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## Harry Broeders' applet

### The two versions of Broeders' applet

I have included Broeders' excellent applet because it elegantly complements ParSer II: his applet graphs the impedance between two port nodes of a circuit as a function of the frequency of the cosinusoidal input voltage to the port. There are two versions:-
• The first is an applet embedded alone in a page; and the user enters an arbitrarily long string to describe the circuit as viewed at the input port. [See the source or a local copy at broeders/Broeders1.html.]
• The second is driven from a JavaScript panel where string input is replaced by data input which restricts the circuit to no more than three elements where the three are R, C, L. [See the source or a local copy at broeders/Broeders2.html .]
Let's play with the first version immediately here. For example, replace each of the "+" by "//" (and press RTN). [Eventually, do more at broeders/Broeders1.html.]

The Broeders applet can be found at various sites:-
Exercise. Sketch a simple interesting RLC ciruit. Input its data to both ParSim II and Broeder's applet. Compare the numerical output of one with the graphical ouput for the other.

Exercise. What are the code steps from the input to the output of ParSer II and Broeders' applet?

Exercise. Here is a circuit which was designed to have an impedance flat over five octaves of freqency. Read the expression from the circuit and input it to Broeders' applet.

Remarks:-
• You may wish to check your expression for the impedance of the circuit against my expression:-
L(44E-8)+R(262E0)+(C(338E-12)//R(469E0))+(C(954E-12)//R(207E0))+(((L(146E-8)//(C(364E-12)+R(9E0))+R(115E0))R(115E0)+(C(333E-12)//(R(168E0)+(L(358E-6)//R(669E0))+(L(111E-6)//R(382E0)))
I have yet to find my error.
• The source of the circuit is Cal Coopman's article on Fractors and the Fractroller.
A grand exercise. Note the comparision between ParSer II and Broeder's applet. Then combine the two into one.

### My discovery of Wolfgang Christian and Harry Broeders

There are two separate threads that eventually merge.

• In the late eighties one of my languages was Smalltalk. I found that I could create an infix operator. For example, I could already write 3 + 4 for the sum of two resistors in series. But, further, I could define, say, # to be the operator for expressing the sum of two resistors in parallel as 3 # 4. The result was that I could write the resistance between a port node of any size circuit as an expression (just like a mathematical expression, with the new operator). [Incidentally, such a circuit must have the series/parallel structure.]
• When I began teaching Internet Programming in the late nineties (in HTML/JavaScript) I found that I could NOT invent a new infix operator. So, for series/parallel resistors as a topic, I replaced 3 + 4 with a function s(3,4) and introduced a function p(3,4), and rewrote the resistance between two nodes in terms of these functions. The calculator for series/parallel resistors was followed by a calculator for series/parallel RLC-circuits where impedance between the input nodes was calculator for an applied cosinusoidal voltage with given frequency.
• This year I have come across Harry Schroeder's applet (in Java) which uses + and // as infix operators). Harry Schroeder created his applet in 1997, which graphed the magnitude of the impedance between the input nodes as a function of the frequency of the applied cosinusoidal voltage.