Posts Tagged #wireless

  • Simple Addition

    Greg Ingersoll

    Thu 07 February 2013 - 15:00:00 CST

    #mathematics #wireless

    Ok, here’s an easy one. When does 17+17=20?

    I was looking at basic WiFi power limits just now and one of the tables caught me off guard for a second until I looked at the units. (Always check units.) One of the tables indicates that a system can have two antennas with output power from each of 17 for a total of 20. How?

    The catch is that the power figures are in dBm which is a logarithmic scale so addition isn’t just addition anymore. And units of dBm give the output power in decibels (dB) relative to 1 milliwatt (which is where the “m” in dBm comes from). 

    So take your output power, say 5mW. Relative to 1mW, this is 5 times larger, or about a 7dB increase:

    $$10\cdot \log_{10}\left(\frac{5\text{mW}}{1\text{mW}}\right) \approx 7\text{dBm}$$

    Likewise, 1mW is 0dBm; there is no increase or decrease from the 1mW reference.

    (Also, if you’ve seen the dB calculation with 20log instead of 10log, that is for amplitude, not power. Power is proportional to amplitude squared so you lose a factor of two after the log. But I digress…)

    Working backwards, 17dBm is equivalent to about 50mW. Twice this is 100mW which is equivalent to 20dBm. 17+17=20.

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