Help me puzzle out a Mystery Circuit!

September 3, 2008 2:37 AM

Later this year, for an electronics course I´m taking, we´ll be given a ¨black box¨ circuit containing various passive elements - resistors, capacitors, and inductors - and asked to design a pre-emphasis circuit that will negate its effect. I´d like to draw up a plan of attack, so: does anyone have any suggestions for experiments to run on the black box to determine the circuit within´s construction? I´ve got access to a function generator and an oscilloscope, of course.
posted by nicolas léonard sadi carnot to technology (5 comments total)

You don't actually need to determine its construction in detail. Just working out its frequency response should be enough. If you program your function generator to generate a swept-frequency sine wave, and lock the scope to the sweep rate, that will give you an amplitude vs. frequency plot. Find the maxima and minima in that, note how fast the response slopes away from those, and provided you've paid attention during the filter design portion of your course, you shouldn't find designing a complementary filter to be too difficult.
posted by flabdablet at 3:26 AM on September 3, 2008 [2 favorites has favorites]

Remember Thévenin's theorem generalized: any two terminal network of resistors, capacitors, and inductors is equivalent to a single complex impedance. So really, you're trying to find an approximate function that describes this impedance (frequency dependent resistance) over a given bandwidth (range of frequencies). Then you need to find the inverse of this function and create some sort of filter (passive? active?) to implement it.

So flabadablet has it. You could also use a noise source and spectrum analyzer.
posted by phrontist at 5:35 AM on September 3, 2008

Allow me to introduce you to the transfer function. This is similar to the complex impedance phrontist talks about.

You can use something called the impulse response. The ideal unit impulse is infinitely high and (1/infinity) long for a total area of 1. The laplace transform of the unit impulse is 1. As you might remember, our transfer function is defined as:

H(s) = Y(s)/X(s)

Where Y(s) is the output
H(s) is the transfer function
X(s) is the input, which in this case is 1, so:

H(s) = Y(s)

The implication of this is: If you apply a unit impulse to the circuit's input, then perform a laplace transform on the output, you will get the system's transfer function.

Once you have the system's transfer function you can invert it, and once you have the inverse transfer function you can build a circuit which has this inverse transfer function.

What I've just said isn't very in depth, but you're presumably at the start of your course at the moment. When the instructor starts talking about unit impulses and designing circuits to give a particular transfer function, listen up and take notes because that's what you need for your assignment.
posted by Mike1024 at 5:39 AM on September 3, 2008

I'm just here to agree with Mike1024 and say that this is a good project for an EE undergrad in a Signals and Systems class. Maybe first semester of sophomore year or so.
posted by mbd1mbd1 at 7:00 AM on September 3, 2008

I read up on the unit impulse / freq response stuff, and pretty much get it. Now I just need to figure out how to apply the theory with our creaky old lab equipment. Thanks everyone! And mbd1, second sem second year, but I´m not an EE major.
posted by nicolas léonard sadi carnot at 8:01 AM on September 3, 2008