What’s a dB
Robert Orndorff, W4BNO
RATS, April 2015
What’s a dB
• It’s one tenth of a Bel
• Named for Alexander Graham Bell
• Originally used in telephone system
measurements in the early 20th century
• Based on MSC (Miles of Standard Cable) and
TU (Transmission Unit)
• Bel is seldom used without “deci”
What’s a dB
•
•
•
•
dB is a ratio
Measurement is compared to a reference level
dB alone is not meaningful
Generally used to measure power or power
changes
• Many uses, only discussing how it is used in
Amateur Radio
What’s a dB
• dBm – dB referenced to 1 milliwatt
• dBV – dB referenced to 1 volt
• dBu – dB referenced to 1 milliwatt into a 600
ohm load, or around 0.7746 millivolts.
Typically used in audio applications
• Have a calculator handy, check my work!
What’s a dB
Formula for dB when referencing Power
 P2 
dBm  10  log10  

 P1 
What’s a dB
Formula for dB when referencing voltage
V 2 
dBV  20  log10  

 V1 
Why use dB?
• When dealing with very small or very large
measurements, dB is useful
• You could say:
 0.000000001 mW
 -90 dBm
Why use dB?
• A negative dBm reading indicates powers of
10 on the right side of the decimal.
• Negative dBm is less than the reference value.
• 0 dBm = 1 milliwatt
• -30 dBm = 0.001 milliwatts
• -50 dBm = 0.00001 milliwatts
• See a pattern here?
Why use dB?
• A positive dBm reading indicates powers of 10
on the left side of the decimal. Positive dBm is
more than the reference value.
• 100 milliwatts is equal to +20 dBm.
• 1 watt (1000 milliwatts) equals +30 dBm
• 10 watts equals +40 dBm
• Power doubles every 3 dB
Why use dB?
•
•
•
•
•
Power doubles every 3.010299956 dB
dB=10*log(P2/P1)
dB=10*log(2)
10*log(2) = 3.010299956……
Close enough to say that power doubles every
3 dB change
3 dB changes
dBm
0
3
6
9
12
15
18
21
24
27
mW
1.00000000
1.99526231
3.98107171
7.94328235
15.84893192
31.62277660
63.09573445
125.89254118
251.18864315
501.18723363
V at 50 ohms
0.22360679775
0.31585299705
0.44615421692
0.63020958209
0.89019469569
1.25743342968
1.77617192929
2.50890953583
3.54392891542
5.00593264850
dBm vs mW
500
450
400
350
milliWatt
300
250
mW
200
150
100
50
0
0
5
10
15
dBm
20
25
30
dBm vs mW (logarithmic scale)
milliWatt
100
mW
10
1
0
5
10
15
dBm
20
25
30
Industry specific use
dBsr is a Scaled Reading. A scaled reading
is obtained when using equipment intended
for 600 ohm systems to read voltages on a
50 ohm system.
Telephone and communications techs doing RF (power line carrier) work.
Watts
0.001
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
11.5
12
dBm
0.0000
26.9897
30.0000
31.7609
33.0103
33.9794
34.7712
35.4407
36.0206
36.5321
36.9897
37.4036
37.7815
38.1291
38.4510
38.7506
39.0309
39.2942
39.5424
39.7772
40.0000
40.2119
40.4139
40.6070
40.7918
dBsr
-10.7918
16.1979
19.2082
20.9691
22.2185
23.1876
23.9794
24.6489
25.2288
25.7403
26.1979
26.6118
26.9897
27.3373
27.6592
27.9588
28.2391
28.5024
28.7506
28.9854
29.2082
29.4201
29.6221
29.8152
30.0000
Volts at Volts at
50 ohms 600 ohms
0.2236
0.7746
5.0000 17.3205
7.0711 24.4949
8.6603 30.0000
10.0000 34.6410
11.1803 38.7298
12.2474 42.4264
13.2288 45.8258
14.1421 48.9898
15.0000 51.9615
15.8114 54.7723
16.5831 57.4456
17.3205 60.0000
18.0278 62.4500
18.7083 64.8074
19.3649 67.0820
20.0000 69.2820
20.6155 71.4143
21.2132 73.4847
21.7945 75.4983
22.3607 77.4597
22.9129 79.3725
23.4521 81.2404
23.9792 83.0662
24.4949 84.8528
P 
dB  10log 2 
 P1 
V 
dB  20log 2  Z of V1 and V2 must be equal
 V1 
 P 
dBm  10log 2  P ower referencedt o1 milliwat t
 0.001
 V2 
dBm  20log
 Z of V1 , V2  50
 0.2236
 V2 
dBm  20log
 Z of V1 , V2  600
 0.7746
 V2 
dBsr  20log
 Z of V2  50, Z of V1  600
 0.7746
 P2 
dBsr  10log

0
.
012


Z of P2  50, P1  P ower in a 50 load at 0.7746volt s
V2  10
P2  10
dB
20
dB
10
 V1
 P1
S units
• The amount of signal strength required to
move an S meter indication from one marking
to the next.
• S meter is a microammeter connected to
detector or in the IF stage, full scale 50 – 100
µA
S units
• S9 originally defined as 50µV at the input of the
receiver (1930s). Input impedance was not
standardized, so this was not necessarily a
measure of power.
• In 1981 the IARU defined S9 as -73 dBm (50µV at
50 ohms) on HF. For VHF S9 is equal to -93 dBm,
or 5µV at 50 ohms
• 1 S unit is equal to 6 dB
• 1 S unit is equal to a voltage ratio of two, or a
power ratio of four
S unit, dBm, milliWatt
S
S0
S1
S2
S3
S4
S5
S6
S7
S8
S9
dBm
-127
-121
-115
-109
-103
-97
-91
-85
-79
-73
mW
mV at 50 ohms
0.000000000000199526
0.00009988149
0.000000000000794328
0.00019928977
0.000000000003162278
0.00039763536
0.000000000012589254
0.00079338686
0.000000000050118723
0.00158301490
0.000000000199526231
0.00315852997
0.000000000794328235
0.00630209582
0.000000003162277660
0.01257433430
0.000000012589254118
0.02508909536
0.000000050118723363
0.05005932649
What about antenna gain?
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•
•
•
•
My antenna has 3 dB gain.
What does that mean?
(group discussion)
Voltage gain?
Power gain?
What about antenna gain?
• My antenna has 3 dB gain.
• Did you mean 3 dBi?
• Did you mean 3 dBd?
What about antenna gain?
• dBi = Gain relative to an isotropic radiator
– An isotropic antenna is an ideal antenna that
radiates its power uniformly in all directions.
•
•
•
•
dBd = Gain relative to a dipole
dBd is 2.15 lower than dBi
3 dBi = 0.85 dBd
Antenna sales brochures and advertisements
say ???.
Top of the Rock, NYC
Questions / Discussion
• http://en.wikipedia.org/wiki/Decibel
• http://en.wikipedia.org/wiki/S_meter
• http://en.wikipedia.org/wiki/Antenna_gain