Page 355 - Integrated Wireless Propagation Models

I n - B u i l d i n g ( P i c o c e l l ) P r e d i c t i o n M o d e l s 333

Time

n - 112 n n + Y 2

..
E H E H E
FIGURE 5.6.2.2.2 The Yee cell demonstrated.

For Eq. (5.6.2.2.5), we transform the E-field equation to the different form:

1
i
i
E;+ (i, j, k)-E;(i, j, k) 1 [H;+ (i, j, k)-H;'+ (i, j -1, k)
L'lt £ !J.y
(5.6.2.2.11)

Then Eq. (5.6.2.2.11) can be rewritten as
[ 1 1 " 1 " 1 :
[ a!J.t
l, ],
l, ],
E " ( i . k) 1 - ] + L'lt H;+2(i, j , k) - H;+2(i, j - 1,k) H +2( · . k)-H +2 ( · . k - 1)
y
y
, ;,
X 2£ E !J. y
1
E;+ (i,j,k) =
[ ]
a!J.t
1 +
2£
(5.6.2.2.12)
For Eq. (5.6.2.2.8), we transform the H-field equation to the different form:
H: (i, j k ) - H: (i, j, k ) _ ..!_[ E ; (i, j, k+ 1)-E ; (i, j, k ) E;(i, j + 1, k)-E;(i, j, k )]
+�
�
-
,
_ (5.6.2.2.13)
L'lt - 11 !J.z !J.y
And Eq. (5.6.2.2.13) can be rewritten as
1 1 • t [E"(i ;· k + 1) - E"(i ;· k) E"( · + 1 k) E"( . . k)]
.
-
H;+2 ( i, j , k) = H;-2 ( i, j , k) +ft- Y ' ' !J.z Y ' ' z z, ; ' !J. y z ! , ] , (5.6.2.2.14)
Assume that we know the E and H values at the very beginning of the first cell (in
3 D ) or grid (in 2 D) at the time (n = 0). Depending on the number of cells or grids, we