Patent ID: 6873922

Claim:
A method of performing a transient response analysis of a capacitor having an impedance in a positive frequency region, wherein the transient response analysis comprises at least the steps of: firstly, inputting an impedance every positive sample frequency expressed by Z ( f n )= R ( f n )+ jX ( f n ) (1) where Z is an impedance, R is real part of Z, X is imaginary part of Z, j is imaginary unit, n (1≦n≦N) is an integer, and f n (f n =nf N /N) is a sample frequency; secondly, generating an impedance every negative sample frequency expressed by Z ( f −n )= R ( f n )− jX ( f n ); (2) thirdly, for an impulse response of Z every sample time expressed by z ( t m )= z R ( t m )+ z X ( t m ) (3) where, z is an impulse response of Z, z R is an impulse response of R, z X is an impulse response of X, m (0≦m≦N) is an integer, and t m (t m =m/2f N ) is a sample time, and for a capacitance at the lowest sample frequency expressed by C ~ 0 = - 1 2 ⁢ π ⁢ ⁢ f 1 ⁢ X ⁡ ( f 1 ) , ( 4 ) setting capacitance C 0 so as to equal to {tilde over (C)} 0 or at least so as to satisfy 0.9× {tilde over (C)} 0 ≦C 0 ≦1.1× {tilde over (C)} 0 ; (5) fourthly, generating an impulse response of X every sample time expressed by z x ⁡ ( t m ) = m 4 ⁢ NC 0 ⁢ f N - 1 2 ⁢ N ⁢ ∑ n = - N n ≠ 0 N - 1 ⁢ X ⁡ ( nf N N ) ⁢ sin ⁡ ( π ⁢ ⁢ mn N ) ; ( 6 ) fifthly, for an extrapolated value of the real part of the impedance at zero frequency expressed by R ~ 0 = f 2 ⁢ R ⁡ ( f 1 ) - f 1 ⁢ R ⁡ ( f 2 ) f 2 - f 1 ( 7 ) setting direct-current resistance R 0 so as to be equal to {tilde over (R)} 0 or at least so as to satisfy 0.9 ×{tilde over (R)} 0 ≦R 0 ≦1.1 ×{tilde over (R)} 0 ; (8) sixthly, generating an impulse response of R every sample time expressed by z R ⁡ ( t m ) = R 0 2 ⁢ N + 1 2 ⁢ N ⁢ ∑ n = - N n ≠ 0 N - 1 ⁢ R ⁡ ( nf N N ) ⁢ cos ⁡ ( π ⁢ ⁢ mn N ) ; ( 9 ) seventhly, inputting an input current every sample time expressed by i(t m ); (10) eighthly, generating a response voltage every sample time expressed by v ⁡ ( t m ) = ∑ m ′ = - N N - 1 ⁢ z ⁡ ( m ′ 2 ⁢ f N ) ⁢ i ⁡ ( m - m ′ 2 ⁢ f N ) ; ( 11 ) and ninthly, outputting at least part of data obtained using Eq. 1 to Eq. 11.