- To introduce the measurement of power in wireless systems.

Power measurements are important in any situation involving data transmission.

Power is often expressed in *decibels*, where

P_{dB} = 10 log_{10}P

Logarithms make the units involved ambiguous, so
in order to relate this to actual units, power can be expressed in
*dBm*, where the power is measured in milliWatts. Thus

P_{dBm} = 10 log_{10}P(mW)

To convert back from dBm to mW, it should be obvious that

P_{out} (mW) = 10^{PdBm/10}

Certain devices, such as amplifiers, can produce *gain* in a
signal, meaning the output is greater than the input. In these cases,
the gain is given by

A = P_{out}/P_{in}

It's often convenient to express gain in decibels, so

G_{dB} = 10 log_{10}(P_{out}/P_{in})

In that case, to get the gain from the gain in decibels,

P_{out}/P_{in} = 10^{PdB/10}

(Note that in this case P_{out} should be *greater
than* P_{in}.)

Many things cause *loss* in a signal, and loss can be considered
as
negative gain, so

L_{dB} = - 10 log_{10}(P_{out}/P_{in})

In that case, to get the loss from the loss in decibels,

P_{out}/P_{in} = 10^{- PdB/10}

(Note that in this case P_{out} must be *less
than* P_{in}.)

Attenuation loss is dependent on wavelength. For radio frequencies,

L_{attenuation-dB} = 10 log_{10}( (4
Π d)/λ^{2})

where d is the distance and λ is the wavelength.

At first glance, using decibels seems more complicated than using
"normal" power units, such as Watts. However, when there are several
elements in a system all producing gain or loss in a signal, it gets
more complex. To get the final output of a system with several gains
and losses, the original signal must be multiplied by the gain (or
loss) of each element in the system. This can be tedious.

On the other hand, if you express everything in dB (or dBm), then gains
and losses are represented by additions and subtractions.

- Fill in the missing quantities in the following table:
**Table 1: Power Measurements**Power in (mW) Power out (mW) Gain (or loss) (dB) 100 10 15 0.2 50 10 0.01 -30 **Related to those above**10 100 2 150 0.01 30

- In many situations, rather than having actual power
measurements, it's easier to use percent (or fractional) changes
in
power.
Fill in the missing quantities in the following table:
**Table 2: Power Measurements**Percent change (%) Fractional change Gain (or loss) (dB) 90 0.9 10 0.1 2 0.01 5 Related to those above 1/2 0.001

**Before you leave the lab, have the lab instructor
sign your lab notebook immediately after your last entry.**

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