# Radio math

## Industrial wireless tutorials: Learn how to determine a link budget, that is, how much power is needed to effectively transmit data over a reliable radio link. See the decibel (dBm) and milliwatt (mW) conversion table.

To properly design a WLAN, there must be a clear understanding of the gains and losses of the system components, including the losses in the medium. To determine a "link budget" or how much power is needed to effectively transmit data over a reliable radio link, the actual power transmitted, along with all losses and gains, must be calculated. Many implementations are done by the seat of the pants, but that method usually results in additional cost in unnecessary equipment or troubleshooting. A small amount of time determining the actual needs will save money and a lot of time troubleshooting.

We've discussed the meanings of the various units used to measure both actual and relative power in a Wi-Fi system. [Radio frequency (RF) power is measured in milliwatts (mW) or in a logarithmic scale of decibels (dB), or decibels referenced to 1 mW of power (dBm).] We will now use these values to do the calculations and conversions required. Some rules of thumb to commit to memory:

The Rule of 10s and 3s:

- For every loss or gain of 10 dBm, divide or multiply the power in mW by 10
- For every loss or gain of 3 dBm, divide or multiply the power in mW by 2.

**Antenna output example**

For example, a transmitter has an output of 10 dBm into a transmission line that has a loss of 3 dBm, which feeds an antenna with a gain of 9 dBm. What is the antenna output in mW?

Remembering that 0 dBm is equivalent to 1mW, transmitter output is converted to 10 mW (10 x 1 mW). The 3 dBm line loss can be equated to halving the power input: 10 mW/2 = 5 mW. Finally, 9 dBm of antenna gain is doubling the value three times, or 5 x 2 = 10 x 2 = 20 x 2 = 40 mW.

Another way to do this is to simply add up the gains and losses: 10 dBm - 3 dBm + 9 dBm = 16 dBm total output (not gain). 16 dBm = 1mW x 10 = 10mW x 2 = 20 mW x 2 = 40 mW. [subhead]

**Link budget calculation **

To determine a link budget, first determine the receiver's sensitivity in dBm. For reliable reception we will assume -80 dBm (.00000001 mW), though sensitivity will range from -70 to -90 dBm. Using an EIRP of 10 dBm (10mW), assume the antennas are 100 ft apart and the receiving antenna has a gain of 3 dB. Radio signals attenuate according to the inverse square rule, and are calculated as Free Space Path Loss (FSPL); as the distance from the antenna doubles, the strength of the signal quarters. A quick way to calculate the loss is to use the "6 dB rule": doubling the distance results in an approximate loss of 6 dB.

Using the numbers above, and a calculated FSPL of 69.32 dB, the calculation for this simple link is: 10 dBm - 69.32 dB + 3 dB = -56.32 dBm received signal strength. This signal will provide a reliable link and falls within an acceptable fade margin of 24 dB. Increasing the output power of the transmitter will allow for more signal at the receiver and increase the "fade margin" of the link, which indicates the margin above the absolute lowest level at which the link becomes unusable; a typical fade margin is 20-25 dB.

The following chart is a handy reference for signal levels:

**dBm and mW conversion table**

dBm | mW | Power level | |
---|---|---|---|

+90 | 1000000000 | 1MW | |

+80 | 100000000 | 100kW | |

+70 | 10000000 | 10kW | |

+60 | 1000000 | 1kW | |

+50 | 100000 | 100W | |

+40 | 10000 | 10W | |

+30 | 1000 | 1W | |

+20 | 100 | .1W | |

+10 | 10 | .01W | |

0 | 1 | .001W, 1mW | |

-10 | .1 | .1mW | |

-20 | .01 | .01mW | |

-30 | .001 | .001mW | |

-40 | .0001 | .0001mW | Very strong signal |

-50 | .00001 | .00001mW | |

-60 | .000001 | .000001mW | Good signal |

-70 | .0000001 | .0000001mW | |

-80 | .00000001 | .00000001mW | |

-90 | .000000001 | .000000001mW | Typical noise floor |

- Daniel E. Capano, owner and president, Diversified Technical Services Inc. of Stamford, Conn., is a certified wireless network administrator (CWNA). Edited by Mark T. Hoske, content manager, CFE Media, *Control Engineering*, mhoske@cfemedia.com.

**ONLINE extras**

www.controleng.com/blogs has other wireless tutorials from Capano on the following topics:

Comparative modulation: Spread spectrum modulation terms and definitions for wireless networking

Radio antenna types

www.controleng.com/webcasts has wireless webcasts, some for PDH credit.

*Control Engineering* has a wireless page.

See related wireless tutorial below from Control Engineering: Murphy's 7 laws of industrial wireless communications