PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

230 Practical MATLAB® Applications for Engineers

because P = i(t)^2 R, then the effective current is given by

I

tt

itdt

t

t






1

21

2

1

2

∫ ()

R.3.13 AC measurements are usually given in RMS values. An AC current x given in RMS
value, through a resistor R is equivalent to the DC current x through R, dissipating
the same power (heat by R).

R.3.14 Let an AC signal be a sinusoidal function of the form x(t) = Xm sin(ωt + θ), then x(t)
can be expressed either in phasor form as X = Xm ∠θ using its peak value, or in
RMS (also known as effective value) as X = (Xm/ √

__

2 ) ∠θ. For example, let an RMS

phasor current be given by I = 8 ∠30°, then the current in the time domain repre-

sentation is either i(t) = 8 √

__

2 cos( ωt + 30°), or i(t) = 8 √

__

2 sin( ωt + 30°).

As a second example, let a voltage v(t) = 16 si n(ωt − 75°). Then v(t) can be trans-

formed into an effective (RMS) phasor voltage representation given by

V



16

2

∠° 75 8 2∠° 75

R.3.15 The form factor ff of x(t) is defi ned by ff = XRMS/XAVG. For a sinusoidal (current or
voltage), the

ff

X

X

m

m





()

()

.

2

2 22

111





R.3.16 The crest factor (CF) of x(t), also known as the peak factor or amplitude factor,
is defi ned by

CF =

Xm

_____

XRMS

For the case of a sinusoid (current or voltage) CF = 1.41.

R.3.17 Recall that the instantaneous power is defi ned by p(t) = v(t)i(t).

R.3.18 Recall that the average power is defi ned by

P

T

AVG pt dt

T

1

0

()

∫

assuming that i(t) and v(t) are the current through and voltage across a given load z,
where i(t) and v(t) are periodic functions with the same period T (or frequency ω).

R.3.19 The PF is defi ned as

PF

P

VI

AVG

RMS RMS

⋅