Filter Response Without Damper

5b505520-1058-4224-9cef-2b3a0ffddbbe 21 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Component Values

L.f 20 μH * :

C.f 100 μF * :

R.out 10 kΩ * :

t0 1 time :

R.Lf 0.1 Ω * :

R.Cf 0.01 Ω * :

j 1 - sqrt :

Frequency

number of decades

n 4 :

points per decade

p 20 :

matrix count

q p 5 p * (range :

10 q p /^vectorize Hz *

f 10 q p /^vectorize Hz * eval :

frequency matrix

Filter Response Without Damper

Inductor

Capacitor

X.C 12 π * f * C.f * / vectorize eval :

X.L 2 π * f * L.f * :

X.L 1 el 0.0013 Ω *

X.C 1 el 159.1549 Ω *

θ.L X.L R.Lf / atan vectorize 180 π / * eval :

θ.C X.C - R.Cf / atan vectorize 180 π / * eval :

θ.L 1 el 0.72

θ.C 1 el 89.9964 -

Z.L R.Lf i X.L * + :

Z.C R.Cf i X.C * - :

Impedance Z2

Z.2 Z.C R.out * Z.C R.out + / vectorize eval :

Z.2 1 el 2.5424 159.1143 i * - (Ω *

θ.2 Z.2 Im Z.2 Re / atan 180 π / * vectorize eval :

θ.2 1 el 89.0846 -

Impedance Z1

Z.1 Z.L Z.2 + :

Z.1 1 el 2.6424 159.1131 i * - (Ω *

θ.1 Z.1 Im Z.1 Re / atan 180 π / * vectorize eval :

θ.1 1 el 89.0486 -

Gain and Phse Shift

Gain.f 20 Z.2 Z.1 / abs vectorize 10 log * vectorize eval :

Phase.f θ.2 θ.1 - :

Gain.f 1 el 2.0336 105 -^* -

Phase.f 1 el 0.036 -

Response

Resp.Gf f Hz / Gain.f augment :

Resp.θf f Hz / Phase.f augment :

Damper Element added in parallel to output filter capacitor

Damper Resistor

Damper Capacitor

R.d L.f C.f / sqrt : 0.4472 Ω *

R.Cd 0.01 Ω * :

C.d 4 C.f * : μF 400

Filter Response with Damper

Damper Impedance

X.Cd 12 π * f * C.d * / vectorize eval :

X.Cd 1 el 39.7887 Ω *

Z.d R.d i X.Cd * - :

Z.d 1 el 0.4472 39.7887 i * - (Ω *

θ.C Z.d Im Z.d Re / atan vectorize 180 π / * eval :

θ.C 1 el 89.356 -

Impedance Z2

Y.2d 1 Z.d / 1 Z.2 / + vectorize eval :

Y.2d 1 el 0.0004 0.0314 i * + (S *

Z.2d 1 Y.2d / vectorize eval :

Z.2d 1 el 0.3879 31.8295 i * - (Ω *

θ.2d Z.2d Im Z.2d Re / atan 180 π / * vectorize eval :

θ.2d 1 el 89.3017 -

Impedance Z1

Z.1d Z.L Z.2d + :

Z.1d 1 el 0.4879 31.8282 i * - (Ω *

θ.1d Z.1d Im Z.1d Re / atan 180 π / * vectorize eval :

θ.1d 1 el 89.1217 -

Gain and Phse Shift

Gain.fd 20 Z.2d Z.1d / abs vectorize 10 log * vectorize eval :

Phase.fd θ.2d θ.1d - :

Gain.fd 1 el 3.2531 105 -^* -

Phase.fd 80 el 147.9626 -

Response

Resp.Gd f Hz / Gain.fd augment :

Resp.θd f Hz / Phase.fd augment :

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Resp.Gf Resp.θf Resp.Gd Resp.θd 4 1 sys

1 time t0 - 7 s *