# A certain formula for antenna system Q

A correspondent questioned the writings of an online expert who opined whilst discussing loaded monopole antennas:

… there is a formula circulating the Internet which states that antenna Q is equal to 360 times the frequency in MHz, divided by the 2:1 VSWR bandwidth in kHz. One has to assume they mean antenna system Q, but that’s not a given. While this formula might give you a comparison between antenna A and antenna B (all else being equal), the actual Q of the antenna (system or otherwise) requires a textbook-full of formulas, and a lot more information than just the 2:1 bandwidth! Fact is, this formula is no more specific than the number of DX contacts a specific antenna garnered.

The formula given is:

Q=360*fc/B(VSWR=2) where fc is the centre frequency.

For example, if a 3.5MHz half wave dipole had a bandwidth of 200kHz, Q=6.3.

If the VSWR curve follows the classic curve of a simple series resonant antenna, the VSWR=2 bandwidth of a matched antenna system is 70.7% of the half power bandwidth (Duffy 2014) .

So we can express the formula above in terms of half power bandwidth B, and convert fc and B to the same units.

Q=360*fc/(0.707*B)/1000=0.509*fc/B.

Wait a minute, the accepted formula is Q=fc/B (Terman 1955), the formula above gives only half that (which hints the error in its derivation / application).

The formula given in the quote for simple series resonant antenna system is indeed wrong.

Contrary to the quote, Calculate Antenna Q from VSWR bandwidth measurement will calculate simple series resonant antenna system Q from centre frequency and bandwidth at some given VSWR.

## References

• Duffy, O. May 2014. Antennas and Q.
• Calculate Antenna Q from VSWR bandwidth measurement
• Terman, Frederick. 1955. Electronic and Radio Engineering – 4th ed. New York: McGraw-Hill.