INDUCTANCES, CAPACITANCES AND RESISTANCES 



The classical filter bears the same relationship to the R-C filter that the 

 attenuator does to potential divider. That is, a classical filter is intended to 

 work between a matched generator and load . Classical filters, like attenuators, 

 are made up of sections which may be T or pi, and any number may be 

 connected in cascade provided they are all designed for the correct character- 

 istic resistance. The overall performance is then the sum of the several 

 performances. 



T-section 



In Figure 5.13 we see such a filter section in the T form, working between 

 impedances Zq. For the present we work entirely in terms of impedance, in 

 the interest of generality. The section comprises elements, as yet unspecified, 

 of impedance Z-^jl in the series arms and Zg in the shunt arm. 



Figure 5.13 



The requirement for matching conditions to be fulfilled is that on removing 

 one of the terminating impedances Zq and looking into the filter, we see an 

 impedance Zq, that is 



■^21 2 ' 



Z2 + 2 I •^o 



whence 



If Zi and Z2 are pure reactances, and the bracketed term is positive, Zq is 

 pure resistive, for both the product and the ratio of y terms are real numbers. 



L/2 





t 



L/2 



Zo 



Figure 5.14 



Low-pass filter 



Value of elements — If the filter is to be low-pass we make Z^ an inductance 

 L and Z^ a capacitance C {Figure 5.14). Then 



jojL\ 



Z 2 — 



^0 = 



(LVI-^ 



84 



