NETW360 Week 1 iLab: Basic RF Calculations
The power emitted from wireless devices, especially in unlicensed bands, such as 2.4 GHz and 5 GHz, are regulated by the Federal Communications Commission (FCC). Wireless network professionals must calculate power levels (or RF signal strength) that are being transmitted by wireless devices to make sure their designs are complaint with FCC regulations. They also need to calculate power levels that are being received by wireless devices to make sure the signal is properly received at the destination.
RF power can be measured in two ways: on the linear scale, by the number of watts that are being transmitted; and on a relative scale, by the number of decibels (dBs) instead of watts.
Decibel milliwatt (dBm) is the logarithmic power ratio (in dB) of the measured power in milliwatts referenced to one milliwatt (mW). Notice that the reference point is specified as 1 mW = 0 dBm.
3’s and 10’s rules are shortcuts for estimating the increase or decrease of these power levels.
In this lab, students will practice basic RF calculations, including
· converting from mW to dBm;
· converting from dBm to mW; and
· estimating power levels using the 3’s and 10’s rules.
Task 1: Converting between dBm and mW
Applying the 3’s and 10’s rules, the relationship between dBm and mW is estimated as shown in the following (partial) table.
3’s rule|10’s rule|
……|……|
0.125 mW = -9 dBm|0.001 mW = -30 dBm|
0.25 mW = -6 dBm|0.01 mW = -20 dBm|
0.5 mW = -3 dBm|0.1 mW = -10 dBm|
1 mW = 0 dBm|1 mW = 0 dBm|
2 mW = 3 dBm|10 mW = 10 dBm|
4 mW = 6 dBm|100 mW = 20 dBm|
8 mW = 9 dBm|1,000 mW = 30 dBm|
……|……|

Notice that as the mW value increases or decreased by the factor of 10, the dBm value increases and decrease by adding or subtracting 10. As the mW value doubles or halves, the corresponding dBm value increases and decrease by adding or subtracting 3.

· Apply 3’s rule to estimate what 16 mWs is in dBm. __12___

· Apply 3’s rule to estimate what 0.0625 mWs is in dBm. __-12___

· Apply 10’s rule to estimate what 10,000 mWs is in dBm. __40___

· Apply 10’s rule to estimate what 0.0001 mWs is in dBm. __-40___

· Apply 3’s rule to estimate what 15 dBm is in mW. __32___

· Apply 3’s rule to estimate what -15 dBm is in mW. __0.03125___

· Apply 10’s rule to estimate what 50 dBm is in mW. __100,000___

· Apply 10’s rule to estimate what -50 dBm is in mW. __0.00001___

Task 2: Estimating power levels using 3’s and 10’s rules

In cascaded systems with power gain and/or loss along a chain of subsystems, power levels given in dB forms can be directly added or subtracted to calculate the total power.

For instance, a transmitter with a power of 9 dBm, after a cable and connector loss of 3 dB, ends up with a power of 9 dBm ˗ 3 dB = 6 dBm or 4 mW. Notice that the simple addition and subtraction here doesn’t apply to powers given in mW.

If one were to subtract 3 dB from 8 mW (i.e., mixed measurement units), 8 mW should be converted to 9 dBm first. The result is in dBm which can be converted to mW when needed.

· Applying the 3’s and 10’s rules, what’s 0.125 mW ˗ 30 dBm in dBm? __-39___

· Applying the 3’s and 10’s rules, what’s 0.125 mW ˗ 30 dBm in mW? __0.00122___

· Applying the 3’s and 10’s rules, what’s 0.0625 mW ˗ 40 dBm in dBm? __-52___

· Applying the 3’s and 10’s rules, what’s 0.0625 mW ˗ 40 dBm in mW? _0.0000064___

· Applying the 3’s and 10’s rules, what’s 8 mW + 30 dBm in dBm? __39___

· Applying the 3’s and 10’s rules, what’s 8 mW + 30 dBm in mW? __8192___

· Applying the 3’s and 10’s rules, what’s 16 mW + 40 dBm in dBm? __52___

· Applying the 3’s and 10’s rules, what’s 16 mW + 40 dBm in mW? __156,250___

The same idea can be applied to conversions from dBm to mW when a dBm value is not readily available in the 3’s and 10’s rules table.

For instance, what is 13 dBm in mW?

First, 13 dBm = 0 dBm + 10 dBm + 3 dBm, where 0 dBm, 10 dBm, and 3 dBm are in the table.

Next, let’s apply the following 3’s and 10’s rules:
· 0 dBm = 1 mW
· When the dBm value increases by adding 10, the mW value increases by the factor of 10.
· When the dBm value increases by adding 3, the mW value increases by the factor of 2.
Finally, we have 13 dBm = 0 dBm + 10 dBm + 3 dBm = 1 mW × 10 × 2 = 20 mW.
· Applying the 3’s and 10’s rules, what’s 7 dBm in mW (must show steps)?
Answer: 7dBm=10dBm-3dBm=10mW/2mW =5mW

· Applying the 3’s and 10’s rules, what’s 4 dBm in mW (must show steps)?
Answer: 4dBm=10dBm-6dBm=10mW/4mW=2.5mW

· Applying the 3’s and 10’s rules, what’s 9 dBm in mW (must show steps)?
Answer: 9dBm=8mW

· Applying the 3’s and 10’s rules, what’s -7 dBm in mW (must show steps)?
Answer: -7dBm=-10dBm+3dBm=0.1mW*2mW=0.2mW