2 solvable examples

959a591b-b4af-4b92-addf-37b838320eb7 65 4 5 decimal

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

Introduction to Laplace RLC circuit

]]> 2 solvable examples

1. RLC excited by unit impulse voltage

R 1 : L 1 : C 0.01 : 13 mat

common to
both circuits x c 10 x ≤ cases :

s I 1 s Z / ≡ (1 R L s * + 1 s C * / + / ≡

s I 1 L / s s 2^s R L / * + 1 L C * / + / (* :

t I s I s t invlaplace maple :

x I x c *

t I t 2 / - exp 399 sqrt t 399 sqrt * 2 / cos * t 399 sqrt * 2 / sin - (* 399 sqrt /

2. RLC excited by unit cosine voltage

R 1 : L 1 : C 1 : ω 1 : 14 mat

experiment =>  C ≤ 1 1 C ≤

s V s s 2^ω 2^+ / :

s I 1 L / s V * s s 2^s R L / * + 1 L C * / + / (* :

t I s I s t invlaplace maple :

x I x c *

t I t 2 / - exp 3 sqrt t 3 sqrt * 2 / cos * - t 3 sqrt * 2 / sin + (* t cos 3 sqrt * + 3 sqrt /

Circuit to be analyzed <= Laplace-Fourier

1. Install the project cycle

components multipliers k 1000 : m 0.001 : u 0.001 m * : n 0.001 u * : 14 mat

Resistors
Inductors
Capacitors
Sampling frequency
applied voltage R mΩ ≡ L μH ≡ C nF ≡ fs kHz ≡ V 51 sys

fs 250 k * : Ts 1 fs / : ω 2 π * fs * : 31 sys

L 4.7 u * : Vdc 12 : Vout 5 : Iout 4 : 41 sys

t I 0 t 0 ≤ Iout Vout 2 L * / 1 Vout Vdc / - (* Ts * - t Vdc Vout - L / (* + 0 t ≤ (t Vout Vdc / Ts * ≤ (& 0 Vout Vdc / Ts * t ≤ (t Ts ≤ (& only one cycle needed4project cases :

1015 -^I 2.7589

The impulse cycle project

x I Vout Vdc / Ts * 0 + 300 red 1 5 mat Ts 0 + 20 red 1 5 mat 3 1 sys

Vout Vdc / Ts * Ts 21 mat 1.6667 106 -^* 4106 -^* 21 mat

The impulse cycle project made visible

x Ts 4 / * I 1.667 6 1.667 2 - 2 2 mat 4 2 4 2 - 2 2 mat 3 1 sys

2. Specify the circuits in the Laplace domain

Input impedance Rin 20 m * : Lin 50 n * : 21 sys

The branches impedances R1 30 m * : R2 5 m * : R3 5 m * : R4 5 m * : 14 mat L1 5 n * : L2 1.5 n * : L3 1.5 n * : L4 1.5 n * : 14 mat C1 470 u * : C2 10 u * : C3 22 u * : C4 33 u * : 14 mat 31 sys

inf 10307^:

s Zin Rin s Lin * + : s Z1 R1 s L1 * + 1 s C1 * / + : s Z2 R2 s L2 * + 1 s C2 * / + : s Z3 R3 s L3 * + 1 s C3 * / + : s Z4 R4 s L4 * + 1 s C4 * / + : 51 sys

s f_Z s Zin inf try s Z1 inf try s Z2 inf try s Z3 inf try s Z4 inf try 51 sys :

s f_Z 110307^* 110307^* 110307^* 110307^* 110307^* 51 sys

on error . . .

clears the divide by zero

in each 'z' branch.

]]>

Lo Δ N X X 0 : i 1 N range X i 1 + el Lo Δ i * + : for X 31 line :

Lo 0 : N 512 : Δ Ts N / : 13 mat vs Lo Δ N X : 31 mat

scaled time vector
covering the length
analyzed for plotting s 1 N range Scale s 1 + el s Δ * u / : for

scaled time vector covering the length analyzed for plot

Scale rows 513

scale Scale 1512 range 11 range el :

Laplace   [j-vs] j 1 i * : n 1 N 1 - (range vs n 1 + el j ω * n * : for 21 line

t I.source t I :

1015 -^I.source 2.7589

Discrete I-source n 1 N range vIs n 1 + el n Δ * I.source : vIs 1 el 2.7589 : 21 line for

λ vIs length :

I-source DFT vFIs vIs λ al_fftc1d :

vFIs

vFIs 1.6678 0.1364 1.2354 i * - 0.3758 - 0.0231 i * + 0.2635 0.1645 i * - 0.1925 - 0.204 i * - 0.0866 0.0527 i * + 0.0074 - 0.2118 i * - 0.0557 - 0.0428 i * + 0.0885 0.1103 i * - 0.0917 - 0.0451 i * - 0.0749 0.0049 i * - 0.039 - 0.1039 i * - 0.0044 0.033 i * + 0.0316 0.0904 i * - 0.0484 - 0.0007 i * + 0.0576 0.0315 i * - 0.0442 - 0.0514 i * - 0.0286 0.0157 i * + 5.2214 105 -^* 0.0706 i * - 0.0178 - 0.0161 i * + 0.0374 0.0445 i * - 0.0374 - 0.0187 i * - 0.0362 0.0026 i * - 0.0175 - 0.0493 i * - 0.0044 0.0166 i * + 0.0175 0.0473 i * - 0.0244 - 0.001 i * + 0.0334 0.018 i * - 0.0243 - 0.0288 i * - 0.0185 0.0091 i * + 0.0006 0.0423 i * - 0.0093 - 0.0103 i * + 0.0242 0.0282 i * - 0.0228 - 0.0112 i * - 0.0248 0.002 i * - 0.011 - 0.0321 i * - 0.0044 0.0113 i * + 0.0123 0.0322 i * - 0.0156 - 0.0013 i * + 0.0241 0.0128 i * - 0.0165 - 0.0196 i * - 0.0144 0.0063 i * + 0.0008 0.0302 i * - 0.0056 - 0.0078 i * + 0.0182 0.0208 i * - 0.016 - 0.0077 i * - 0.0193 0.0017 i * - 0.0079 - 0.0237 i * - 0.0044 0.0086 i * + 0.0097 0.0244 i * - 0.0111 - 0.0015 i * + 0.0191 0.0101 i * - 0.0123 - 0.0147 i * - 0.0121 0.0049 i * + 0.0009 0.0234 i * - 0.0035 - 0.0065 i * + 0.0148 0.0166 i * - 0.0122 - 0.0056 i * - 0.0161 0.0015 i * - 0.0061 - 0.0186 i * - 0.0044 0.0071 i * + 0.008 0.0197 i * - 0.0083 - 0.0016 i * + 0.0161 0.0084 i * - 0.0097 - 0.0116 i * - 0.0107 0.004 i * + 0.0009 0.0191 i * - 0.0021 - 0.0057 i * + 0.0126 0.0138 i * - 0.0097 - 0.0042 i * - 0.0141 0.0013 i * - 0.0049 - 0.0153 i * - 0.0044 0.0061 i * + 0.0069 0.0166 i * - 0.0064 - 0.0018 i * + 0.014 0.0072 i * - 0.008 - 0.0094 i * - 0.0098 0.0034 i * + 0.0009 0.0161 i * - 0.0012 - 0.0052 i * + 0.011 0.0119 i * - 0.0079 - 0.0032 i * - 0.0126 0.0012 i * - 0.004 - 0.0129 i * - 0.0045 0.0055 i * + 0.0062 0.0143 i * - 0.0051 - 0.0019 i * + 0.0125 0.0063 i * - 0.0067 - 0.0078 i * - 0.0091 0.0031 i * + 0.0009 0.0139 i * - 0.0005 - 0.0048 i * + 0.0099 0.0105 i * - 0.0066 - 0.0024 i * - 0.0115 0.0011 i * - 0.0034 - 0.0111 i * - 0.0045 0.005 i * + 0.0056 0.0126 i * - 0.0041 - 0.0021 i * + 0.0114 0.0057 i * - 0.0058 - 0.0066 i * - 0.0086 0.0028 i * + 0.0009 0.0123 i * - 2.2274 105 -^* 0.0046 i * + 0.009 0.0094 i * - 0.0056 - 0.0018 i * - 0.0107 0.001 i * - 0.003 - 0.0097 i * - 0.0045 0.0047 i * + 0.0051 0.0113 i * - 0.0033 - 0.0022 i * + 0.0106 0.0052 i * - 0.005 - 0.0056 i * - 0.0082 0.0026 i * + 0.0008 0.0109 i * - 0.0004 0.0044 i * + 0.0083 0.0085 i * - 0.0049 - 0.0012 i * - 0.0101 0.0009 i * - 0.0026 - 0.0085 i * - 0.0045 0.0044 i * + 0.0047 0.0102 i * - 0.0027 - 0.0024 i * + 0.0099 0.0047 i * - 0.0045 - 0.0048 i * - 0.0079 0.0024 i * + 0.0008 0.0098 i * - 0.0008 0.0043 i * + 0.0078 0.0078 i * - 0.0043 - 0.0008 i * - 0.0096 0.0008 i * - 0.0024 - 0.0076 i * - 0.0046 0.0042 i * + 0.0044 0.0093 i * - 0.0022 - 0.0025 i * + 0.0093 0.0044 i * - 0.004 - 0.0041 i * - 0.0076 0.0023 i * + 0.0008 0.0089 i * - 0.0011 0.0042 i * + 0.0073 0.0072 i * - 0.0038 - 0.0004 i * - 0.0092 0.0007 i * - 0.0022 - 0.0068 i * - 0.0046 0.0041 i * + 0.0042 0.0086 i * - 0.0018 - 0.0026 i * + 0.0089 0.0041 i * - 0.0036 - 0.0035 i * - 0.0074 0.0023 i * + 0.0007 0.0082 i * - 0.0013 0.0042 i * + 0.0069 0.0067 i * - 0.0033 - 1.4128 105 -^* i * - 0.0089 0.0006 i * - 0.002 - 0.0061 i * - 0.0046 0.004 i * + 0.0039 0.008 i * - 0.0014 - 0.0028 i * + 0.0085 0.0038 i * - 0.0033 - 0.003 i * - 0.0073 0.0023 i * + 0.0007 0.0075 i * - 0.0015 0.0042 i * + 0.0066 0.0063 i * - 0.003 - 0.0003 i * + 0.0086 0.0006 i * - 0.0019 - 0.0055 i * - 0.0047 0.004 i * + 0.0037 0.0074 i * - 0.0011 - 0.003 i * + 0.0082 0.0036 i * - 0.0031 - 0.0025 i * - 0.0072 0.0022 i * + 0.0006 0.0069 i * - 0.0017 0.0043 i * + 0.0064 0.0059 i * - 0.0027 - 0.0006 i * + 0.0084 0.0005 i * - 0.0018 - 0.005 i * - 0.0047 0.004 i * + 0.0036 0.007 i * - 0.0009 - 0.0031 i * + 0.008 0.0034 i * - 0.0029 - 0.0021 i * - 0.0071 0.0022 i * + 0.0006 0.0064 i * - 0.0019 0.0043 i * + 0.0061 0.0056 i * - 0.0025 - 0.0009 i * + 0.0082 0.0004 i * - 0.0017 - 0.0045 i * - 0.0048 0.004 i * + 0.0034 0.0066 i * - 0.0006 - 0.0033 i * + 0.0077 0.0032 i * - 0.0028 - 0.0017 i * - 0.0071 0.0023 i * + 0.0005 0.006 i * - 0.0021 0.0044 i * + 0.0059 0.0053 i * - 0.0023 - 0.0012 i * + 0.0081 0.0003 i * - 0.0017 - 0.0041 i * - 0.0049 0.004 i * + 0.0032 0.0062 i * - 0.0005 - 0.0035 i * + 0.0076 0.003 i * - 0.0026 - 0.0013 i * - 0.007 0.0023 i * + 0.0005 0.0056 i * - 0.0022 0.0045 i * + 0.0057 0.0051 i * - 0.0021 - 0.0015 i * + 0.0079 0.0003 i * - 0.0017 - 0.0037 i * - 0.0049 0.0041 i * + 0.0031 0.0059 i * - 0.0003 - 0.0037 i * + 0.0074 0.0029 i * - 0.0025 - 0.001 i * - 0.007 0.0023 i * + 0.0004 0.0053 i * - 0.0023 0.0047 i * + 0.0056 0.0049 i * - 0.002 - 0.0018 i * + 0.0079 0.0002 i * - 0.0017 - 0.0033 i * - 0.005 0.0042 i * + 0.003 0.0056 i * - 0.0001 - 0.0039 i * + 0.0073 0.0028 i * - 0.0025 - 0.0007 i * - 0.007 0.0024 i * + 0.0003 0.0049 i * - 0.0025 0.0048 i * + 0.0054 0.0047 i * - 0.0019 - 0.0021 i * + 0.0078 0.0001 i * - 0.0017 - 0.003 i * - 0.0051 0.0043 i * + 0.0028 0.0054 i * - 6.9593 106 -^* - 0.0041 i * + 0.0072 0.0027 i * - 0.0024 - 0.0003 i * - 0.0071 0.0025 i * + 0.0002 0.0047 i * - 0.0026 0.005 i * + 0.0053 0.0045 i * - 0.0018 - 0.0024 i * + 0.0078 3.6496 105 -^* i * - 0.0017 - 0.0027 i * - 0.0052 0.0044 i * + 0.0027 0.0052 i * - 0.0001 0.0044 i * + 0.0071 0.0026 i * - 0.0024 - 0.0071 0.0026 i * + 0.0001 0.0044 i * - 0.0027 0.0052 i * + 0.0052 0.0044 i * - 0.0017 - 0.0027 i * + 0.0078 3.6496 105 -^* i * + 0.0018 - 0.0024 i * - 0.0053 0.0045 i * + 0.0026 0.005 i * - 0.0002 0.0047 i * + 0.0071 0.0025 i * - 0.0024 - 0.0003 i * + 0.0072 0.0027 i * + 6.9593 106 -^* - 0.0041 i * - 0.0028 0.0054 i * + 0.0051 0.0043 i * - 0.0017 - 0.003 i * + 0.0078 0.0001 i * + 0.0019 - 0.0021 i * - 0.0054 0.0047 i * + 0.0025 0.0048 i * - 0.0003 0.0049 i * + 0.007 0.0024 i * - 0.0025 - 0.0007 i * + 0.0073 0.0028 i * + 0.0001 - 0.0039 i * - 0.003 0.0056 i * + 0.005 0.0042 i * - 0.0017 - 0.0033 i * + 0.0079 0.0002 i * + 0.002 - 0.0018 i * - 0.0056 0.0049 i * + 0.0023 0.0047 i * - 0.0004 0.0053 i * + 0.007 0.0023 i * - 0.0025 - 0.001 i * + 0.0074 0.0029 i * + 0.0003 - 0.0037 i * - 0.0031 0.0059 i * + 0.0049 0.0041 i * - 0.0017 - 0.0037 i * + 0.0079 0.0003 i * + 0.0021 - 0.0015 i * - 0.0057 0.0051 i * + 0.0022 0.0045 i * - 0.0005 0.0056 i * + 0.007 0.0023 i * - 0.0026 - 0.0013 i * + 0.0076 0.003 i * + 0.0005 - 0.0035 i * - 0.0032 0.0062 i * + 0.0049 0.004 i * - 0.0017 - 0.0041 i * + 0.0081 0.0003 i * + 0.0023 - 0.0012 i * - 0.0059 0.0053 i * + 0.0021 0.0044 i * - 0.0005 0.006 i * + 0.0071 0.0023 i * - 0.0028 - 0.0017 i * + 0.0077 0.0032 i * + 0.0006 - 0.0033 i * - 0.0034 0.0066 i * + 0.0048 0.004 i * - 0.0017 - 0.0045 i * + 0.0082 0.0004 i * + 0.0025 - 0.0009 i * - 0.0061 0.0056 i * + 0.0019 0.0043 i * - 0.0006 0.0064 i * + 0.0071 0.0022 i * - 0.0029 - 0.0021 i * + 0.008 0.0034 i * + 0.0009 - 0.0031 i * - 0.0036 0.007 i * + 0.0047 0.004 i * - 0.0018 - 0.005 i * + 0.0084 0.0005 i * + 0.0027 - 0.0006 i * - 0.0064 0.0059 i * + 0.0017 0.0043 i * - 0.0006 0.0069 i * + 0.0072 0.0022 i * - 0.0031 - 0.0025 i * + 0.0082 0.0036 i * + 0.0011 - 0.003 i * - 0.0037 0.0074 i * + 0.0047 0.004 i * - 0.0019 - 0.0055 i * + 0.0086 0.0006 i * + 0.003 - 0.0003 i * - 0.0066 0.0063 i * + 0.0015 0.0042 i * - 0.0007 0.0075 i * + 0.0073 0.0023 i * - 0.0033 - 0.003 i * + 0.0085 0.0038 i * + 0.0014 - 0.0028 i * - 0.0039 0.008 i * + 0.0046 0.004 i * - 0.002 - 0.0061 i * + 0.0089 0.0006 i * + 0.0033 - 1.4128 105 -^* i * + 0.0069 0.0067 i * + 0.0013 0.0042 i * - 0.0007 0.0082 i * + 0.0074 0.0023 i * - 0.0036 - 0.0035 i * + 0.0089 0.0041 i * + 0.0018 - 0.0026 i * - 0.0042 0.0086 i * + 0.0046 0.0041 i * - 0.0022 - 0.0068 i * + 0.0092 0.0007 i * + 0.0038 - 0.0004 i * + 0.0073 0.0072 i * + 0.0011 0.0042 i * - 0.0008 0.0089 i * + 0.0076 0.0023 i * - 0.004 - 0.0041 i * + 0.0093 0.0044 i * + 0.0022 - 0.0025 i * - 0.0044 0.0093 i * + 0.0046 0.0042 i * - 0.0024 - 0.0076 i * + 0.0096 0.0008 i * + 0.0043 - 0.0008 i * + 0.0078 0.0078 i * + 0.0008 0.0043 i * - 0.0008 0.0098 i * + 0.0079 0.0024 i * - 0.0045 - 0.0048 i * + 0.0099 0.0047 i * + 0.0027 - 0.0024 i * - 0.0047 0.0102 i * + 0.0045 0.0044 i * - 0.0026 - 0.0085 i * + 0.0101 0.0009 i * + 0.0049 - 0.0012 i * + 0.0083 0.0085 i * + 0.0004 0.0044 i * - 0.0008 0.0109 i * + 0.0082 0.0026 i * - 0.005 - 0.0056 i * + 0.0106 0.0052 i * + 0.0033 - 0.0022 i * - 0.0051 0.0113 i * + 0.0045 0.0047 i * - 0.003 - 0.0097 i * + 0.0107 0.001 i * + 0.0056 - 0.0018 i * + 0.009 0.0094 i * + 2.2274 105 -^* 0.0046 i * - 0.0009 0.0123 i * + 0.0086 0.0028 i * - 0.0058 - 0.0066 i * + 0.0114 0.0057 i * + 0.0041 - 0.0021 i * - 0.0056 0.0126 i * + 0.0045 0.005 i * - 0.0034 - 0.0111 i * + 0.0115 0.0011 i * + 0.0066 - 0.0024 i * + 0.0099 0.0105 i * + 0.0005 - 0.0048 i * - 0.0009 0.0139 i * + 0.0091 0.0031 i * - 0.0067 - 0.0078 i * + 0.0125 0.0063 i * + 0.0051 - 0.0019 i * - 0.0062 0.0143 i * + 0.0045 0.0055 i * - 0.004 - 0.0129 i * + 0.0126 0.0012 i * + 0.0079 - 0.0032 i * + 0.011 0.0119 i * + 0.0012 - 0.0052 i * - 0.0009 0.0161 i * + 0.0098 0.0034 i * - 0.008 - 0.0094 i * + 0.014 0.0072 i * + 0.0064 - 0.0018 i * - 0.0069 0.0166 i * + 0.0044 0.0061 i * - 0.0049 - 0.0153 i * + 0.0141 0.0013 i * + 0.0097 - 0.0042 i * + 0.0126 0.0138 i * + 0.0021 - 0.0057 i * - 0.0009 0.0191 i * + 0.0107 0.004 i * - 0.0097 - 0.0116 i * + 0.0161 0.0084 i * + 0.0083 - 0.0016 i * - 0.008 0.0197 i * + 0.0044 0.0071 i * - 0.0061 - 0.0186 i * + 0.0161 0.0015 i * + 0.0122 - 0.0056 i * + 0.0148 0.0166 i * + 0.0035 - 0.0065 i * - 0.0009 0.0234 i * + 0.0121 0.0049 i * - 0.0123 - 0.0147 i * + 0.0191 0.0101 i * + 0.0111 - 0.0015 i * - 0.0097 0.0244 i * + 0.0044 0.0086 i * - 0.0079 - 0.0237 i * + 0.0193 0.0017 i * + 0.016 - 0.0077 i * + 0.0182 0.0208 i * + 0.0056 - 0.0078 i * - 0.0008 0.0302 i * + 0.0144 0.0063 i * - 0.0165 - 0.0196 i * + 0.0241 0.0128 i * + 0.0156 - 0.0013 i * - 0.0123 0.0322 i * + 0.0044 0.0113 i * - 0.011 - 0.0321 i * + 0.0248 0.002 i * + 0.0228 - 0.0112 i * + 0.0242 0.0282 i * + 0.0093 - 0.0103 i * - 0.0006 0.0423 i * + 0.0185 0.0091 i * - 0.0243 - 0.0288 i * + 0.0334 0.018 i * + 0.0244 - 0.001 i * - 0.0175 0.0473 i * + 0.0044 0.0166 i * - 0.0175 - 0.0493 i * + 0.0362 0.0026 i * + 0.0374 - 0.0187 i * + 0.0374 0.0445 i * + 0.0178 - 0.0161 i * - 5.2214 105 -^* 0.0706 i * + 0.0286 0.0157 i * - 0.0442 - 0.0514 i * + 0.0576 0.0315 i * + 0.0484 - 0.0007 i * - 0.0316 0.0904 i * + 0.0044 0.033 i * - 0.039 - 0.1039 i * + 0.0749 0.0049 i * + 0.0917 - 0.0451 i * + 0.0885 0.1103 i * + 0.0557 - 0.0428 i * - 0.0074 - 0.2118 i * + 0.0866 0.0527 i * - 0.1925 - 0.204 i * + 0.2635 0.1645 i * + 0.3758 - 0.0231 i * - 0.1364 1.2354 i * + 5121 mat :

Stem Module

Spectrum stem plot for QuickPlot unicolor data Stem stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

sub vFIs 120 range 11 range el :

Alternate for stem style S t 1 sub length range : Fo sub mwabs : t Fo augment 31 line :

spectrum S Stem :

Fake to view DC DC 0.875 0 0.875 spectrum 12 el 1.125 spectrum 12 el 1.125 042 mat :

Partial I-source spectrum scaled 1/(λ-1)

spectrum DC 2 1 sys

vs rows 513

vs vs 1512 range 11 range el :

3. Solving the project

ii 1 vs rows range Z1 ii el 1 vs ii el f_Z 1 el / : for

ii 1 vs rows range Z2 ii el 1 vs ii el f_Z 2 el / : for

ii 1 vs rows range Z3 ii el 1 vs ii el f_Z 3 el / : for

ii 1 vs rows range Z4 ii el 1 vs ii el f_Z 4 el / : for

ii 1 vs rows range Z5 ii el 1 vs ii el f_Z 5 el / : for

Z2 1 el 0 : Z3 1 el 0 : Z4 1 el 0 : Z5 1 el 0 : 14 mat

Discrete Laplace impedances Y Z1 Z2 Z3 Z4 Z5 15 mat :

The current divisor U Y transpose : i 1 N range Ysum i el U 1 el (i el U 2 el (i el + U 3 el (i el + U 4 el (i el + U 5 el (i el + : for 21 line

check respective lengths Ysum rows Y 11 el rows scale rows vFIs rows 41 mat 51251251251241 mat

DFT complex admittances i 1 N range j 15 range FIz i j el Y j el i el Ysum i el / (vFIs i el * eval : for for

sanity MCD 1/1

can't confirm 1/1 sanity

Iz5 MCD 1.109 1.11 1.111 1.113 0.463 - 0.467 - 0.472 - 0.477 - 81 mat

Iz1 scale Iz 1 el augment : Iz2 scale Iz 2 el augment : Iz3 scale Iz 3 el augment : Iz4 scale Iz 4 el augment : Iz5 scale Iz 5 el augment : 51 sys

Iz FIz 1 col mwifft Re FIz 2 col mwifft Re FIz 3 col mwifft Re FIz 4 col mwifft Re FIz 5 col mwifft Re 51 sys :

Source of the project: Mark Solution doctored by: Lou September 04 2009 Mathsoft.

Don't understand MCD 
switch. Might be a left
over code undocumented.
Many of those codes were
discovered. Accordingly
to Lou, it did meet a
Lab Analyzer. 21321421 sys

Submatrix system

Iz1_0 Iz1 121212 submatrix : Iz2_0 Iz2 121212 submatrix : Iz3_0 Iz3 121212 submatrix : Iz4_0 Iz4 121212 submatrix : Iz5_0 Iz5 121212 submatrix : 51 sys

Iz1_1 Iz1 21351212 submatrix : Iz2_1 Iz2 21351212 submatrix : Iz3_1 Iz3 21351212 submatrix : Iz4_1 Iz4 21351212 submatrix : Iz5_1 Iz5 21351212 submatrix : 51 sys

I1 Iz1_0 Iz1_1 1 col reverse Iz1_1 2 col augment stack : I2 Iz2_0 Iz2_1 1 col reverse Iz2_1 2 col augment stack : I3 Iz3_0 Iz3_1 1 col reverse Iz3_1 2 col augment stack : I4 Iz4_0 Iz4_1 1 col reverse Iz4_1 2 col augment stack : I5 Iz5_0 Iz5_1 1 col reverse Iz5_1 2 col augment stack : 51 sys

I1 I2 I3 I4 I5 5 1 sys I1 I2 I3 I4 I5 1.667 0.25 1.667 0.25 - 2 2 mat 0 7 1 sys