2. 8 COMBINING dBm AND dB
™ Power amplification means that the output power
ÂÂ larger than the input power by the amplification
factor ⇒⇒ G
™ If G = 100  an input power of 1 mW  amplified
and the output power will be
1 mW x 100 = 100 mW
™ Power amplification  described in term of:
dBm ⇒⇒ input and output power amplification
™ dB ⇒⇒ G
™ dBm + dB ⇒⇒ has physical meaning
™ The input power dBm ⇒⇒ multiplied by the gain
G ⇒⇒ dB
Which leads to the power amplification in term of dB
1
™ Important (in)
dBm + dB (G) = dBm (out) FF power amplification
dBm - dB = dBm FF power attenuation
Operation
dB + dB
dB - dB
dBm + dBm
Resulting
Units
dB
dB
XX
dBm - dBm
dB
dBm + dB
dBm
dBm - dB
dBm
Meaning
product of two
numbers
comparing two
numbers
multiplying two
powers
comparing two
powers
power
amplification
power
attenuation
Allowed
yes
yes
no
yes
yes
yes
Table 2.2 summarizes all possible combinations of
dBm.
2
EXERCISES
1. 5 dB + 19 dB =
2.
26 dB + 57 dB =
3.
64 dB - 3 dB =
4.
29 dB - 44 dB =
5.
-7 dB - 20 dB =
6.
-24 dB - 30 dB =
7.
-20 dB - (-60 dB) =
8.
-12 dB - (- 90 dB) =
9.
3 dBm + 4 dB =
10.
2 dBm + (-6 dBm) =
11.
-23 dBm + (-40 dBm) =
12.
9 dBm - 0 dB =
13.
24 dBm - 3 dBm =
14.
-6 dBm - 5 dBm =
15.
-15 dBm - (- 10 dBm) =
16.
-24 dBm - (-24 dBm) =
17.
-30 dBm - (- 60 dBm) =
18.
10 dBm - (- 80 dBm) =
19.
4 dBm + 10 dB =
20.
-4 dBm + 20 dB =
3
21.
-46 dBm + 10 dB =
22.
-90 dBm + 100 dB =
23.
3 dBm - 10 dB =
24.
-14 dBm - 20 dB =
25.
-62 dBm - 3 dB =
1. 9. VOLTAGE RATIO
™ In microwave ⇒⇒ power amplification ⇒⇒ an
important factor.
™ In
low
frequency
electronics
⇒⇒
voltage
amplification ⇒⇒ an important factor.
Power = V2/ R
™ Voltage gain ⇒⇒ can be expressed as a ratio ⇒⇒
but can not converted to dB
Since
Power A = V2A/ RA
Power B = V2B / RB
4
™ If
the
power
generated
by
two
separate
voltages ⇒⇒ VA and VB ⇒⇒ compared when
applied across resistors of equals values.
RA = RB
then
dB = 10 log (V2A/V2B)
= 20 log (VA / VB)
™ 10 dB power gain ⇒⇒ mean that power A is 10
times power B
™ If voltage A is 10 times voltage B ⇒⇒ power gain is
20 dB.
™ This is because a 10 times voltage increases across
a resistor ⇒⇒ ten times current increase.
P = IV = 100 = 102 = 20 dB
2.10. NEPER
x
™ dB and log ⇒⇒ base 10 ⇒⇒ 10 ⇒⇒ 10 is the base
of x
™ e = 2.718 ⇒⇒ a natural number in mathematics
™ π = 3.1416 is the natural number also.
5
Power A and B
dB = 10x log (PA / PB)
Neper = ln (PA / PB)
Example (2.10.1)
PA = 4mW
PB = 8mW
Neper = ln (8/4) = ln 2 = 0.69 Neper
Example (2.10.2)
PA = 100 mW
PB = 10 mW
Neper = ln (100 / 10) = ln 10 = 2.30 Neper
Example (2.10.3)
PA = 1 mW
PB = 10 mW
Neper = ln (1/ 10) = ln 0.1 = - 2.30 Neper
6
Example (2.10.4)
PA = 6 mW
PB = 1000 mW
Neper = ln (6/ 1000) = ln 0.006 = - 5.11 Neper
In general ⇒⇒ the natural logarithm and the Neper
are much less important than the dB.
This chapter from Ref. (1)
7