# “No short antenna is more efficient than a resonant-length antenna”

A recent online posting asserted that an antenna is optimal when itself resonant, and fed with a resonant feed line length so delivering a purely resistive load to a source, and further that implementors needed to be careful that a shorter dipole could be offset to some extent by a longer feed line but it would be inferior because:

no short antenna is more efficient than a resonant-length antenna

… but does that stand scrutiny?

## An NEC experiment

Lets walk though an experiment using NEC-4.2 models of a dipole of 2mm copper wire at 10m height at 7.1MHz over average ground (σ=0.005, εr=13).

Key assumptions:

1. source has a Thevenin equivalent source impedance of 50+j0Ω;
2. feed line is lossless.

The results are sensitive to the model assumptions.

We will calculate the ratio of radiated power to the power delivered by the transmitter to a matched load, let us call it TransmitEfficiency for the purposes of this article.

### Scenario 1: shortened half wave dipole fed with the shortest electrical length of lossless 75Ω line that delivers in input impedance of approximately 50+j0Ω.

Length is 19.932m, feed point impedance is 74.9-j30.8Ω. Input impedance looking into 6.033m of 75Ω line is 49.9+j0.48Ω (approximately matched). RadationEefficiency is 75.85% or -1.200dB, and MismatchLoss at the source is 0.0001dB so TransmitEfficiency is RadiationEfficiency-MismatchLoss=-1.2001dB or 75.85%.

### Scenario 2: resonant half wave dipole fed with the same electrical length of lossless 50Ω line.

Length is 20.246m, feed point impedance is 79.9-j0.1Ω. Input impedance looking into 6.033m of 50Ω line is 40.94-j19.39Ω. RadationEefficiency is 75.91% or -1.197dB, and MismatchLoss at the source is 0.24dB so TransmitEfficiency is RadiationEfficiency-MismatchLoss=-1.437dB or 71.83%.

### Scenario 3: resonant half wave dipole fed with an electrical half wave of lossless 50Ω line.

Length is 20.246m, feed point impedance is 79.9-j0.1Ω. Input impedance looking into 6.033m of 50Ω line is 79.9-j0.1Ω. RadationEefficiency is 75.91% or -1.197dB, and MismatchLoss at the source is 0.24dB so TransmitEfficiency is RadiationEfficiency-MismatchLoss=-1.437dB or 71.83%.

## Effect of line loss

The above solutions were solved using lossless line.

Scenario 1 lengths would need to be adjusted very slightly to achieve a match looking into lossy line, and there would be an additional loss due to the line operating under standing waves, eg about 0.13dB for Belden 1694A RG6 for a TransmitEfficiency of -1.3dB or 74%.

Scenario 2 would also sustain additional loss due to the line operating under standing waves, eg about 0.095dB for Belden 8276 RG213 for a TransmitEfficiency of -1.5dB or 71%.

Scenario 3 would also sustain additional loss due to the line operating under standing waves, eg about 0.23dB for Belden 1694A RG6 for a TransmitEfficiency of -1.7dB or 68%.

## Analysis

The assumption that the source has a Thevenin equivalent source impedance of 50+j0Ω is not to imply that ham transmitters always, mostly or sometimes have such a characteristic, but you would expect a laboratory Standard Signal Generator to have such a characteristic and the experimental results could be verified with such a source.

The best TransmitEfficiency is that of Scenario 1, the shortened dipole with a length of 75Ω line to provide a match to the source.

Further, that Scenario 3 which uses a resonant dipole and resonant line length is the worst TransmitEfficiency, the increase in line to a resonant length increases transmission line loss and does nothing for MismatchLoss at the source.

There is no magic to the resonant dipole scenarios that makes them work significantly better than the non-resonant dipole scenario.

Radiator resonance is not a necessary condition for an efficient antenna, nor is it sufficient condition for an efficient antenna.

Applying the effect of minimal practical line loss does not change the ranking, the best performer is Scenario 1 in which neither dipole nor feed line are themselves resonant.

Scenario 1 does not come about by accident, it is designed to present a match to the source and to do so with high TransmitEfficiency. It is probably fair to say that the design concepts might not be part of the knowledge set of some hams, hams who may recite the mantra “resonant antennas always work better” to reinforce their own belief.

It takes only one valid experiment to show that the general statement  no short antenna is more efficient than a resonant-length antenna is not true.