By A. M. P. Brookes and P. Hammond (Auth.)

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3 Ans: CiRi = C2R3; L = C2R2R3 4. c. bridge shown in Fig. 4. FIG. 4 Ans: R1R4 =-- R2R3 = L/C 50 ADVANCED ELECTRIC CIRCUITS 5. c. bridge shown in Fig. 5. FIG. c. bridge networks discussed in the previous chapter are tuned. Similarly an electrical filter is a network which offers less impedance to currents of certain frequencies than to those at other frequencies and so a filter is also a tuned network. The relationship between any chosen parameters for the network is known as its response curve or characteristic and it is usually the aim of the designer of a network to achieve a characteristic as close to an ideal one as is possible with reasonable economy.

3 shows a circuit with voltage excitations represented by 5 and (5 +j) V acting as shown. The impedances are all in ohms. d. across AB. ) - J VW =j=-j20fl 5Volts 1 Q) |(5+j)Volts B FIG. 3 lOOj. Am: Complex potential is ~^; 0-497 V, -90° 33 NETWORK THEOREMS 4. Represent the excitations in Fig. 4 by complex exponentials. Then set up the mesh equations for h and h. Solve for h and turn the complex current back into a physical one. -HI2 sin cut I (

Clearly the by-passing effect of Z will be small unless the value of Z at the unwanted frequencies is small in comparison with R—less than one-tenth of R, say. It is less obvious that Z must also be small compared with Ro, but if Ro were negligible, the only effect of adding Z would be to draw additional current from the generator; the current through the load would have the constant value EjR. The circuit operates efficiently only if the additional current through Z causes a large voltage drop across Ro and thus reduces the current through R at the unwanted frequency.