REFERENCES 



Steady value to another; (2) the sine wave of constant amplitude and variable 

 frequency {Figure 1.6). 



The apparatus performance may then be described in terms of the transient 

 response to the apphcation of the step-function, with the introduction of 

 terms such as 'overshoot', 'lag', 'time constant', or in terms oi Xht frequency 

 response or steady-state response to the sine wave, describing the amphtude 

 and relative phase of the output as the frequency of the input — of constant 

 amphtude — is varied. Phrases such as 'jc decibels down at j' cycles per second' 

 are part of steady-state jargon. 



Frequency! Frequency2 Frequency3 



{Voltage 

 or 

 current 



Time 



m NM AM 



Figure 1.6 



Transient response analysis and steady-state analysis, then, are the methods 

 by which the behaviour of component networks in control engineering are 

 discussed. Historically the two analyses spring from rather diiferent engi- 

 neering fields ; the former from radar and television, the latter from telephone 

 engineering and radio. Radar and television are 'pulse' techniques, interested 

 in angular waveforms like the step-function, whereas sound waveforms are 

 smoother affairs, more obviously composed of a number of sine waves. In 

 electronics as applied to biological research both kinds of waveform occur 

 and both analyses are relevant. Both analyses are really describing the same 

 thing, being connected by the Fourier transform: 



e^'"' F(co) d(o 



fit) = lim f 



A~-coJ — 



A 



The step-function response /(/) is composed of the sum of a large number of 

 component sine waves, but the numerical production of the transient response 

 of a network whose steady-state response is known, or vice versa, is apt to 

 be a tedious business^'^'^. 



In this book the emphasis is upon steady-state response, though transient 

 response is discussed in the simpler and more ubiquitous cases. The evalua- 

 tion of steady-state response is easier mathematically, elementary algebra 

 being all that is required, whereas the solution of the most simple transient 

 response problem involves a differential equation. Furthermore, in the 

 writer's opinion, steady-state response of actual apparatus is easier to measure. 



The reason for the introduction of the four kinds of ideal generator is 

 now evident; the alternating voltage and current generators are for inves- 

 tigating steady-state behaviour; the direct generators are for obtaining a 

 step-function of voltage or current. 



REFERENCES 



^ RODDAM, T. Calculating transient response Wireless World 63 (1952) 292 



^ LuDBROOK L. C. Step to frequency response transforms Electron. Engng. 26, 



(1954) 27 

 ^ Jaworski, Z. E. Empirical transient formulae Electron. Engng. 26 (1954) 397 



5 



