**4.2** *RC* **admittance synthesis**

The synthesis method for an *RC* admittance (*YRC*) developed in [15] can be used also for an *RC* impedance (*ZRC* = 1/*YRC*) with some minor modifications, and it is presented in the following.

A function *F*(*s*) of a complex variable *s* is an *RC* admittance if and only if the following conditions are fulfilled:


Replacing *s* with *jω*, (where *ω=2πf* and *f* is the frequency) the shape of the *RC* admittance modulus curve |*YRC*(*jω*)| versus *ω* is defined by the poles and zeros location. Sweeping the *ω* axis starting from the origin, it can be observed that the location of a zero is associated with a slope change of 20 dB/decade and the location of a pole is associated with a slope change of 20 dB/decade. This is because the characteristic |*YRC*(*jω*)| has asymptotes whose slopes are 20 dB/decade, 0, 20 dB/ decade, 0, and so on. The |*YRC*(*jω*)| characteristic approximation by asymptotes has the maximum error of 3 dB at the asymptote intersection (**Figure 8**) [16].

A natural way to approximate the |*YRC*(*jω*)| characteristic is to consider a smaller asymptote number than that corresponding to the measured characteristic. A greater error *ε* between measured and simulated values leads to a simpler circuit (**Figure 8**).

**Figure 8.** *The* |YRC*(*jω*)*| *characteristic approximation by asymptotes.*
