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Idiomas disponibles
Idiomas disponibles
Basics of measurement
Attenuation and amplifi cation
The following picture shows a circuit with an inut voltage V
and an output voltage V
. In order to simplify let the input
o
impedance R
= output impedance R
i
I i
Input signal with
V i
R
i
power level
P i
V o
g v
Voltage amplification:
=
V i
I o
g c
Current amplification:
=
I i
P o
V i x I i
g p
Power amplification :
=
=
P i
V o x I o
Decibel dB
In cases where signals may differ by orders of magnitude it
is advantageous to display them on a logarithmic scale. Also,
as seen from the above, the amplifi cations or attenuations of
succeeding stages are multiplied, hence it is advantageous to
use a logarithmic measure, this is the Bel resp. the decibel.
Multiplication thus is reduced to the addition of logarithms
resp. the addition of bels (B) or decibels (dB), division to the
subtraction of Bels or decibels.
1 Bel = lg X
/ X
.
1
2
Both nominator and denominator must use the same units. The
Bel or decibel is thus always a pure number. It denotes only the
quotient of two numbers and does not represent a level.
Relative level
The quotient of two voltages or currents is given in dB by:
V1
g
= 20 lg –––
u
V2
I
1
g
= 20 lg –––
i
I
2
The quotient of two powers is given by:
P
1
g
= 20 lg
–––
p
P
2
In general:
2
V
o
–––
2
R
V
R
o
o
g
= ––––– = 10 lg [ –––– x –––– ] = 20 lg ––– + 10 lg –––
p
2
2
V
V
R
i
i
–––
R
i
In the special case that R
zero, so the decibels of voltage, current and power
become identical.
HINT
.
o
I o
Two-port
Output signal with
V o
R
o
power level
V i
d v =
Attenuation:
=
V o
I i
d c =
Attenuation:
=
I o
or efficiency factor
g u x g i
=
or
Vo
R
i
i
V
R
o
i
o
= R
the logarithm of 1 is
i
o
Absolute level
As mentioned decibel values do not represent absolute va-
lues but only quotients. However, it has become practical to
base decibels in special applications upon fi xed numbers, so
that a dB value with an affi x describing the base denotes an
absolute level.
i
The following standards are in use:
Absolute voltage levels:
V
20 lg ––––
P o
1V
V
20 lg ––––
1mV
1
g v
V
20 lg ––––
1
1µV
g c
Absolute power levels:
η
P
10 lg ––––
1W
P
10 lg ––––
1mW
this is equivalent to 224 mV across a 50 Ω load.
V gen =
~
2 x V 0
Attenuation
Input signal
P i
If P
> P
amplifi cation takes place, hence the quotient P
o
i
> 1, hence 10 lg P
If P
< P
attenuation takes place, hence the quotient P
o
i
< 1, hence 10 lg P
B a s i c s o f m e a s u r e m e n t
in dBV
in dBmV
in dBµV
in dBW
in dBmW
generator
cable
Z = 50 Ω
R i
V 0 = 224 mV
Power match
R i = Z = Ra = 50Ω
P 0 = 1 mW = 0 dBm
Two-port
Output signal
/P
> 0.
o
i
/P
< 0
o
i
Subject to change without notice
load
R L
P o
/P
o
i
/P
o
i
29
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