General Parallel Adaptor for Force Waves

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In the more general case of wave digital element ports being connected in parallel, we have the physical constraints

		$\displaystyle f_1(n) = f_2(n) = \cdots = f_N(n) \isdef f_J(n)$	(Q.14)
		$\displaystyle v_1(n) + v_2(n) + \cdots + v_N(n) = 0$	(Q.15)

The derivation for the two-port case extends to the

-port case without modification:

0	$\displaystyle =$	$\displaystyle \sum_{i=1}^N v_i$
	$\displaystyle =$	$\displaystyle \sum_{i=1}^N\frac{f^{{+}}_i-f^{{-}}_i}{R_i}$
	$\displaystyle =$	$\displaystyle \sum_{i=1}^N\frac{2f^{{+}}_i-f_J}{R_i}$
	$\displaystyle \isdef$	$\displaystyle \sum_{i=1}^N \left(2\Gamma _if^{{+}}_i-\Gamma _i f_J \right)$
$\displaystyle \,\,\Rightarrow\,\, \sum_{j=1}^N \Gamma _j f_J$	$\displaystyle =$	$\displaystyle \sum_{i=1}^N 2\Gamma _i f^{{+}}_i$
$\displaystyle \,\,\Rightarrow\,\, f_J$	$\displaystyle =$

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