. The thermionic vacuum tube and its applications . Fig. 105. shunt with the capacity Co between the filament and plate. Zgrepresents the unpedance as measured between filament and gridand is the effectiv^e input impedance. Remembering that a poten-tial eg impressed on the grid introduces an equal to ^egin the plate circuit, the input impedance Zg can be obtained byincluding in the plate circuit a ficntious generator giving ^xeg asindicated in the diagram and solving the Ivirchofif equations for thenetwork. THE THERMIONIC AMPLIFIER 207 Unless the frequency is very high (over a million c


. The thermionic vacuum tube and its applications . Fig. 105. shunt with the capacity Co between the filament and plate. Zgrepresents the unpedance as measured between filament and gridand is the effectiv^e input impedance. Remembering that a poten-tial eg impressed on the grid introduces an equal to ^egin the plate circuit, the input impedance Zg can be obtained byincluding in the plate circuit a ficntious generator giving ^xeg asindicated in the diagram and solving the Ivirchofif equations for thenetwork. THE THERMIONIC AMPLIFIER 207 Unless the frequency is very high (over a million cycles persecond) we can neglect the capacity C2 between filament andplate, since it is shunted by the plate resistance which is thenlow compared with the impedance due to C2. The equation givenby Nichols for the effective input impedance is:1 l+icoCsTT Zo = where W = (51) cj is 2xX frequency, and j is the imaginary unit V—1. The other quantities are indicated in Fig. For most tubes used at present this equation is applicable forfrequencies up to about a million cycles per second. Let the external output impedance take the general formZQ=rQ-\-jxQ. Then equation (51) can be transformed into: „ _ ac-\—bc r52) (53) c2 + d2 = -rs+jXi;where the coeflEicients have the values a=rp+ro— corproCs h = corproC3-\-xo c = co2rproCiC3 + wXo(Ci+C3+MC3) d = co2r^i,CiC3 - a;r^(Ci +C3) - a;ro(Ci+C3+MC3) It will be seen from inspection that the effective input im-pedance will generally comprise a resistance Vg which may bepositive or negative, and a reactance Xg which is capacitive. 70. Case 1. Low Frequencies: a)<10^. In this case wecan neglect co-tenns where they occur in the same expression withterms containing w in a lower order, , neglect w^ in comparisonwith CO. 208 THERMIONIC VACUUM TUBE Let the output impedance be inductive xo = -Loaj. Evaluationof the coefficients (53) gives for the input resistance: _ rpCsirpToCs+ro^i^Cs-^rQ^Cs - m^o) and


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