
    <h1>Power Measurement and Antenna Gain</h1>
    <p>HPR show by Paulj, May 2025.</p>
    <h2>1.0 Power expressed in dB (also written as dBW)</h2>
    <p>&nbsp;&nbsp;&nbsp;&nbsp;Power P<sub>dB</sub> = 10 . log<sub>10</sub><b>P</b></p>
    <p><br>
    </p>
    <p>Where <b>P</b> is the power expressed in Watts.</p>
    <h2>2.0 Power expressed in dBm</h2>
    <p>&nbsp;&nbsp;&nbsp;&nbsp;Power <b>P<sub>dBm</sub></b> = 10 . log<sub>10</sub><b>P</b></p>
    <p><br>
    </p>
    <p>Where <b>P</b> is the power expressed in milliwatts.</p>
    <p><br>
      <br>
    </p>
    <p>1W = 1000mW<br>
    </p>
    <p>&nbsp;&nbsp;&nbsp;&nbsp;Power <b>P<sub>dBm</sub></b> = 10 . log<sub>10</sub><b>1000mW</b><br>
    </p>
    <p>&nbsp;&nbsp;&nbsp;&nbsp;Power <b>P<sub>dBm</sub></b> = <b>30
        dBm</b><br>
    </p>
    <p>&nbsp;&nbsp;&nbsp;&nbsp;so:</p>
    <ul>
      <b>0 dB = 30 dBm</b>
    </ul>
    <h2>3.0 Power expressed relative to an isotropic antenna - dBi</h2>
    <p>An Isotropic antenna is an theoretical ideal antenna which
      radiates equally in all directions. Imagine the antenna is at the
      centre of a sphere, the signal strength at the surface of the
      sphere is equal at all points. The gain of an isotropic antenna is
      defined as 1, meaning: <br>
    </p>
    <p>&nbsp;&nbsp;&nbsp;&nbsp;</p>
    <ul>
      <b>10 dB = 10 dBi</b>
    </ul>
    <h2>4.0 Power expressed relative to a half wave dipole antenna - dBd</h2>
    <p>The simplest practical antenna is a half wave dipole antenna,
      where each of the two legs is a quarter wave length long. The feed
      is at the centre, and the two legs are generally horizontal, and
      aligned away from the feed point 180 degrees apart. The dipole
      antenna exhibits gain perpendicular to the legs. The maximum gain
      is 1.64 times the isotropic antenna - a gain of approximately
      2.15dBi. The gain off the ends of the dipole is much lower - the
      total power radiated by the antenna can not exceed the power being
      input, so if there is more radiation (gain) in one direction,
      there must be a corresponding reduction in a different direction.
      So:</p>
    <p>&nbsp;&nbsp;&nbsp;&nbsp;</p>
    <ul>
      <b>2.15 dBi = 0 dBd</b>
    </ul>
    <h2>5.0 Effective Radiated Power - ERP and EIRP</h2>
    <p>ERP and EIRP are both used to indicate the power achieved using
      an antenna.ERP compares the antenna performance with a dipole, and
      EIRP compares the performance with an isotropic antenna. So, the
      ERP is the power which would need to be fed into a dipole antenna,
      to get the same effect in the direction your antenna is pointing.
      EIRP is the power required for an isotropic antenna to gain
      equivalence.</p>
    <p><br>
    </p>
    <p>Practical example: My KX3 can transmit 15W. using the formula
      above, this is 11.77 dB. If I attach a Yagi-Uda antenna with a
      gain of 10dB, the <b>ERP</b> is 21.77 dB. Using the formula
      above, from this number you can calculate that this is the
      equivalent of 150.3142 Watts ERP. To understand the EIRP, we need
      to add 2.15 to the 21.77 dB value, giving 23.92 dB <b>EIRP</b>.
      Again, converting to actual power gives 246.515 Watts EIRP.</p>
    <p><br>
    </p>
    <ul>
      <li>If you are comparing antennas, make sure the same units are
        being used in all cases (either EIRP or ERP) - some sellers will
        use EIRP, because the values are higher!
      </li>
      <li>Check your licence conditions. Power output limits are often
        at the antenna, and don't include antenna gain. You can set your
        transmitter to output sufficient power to overcome any feed line
        losses, and present up to the power permitted to the antenna. A
        good antenna can then be used to get the transmitted power out
        and across the world. For feedline loses, the value is given in
        dB per 10 metres. For example, RG58 is 2dB / 10 metres (at
        100MHz - choose the right feeder coax for your target
        frequency!). If you have 15 metres, then you will have 3 dB
        feeder loss, so half of your transmitter power will be lost in
        the feed line. If you know this and your transmitter can output
        more, then you can increase the transmitter power accordingly.
        So for 25W at the transmitter, with 3dB loss in the feeder, you
        can set the output to 50W.
      </li>
      <li>Some transmit power limits are set in ERP or EIRP, so you will
        need to calculate back from the antenna to see the maximum
        allowable transmitter power, to stay within the rules.
      </li>
    </ul>
    <h2>6.0 Combining values</h2>
    <p>One result of the use of dB is that you can add the values
      together to understand the whole system gain. So, with our example
      above, if we have 11.77 dB of output power, then -1 dB insertion
      loss for a bandpass filter, -3 dB loss for the feeder, and 5dB
      gain on the antenna, the overall ERP is 12.77 dB. You can convert
      this back to Watts, to get 18.92W ERP.</p>
    <h2>7.0 Links</h2>
    <ul>
      <li><a href="https://www.antenna-theory.com/antennas/dipole.php">Dipole
          information</a>
      </li>
      <li><a
          href="https://www.antenna-theory.com/antennas/travelling/yagi.php">Yagi-Uda
          information</a>
      </li>
      <li><a href="https://en.wikipedia.org/wiki/Decibel">Wikipedia
          information on Decibels</a>
      </li>
      <li><a
          href="https://en.wikipedia.org/wiki/Effective_radiated_power">Wikipedia
          information on ERP and EIRP</a>
      </li>
      <li><a href="https://en.wikipedia.org/wiki/Gain_(antenna)">Wikipedia
          information on Antenna Gain</a>
      </li>
      <li><a href="https://m0ukd.com/calculators/erp-eirp-calculator">ERP
          &amp; EIRP calculator from M0UKD</a>
      </li>
    </ul>
