Estimating the schematic of a black box using the measured impedance curve
This sounds very much like a homework question to me but as its Xmas...

Barry is quite correct if we were to consider every possibility but let us assume for this particular case that the question is actually solvable or at least approachable. i.e. the box contains only a few passive components arranged in a simple circuit. How could we approach it?



Consider a generalised black box - terminals A and B are the inputs and terminals C and D are the outputs.

Use the information you have - You have been told that it is a (simple?) demodulator - so there's a good chance it will have a diode somewhere in the circuit and possibly a capacitor.  

A first approach would be with resistance (continuity) measurements. If you are lucky B and C are connected together to form a common connection which simplifies things a bit. 

Measuring resistance/continuity between two points and reversing the measurement voltage ( e.g A -> B and B -> A) should pick up a diode (or rectifier type junction) connected between those terminals. A bi-directional low resistance may indicate a wire or an inductor. A changing resistance value may indicate a capacitor as it charges up - short it out and see if it charges up again.

The next step would be to try putting some form of signal into the box and see what comes out (into a known load such as a resistor), measuring input voltage, current and phase (useful for capacitance/inductance type circuits). You could also try using a variable DC input of some sort as well as a variable AC source. An oscilloscope would be an invaluable tool to see the waveforms as well as measure inputs and outputs. 

This is where the possibilities for the unknown circuit multiply but by using logic and reason (based on the characteristics of different devices) to suggest the most probable solution you can take the analysis a bit further. For example, if there was no continuity between input and output terminals for a DC voltage BUT an AC signal could get through then you could be dealing with either a capacitive (series) circuit OR a transformer. Think about how you would eliminate one choice or the other. 

As a training exercise use this approach to analyse the circuit below and see if you can answer the following questions - 



(1) How would you know there was a diode between A and C?

(2) How would you know it was a Germanium diode and NOT a Silicon one? 

(3) How would you know there was a 10k resistor across the inputs?

(4) How could you determine the value of the 0.1uF capacitor from outside the box?