zLim,d1,ls1],{zo,50},{d1,0,2.65,0.001},{zLre,50},{zLim,50},{ls1,0.001,.5,.001}]