Logarithmic Representation of signal Levels “Decibel Notation dB” Original unit was “bel” ...
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Transcript of Logarithmic Representation of signal Levels “Decibel Notation dB” Original unit was “bel” ...
Logarithmic Representation of signal Levels
“Decibel Notation dB”Original unit was “bel”
The prefix “deci” means one tenth
Hence, the “decible” is one tenth of a “bel”
dB expresses logarithmically the ratio between two signal levels (ex.: Vo/Vi = Gain)
dB is dimensionless
Either way, a drop of 3dB represents half the power and vice versa.
The basic equations to calculate decibels
in
o
I
IdB log20
in
o
V
VdB log20
in
o
P
PdB log10
Iin Io
Vo
Po
Vin
Pin
Adding it all up
2001.0
2.011
inV
VA
5.02.0
1.0
1
2 V
VAtten
151.0
5.1
2
32 V
VA
45.1
6
33 V
VA o
600321 AAAttenAAV
6.55600log20 dBA
Converting between dB and Gain notationFor dB = 20 log (Vo/Vin)
if it is needed to convert from dB to output-input ratio i.e. Vo/Vin
Vo = Vin 10dB/20
or Vo = Vin EXP(dB/20)
Ex: calculate the output voltage Vo if the input voltage Vin=1mV and an amplifier of +20 dB is used:
Vo=(0.001V) 10(20/20)
=(0.001) (10) = 0.01V
Av=20dB
1 mVVo?
Vin
special decibel scales: dBmdBmdBm: used in radio frequency
measurements (RF)0 dBm is defined as 1 mW of RF signal
dissipated in 50-Ω resistive loaddBm = 10 log (P/1 mW)
EX: What is the signal level 9 mW as expressed in dBm?dBm = 10 log (P/1 mW)
dBm = 10 log (9 mW/1 mW) = 9.54 dBm
Converting dBm to voltage or voltage to dBm
Converting voltage to dBm : Converting voltage to dBm : Use the expression P=V2/R=V2/50 to find milliwatts, and then use the equation of dBmEX: Express a signal level of 800 μV rms in dBm
P=V2/50 P=0.00000064 V / 50 Ω→p=0.0000128 mW dBm = 10log(P/1mW)= -48.9
Converting dBm to voltage : Converting dBm to voltage : Find the power level represented by the dBm level, and then calculate the voltage using 50 Ω as the load.EX: what voltage exists across a 50- Ω resistive load
when -6 dBm is dissipated in the load?P=(1 mW)(10dBm/10) P =(1 mW)(10-6 dBm/10) =(1 mW)(10-0.6) =(1 mW)(0.25)=0.25 mW If P=V2/50, then V = (50P)1/2 = 7.07(P1/2), V = (7.07)(P1/2) = (7.07)(0.251/2) = 3.54 mV