co 2) 327) 
ee | [95] 
— on or Q 2Q 2K, 
The solution for the constant-temperature bare wire may be found by letting a = 0 in the 
foregoing relations. Then 
Mi )eateotis @ [96] 
on 
The characteristic values of €, 6 are determined from the equation 
= Fe = — - [97] 
K 
In the expression for B,, the denominator reduces fo 5, and Z, (¢, a) becomes 
ASA] 
Zy (C,2)=- 2 = 2 [98] 
n 
Then the response of the bare wire becomes 
(Q + 2 pin EF 
oe 3G, 
Qu (t)=-—_S _— 1+ —c 
Niece ate n=1 iy Ee | 
% H, 2H, 2 ky 
Thus the bare|wire responds with a step-function which overshoots its final value. 
[99] 
TIME CONSTANT AND FREQUENCY RESPONSE OF COATED WIRES 
Although the response of a coated hot wire to a step-like change in one of its parameters 
is given by an infinite sum of transient terms, efforts will be made to find out how well a single 
transient term can approximate the sum. An equivalent time constant for the coated wire will 
be determined and its frequency response will be investigated. In addition, sample calcula- 
tions of the time constants and frequency responses will be presented. 
If the response of a system to a step-like disturbance g is characterized by an exponen- 
tial function such as 
f(t)=g fl -e /™) [100] 
the time constant M is defined as the time in which f(¢) attains 1 — e~! of its final value. 
If, on the hand, the initiating disturbance starts with a step but is also a function of 
the time, the response of the system may be found from the solution for the simple step 
20 
