POINTS PER DECADE FOR LOOP VERSION

0aa89e35-a212-4eea-9dcb-190774e87c87 147 3 12 decimal

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

TEST OF TDFD COUPLING TO TM-LINE BY CONSTANT DOUBLE EXPONENTIAL E-FIELD

POINTS PER DECADE SNIPPET

MUST DEFINE THE FOLLOWING PARAMETERS BEFORE INSERTING THE SNIPPET

NUMBER OF POINTS PER DECADE = NPD:

DECADE GRID SIZE

POWER OF START POINT = NFS

POWER OF END POINT = NFF

TOTAL NUMBER OF POINS = Nt

NFS NFF NPD PPD Δ 9.9 1 - NPD / : i 1 NPD range j 1 NFF NFS - (range FF i j el 1 i Δ * + (10 j NFS + 1 - (^* : for for ColF.1 FF 1 col : V ColF.1 : i 2 FF cols ((range V V FF i col stack : for V 61 line :

Define more time points per decade using snippet.

Points/Decade =

NPD 5 :

Power of Starting Point

NFS 9 - :

Power of End Point

NFF 1 - :

t NFS NFF NPD PPD :

t length 40

t max 9.9 102 -^*

k 1 t length range :

Nt t length : 40

Nt 40

DEFINE CONSTANT DRIVING FIELD ALONG TM LINE

t rows 40

E.o 5105^* :

α 4106^* :

β 480106^* :

t min 2.78 109 -^*

t.o β α / ln β α - / : 1.0058 108 -^*

Norm α t.o * - exp β t.o * - exp - : 0.9526

t 0.00000000278 0.00000000456 0.00000000634 0.00000000812 0.0000000099 0.0000000278 0.0000000456 71 mat

k 1 t rows range 1 - t k el β α - (* exp + t k el β * exp / 1010 -^≤ EE k el 1010 -^: EE k el E.o Norm / 1 - t k el β α - (* exp + t k el β * exp / (* : if for

1 - t t rows el β α - (* exp + t t rows el β * exp / #

t t rows el 0.099

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t rows EE rows 21 mat 401521 mat

@ some values of 't' exp(,) is above 10^307

EE Max 499988

EE Min 10006

Q 380880.663682605 456596.792906302 486727.399636462 497474.438869479 499987.744419904 469658.380421549 437382.181791019 407323.361967068 379330.315795378 353261.074411543 172639.804853289 84707.7732319033 41562.8762555926 20393.319488032 10006.2247180248 151 mat

EE rows 15

CABLE PARAMETERS FOR TDFD COUPLING TO BURIED CABLE

σ.g 1103 -^* :

μ.o 4 π * 107 -^* :

σ.c 5.8 107^* :

c 3108^* :

ε.rg 16 :

ε.o 1 μ.o c 2^* / :

a.o 102 -^:

ε.g ε.rg ε.o * :

Ncell 10 :

Δz 10 :

Lz Ncell Δz * : 1102^*

Δt k el k 1 ≤ t k el t k el t k 1 - el - if :

Do Time Iteration:

k 1 Nt 1 - (range :

Δt k 2 Nt range Δ k el t k el t k 1 - el - : Δ 1 el t 1 el : 21 line for Δ 21 line :

k length 39

t 0.00000000278 0.00000000456 0.00000000634 0.00000000812 0.0000000099 0.0000000278 0.0000000456 0.0000000634 0.0000000812 0.000000099 0.000000278 0.000000456 0.000000634 0.000000812 0.00000099 0.00000278 0.00000456 0.00000634 0.00000812 0.0000099 0.0000278 0.0000456 0.0000634 0.0000812 0.000099 0.000278 0.000456 0.000634 0.000812 0.00099 0.00278 0.00456 0.00634 0.00812 0.0099 0.0278 0.0456 0.0634 0.0812 0.099 401 mat :

Δt 11 mat 0.00000000278 0.00000000178 0.00000000178 0.00000000178 0.00000000178 0.0000000179 0.0000000178 0.0000000178 0.0000000178 0.0000000178 0.000000179 0.000000178 0.000000178 0.000000178 0.000000178 0.00000179 0.00000178 0.00000178 0.00000178 0.00000178 0.0000179 0.0000178 0.0000178 0.0000178 0.0000178 0.000179 0.000178 0.000178 0.000178 0.000178 0.00179 0.00178 0.00178 0.00178 0.00178 0.0179 0.0178 0.0178 0.0178 0.0178 401 mat 11 mat

t 11 mat 0.00000000278 0.00000000456 0.00000000634 0.00000000812 0.0000000099 0.0000000278 0.0000000456 0.0000000634 0.0000000812 0.000000099 0.000000278 0.000000456 0.000000634 0.000000812 0.00000099 0.00000278 0.00000456 0.00000634 0.00000812 0.0000099 0.0000278 0.0000456 0.0000634 0.0000812 0.000099 0.000278 0.000456 0.000634 0.000812 0.00099 0.00278 0.00456 0.00634 0.00812 0.0099 0.0278 0.0456 0.0634 0.0812 0.099 401 mat 11 mat

δ k el 2 t k el * μ.o σ.g * / sqrt :

Rc k el 1 π a.o 2^* σ.c * / :

Rs k el μ.o 4 π * t k el * / :

R k el Rc k el Rs k el + :

k 1 t rows range :

k 1 t rows range Rc k el 1 π a.o 2^* σ.c * / : for

k 1 t rows range Rs k el 1 π a.o 2^* σ.c * / : for

k 1 t rows range δ k el 2 t k el * μ.o σ.g * / sqrt : for

R Rc Rs + vectorize :

Rc 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 101 mat

Rs 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 0.000054881014859 101 mat

R 0.000109762029719 0.000109762029719 0.000109762029719 0.000109762029719 0.000109762029719 0.000109762029719 0.000109762029719 0.000109762029719 0.000109762029719 0.000109762029719 101 mat

δ 2.10345131104923 2.69396833778544 3.1765426790815 3.59491048276059 3.96942557130095 6.65169709018287 8.51907589177986 10.0451099506308 11.368105109939 12.5524258078261 101 mat

δ k el δ k el 0 ≤ 1.0000 a.o * 0 δ k el < (δ k el Lz < (& δ k el Lz if if :

δ 2.103 2.694 3.177 3.595 3.969 6.652 8.519 10.045 11.368 12.552 101 mat

δ max 1.14 104^*

Lg k el μ.o 2 π * / δ k el a.o / ln * :

L k el Lg k el :

Gg k el 2 π * σ.g * δ k el a.o / ln / :

CCg k el 2 π * ε.g * δ k el a.o / ln / :

ZT.0 1 :

ZT.Ncell 1 :

Approximation to incident E-field reflection terms at the ground surface by substituting 1/t for iω to get the net driving field.

Refl k el 2 μ.o t k el / σ.g ε.g t k el / - (* sqrt * c μ.o * σ.g ε.g t k el / - (* μ.o t k el / σ.g ε.g t k el / - (* sqrt + / :

Refl rows 40

Net Driving Field for the TM Line

EE rows 15

E k el EE k el Refl k el * Re :

E EE Refl * vectorize :

E Max #

E Min #

E #

UNCOUPLED TDFD CALCULATION

E max #

I I Clear k 1 Nt 1 - (range k 1 ≤ I k el 1010 -^: I k el I k 1 - el Δt k el L k el / E k el * + 1 Δt k el L k el / R k el * + / : if for I 31 line :

R max 1.1 104 -^*

R min 1.1 104 -^*

L max 1.84 106 -^*

L min 0

Gg max 6.82 104 -^*

CCg max 9.65 1011 -^*

I I :

t length 40

I length 39

I max 1.68 104^*

I min 11010 -^*

Nt 40

Ncell 10

ZT.0 1 :

ZT.Ncell 1 :

Δz 10

Lz 100

Δt length 39

COUPLED TDFD ROUTINE

COUPLED TDFD ROUTINE

Ans AI VG Ncell Nt matrix : (: k 2 Nt 1 - (range j 1 Ncell range j 1 ≤ ΔI AI j k 1 - el eval : ΔI AI j k 1 - el AI j 1 - k 1 - el - eval : if j 1 ≡ VG AI ZT.0 * eval : j Ncell ≡ VG AI ZT.Ncell * eval : VG j k el VG j k 1 - el ΔI Δz / Δt k el CCg k el / * - 1 Δt k el CCg k el / Gg k el * + / : if if 21 line for VT VG : n 1 Ncell 1 - (range ΔV VT n 1 + k el VG n k el - eval : AI n k el AI n k 1 - el Δt k el L k el / E k el ΔV Δz / - (* + 1 Δt k el L k el / R k el * + / : 21 line for 31 line for 11 line VT AI 21 mat 31 line :

Initialize Results to Zero

Time Loop on k

Spatial Loop on j for Voltage

Currents From Previous Time k-1

Votage at End Point Terminations ZT

Voltage at Remaining Cable Points

Spatial Loop on n for Current

Voltages at Present Time k

Current at Point n and Present Time k

Ans1 Ans eval :

V Ans1 1 Ncell 1 Nt 1 - submatrix eval :

V Ans1 1 el :

I Ans1 Ncell 2 Ncell * 1 Nt 1 - submatrix eval :

I Ans1 2 el :

Ans1 rows #

Ans1 cols #

str

Voltage V Ncell 2 / k el transpose eval :

Current I Ncell 2 / k el transpose eval :

Current max #

Voltage max #

lastError Ans1 - not defined.