RESISTANCES AND CAPACITANCES 



and the equivalent circuit is thus (Figure 3.28) an unloaded filter. The 

 transmission characteristic is again moved to the right such that the turn-over 

 frequency is raised by a factor (R + Rj)lR, and it is also moved downward 

 an amount 20 logio [R + Rl)IJ^ dB's. 



RR, 



L 



PjRi 

 WVWW— 1 



Figure 3.28 



Low-pass R-C filter fed from a real generator 



When a low-pass filter is fed from a real generator of internal resistance r, 

 the eifect is to alter the value of resistance required in the filter. For a given 

 turn-over frequency cjq, the total R required {Figure 3.29) is If Ceo. Since 



R=\/Cmc 



r 



^y^ 



t'out 



Figure 3.29 



we already have r, the value of R' required is only (IjCoj) — r. There is no 

 reason why we should not dispense with R' altogether, connecting C directly 

 across the terminals of the generator. Then the value of C required is simply 

 l/cocrf (Figure 3.30). 



Figure 3.30 

 High-pass filter fed from real generator 

 This case (Figure 3.31) is a little more complicated. As before, the value 



«'=a/Ca;c)-r 



'out 



Figure 3.31 



of R' required is (1/Cco) — r. The output appears across both R' and r, 

 but only the proportion across R' is usable. The filter therefore introduces — 

 in addition to the frequency dependent attenuation — a fixed attenuation 

 20 log^o (R' + r)lR' dB's. 



38 



