Type II: Current-centered Mesh

This arrangement is the dual to the previous case. We now set

$$Z_{x^{+},i+\frac{1}{2},j} = Z_{x^{-},i+\frac{1}{2},j} = v_{0}l_{i+\frac{1}{2},j}$$ (4.76)

$$Z_{y^{+},i,j+\frac{1}{2}} = Z_{y^{-},i,j+\frac{1}{2}} = v_{0}l_{i,j+\frac{1}{2}}$$ (4.77)

$$Z_{c,i+\frac{1}{2},j} = Z_{c,i,j+\frac{1}{2}} = 0$$ (4.78)

and

$$Y_{c,i,j} = -\frac{1}{v_{0}}\left(\frac{1}{l_{i+\frac{1}{2},j}}+\... ...1}{2},j} + c_{i-\frac{1}{2},j}+c_{i,j+\frac{1}{2}} + c_{i,j-\frac{1}{2}}\right)$$

We then have

$$v_{0}\geq \max_{2(k+p)\hspace{0.05in}{\rm odd}}\left(\sqrt{\frac{2}{l_{k,p}c_{k,p}}}\right)$$ (4.79)

for half-integer $k$ and $p$. It is rather interesting that in (2+1)D, if we have $r=0$ and $e=f=0$, this arrangement (and not that of type I) allows the series junctions to be treated as throughs (with sign inversion). We may thus operate at a reduced sample rate in this case. This particular choice of immittances, in the constant-coefficient, lossless and source-free case with $v_{0} = \sqrt{2/(lc)}$, yields the original form of the waveguide mesh proposed in [198], and mentioned in §4.2.7. We also note that networks such as this and type I, for which the connecting immittances may vary spatially have also been explored in TLM [29,159].