Analog and Digital Filters: Design and Realization by Harry Y. F. Lam

By Harry Y. F. Lam

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V1 Fig. PI-7 (c) v,(t) = cos 10 8 t (d) Based on the results of (a), (b), and (c), what type of filter is V1/V,? V2 /V, ? V3/V. (e) Find the transfer functions where i = 1,2,3. (0 Sketch the magnitude functions IHi(jco) I for i = 1,2,3. (g) Sketch the phase functions c/Jlco) of Hls) for i = 1,2,3. 1-8. Consider a filter Fwhose frequency characteristics are shown in Fig. w 2 BUILDING BLOCKS A port, as shown in Fig. 2-I(a), is a pair of terminals with the condition that the instantaneous current entering one terminal will always equal the instantaneous current leaving the other terminal of the port.

Normally, the op. amp. connection to ground is not shown but is understood to be present. 2 Building Blocks / 21 Before we proceed further, it should be emphasized that these basic building blocks are ideal elements only; they are of paper and pencil type and not of the real physical world type. In general, the electrical performance of a real physical element can be modeled to a sufficient degree of accuracy by a combination of these ideal elements. For example, an actual inductor, in most cases, can be adequately modeled by a series combination of an ideal resistor and an ideal inductor.

Consider the circuit shown in Fig. P2-5, where the 2-port network N z has an admittance representation II =y 11 V1 +Y12V2 12 = Y21 VI + y 22 V2 Find the driving-point admittance function Y(s). r $ $ N2 y(s) Fig. P2-5 2-6. Given the transmission matrix of a 2-port network N in Fig. @ (a) Fig. P2-6(a) 42 + v, I Chap. 2 Building Blocks ~ I ® N ~ ~ I- I I- ~$~ @ ® - @ (b) N (e) Fig. P2-6(b), (c) Find the transfer functions Vo/Vi of the circuits shown in Fig. P2-6(b) and (c). 2-7. Find the transmission matrix of the circuit shown in Fig.

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