405791d9-1bc7-4a82-a628-898b707a1065 342 4 5 false false false 0 3 decimal

Using superposition with MNA method

Utilities

Instead simplfiy x# SN x# num2str eval str2num 11 line :

Complex Signum z csign z Re sign z Re 0 ≠ z Im sign cases 11 line :

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 V1s 16 mat transpose :

V A 1 -^B * SN :

Complex Freq

s C1 H V 2 el V 1 el / SN :

s C1 R1 XT RT \002E\\002E\\002E\ H

Symbolic Soltuions

t v.12 t f v.1 t v.2 - :

As time function only, faster.

t v.2 2 κ * 1 - H.n t i 2 * π * f * 2 κ * 1 - V.1 * κ 1 Σmax sum :

t f C v.12 t f v.1 t f C v.2 - :

As function of several variables

t f C v.2 i 2 κ * 1 - (* 2 * π * f * C H t i 2 * π * f * 2 κ * 1 - V.1 * κ 1 Σmax sum :

Square Wave

t f v.1 Vo i e i 2 * π * f * t *^* - csign * :

t s n V.1 i 4 Vo * n π * / * e n s * t *^* - :

Values

R1 327.1 kΩ * :

C1 200 pF * :

Vo 0.8 V * :

Π x τ * f v.1 Re x τ * v.2 Re x τ * v.12 Re 31 sys :

RT 9 MΩ * :

CT 12.78 pF * :

LK 250 nH * :

RK 1.5 Ω * :

CK 100 pF * :

Σmax 10 :

RO 1 MΩ * :

CO 15 pF * :

Frequency

f 1000 Hz * :

n H.n i n * 2 * π * f * C1 H SN :

τ 1 f / :

Π 1 1 line

Transfer function

Co 0.1 510 stack pF * :

k 13 range :

sx i 2 * π * 10 x^* Hz * :

δ k el PH'Traces#@'LineStyle'LineColor:"blue" @ k 1 - num2str strrep str2num : δ k el PH'Traces#@'LineStyle'LineColor:"red" @ k 1 - 3 + num2str strrep str2num : 21 line

δ dummy ≡

Π1 δ k el sx Co k el H Re : mat2sys.1 δ k el sx Co k el H Im : mat2sys.1 21 sys :

Π2 δ k el sx Co k el H abs : mat2sys.1 δ k el sx Co k el H arg : mat2sys.1 21 sys :

Π1 1 1 line Π2 1 1 line

Utility

y a NR iter 11 range ya yδ 12 mat y t a ≡ at y t a Δt + ≡ at 12 mat : a a ya Δt * yδ ya - / - eval : 21 line for a 21 line :

Δt 0.00001 s * :

Freqs

f Clear 1

nf 110 range :

X nf 1 - 101 - / 3 * 50 log10 + :

F 10 X^vectorize Hz * :

τ 1 F / vectorize :

Caps

Co 0.1 5 stack pF * :

nc 1 Co length range :

Measures

VPP1 nf nc el 0.5 τ nf el * F nf el v.1 0 F nf el v.1 - :

V2PP nf nc el 0.5 τ nf el * F nf el Co nc el v.2 0 F nf el Co nc el v.2 - Re :

V12PP nf nc el 0.5 τ nf el * F nf el Co nc el v.12 0 F nf el Co nc el v.12 - Re :

t1 nf nc el 0 :

t2 nf nc el t F nf el Co nc el v.2 Re 0 NR τ nf el mod s * :

t12 nf nc el t F nf el Co nc el v.12 Re 0 NR τ nf el mod s * :

Δt2 nf nc el t1 nf nc el t2 nf nc el - :

Δt12 nf nc el t1 nf nc el t12 nf nc el - :

Pha2 nf nc el 2 π * F nf el * Δt2 nf nc el * :

Pha12 nf nc el 2 π * F nf el * Δt12 nf nc el * :

tbl F VPP1 1 col V2PP 1 col V12PP 1 col Pha2 1 col Pha12 1 col augment :

tbl tbl VPP1 2 col V2PP 2 col V12PP 2 col Pha2 2 col Pha12 2 col augment :

tblH S:VPP1 S:VPP2 S:VPP12 S:Pha2 S:Pha12 S:'V S:'V S:'V S:'deg S:'deg 25 mat :

tblH S:Freq S:'Hz 21 mat tblH tblH augment eval :

tblU tblH str2num vectorize 2 row eval :

< - - - - - - - Co1 - - - - - - - - - - >< - - - - - - Co2 - - - - - - - - - - >

tblU S tbl Pha12 Pha2 Δt12 Δt2 t12 t2 t1 V12PP V2PP VPP1 F X nf Δt NR sx τ H.n CO RO CK RK LK CT RT Vo C1 R1 V.1 v.1 v.2 v.12 H csign SN tblU S tblH tbl nc F X nf Δt NR Π2 Π1 δ sx k Co τ H.n CO RO CK RK LK CT RT Π Vo C1 R1 V.1 v.1 v.2 v.12 H V B csign SN tblU S F X nf Δt sx τ H.n CO RO CK RK LK CT RT Vo C1 R1 V.1 v.1 v.12 H

tbl
50.00	1.60	0.02	1.57	-0.06	-0.09	1.60	0.03	1.56	-0.09	-0.08
107.70	1.60	0.04	1.55	-0.14	-0.19	1.60	0.06	1.53	-0.20	-0.19
232.10	1.60	0.10	1.49	-0.30	-0.42	1.60	0.14	1.45	-0.43	-0.41
500.00	1.60	0.22	1.37	-0.66	-0.95	1.60	0.31	1.28	-0.92	-0.89
1077.00	1.60	0.45	1.14	-1.41	-2.27	1.60	0.60	0.99	-1.94	-1.93
2321.00	1.60	0.80	0.79	-3.12	-6.36	1.60	0.97	0.62	-3.99	-4.49
5000.00	1.60	1.14	0.45	-8.30	-11.40	1.60	1.25	0.34	-9.63	-7.23
10770.00	1.60	1.35	0.24	-19.55	-18.57	1.60	1.41	0.18	-21.94	-10.40
23210.00	1.60	1.44	0.15	-43.25	-31.47	1.60	1.43	0.16	-47.26	-20.76
50000.00	1.60	1.31	0.28	-90.00	-90.00	1.60	1.12	0.47	-90.00	-90.00
1·1/s	1 (kg m^2)/(A s^3)	1 (kg m^2)/(A s^3)	1 (kg m^2)/(A s^3)	0.02	0.02	1 (kg m^2)/(A s^3)	1 (kg m^2)/(A s^3)	1 (kg m^2)/(A s^3)	0.02	0.02
S:Freq	S:VPP1	S:VPP2	S:VPP12	S:Pha2	S:Pha12	S:VPP1	S:VPP2	S:VPP12	S:Pha2	S:Pha12
S:'Hz	S:'V	S:'V	S:'V	S:'deg	S:'deg	S:'V	S:'V	S:'V	S:'deg	S:'deg
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Alvaro

4 appVersion 1.74.9654.0