Page 115 - Circuit Analysis II with MATLAB Applications

Summary

int(d) % Integrate the delta function

ans =
Heaviside(t-a)*k

3.8 Summary

x The unit step function u t that is defined as
0

­ 0 t 0
u t = ®
0
¯ 1 t ! 0
x The unit step function offers a convenient method of describing the sudden application of a volt-
age or current source.

x The unit ramp function, denoted as u t , is defined as
1
t
d
u t = ³ u W W
0
1
– f
x The unit impulse or delta function, denoted as G t , is the derivative of the unit step u t . It is also
0
defined as
t
d
³ GW W = u t
0
– f
and
G t = 0for allt z 0

x The sampling property of the delta function states that

f t G t – a = fa G t

or, when a = , 0
f t G t = f0 G t

x The sifting property of the delta function states that
f
d

³ ft G t – D t = f D

– f
x The sampling property of the doublet function G' t states that
f t G' t – a = fa G' t – a – f ' a G t – a

Circuit Analysis II with MATLAB Applications 3-19
Orchard Publications