Download AC Signals

AC Signals
Sinusoidal Signal
 An ideal generator produces
1 period = T
an induced emf that oscillates.
0
• Sine or cosine wave
t
 The oscillation is characterized
by its period.
2t
   0 cos
T
   0 cos 2ft
   0 cos t
 The inverse of the period is the
frequency.
• f = 1/T
• Cycles per sec, or Hz
• Angular frequency in radians
Amplitude
 The amplitude of a sinusoidal
signal is the peak value.
• Also maximum negative value
 The average value is zero.
• equally above and below zero
0
t
-0
 The average value of the
square is half the peak
squared.
02
• Root mean square value
 rms 
 02
2

0
2
0
t
Phase
 The phase of a signal
f = t/T
compares the time at a point to
the time for the peak.
0
• Fraction of a period
t
 Phase is measured as an
angle.
2t
f
T
t
f  360
T
• Divided into 2 radians
• Compare to 360°
Phasor
 A phasor diagram maps the
cosine onto the x-axis of a
circle.
• x =  cos t
 A vector represents a changing
value like voltage.
• Magnitude for amplitude
• Angle for phase
• Moves counterclockwise with
time

q
 cos q
AC Resistance
 An AC source and resistor
make a one-loop circuit.
v
R
 The resistor voltage must
vR  V0 cos t
i
i
V0
cos t
R
V0
cos 2ft
R
balance the source voltage.
• Lower case for AC
 The current follows from
Ohm’s law.
• Oscillates as well
Power Loss
 Power loss in an AC circuit depends on the
instantaneous voltage and current.
v2
p  vi   i 2 R
R
P
2
I0 R
0
t
Average Power
 It’s more useful to look at the
2
Prms  I rms
R
average power loss.
• Use RMS voltage or current.
 The form can reflect current,
2
Vrms

R
voltage or both.
Prms
P
Prms  Vrms I rms
2
I0 R
Prms
0
t
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