Engineering How to determine circuit components of ´Mystery Box’ ?

[JoeBeef]

Homework Statement

Hi, I am tasked with finding the configuration of a ´Mystery box’ circuit that can contain up to a maximum of 3 total components.
Components can be resistors, capacitors or inductors (R, L or C).
The circuit has 2 unknown impedances Z1 and Z2, which are in series. Z1 and Z2 can be any combination of R,L or C components in parallel or in series.

So, example configurations could be Z1= C||R and Z2 = R, to make a C||R R circuit (C and R in parallel, then another resistor in series to the parallel component.)
Other examples could be R-L-C, or R-R||L and so on.

Relevant Equations

N/A

I measured the resistances across Z1 and Z2 with a multimeter and found Z1 = 473Ohm and Z2 = 164Ohm. Next I used a function generator and oscilloscope to observe the AC response.

I observed that the circuit blocks lower frequencies and allows higher frequencies through (high pass filter) which would be consistent with a RL or CR type circuit. I observed a square wave Vin input and the Vout response consistent with high pass filter response.

However, since I was able to measure resistances across Z1 and Z2, there cannot be a capacitor in series as it would block the small current from the multimeter.

I am stuck here. Possible configurations for high pass filters given the rules and the absence of a capacitor in series tell me it could be
C||R R,
R R||L or
R RL.
How can I differentiate between these high pass filters? What is another test I could do to steer me in the right direction? Thanks.

 

[berkeman]

Welcome to PF.

Does this black box have 3 or 4 terminals? Can you show which terminals you connected to for each of the measurements? Thanks.

 

[JoeBeef]

 

[JoeBeef]

I measured impedance of Z1 across the two BNC connectors, Z2 by measuring from the right BNC connector to ground, and took my oscilloscope measurements by connected Vin to the left BNC connector and Vout to the right BNC connector.

 

[DaveE]

OK, so you've measure the DC resistance of each element. Note that you didn't get values of 0 or ∞ for either. That should tell you something about where capacitors (∞Ω) or inductors (0Ω) can't be. What are all of the other possibilities that will also give a HPF response? Do a bit of simple math to look at the transfer function, I/O impedances etc. of those possibilities.

Can you also make impedance measurements at high frequencies? Adding a source or load resistance would also give you more information.

You've done good work at DC, can you do something similar at high frequencies, where you might be able to approximate inductors as ∞Ω and capacitors as 0Ω?