= 6 = 
645 
(1) High-frequency response. In an ordinary resistance-coupled ampli- 
fier stage, the high-frequency response falls to zero with increasing fre- 
quency because of the shunting capacity of circuit elements (tubes, resis- 
tors, wiring) in parallel with the load resistor across which the response 
signal is developed. 
The relative response of this circuit to a signal of frequency f is 
given by 
(1) Fw) = (1 * (wr)2I8, 
where w = 27f and the "time constant" 7 = RC — where R is the load resist- 
ance and C is the total circuit capacitance in parallel with it. The quan- 
tity 7 can be evaluated from the response curve, as it is equal to 1/2nf.> 
where f, is the frequency at which the response has fallen to 70 percent of 
its value at lower frequencies, The admittance function, of which the re- 
sponse F(w) is the modulus, is 
(2) F(p) = 7eaFe 
where p = iw and i = w= 1, The transient response resulting from the 
action of this or any other admittance function on a transient pulse F(t) 
is most easily obtained by the use of Fourier transforms, or pairs, if 
these can be found for the functions involved, An extensive table of these 
pairs compiled by Campbell and Roster ee hereafter referred to as C-F, 
simplifies this procedure. 
An applied transient S(t) in the form of a negative exponential 
(3) S(t) = de 
has the transform 
M(s(t)] = A/(p + 1/e).  [C-F, Pair 438] 
2/ ; 
Ge A. Campbell and R, A. Foster, Fourier integrals for practical 
applications, Bell Telephone System Monograph B-50h. 
