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There are generally 3 references: dBi (Isotropic), dBq (quarter waveradiator reference), and dBd (half wave or Dipole) reference.

An antenna generates a pattern of energy: an isotrope generates a perfect sphere. A dipole generates a torus (donut) shaped pattern. Since gain is related to the concentration of energy, there is more energy on the surface of a torus than there is on the surface of a sphere the same diameter. This is because there is more surface area on the sphere to distribute the same amount of energy (the input power). A 1/4 wave antenna exhibits a flattened sphere, so it too has a smaller surface area than a sphere of equal diameter.

Assuming a perfect spherical radiator (an isotrope) is a 0 dB gain reference, a quarter wave antenna would exhibit 0.15 dB of gain, and a dipole would exhibit 2.15 dB of gain over the isotrope. The reason for this is that no real world antenna can produce a perfect sphere of radiation, so there is some intrinsic gain in a resonant antenna.

So in your case of a 3.5 dBq antenna, this would be the eqivalent of 3.35 dBi (0.15 dB less) and 5.5 dBd (2 dB greater).

Some reputable manufacturers are quoting antenna gain in dBq, but these were antennas designed for low frequency (no more than 30 MHz) operation, where vertical monopoles are space efficient radiators (think AM broadcast).

One other occasion where the dBq number noted is by manufacturers of mobile antennas (think CB Radio) who are trying to make their antenna look better than the competition when selling to uninformed consumers (My antenna has 3 dB gain! Double your power!) In the end, it's the same antenna, just a marketing hype to make one product more appealing to the uninitiated.

In the VHF UHF bands dBd or dBi are the common references.

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