Design of a Composite Filter

The m corresponding to an a = 10,300/8400 = 1.225 is, from equation 96, m = 0.577, From Fig, 44 it is seen that this m will give good impedance match, and hence one m-derived section can be used to obtain both the infinite attenuation and the good impedance match.

From equations 74 and 75 for the constant-k sections, L₁ = 600/(3.1416 X 8400) = 22.7 millihenrys; also.. C₂ = 1/(3.1416 X 8400 X 600) = 0.0632 microfarad. For the m-derived sections (see Fig. 42), mL₁/2 = (0.577 X 22.7) /2 = 6.55 millihenrys. The value of the shunt capacitor is mC₂ = 0.577 X 0.0632 = 0.0365 microfarad. Also, (1-m²)L₁/4m = [(1 - 0.577²) X 22.7]/(4 X 0.577) = 6.55 millihenrys. In the preceding paragraph an m-derived T section was designed.

Half of this is to be used to terminate each end of the constant-k sections. The complete filter will then consist of the sections of Fig. 45(a). The units would, for economy, be combined as shown in Fig. 45(b). In the final filter it is of interest to find that the 13.1-milli-henry inductors and the 0.0183-microfarad capacitors shunting each end of the filter are tuned to a frequency of approximately 10,300 cycles, the frequency at which infinite attenuation is desired. The measured attenuation characteristics are shown in Fig. 46.

Figure 46. Attenuation characteristics of the composite filter of Fig. 45, and estimated contribution made by each portion.

Suppose that a very sharp cutoff had been desired, with an infinite attenuation at about 9240 cycles, giving an a = 9240/8400 = 1.1. According to Fig. 44, an a of 1.1 or an m of 0.416 would not give a good termination. Therefore, one m-derived T section of a = 1.1 would be added internally to the composite filter of Fig. 45. Although in the previous discussions only a low-pass filter was designed, the procedure is the same for a high-pass composite filter.