EE511 Day 3 Class Notes
Laurence Hassebrook
Updated 9-3-03
Wednesday 9-3-03
INTEGRATION CONTINUED
DC VALUE
A commonly measured component of a signal is the “dc” value
Wdc 
lim 1 T / 2
lim
wt dt 
wt 

T   T T / 2
T 
POWER
If we can separate signal power from noise power sufficiently, the signal can be detected. Thus, we
need a definition of power.
Example: Consider an electronic device s.t. the instantaneous power is p(t)=v(t)i(t). The average
power is
Pave  pt  
1 T
vt it dt
T 0
Example: let v(t) = V cos(2fot) and i(t)=I cos(2fot)
The instantaneous power is
 1  cos 4f o t 
pt   VI cos 2 2f o t   VI 

2


The average power for T=1/fo is
VI
VI
VI
 VI  1 T
Pave  pt      1  cos 4f o t dt   1  cos 4f o t   1  0  
2
2
2
 2 T 0
RMS VALUE
WRMS 
w2 t 
Given v(t) and i(t) = v(t)/R, the instantaneous power is p(t) = v(t) i(t) = v2(t)/R = i2(t)R and
Pave 
v 2 t 
R
 i 2 t  R 
2
VRMS
2
 I RMS
R  VRMS I RMS
R
Solve the above?
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NORMALIZED POWER: Assume R=1
The average normalized power is
lim
w 2 t 
T 
where w(t) is v(t) or i(t).
P
ENERGY
The definition of energy is
E
lim T / 2
lim
wt dt 
T wt 

T   T / 2
T 
ENERGY AND POWER SIGNALS
The definition of “energy” signals is that their E value must be finite and the definition of “power”
signals is that their average power must be finite. All non-zero periodic signals cannot be “energy”
signals but, if their periodic function is finite then they are “power” signals. All finite length signals
with finite values are “Energy” signals.
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