By Hercules G. Dimopoulos
Knowledgeable by way of the authors' lengthy adventure within the topic, this step by step presentation of the subject presents a coherent and seamless framework that encompasses passive and energetic filters and comprises the main sleek and updated layout methodologies.
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Extra resources for Analog Electronic Filters: Theory, Design and Synthesis
Nodes with only inductors or capacitors connected to them. A further reduction is due to the existence of closed paths (loops) consisting exclusively of inductors (L-loops) or capacitors (C-loops). In fact each L-node, C-node, L-loop or C-loop reduces the order by 1. In the circuit of Fig. 40a, there are one L-node and one C-loop. If this is not obvious, see the circuit of Fig. 40b, which is the same circuit redrawn to make the L-node and the C-loop apparent. Since the number of reactive elements is 7 (3 inductors and 4 capacitors), the order of the circuit will be n = 7 − 1 − 1 = 5, which is independent of the element values.
22. However, this is not enough since the gain function must satisfy some more realizability conditions. e. the magnitude of the transfer function H (s) of a linear time invariant circuit for s = j Ω, is an even function of Ω and G2 (Ω) is an even rational function. In addition, we know that the poles of H (s) must be located in the left-hand half s-plane. These fundamental necessary conditions for G(Ω) and H (s) limit the number of possible solutions. 15) is not an even function, nor is its square, and this implies that there is no linear time invariant circuit with this gain function.
Suppose that the transfer function of the 3rd order passive filter of Fig. e. C1 (RS , RL , ωC , αmax ), L2 (RS , RL , ωC , αmax ) and C3 (RS , RL , ωC , αmax ). In order to create a table giving the values of C1 , L2 and C3 for given RS , RL , ωC and αmax , a table like the one shown in Fig. 34 will be necessary. For the table to be useful, at least 100 RS values and 100 RL values are necessary. For the cutoff frequency more than 1000 entries, if not many more, will be needed. Finally, for αmax , we will limit the table values to only 10.