Basics Of Easurement; Attenuation And Amplification; Dezibel Db; Relative Level - Hameg HM5510 Handbuch

Basics of measurement

Attenuation and amplification

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
P i
power level
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 amplifications 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:
V
1
g = 20 lg ––– or
u
V
2
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
o o
[
g = ––––– = 10 lg ––––– x –––––
p
2 2
V V
i i
–––
R
i
STOP
In the special case that Ri = Ro the logarithm of 1 is
zero, so the decibels of voltage, current and power
become identical.
TiPP
.
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
g u x g i
=
R Vo
i
]
= 20 lg –––– + 10 lg––––
R V
o i
B a s i c s o f m e a s u r e m e n t

Absolute level

As mentioned decibel values do not represent absolute values
but only quotients. However, it has become practical to base
decibels in special applications upon fixed numbers, so that a
dB value with an affix describing the base denotes an absolu-
te level.
i
The following standards are in use:
Absolute voltage levels:
V
P o
20lg ––– = dBV
1V
V
1 20lg –––– = dBmV
1mV
g v
V
1
20lg –––– = dBµV
g c
1µV
Absolute power levels:
P
10lg –––– = dBW
1W
P
10lg –––– = dBmW
1mW
this is equivalent to 224 mV across a 50 ohm load.
V gen = ~
2 x V 0
Attenuation
Input signal P e
If Po > Pi amplification takes place, hence the quotient Po/Pi
> 1, hence 10 lg Po/Pi > 0.
R
i
R
o
If Po < Pi attenuation takes place, hence the quotient Po/Pi <
1, hence 10 lg Po/Pi < 0
generator cable load
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 o
Subject to change without notice
R L
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