By Crossley J.N. (ed.)

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**Extra resources for Algebra and logic: Proceedings Clayton, 1974**

**Sample text**

6. 7. 8. 55 A L G E B R A OP F O U R - T E R M I N A L N E T W O R K S ΖΛΛ = G A 7T~C~~ Ζ Λ9 = 1 ^21 — ~c ~ D C ~ D ~B~~ A Zu = 9. Z \2 = 10. Z 2l = ^22 = = y Z = r„=- \2 Y 1 — B ~ = — _ z~212l _ A __ ~B~~ Az A. B ^22 Λ 12 A = fr \2 Z 1^_ _ Z 22 ^2\2 1 T7~ ^ K= 22 1 D ~ A =(AD = Z c = ^22 Δζ Z ~D~~~ ^22 _ = = = ^12^21) (^11 ^22 4> = ( Λ ΐ Λ 2 — ^12^21) Ä l2^2l) *11 Λ22 - 1 22 14. 15. A 16. Ä 17. /111 1 = ll III 18. ^11 =_ — BG) (^11^22 13. V = = 11. 12. ^2 22 2 ^ 4 V 111-, n y ^ 1 = h9 19. = K 20.

2: With similar reasoning as with Fig. 1, the transmission matrix of this composite network will be also synthesized from 25 ALGEBRA OF FOUR-TERMINAL NETWORKS the elementary Y and Z matrices. 12) and cascade the transmission matrices in the same I2 I I CHZh Γθ + v2 Y FIG. 2. The four-terminal network of cascaded Y and Z elements order as the elements in the composite network shown in Fig. 11) The input-output quantities of the composite network in Fig. 14) 26 BASIC MATRIX ALGEBRA AND TRANSISTOR CIRCUITS These equations completely define the equilibrium conditions of the network shown in Fig.

8) D I t is recognized t h a t in the notation used in Fig. 17) which has been obtained by simple synthesis and matrix multiplication. (b) T H E π NETWORK The equilibrium conditions of a Fig. 2 are conveniently written in Using Kirchhoff's Law, a pair of equation can be formulated with variables. Λ = Γ ΐ ( Γ ΐ + Ym)~ -I2=-V1Ym+V2(Y2+Ym) n network as shown in terms of nodal equations. 10): v, 2 -o— -co- T I M Yi I I 3 V2 4 -o · FIG. 2. 17) are in the desired form with the input quantities Vx and Ιλ as dependent variables.