By Wai-Kai Chen
Lively community and suggestions Amplifier thought
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Additional info for Active Network Analysis. Feedback Amplifier Theory
45) Let uk (t), k = 1, 2, . . , n, be n linearly independent excitations that can be supported by the n-port under consideration. Since in deriving Eq. 45) u0 (t) is an arbitrary excitation, Eq. 45) is also applicable to uk (t). Applying it to uk (t) successively gives uk (t)y(t) = 0 k = 1, 2, . . 46) or, more compactly, [u1 (t), u2 (t), . . 47) Since the vectors uk (t) are linearly independent, the coefficient matrix is nonsingular. 52) This completes the proof of the theorem. The ideal one-port short circuit is noncausal under voltage excitation-current response because it admits an infinitude of responses for the sole excitation September 1, 2016 10:33 Active Network Analysis: Feedback …– 9in x 6in b2428-ch01 page 21 CHARACTERIZATIONS OF NETWORKS 21 v(t) = 0.
17 by open-circuiting the output port. In a similar manner, we can compute z 12 (s) and z 22 (s). 70) we let u(s) ˜ = [V1 (s), V2 (s)] and y˜ (s) = [I1 (s), I2 (s)] . From Eq. 71b) September 1, 2016 10:33 Active Network Analysis: Feedback …– 9in x 6in b2428-ch01 page 26 26 ACTIVE NETWORK ANALYSIS They are obtained by short-circuiting the output port of the two-port network of Fig. 17. In a similar fashion, we can compute y12 (s) and y22 (s). 72) Finally, suppose that we take u(s) ˜ = V2 (s), −I2 (s) as the excitation and y˜ (s) = [V1 (s), I1 (s)] as the response.
In the piecewise-linear analysis of a regenerative oscillator, such as the blocking oscillator, a somewhat similar problem is posed by the question of designing a pulse circuit of minimum rise time. More precisely, given an active device, what is the smallest time constant for an exponentially increasing signal that the device can produce? For this we introduce the concept of fastest regenerative mode. 11: Fastest regenerative mode The largest σ on the nonnegative σ -axis at which an n-port network is active is called the fastest regenerative mode of the n-port network.
Active Network Analysis. Feedback Amplifier Theory by Wai-Kai Chen