bdd726a9-cdb1-4e34-bdeb-d2e1c1f67ff8 46 4 5 decimal

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

Admittances for the various elements are simply the inverse of their impedances. The expressions for inductors and capacitors should be expressed in terms of the operating frequency for the circuit. Using the admittance matrix, it is possible to find the resonnant frequency for the network, and the general frequency response. Admittance formulae for capacitors and inductors are shown below

ω Y.L 1 j ω * L * / ≡

c 299792458 m s / * :

j 1 - sqrt :

ω Y.C j ω * C * ≡

MHz Hz 106^* :

μF 106 -^:

μH 106 -^:

Hz 1 :

Ω 1 :

ω A 01 Ω / * 01 Ω / * 01 Ω / * 1 j ω * 100 * μH * / j ω * 10 * μF * 01 Ω / * 01 Ω / * 1 j ω * 200 * μH * / 01 Ω / * 01 Ω / * 01 Ω / * 01 Ω / * 01 Ω / * 150 Ω * / 1 0.5 Ω * / 01 Ω / * 01 Ω / * 01 Ω / * 01 Ω / * 01 Ω / * 01 Ω / * 01 Ω / * 01 Ω / * 01 Ω / * 01 Ω / * 55 mat :

ω AS ω A ω A transpose + :

1 Hz * AS 00010000 i * - 1105 -^* i * 005000 i * - 0005000 i * - 0 0.02 210000 i * - 0 0.02 001105 -^* i * 020055 mat

i 11 Hz * A rows 1 - (range : k 11 Hz * A rows 1 - (range : 21 line

ω i k F ω AS - (i 2 + k 2 + el i k ≠ ω AS i 2 + col sum cases :

ω Y ω 00 F ω 01 F ω 02 F ω 03 F ω 10 F ω 11 F ω 12 F ω 13 F ω 20 F ω 21 F ω 22 F ω 23 F ω 30 F ω 31 F ω 32 F ω 33 F 44 mat :

sanity checked 1 Hz * Y 5000 i * - 5000 i * 005000 i * 2.02 5000 i * - 0.02 - 2 - 0 0.02 - 0.02 10000 i * - 002 - 021105 -^* i * + 44 mat

ω V ω Y 1 -^100041 mat * :

sanity checked 1 Hz * V 49.99999 0.0247 i * - 49.99999 0.0249 i * - 5108 -^* 0.0001 i * + 49.99999 0.02515 i * - 41 mat

f.min 100 Hz * :

f.max 0.5 MHz * :

r f.max Hz / log10 f.min Hz / log10 - :

sanity checked r 3.699

n 050 range f n 1 + el f.min 10 0.02 r * n *^* eval : for m 1 f rows range G m el 2 π * f m el * V 4 el 2 π * f m el * V 1 el / eval : for j 1 G rows range Bode j el 20 G j el abs log10 * eval : for 31 line

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

Bode max 13.8

Bode f Bode augment : bode Bode o 5 black plot : 21 line

Bode 3577 20 3577 10 - 2 2 mat bode 3 1 sys

Bode 100 0.01 118.57 0.01 140.59 0.01 166.7 0.02 197.66 0.03 234.37 0.04 277.89 0.05 329.5 0.07 390.69 0.1 463.25 0.15 549.28 0.21 651.29 0.29 772.24 0.41 915.66 0.59 1085.7 0.83 1287.33 1.2 1526.41 1.73 1809.88 2.54 2146 3.8 2544.54 5.91 3017.09 9.75 3577.4 13.84 4241.77 6.16 5029.52 0.41 - 5963.56 5.37 - 252 mat

XY1 Bode 122 range 12 range el : XY2 Bode 2350 range 12 range el : 21 line

x S1 XY1 1 col XY1 2 col x ainterp 100 x ≤ (x 3577.4 ≤ (& S2(x) cases : x S2 XY2 1 col XY2 2 col x ainterp 3577.4 x ≤ (x 5105^* ≤ (& S1(x) cases : 21 line

x S1 x S2 3577.4 20 3577.4 5 - 2 2 mat 3 1 sys

bode_zed bode 1 col bode 2 col augment :

ZED GRAPH REGION [alyles]

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Bode bode_zed 2 1 sys

j 1 G rows range Φ j el 180 π / G j el arg * eval : for

phase f Φ augment : phase_zed phase : 21 line

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phase phase_zed 180 - 3 1 sys

more generally z Φase 180 π / z arg * 3601 z arg 0 ≥ 0 cases * - :

n 1 G rows range Φase n el 180 π / G n el arg * 3601 G n el arg 0 ≥ 0 cases * - eval : for

Φase 0.3243 - 0.3846 - 0.4562 - 0.5413 - 0.6424 - 0.7626 - 0.9059 - 1.0768 - 1.2812 - 1.5266 - 1.8228 - 2.1828 - 2.6248 - 3.1754 - 3.8756 - 4.7929 - 6.0476 - 7.879 - 10.8377 - 16.5122 - 31.6579 - 94.6632 - 150.7509 - 231 mat