Stee 651 
Under such conditions, the area under the response curve is independent of 
the high-frequency response characteristics and is, except for the instrument 
factor $(w)} equal to the area under the applied signal. It is difficult to 
state any very general condition on the functions S(X) and F(X) sufficient 
to insure this result, but its legitimacy can be readily determined for any 
fairly definite set of conditions, 
(ii) Low-frequency response. The failure of electrical circuits to 
have a finite response as the frequency approaches zero is usually due to 
the presence of capacitance in the circuit as a series elenenee In the 
case of conventional voltage amplifiers, successive stages are coupled by 
condensers in order not to cascade operating potentials of the tubes, If the 
plate of one stage is coupled to the next grid by 2 capacitor © in series 
with the grid resistor R, the signal applied to the grid has the magnitude 
F(w) x | aes 
a + (JA) |2 
relative to the signal across the network, where 1 = RC. The admittance 
function is then 
Fe) = BAS. 
The response R(t) to an applied exponential transient S(t) = s(0)e7*/® 
is given by the Fourier transform 
a(t) =u [P(p) w fs())] = 500) w p-RS og 
The solution of this equation is 
-t/e -(4-4 
(11) R(t) = 8(0) 2-5 [1-26 hating Ws 
1 
~— 
3 sa 
=—Gauges which have an internal impedance equivalent to a capacitance 
will also have zero response at zero frequency if shunted by any resistance 
element, These conditions occur, for example, with a piezoelectric gauge 
shunted by the input resistance of an amplifier circuit. The analysis of the 
case is similar to that for the amplifier-coupling circuit. 
