# Electrically short antenna

I am trying to understand fully the problem with using electrically short antenna to transmit RF signals (i.e length significantly shorter than the intended wavelength).

Currently my understanding is that such an antenna does not radiate : since the length of the antenna is much shorter than the wavelength the voltage distribution on the antenna at any given moment is roughly uniform. In particular there is no voltage fluctuation on the antenna and hence no magnetic field and hence no radiation.

I have been trying to quantify this explanation. The simplest quantification is that the impedance of an electrically short antenna is large, so the power transmitted to the antenna is small. But let's suppose I match the input impedance with the antenna impedance and I crank up the voltage to such an extent that the power transmitted to the antenna is now large. Now even the small variation in the roughly uniform voltage distribution are magnified and a magnetic field appear.

I am wondering if the high impedance is really the only issue that prevents an electrically short antenna from radiating? (Indeed, the antenna now behaves like an RC circuit, but I don't see why this is a problem if for example R = 50, C = 10k and the frequency is in the 10Mhz range and the voltage is very large).

• VLF/ELF antennas? Note that an electrically short dipole is the "dual" of an electrically small loop antenna. Rather than a (lossy!) transformer, use resoance for Z-match to produce hi volts: add a baseload inductor to your short whip antenna, as with 160M mobile (or add a capacitor across your small loop.) Remember, tiny antennas needing to create intense fields at 1/2-wave distance will heat up, and have very poor efficiency. Perhaps a wide foil loop antenna with a large low-loss capacitor would be more efficient than adding a low-Q multi-turn inductor to a whip or dipole antenna. Jan 17 at 13:53

am trying to understand fully the problem with using electrically short antenna to transmit RF signals (i.e length significantly shorter than the intended wavelength).

Currently my understanding is that such an antenna does not radiate

It radiates, but with a slightly different radiation pattern, and an efficiency problem related to its impedance.

since the length of the antenna is much shorter than the wavelength the voltage distribution on the antenna at any given moment is roughly uniform. In particular there is no voltage fluctuation on the antenna and hence no magnetic field and hence no radiation.

A short antenna has predominantly capacitative reactance. Current does flow, just not alot.

But let's suppose I match the input impedance with the antenna impedance

I am wondering if the high impedance is really the only issue that prevents an electrically short antenna from radiating?

Again, a short antenna does radiate. But there is a problem you have missed. You are correct, the impedance for a short antenna is high. As I mentioned, there is a very high capacitative component to that impedance. What I didn't mention is that the resistive component, or more precisely the radiation resistance can very small (1 or 2 Ohms). When matching the impedance, the ohmic resistance of the loading coil might be comparable to, or larger than the radiation resistance. That means more power lost to heat, and less power radiated.

• To be clear when I said "does not radiate" I mean "radiate negligibly". Of course everything with some non-zero current variation radiates some non-zero amount. Jan 17 at 7:05

There are graphs (and formula) that tell you what the impedance is. For instance this one for a monopole vs height (length of antenna): -

At approximately a quarter wavelength the impedance is 37.5 + j21.25 Ω as per this wiki article.

As monopole length decreases, the reactance dominates (capacitive) and radiation resistance drops considerably. This means you have to counter the capacitive reactance and impedance match to get anything like a decent power transmission efficiency.

But, as the antenna length reduces (and radiation resistance falls), the antenna losses become a bigger part of the net resistance projected by the antenna to the driving circuit so it's a bit of a losing game trying to get the same efficiency as a proper length quarter wave monopole or half wave dipole (for instance).

Not much a problem for a receiver though - think crystal radios - they never had anything like full length antennas and always operated "short" and the extra capacitive reactance and the tuning coil worked together to give selective reception.