Passive, active, and digital filters (3ed., CRC, 2009) - tiera.ru

3-10 Passive, Active, and Digital Filtersl nI nBWc nc n /BW(a)LPBWω o 2 c nBP1.032.82×10 –6 5.36×10 –6 33.974×10 –6 5.177×10 –6 25.2×10 –6 6.982×10 –6+V in–103.2×10 –6129.1×10 –6134.4×10 –61.705×10 –6 1.264×10 –6 1.309×10 –60.2242+V out–(b)FIGURE 3.8 (a) LPP to bandpass network element transformations and (b) bandpass network derived from LPPnetwork of Figure 3.3a.an inductor with value L s and a capacitor with value C s and capacitors in the LPP are replaced by theparallel combination of a capacitor C p and inductor L p . This is illustrated in Figure 3.8. As with othertransformations, resistors remain unchanged since they are not frequency dependent.Example 3.3Consider the LPP network shown in Figure 3.3a with specifications Ap ¼ 2 dB, As ¼ 45 dB, and V s ¼ 1.6.Derive a bandpass network using the parameters calculated in Example 3.2: v 2 o ¼ (2p)2 144, BW ¼2p 4.4 krad=s.SolutionStraightforward application of the relations shown in Figure 3.8a leads to the network of Figure 3.8b.3.5 Low-Pass to Band-Reject TransformationThis transformation is characterized byS ¼ BWpp 2 þ v 2 o(3:21)and it can be best visualized as a sequence of two transformations through the intermediate complexfrequency variables s 0 ¼ u 0 þ jV 0 3 1. A normalized LPP to high-pass transformationss ¼ 1 s 0 (3:22)