Black Box Analysis, Amplifiers, Filters

Let us consider a black box containing some series combination of ideal components one resistor, one or no battery, and one or no capacitor. By external measurements, we shall find the component values in three different cases. 

Second, DC method. To find out, we must add something to the measurement. For instance, by varying V, the current I also varies. By applying V = 0, we still have a current flowing, which must be 1 = Vb/R. We can then assume that there must be a battery in the circuit. 

DC/AC method. To obtain this information, we actually have to superimpose a varying signal, an AC voltage, on the DC voltage. In addition, fliis manual method cannot be used if we want to continuously monitor changing values of Vb and R. 

If R and B are nonideal with current depending values, as in an electrolytic electrode system, the DC approach cannot be used. A better approach is to superimpose a small, continuous sine wave voltage on the applied DC voltage. Our current measuring device must then be able to measure both AC current with phase and DC. The battery (being ideal with zero internal resistance) will not influence the AC current, and we consequently measure the resistance of R at AC, but a different R at DC. Because there is no phase shift, we then know that the battery is in the circuit. If we repeat the measurement on many frequencies and the results are identical, we know that there is no capacitor inside the black box. 

The current measuring circuit is very attractive instead of introducing a current reading shunt resistor with the necessary (even if small) voltage drop. The voltage drop in this circuit is virtually zero. 

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