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resistor ladder



Hi --

If you want a follow-on exercise to the "resistor
cube", try the R-2R ladder.

*) This has vastly more engineering significance
than the resistor cube. It's used for digital-to-
analog converters (although other techniques are
used also, especially in the lowest and highest
frequency ranges).

*) It reinforces the symmetry lesson that we began
with the cube. The symmetry of the ladder is very
different from the symmetry of the cube, but it's
a symmetry nevertheless, and it would be madness to
analyze the ladder network without exploiting this
symmetry.

*) If you handle it right, you can use it to teach
the kids not to be intimidated by problems that
_look_ hard. If they've been doing "resistors in
parallel" and "resistors in series" and suddenly
they see an R-2R ladder with 13 stages, their first
reaction is usually abject terror. They think they
will be there until a year from July analyzing it.
But the symmetry makes it go really fast.

So far all the references I've been able to find
implement the ladder in ways that are unnecessarily
fancy, using op-amps and other stuff that is not
on the high-school syllabus.
Horowitz and Hill (look up digital-to-analog)
or
http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/dac.html#c3

But (!) you can perfectly well do it with nothing
more than resistors, double-throw switches, and an
ammeter or voltmeter.