HARD VALVES 



Miller effect 



The other disadvantage is perhaps rather unexpected — it is that the input 

 capacitance is high; the valve seems, looking in at the grid, to have an 

 appreciable capacitance between grid and cathode. One of the most impor- 

 tant reasons for using valves is that the input impedance is high, which means 

 that not only the input resistance but also the input reactance is large. This 

 appreciable virtual input capacitance of triodes is called 'Miller effect' and 

 arises in the following way. 



Suppose we have a generator, a hypothetical 'charge-meter', perhaps a 

 balhstic galvanometer, a capacitance and a 'black box', all in series as in 

 Figure 8.18, and suppose initially that the black box contains nothing but a 



Charge-meter 



X — 



Figure 8.18 



piece of wire joining the two terminals. Then on switching on the generator 

 of e.m.f. E a charge Q^ is displaced round the circuit which we measure on 

 our charge-meter, and we construe that the capacitance has a value C = QjE. 

 Now let the black box contain a device which, when the generator is switched 

 on, immediately makes the right-hand plate of the capacitance AE volts 

 negative to earth. Then the actual voltage across the capacitance = E{\ -\- A)y 

 and the charge displaced will be go = ^^(1 + ^) instead of Q^ = CE. 

 The circuit therefore behaves as if the black box contained once more just the 

 piece of wire, but as if the capacitance were not C but C(l + A). 



This is precisely the state of affairs with the triode amplifier. The grid 

 has a capacitance Cg^. to the cathode and Q„ to the anode. A unit change 

 of grid potential produces a potential change at the anode of —A, where A 

 is the gain. The apparent input capacitance is therefore not {Cgj^ + C'sJ ^^^ 



C,, + (1 + A)Cg,. 



A triode might have C^^ = 5 f^/uF and Cg^ = 3 ju/liF. If the input capaci- 

 tance were only 8 /^/^F this would not be very serious, as the reactance at 

 10,000 c/s would be 



1 



In X 10,000 X 8 X 10-12 



which is about 2 megohms. However, if A = 50, the input capacitance is 

 5 /^/^F + 3 X 51 ///^F :^ 160 ///fF. At 10,000 cycles the reactance of this is 



1 



2 X 10,000 X 160 X 10 



-12 



which is only about 100,000 Cl, and is for many purposes intolerably low. 



In the tetrode a second grid is placed between the 'control grid' and the 

 anode, called the 'screen' grid, and in use this is maintained at a fixed positive 



144 



