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Abstract:  The db (decibel) is a relative unit of
measurement commonly used in communications for providing a
reference for input and output levels.  This tutorial provides an
overview of the use of the dB in communication systems.  The
tutorial also includes a table of standard dB terms.         

The term dB or decibel is a relative unit of
measurement used frequently in electronic communications to
describe power gain or loss.  Decibels are used to specify measured
and calculated values in audio systems, microwave system gain
calculations, satellite system link-budget analysis, antenna power
gain, light-budget calculations and in many other communication
system measurements.  In each case the dB value is calculated with
respect to a standard or specified reference.

The dB value is calculated by taking the log of the ratio of
the measured or calculated power (P2) with respect to a reference
power (P1).  This result is then multiplied by 10 to obtain the
value in dB.  The formula for calculating the dB value of two
ratios is shown in equation 1.  Equation 1 is commonly referred to
as the power ratio form for dB.

                                 

Equation 1 can be modified to provide a dB value based on
the ratio of two voltages.  By using the power relationship P =
V^2/R, the relationship shown in equation 2 is obtained.

                                                                  
           

By simplifying the equation, a dB relationship based on voltage
ratios instead of power is obtained.  The voltage gain calculation
is shown below in equation 3.

      
                                                                  
               

The dB unit is often used in specifying input and output
signal level requirements for different communication systems.  An
example of specified audio levels can be found in microwave
transmitters.  It is common for a +8dBm input level to be
specified.  Notice that a lower case m has been attached to
the dB value.  This indicates that the specified dB level is
relative to a 1 milliwatt reference.  In standard audio systems
0dBm is defined as .001 watt measured with respect to a load
termination of 600 ohms.  A 600 ohm balanced audio line is the
standard for professional audio and telecommunications.

The voltage measured across a 600 ohm load for an 0dBm level
is .775 volts.  This value is derived below using equation 1.

        
                           

Since 1mW is the specified reference for 0dBm, the voltage
reference can be derived as shown in equation 4.

        
                    

This is the voltage reference for 0dB with respect to a 600 ohm
load.  To determine the voltage required at the input of the
microwave transmitter to provide a +8dBm level, use the voltage
gain equation 3 letting V1 equal the .775 reference in the equation

To solve for V2 for a +8dBm level;

Thus for a +8 dBm level to be present at the input of the
microwave transmitter, approximately 1.95 volts must be present
across the 600 ohm input.

The term dBm also applies to communication systems which have
a standard termination impedance other than 600 ohms.  For example,
video and some RF systems are terminated with 75 ohms.  The 0dBm
value is still defined as 1mW but measured with respect to a 75 ohm
termination instead of 600 ohms.  Therefore the voltage reference
for an 0dBm system with respect to 75 ohms is;

        
                           

To calculate the voltage gain or loss with respect to a 75 ohm
load use equation 5 if a voltage is specified and the dB value is
needed.

                                                                  
                       

More commonly encountered in communications are 50 ohm systems.
The dBm voltage reference for a 50 ohm system is:

To calculate the voltage gain or loss, expressed in dB for a 50
ohm system, use equation 3 with the value for V2=.2236.  This
relationship is shown in equation 5.

It is common for power to be expressed in watts instead of
milliwatts.  In this case the dB unit is obtained with respect to
1 watt and the dB values are expressed as dBW.

Remember, dB is a relative measurement.  As shown by equations
1 and 3, both power and voltage gains can be expressed,in dB,
relative to a reference value.  In the case of dBW the reference is
1 watt, therefore equation 1 is written with 1 watt replacing the
reference P1.  This gives equation 6.

                                                                  
                       

It is common in communication receivers to express voltage
measurements in terms of dBuV, dB-microvolts.  For voltage gain
calculations involving dBuV use equation 3 and specify 1uV as
the reference (V1) in the calculations as shown in equation 7.

There are a multitude of applications involving the use of dB
for calculations involving relative values.  The important thing to
remember is that a relative reference is typically specified or
understood when calculating or measuring a dB value.

  

II. dB Reference Table

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dBm 1 milliwatt (.001W), Typical measurement for audio
input/output specifications.  Also used in low power optical
transmitter specifications.

dBm(600)  The standard audio reference power level
defined by 1 milliwatt measured with respect to a 600 ohm load.
This measurement is commonly used in broadcasting, professional
audio applications and is a common telephone communications
standard.

dBm(50) This standard is defined by 1 milliwatt measured
with respect to a 50 ohm load.  This measurement is commonly used
in RF transmissions/receiving systems.

dBm(75) This standard is defined by 1 milliwatt measured
with respect to a 75 ohm load.  This standard is common in some RF
systems particularly cable TV systems.

dBmW  This is the generic form for a 1 milliwatt
reference, also written as dBm. This term usually has an
inferred load reference, depending on the application.

dBW This is a common form for power amplification
relative to a 1 watt reference (usually 50 ohms).  Typical
applications are found in RF Power Amplifiers and High Power Audio
Amplifiers specifications.

dBuV  This is a common form for specifying input RF
levels to a communications receiver.  This is called dB microvolt
where 1 microvolt = 1*10E-6V.

dbV While this dB term is defined, it is rarely used
in defining communication systems.  The dB value is obtained with
respect to 1 Volt.

dB/bit This is a common term used for specifying the
dynamic range or resolution for a Pulse Coded Modulation (PCM)
system such as a CD player.  This reference is defined by
20 Log(2)/bit = 6.02dB/bit.

dBi This is dB isotropic .  It is used as the reference
when defining Antenna Gain.

dB/Hz This is relative noise power in 1-Hz bandwidth.  This
term is used often in digital communications and in defining a
laser's Relative Intensity Noise (RIN).  For a laser system,
this is an electrical not an optical measurement.  A typical¹ RIN
for a semiconductor laser is -150 dB/Hz.

dBW/K-Hz  This is a common term used when analyzing
carrier-to-noise (C/N) in a communications link such as a satellite
link budget.  This value is based on the Boltzmann's
constant expressed in dB as 10 Log(1.38*10E-23) = -228.6 dBW/K-Hz.