Equations for One Resistor Two Capacitor Circuits

Impedance is the preferred parameter characterizing the two resistors, one capacitor series circuit, because it is defined by one unique time constant Xz (Eq. (12.8)). This time constant is independent of R, as if the circuit was current driven. The impedance parameter therefore has the advantage that measured characteristic frequency determining Xz is directly related to the capacitance and parallel conductance (e.g., membrane effects in tissue), undisturbed by an access resistance. The same is not true for the admittance the admittance is dependent both on xz and X2, and therefore on both R and G. 

It is important to analyze this circuit with respect to selectivity let us assume that our black box contains the two resistors—one capacitor series circuit. Under what conditions will measured Y be proportional to the unknown G and not be disturbed by variations in R and C And correspondingly under what conditions will measured Y be proportional to unknown C and not be disturbed by variations in R and G  

From Eq. (12.10) we see that Y is proportional to G only if the following three conditions are met  

If the conditions for Y are satisfied, it will be possible to follow, for example, the unknown C directly by single frequeney measurement of Y, without ealeulations based on results from measurements on several frequeneies. 

The admittance time constant is uniquely defined by ty, independent of G, as if the circuit were voltage driven. The admittance parameter therefore has the advantage that the measured characteristic frequency determining xy is directly related to the capacitance (membrane effects) and series resistance in tissue. The same is not true for impedance the impedanee is defined by both ty and X2. 

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