SLVUBB4 User guide

SLVUBB4B November 2017 – February 2023

13.4 Damping Factor

$f_{d a m p}$ is the filter frequency of the filter inductor and the parallel input/output capacitor and damping capacitor network.

Equation 123.

X_{C i n / o u t} = \frac{1}{2 \times π \times f_{d a m p} \times C_{I N / O U T}}

Equation 124.

X_{C d} = \frac{1}{2 \times π \times f_{d a m p} \times C_{D}}

Effective impedance at $f_{d a m p}$ .

Equation 125.

Z_{e f f} = \frac{\sqrt{{E S R}_{I N / O U T}^{2} + {X_{C i n / o u t}}^{2}} \times \sqrt{{({R_{D} + E S R}_{D})}^{2} + {X_{C d}}^{2}}}{\sqrt{{({R_{D} + E S R}_{D} + {E S R}_{I N / O U T})}^{2} + {(X_{C d} + X_{C i n / o u t})}^{2}}}

Effective phase angle at $f_{d a m p}$ .

Equation 126.

φ_{e f f} = \tan^{- 1} (\frac{X_{C i n / o u t}}{{E S R}_{I N / O U T}}) + \tan^{- 1} (\frac{X_{C d}}{{R_{D} + E S R}_{D}}) - \tan^{- 1} (\frac{X_{C i n / o u t} + X_{C d}}{{E S R}_{I N / O U T} + {R_{D} + E S R}_{D}})

Effective capacitance:

Equation 127.

C_{e f f} = \frac{1}{2 \times π \times f_{d a m p} \times Z_{e f f} \times \sin (φ_{e f f})}

Effective ESR:

Equation 128.

{E S R}_{e f f} = Z_{e f f} \times \cos (φ_{e f f})

Damping factor:

Equation 129.

δ = 0.5 \times (\frac{D C R + {E S R}_{e f f}}{\sqrt{\frac{L_{F}}{C_{e f f}}}} + \frac{\sqrt{\frac{L_{F}}{C_{e f f}}}}{- \frac{V_{i n}}{I_{i n}}})