POINTS PER DECADE FOR LOOP VERSION

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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 eval :

Nt 40

DEFINE CONSTANT DRIVING FIELD ALONG TM LINE

E.o 5105^* :

α 4106^* :

β 480106^* :

t min 2.78 109 -^*

t.o β α / ln β α - / :

t.o 1.0058 108 -^*

Norm α t.o * - exp β t.o * - exp - :

Norm 0.9526

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

EE max 5105^*

EE min 11010 -^*

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 * :

Lz 1102^*

Do Time Iteration:

k 1 Nt 1 - (range :

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

k length 39

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 + :

δ k el 2 t k el * μ.o σ.g * / sqrt :

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 :

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 / :

δ max 1102^*

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 + / :

Net Driving Field for the TM Line

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

E max 1.22 105^*

E min 6.598 1014 -^*

UNCOUPLED TDFD CALCULATION

E max 1.2174 105^*

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 35.97

R min 5.61 105 -^*

L max 1.84 106 -^*

L min 1.07 106 -^*

Gg max 1.17 103 -^*

CCg max 1.66 1010 -^*

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.