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X-Parameters by Jason Horn, Jan Verspecht, David E. Root

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Appendix E: Solutions to exercises

Exercise 1.1 Referring to Figure 1.9, Eq. (1.5) is used to write KCL at the internal node according to (E.1):

i(t)=i2(1)(t)+i1(2)(t)=0=a2(1)(t)−b2(1)(t)+a1(2)(t)−b1(2)(t).
(E.1)

The voltage at the internal node can be written using Eq. (1.5) according to (E.2):

v(t)=a2(1)(t)+b2(1)(t)=a1(2)(t)+b1(2)(t).
(E.2)

Solving (E.2) for a2(1)(t) yields

a2(1)(t)=−b2(1)(t)+a1(2)(t)+b1(2)(t).
(E.3)

Substituting for using (E.3) into (E.1) results in (E.4):

(E.4)

Substituting (E.4) ...

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