PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Alternating Current Analysis 227

where j = √

___

−1 (Euler’s identity) and

e

n

n

(^)
  1
23
23
!!

,,

!

(Taylor s series)’

cos( )

!!!

 1

246

246

− 

sin( )

!!!

  

357

357

Recall that cos(θ) = real[ejθ] (from Chapter 5 of the book titled Practical MATLAB®

Basics for Engineers), sin(θ) = imaginary [e−jθ], and ejθ = √

_____________

co s^2 θ + si n^2 θ = 1.

R.3.6 The average value of a given signal x(t) is given by

X

T

AVG xt dt

T

1

0

∫ ()

assuming that x(t) is a periodic wave with period T.

R.3.7 A DC voltmeter connected across an AC drop will indicate its average value.

R.3.8 The average value of a sinusoidal wave with period T is given by

X

T

AVG Xtdtm

T

1

0

∫ sin()

which is also equal to

X

X

AVG

m td t

2

0

0

2



sin() ( )

π

∫

R.3.9 The average value of a sinusoidal wave over 1/2 period (T) is given by

X

T

AVG Xtdtm

T








1

(^20)
2
∫ sin()
or by

X

X

AVG
 m td t



sin() ( )

0

π

∫

which is equal to

(^) XXAVG
^2064 m
Xm
.