TUNED AMPLIFIERS 



required = l/oj^ = 1/3,600 henry farads. The largest paper-insulated 

 capacitors commonly available have a value of 8 f^F. If we employ one of 

 these the inductance required 



^ ^ 3,600 X 8 X 10-« = ^^ ^ 



8 /nF paper capacitors and 35 henry inductors are bulky and expensive com- 

 ponents. As has been hinted before, inductors are a nuisance in electronic 

 designs. They usually have to be home-made and they ought to be enclosed 

 in expensive mumetal screening boxes. 



An alternative approach lies through networks which use only resistances 

 and capacitances. We have met the twin T, which clearly has a rejector 

 characteristic, and a network exhibiting an acceptor characteristic is the 

 band-pass filter for a = I. These are clearly very unselective circuits. 



The Q factor of inductance-capacitance tuned circuits may be variously 

 defined. Up till now we have called it mL/R, or (LICR^Y^^. If a response 

 curve for a circuit of resonant frequency cOg is available, Q may be measured 

 off as follows: find the points on the curve at which the response is 1/(2)^/^ 

 of its maximum value. If the difference between the frequencies at which this 

 occurs is doj, then Q = cojdoj (Figure 13.3). Strictly speaking this is only 



1 



707 



! ! 1 



S(jo 



Figure 13.3 



true when Q is quite large, but the relationship gives a very fair indication 

 even for Q values less than 1. This gives us a basis for allotting an 'effective 

 Q factor' to any resonance-like curve. Thus in Graph 14 we see that when 

 a = 1 the filter has Kout/Km = 0-37 at 'resonance'. l/(2)i/2 of this is 0-245, 

 and we see the curve has these values of Kout/f^in at 3/Ci? and 0-331 CR. 

 Hence 



^ICR 



O = = 0-375 



^ 3/C/? - 0-33/C7? 



Similarly, measurement from the twin F characteristic (Graph 18) reveals a 

 Q factor of only about J. The output falls from its maximum value, 1, to 

 1/(2)1/2 0^ frequencies of approximately AjCR and 0-251 CR. These values do 

 not look very good beside the g's of 100 or so obtainable from an inductance- 

 capacitance tuned circuit. 

 There are three approaches by which we can improve matters. They involve 



14 197 



