# Comparing antenna effeciency

Let's say I have three dipoles, one is resonant at some frequency and is matched at the antenna, the second is shortened with loading coals and is also matched at the antenna, the third is shortened but has no loading coils and is also matched at the antenna.

Supposing that all three are matched to 50 ohms and I use a short (ish) piece of coax to the antenna, how would they perform with regard to efficiency, gain, etcetera?

Assuming at least a half wavelength above ground at the same location, only one antenna installed at a time.

• If the third antenna is shortened and has no loading coils, then how is it still matched? – Phil Frost - W8II Mar 28 '14 at 13:23
• Assuming all three antennas have some soft of matching network between the antenna and the feedline. – s3c Mar 28 '14 at 13:27
• A loading coil is a matching network. If you take the loading coils out, then the "matching network" you need is exactly the inductance you just took out. We can't exactly compare the performance of antennas that are specified so vaguely. – Phil Frost - W8II Mar 28 '14 at 13:30

Antenna efficiency can be defined as the ratio of the radiation resistance to the total resistance of the antenna (radiation resistance, plus ohmic resistance of the antenna, plus ground losses, etc), normalized to the feedpoint impedance. If radiation resistance is the only resistance in the antenna, then it's 100% efficient.

$$\text{efficiency} = \frac{R_\text{radiation}}{R_\text{radiation} + R_\text{ohmic} + R_\text{ground}+R_\text{any other kind}}$$

Performing this calculation can be tricky since there are so many potential sources of loss which may not be thought of as a "resistance", but can be expressed as such. Dielectric losses are a good example.

Loading coils and matching networks are significant only to the extent that they introduce additional loss. Sources of loss might include:

• resistive losses in the coils
• magnetic hysteresis losses in the core material of inductors
• dielectric losses in capacitors
• unintentional near-field coupling to nearby lossy materials (mast, trees, etc)

Shortening the antenna tends to decrease the radiation resistance. This doesn't make the antenna less efficient itself: it just makes other losses more significant, since they are now a greater fraction of the effective total resistance of the antenna.