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Using superposition with MNA method

Circuit and admittance matrix, by hand or using MNA function from the other worksheet.

V1 1 0R1 1 2C1 2 0RT 2 3CT 2 3LK 3 4RK 4 5CK 5 0RO 5 0CO 5 0 χ χ :

A 1 R1 / 1 R1 / - 00011 R1 / - R1 1 s CT * RT * + s C1 * RT * + (* RT + R1 RT * / 1 s CT * RT * + RT / - 00001 s CT * RT * + RT / - RT 1 s 2^CT * LK * + (* s LK * + s LK * RT * / 1 s LK * / - 00001 s LK * / - RK s LK * + s LK * RK * / 1 RK / - 00001 RK / - RK 1 s CO * RO * + s CK * RO * + (* RO + RK RO * / 010000066 mat :

Solve the linear system

B 00000 f n V.1 16 mat transpose :

V A 1 -^B * :

Complex freq

s 0 i n * 2 * π * f * + :

t f n v.2 V 2 el :

Values

R1 327.1 kΩ * :

C1 200 pF * :

Vo 0.8 V * :

RT 9 MΩ * :

CT 12.78 pF * :

LK 250 nH * :

RK 1.5 Ω * :

CK 100 pF * :

nmax 8 :

RO 1 MΩ * :

CO 15 pF * :

Square wave

t f v.1 Vo 2 π * f * t * sin sign * :

f n V.1 i 4 Vo * n π * / * - :

Solution

t f v.2 t f 2 k * 1 - v.2 e 2 k * 1 - (i * 2 * π * f * t *^* k 1 nmax sum :

Frequency

f 2314 Hz * :

T 1200 range 1 - 2001 - / 2 f / * 4 f / + :

Using spice#

.TRAN 0 {6/freq} {4/freq} {0.01/freq}.SAVE V(1) V(2) I(R1).PARAM freq=@ χM χM :

V1 1 0 V1sR1 1 2 327.1kC1 2 0 200pRT 2 3 9MEGCT 2 3 12.78pLK 3 4 250nRK 4 5 1.5CK 5 0 100pRO 5 0 1MEGCO 5 0 15p χVer χVer :

CR \ 000D \ concat str2num num2str :

wave PULSE(-0.8 0.8 0 1u 1u {1/freq/2-1u} {1/freq}) :

circ χVer description V1s wave strrep :

mode χM description @ f s * eval num2str strrep :

M {CR}{circ}{CR}{mode}{CR}.END_spice# :

T.M V.1 V.2 13 mat M 1 col s * M 2 col V * M 3 col V * 13 mat :

M rows 239

from above

Compare both solutions

T f * V1.n T f v.1 Re vectorize eval : augment T f * V2.n T f v.2 Re vectorize eval : augment T f * V1.n V2.n - augment T.M f * V.1 . 6 blue augment T.M f * V.2 . 6 red augment T.M f * V.1 V.2 - . 6 green augment 6 1 sys

Alvaro

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