EE433
Gain and dB Quick Reference
Fall 2015
EE 3433 -- Gain and dB Quick Reference Handout
For a single element in a communication system
 pOUT , pIN in linear units [Watts or mWatts]
Gain as a Ratio : g1 
pin [mW]
g1
pout [mW]
pOUT
pIN
p
Gain in dB : G1  10log10  OUT
 pIN

 vOUT 
 , G1  20log10 


 vIN 
Gain in dB : G1  10log10  pOUT  10log10  pIN 
For cascaded elements in a communication system
pin [mW]
g1
g2
gn
 pOUT , pIN in linear units [Watts or mWatts]
Gain as a Ratio : gTotal 
pOUT ,Total
pIN
 g1 g 2  g n
 pOUT ,Total
Gain in dB : GTotal  10log10 
 pIN
Gain in dB : GTotal  G1  A2    GN

 vOUT ,Total 
 , GTotal  20log10 


 vIN 
Pout, Total [mW]
EE433
Gain and dB Quick Reference
Fall 2015
Gain and Power in dB units
Given a system with a power in, pIN, a power out, pOUT, and an overall gain/attenuation ap (expressed as a
p
ratio a p  OUT ), then we can express the powers and gain in dB units by using the following
pIN
relationships:
pin [mW]
Pin [dBm]
g1
G1
pout [mW]
Pout [dBm]
We can express powers in dB units with respect to a specific reference power, usually 1 Watt or 1
milliwatt.
Note That: Power must be expressed in the same units as our reference power. Using a 1 Watt reference
power, power must be expressed in terms of Watts (e.g., 10 µW would be 10  10 6 W ); using a 1 mW
reference power, power must be expressed in terms of milliwatts (e.g., 10 µW would be 10  10 3 mW ).
Then, we can convert to dB notation:
p
[Watts] 
POUT [dBW ] 10log10  OUT

 1 Watt

p
[milliwatts ] 
POUT [dBm] 10log10  OUT

 1 milliwatt

When in dB notation, due to the properties of the logarithm, the gain can be expressed in terms of the
difference between the output and input powers:
p 
G1 [dB]  10log10  OUT   pOUT [dBW ]  pIN [dBW ]
 pIN 
p 
G1 [dB]  10log10  OUT   POUT [dBm]  PIN [dBm]
 pIN 
Note That: Powers expressed in dB units cannot be directly added (e.g., 20 dBm + 20 dBm ≠ 40 dBm).
They must first be converted back to linear units, added, and then converted back to dB units. For
example:
P1  30 dBm, P2  20dBm
30
20
P1  P2  10 10  10 10  1000 mW  100 mW  1100 mW
P1  P2 dBm   10 log 10 1100 mW   30.4 dBm