By Wai-Kai Chen
Lively community and suggestions Amplifier thought
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Extra resources for Active Network Analysis. Feedback Amplifier Theory
When we say that A is analytic in a region, we mean that every element of A is analytic in the region. On the other hand, when we say that A has a pole at s0, we mean that at least one element of A has a pole at s0. 6: Positive-real matrix An n × n matrix function A(s) of the complex variable s is said to be a positive-real matrix if it satisfies the following three conditions: 1. A(s) is analytic in the open RHS. 2. A(s) = A(s) for all s in the open RHS. 3. Its hermitian part Ah (s) is nonnegative definite for all s in the open RHS.
64) The matrix Y(s) is called the short-circuit admittance matrix or simply the admittance matrix, whose elements are referred to as the short-circuit admittance parameters or admittance parameters. We illustrate the above results by the following example. 4 Consider the high-frequency equivalent network of a bipolar transistor as shown in Fig. 17. Let u(s) ˜ = [I1 (s), V2 (s)] and y˜ (s) = V1 (s), I2 (s) , where Vk (s) and Ik (s) are the transforms of vk (t) and i k (t), respectively. 17 A high-frequency equivalent network of a bipolar transistor.
We emphasize the difference of the concepts that an n-port is passive and that an n-port is passive at a closed RHS point s0 . 135) for all complex n-vectors u0 . 136) u0∗ Hh (s0 )u0 |s0 | 0 for all complex n-vectors u0 . As demonstrated in Eq. 131), Eq. 136) is a consequence of positive realness of H(s). However, the converse is not necessarily true. 3. 127). The definitions of passivity and activity at a single complex frequency s0 in the closed RHS suggest that for any given n-port, the closed right half of the complex frequency s-plane can be partitioned into regions of passivity and activity.
Active Network Analysis. Feedback Amplifier Theory by Wai-Kai Chen