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I'm studying this scientific paper where a capacitance measurement is done with the circuit shown at page 3. For simplicity I reported it here:

enter image description here

A sinusoidal signal is applied at the input through a function generator. The goal is to measure the associated capacitance of Zcell impedance by evaluating the phase shift between the input and the output signal. The author of this study says that the capacitance value is extracted by using the following formulas (reported at page 2):

enter image description here

Unfortunately I've not understood the meaning of these formulas. For example formulas (1), (2) report the same expression (maybe an error?).

How does this circuit work and, in particular, how are these formulas used?

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  • \$\begingroup\$ If you look at section 2.3, you'll notice they decided to name both of the capacitors as Cf and both of the resistors as Rf (even though they have different values), and didn't even label them at all in the circuit diagram. \$\endgroup\$
    – Dan Mašek
    Jan 5 at 20:30
  • \$\begingroup\$ I don't understand how they took into account the phase shift introduced by the TL081. \$\endgroup\$
    – Antonio51
    Jan 6 at 11:36

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