Patent ID: 8228140

Claim:
A device associated with the control of a tractable filter, comprising: an induction coil having a series resistance, a series inductance, a parallel resistance, a parallel inductance and a parallel capacitance that are determined in accordance with the following relationships: R p = Q · L · ω 0 ; C p = 1 L · ω 0 2 ; L p = L ; Y coil = 1 R p + j ( C p ⁢ ω 0 = 1 L p ⁢ ω 0 ) ; α = 1 R p ; β = - ( C p ⁢ ω 0 - 1 L p ⁢ ω 0 ) ; Z coil = 1 Y coil = ( α α 2 + β 2 ) + j ( β α 2 + β 2 ) ; R s = α α 2 + β 2 ; and L s = 1 / ω 0 ⁡ [ β α 2 + β 2 ] ; wherein: Q is an overvoltage coefficient of the inductance; L is an initial inductance value that is chosen in accordance with a working resonant frequency and the application; ω 0 is the working resonant frequency; L p is a parallel inductance value of the induction coil; R p is a parallel resistance value of the induction coil; C p is a parallel capacitance value of the induction coil; Y coil is an equivalent admittance of the induction coil; Z coil is an equivalent impedance of the induction coil; R s is a series resistance value of the induction coil; and L s is a series inductance value of the induction coil; and a series resistance in series with the induction coil, the series resistance having a value determined in accordance with the following relationships: R = 0.99 · R p ± ( 0.99 ⁢ ⁢ R p ) 2 - 4 · L 0 2 ⁢ ω 0 2 2 ; and r series =R−Rs wherein: R p is the parallel resistance of the induction coil; L 0 is the inductance of the induction coil at a resonant frequency; ω 0 is the working resonant frequency; r series is the series resistance in series with the induction coil; and R is a lowest resistance value solution to the respective relationship.