Theoretical maximum gain and bandwidth of an antenna

Theoretical maximum gain and bandwidth of an antenna.

Picture of an antenna in a sphere of radius a


Frequency:	f =	Hz
Minimum radius of a sphere containing the antenna:	a =	m
Maximum antenna gain:	G <	dBi
Maximum quality factor:	Q <	1/1
Minimum band width:	BW >	Hz

Enter the frequency f and one value (either a, G, Q or BW) and click the "Calculate" button next to it to compute the three other values.

These values are only valid for perfect antennas (no losses). For real antennas (with losses) the gain lower and the bandwidth is wider.
Bandwidth can only calculated when the condition Q>>1 is true and it's only valid for linear polarized antennas.

Bibliography:

Gain:		L. J. Chu, Physical limitations of omni-directional antennas, Journal of Applied Physics, vol. 19, pp. 1163-1175, December 1948.
Bandwidth:		R. F. Harrington, Time-Harmonic Electromagnetic Fields, Electrical and Electronical Engineering, McGrow-Hill, New York, 1961.
Newton's method:		J. Rappaz, Analyse numérique, Notes de cours: Leçons 1 à 10, École Polytechnique Fédérale de Lausanne, 1994, pp. 64-66.

How far(long) the transmitter cover?

The transmission range depends on many factors. The true distance is based on the antenna installing height , antenna gain, using environment like building and other obstructions , sensitivity of the receiver, antenna of the receiver . Installing antenna more high and using in the countryside , the distance will much more far.

EXAMPLE 5W FM Transmitter use in the city and hometown:

I have a USA customer use 5W fm transmitter with GP antenna in his hometown ,and he test it with a car, it cover 10km(6.21mile).

I test the 5W fm transmitter with GP antenna in my hometown ,it cover about 2km(1.24mile).

I test the 5W fm transmitter with GP antenna in Guangzhou city ,it cover about only 300meter(984ft).

Below are the approximate range of different power FM Transmitters. ( The range is diameter )

0.1W ~ 5W FM Transmitter ：100M ~1KM

5W ~15W FM Ttransmitter : 1KM ~ 3KM

15W ~ 80W FM Transmitter : 3KM ~10KM

80W ~500W FM Transmitter : 10KM ~30KM

500W ~1000W FM Transmitter : 30KM ~ 50KM

1KW ~ 2KW FM Transmitter : 50KM ~100KM

2KW ~5KW FM Transmitter : 100KM ~150KM

5KW ~10KW FM Transmitter : 150KM ~200KM

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1.How far you want to cover in diameter ?
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