The purpose of this short web page is to present some experimental impedance measurements on simple dipoles at around 800 MHz, made with a network analyser. The results are presented in the form of three red impedance curves plotted on a Smith chart, which is centred on the 200 ohms transmission line impedance formed from transforming the 50 ohm coaxial feeder impedance with a balun.
The antennas measured were 1) a simple half wave dipole, 2) a folded dipole, and 3) a folded dipole with the ends (folds) cut off. The lengths of the dipoles were about 16 cm in each case. They were constructed from 14 swg copper wire, diameter about 2 mm.
The centre frequency of the plots is 785MHz in each case, and the span is 100 MHz. Thus the curves move from 735 to 835 MHz in a counter-clockwise direction around the Smith chart.
Of course, the centre of the dipole contained the balun matching cable and the feed points of the two rods were about 5mm apart. Since there is significant coupled structure in the near field, we do not expect precise agreement between theory and experiment. Thus we begin to get an idea of the limitations of standard theory, in real applications, because the resistive point for our measured dipole is close to 830 MHz. The measured plot is presented here...
The standard story in the textbooks, when talking about the folded half wave dipole, is that it presents a driving point impedance of about 300 ohms resistive (4 times 75 ohms) to the feeder. We can easily measure this and the results of our measurements are presented here. In our example, the dipole rods are spaced by 14mm and the wire diameter is 2mm. The overall length of the dipole is again 16.1 cms, all measurements plus or minus 5%. In this picture the normalised impedance of the SMITH chart is 200 ohms.
Why is the impedance raised by adding the extra rod? The argument is that the current in the extra rod mirrors the current in the driven rod.
In a single lambda/4 rod (one rod of the two forming the dipole) the current is maximum at the feed point, then decays co-sinusoidally to zero at the end.
In the case of the folded dipole, with a conductor bridge at the fold end, the two parallel conductors (closely spaced) form a parallel wire transmission line, of length lambda/4, and shorted at the fold. Thus at the other (feed) end, the parallel rod combination (whatever its characteristic impedance) presents an open circuit to differential driving signals. There can therefore be NO differential current between the feed ends of the two rods, and the currents in one rod must equal the current in the other, and be in the same direction(at the feed end). Since a single rod has the co-sinusoidal distribution specified above, this must also be the common-mode current distribution in the parallel rod.
The differential mode current, as we have seen, is zero at the feed end, but a quarter wavelength away along the double rods it has risen to V/2Zo, where V/2 is half the antenna driving point voltage and Zo is the impedance, not of the radiating antenna, but of the transmission line formed by the two parallel rods. Of course, the differential current contributes very little to the radiation from the antenna as there are equal and opposite contributions on the two rods.
The common-mode current which radiates is therefore twice the current delivered by the feeder to the real radiation impedance, and for the same total radiated power P = (IIR), the current I consists of two parts: I/2 from the feed and I/2 in the parallel rod. Halving the feed current must quadruple the radiation resistance. ([I/2][I/2][4R]) = (IIR) = P.
In this case, the "two quarter wave open circuit parallel wire transmission lines" which form the upper and lower quarter wave sections of the dipole, present short circuits to differential mode currents. This is because a quarter wave transmission line feeding an open circuit has short circuit input impedance. Thus the current in the extra rod is OPPOSITELY DIRECTED to the current in the driven rod, and the effect is to present a short circuit to the feeder. This we clearly see in the measurements below; the only difference between this measurement and the picture above for the folded dipole is that we have cut the folded ends off. The folded dipole with open circuit ends is therefore a very inefficient radiator; the oppositely-directed currents cancel out each other's radiation in the far field. Cutting the ends off the dipole eliminates the differential mode currents which were flowing in the ends.
I am very grateful to Mike Blewett for constructing and measuring the dipoles.
I am also very grateful to Paul Dent for pointing out the even-and-odd mode properties of folded dipoles in more detail than I had grasped.
Copyright D.Jefferies 1998, 2000.