082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

380 Chapter 10 Differentiation
I
Bias current
Operating
point
dV
dI
Bias
voltage
Tangent
approximation
V
Figure10.17
Diode characteristic showing
operating point and tangent
approximation.
sinceI s
isconstant.
It is usual to write small changes in current and voltage as δI and δV. Therefore,
since
δI
δV ≈ dI
dV
δI ≈ 40I s
e 40V δV
Thisexpressionallowsthechangeindiodecurrent, δI,tobeestimatedgivenachange
indiodevoltage, δV,providedtheoperatingpointisknownandthechangesaresmall.
Example10.15 Findthe derivative ofy = e −t +t 2 , when
(a)t=1
(b)t=0
Solution
y=e −t +t 2
y ′ = −e −t +2t
(a) Whent = 1,y ′ = −e −1 +2 = 1.632, thatisy ′ (1) = 1.632.
(b) Whent = 0,y ′ = −1,thatisy ′ (0) = −1.
Engineeringapplication10.6
Obtainingalinearmodelforasimplefluidsystem
Consider the fluid system illustrated in Figure 10.18. The pump is driven by a d.c.
motor. The pump/motor can be modelled by a linear relationship in which the fluid
flowrate,q i
, isproportionaltothe control voltage, v in
, thatis
q i
=k p
v in