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ESREquivalent resistance models
The technical capacitor model shows that the impedance real part is the sum of two contributions: the capacitor series resistance serie rs and the parallel resistance rp.
Equivalent Series Resistance (ESR)All the dissipative composants are collected in a new resistance which is called the Equivalent Series Resistance and is specified as "ESR". The impedance in the technical capacitor model is given by: Z = R + j X = (rs + rp/a) + jw(L - C rp2/a) where a = 1 +(w C rp)2 The impedance in the Equivalent Series Resistance model is given by: Z = ESR - j/wCs Comparing both the real and imaginary part, it gives: ESR = rs + rp/a and Cs= 1/w2/(C rp2/a-L) The plot below shows a simulation of the ESR with: C = 100 nF L = 100 nH rs = 10 mΩ rp = 100 kΩ At the resonnance the impedance module is equal to the real part of the impedance. At a given frequency the power losses are given by: PL = ESR i2. Source: Garmanage: Roland Gallay
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