Antenna Q Factor

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The Q or Quality of an antenna is a measure of the bandwidth of an antenna relative to the center frequency of the bandwidth. If the antenna operates over a band between f1 and f2 with center frequency fc=(f1+f2)/2, then the Q is given by:

antenna Q quality factor

Q = ----
   f2 - f1

Antennas with a high Q are narrowband, antennas with a low Q are wideband. The higher the value of Q, the more sensitive the input impedance is to small changes in frequency.

Q factor defines the damping of a resonator. Q factor is defined as the ratio of the energy stored in the oscillator to the energy that must be imparted per cycle to keep the oscillator cycling.

Q = 2π x Energy Stored / Energy Lost Per Cycle

When you trim an antenna’s length you are adjusting the resonant frequency by changing the distance that current has to flow from end to end of the element. Antennas used with oscillators have a high Q value, so a revised more practical formula is used.

Q = ƒc ÷ (ƒ2 – ƒ1)

This is the same as the top formula. Now to explain the formula as it applies to antennas:

  • ƒc is the frequency of resonance
  • ƒ1 and ƒ2 are the frequencies above and below the center

An antenna that operates well well over a broad band of frequencies (ƒ2 – ƒ1) is going to result in a relatively low Q value. An antenna that operates well across only a very narrow range of frequencies is going to generate a relatively high Q value. A mobile whip antenna with a loading coil to operate on the 80m ham radio band will have a high Q value. It will have a very narrow range of frequencies that it can be used on.

A low Q antenna is somewhat more damped and may require slightly more reinforcing energy, it can oscillate well across a much broader range of frequencies.

  • Broad frequency range antennas have low Q but are less efficient at radiating energy
  • Narrow frequency range antennas have high Q and may be more efficient at radiating energy on the resonate frequency.

When an antenna is physically shortened for the desired operating frequency and a loading coil is added to help it resonate at that desired frequency anyway, the Q factor is increased, like our 80m mobile antenna example. The inductive coil’s effect is to reduce damping in the antenna circuit at the desired operating frequency. Greater loading. thus having higher Q, allows physically shorter antennas for a given frequency.

For mobile operation on the HF ham radio bands you will often see a high Q antenna with its shortened length. It will have a loading coil and perhaps a disk, spoke, or swirled looking capacitance hat. Sometimes these mobile antennas have a motorized movable tap on a large loading coil so that the number of turns used by the antenna changes commensurately with the desired operating frequency. This way the narrow bandwidth is overcome by the ability to dynamically tune the antenna. These motorized tuning antennas are called screwdriver antennas. There are manually tunable versions which require adjustment or chaing of the matching component.