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Beta Match - Hairpin, Stub affecting the element

Yuri Blanarovich, K3BU

Recent query by I0JX and discussion on the Antenna Newsgroup about the behavior of Beta Match - "trombone" or loading stub - hairpin on the performance of the antenna stirred some interesting arguments. Wes Stewart, N7WS argued that my remarks stating that Beta Match shortens the physical length of the resonant radiator and exhibits slight drop in efficiency are not valid. I suggested that better way to match would be using coil inductor in place of the Beta stub or tapping the element at the 50 ohm impedance point, off center, along it's full length.

When I was P40A from Aruba and wanted to operate on 40m using Inv. V dipole strung from the hotel roof, I was presented with the lower than 50 ohm impedance (antenna close to the building). When I used the hairpin stub to match the 50 ohm feedline I realized that by folding the portion of the dipole into a hairpin I could find the 50 ohm point, but had to extend the length of the dipole to maintain the resonance. Anyone who has experienced using the Beta Match knows that in order to maintain the resonant frequency of the element, the element has to be shortened (inductive loading by hairpin stub at the center) from its length without the hairpin.

My reasoning about the efficiency of Beta matched element was based on the experience with using loading elements (coil, stub, top hat) and their effect on the resonant length of the radiator. More light on the subject and distribution of antenna current along the radiator and loading elements can be seen in my other article Current distribution in the Antenna Loading Coils.

The basis for understanding the problem is to realize that we are dealing with antenna element - standing wave circuit, that has the current distributed along the element in the cosine curve fashion. Minimum at the ends and maximum in the center of the resonant half wave dipole element. The vertical quarter wave radiator has minimum (zero) current at the tip and maximum at the feed point. If we introduce the loading element along the length of the element, we see the distortion in the shape of the "perfect" cosine curve that unloaded element would have.  Depending on the point of insertion we can see drop along the loading element, if inserted say in the middle of the dipole (half) leg, or no drop if inserted in the middle of the dipole (but drop between the center of the loading element and its ends.)

The antenna efficiency is roughly proportional to the area under the current distribution curve along the element. Maximum would be with full size half wave resonant dipole element, having full undistorted cosine curve. Reduced efficiency would be with physically shortened element having loading element (coil, stub) exhibiting the current drop along its length and causing the distorted cosine curve, with less area underneath it.

Lets look at the simplified basic situation with dipole and modeling it EZNEC.

We have full size half wave dipole, about half wave above ground, fed at the center, having 75 ohm impedance and the following current distribution:

Here is the SWR plot and impedance information:

 

Here is the radiation diagram and gain

 

Now have look at the half wave Dipole with 2m Beta Match or hairpin inserted in the middle.

 

We can see that hairpin stub has portion of the element current along its length and by careful examination we would see that the current is at maximum in segment 3 at end of the stub and slightly decreases towards the element. The element physical length has to be reduced to compensate for loading, impedance decreases at the feedpoint and to find 75 ohm point we have to go to about 70% point from the end as marked by the red circle.

 

Here we see the now shortened element resonant back to 7.2 MHz and impedance at the moved feedpoint and also narrower bandwidth.

Here we see the pattern and gain, now dropping to 6.92 dBi from 7.07 dBi  indicating the drop in efficiency that corresponds roughly to drop in the area under the new curve, with its "missing" center portion now folded along the "boom" over the Beta stub.

If the element is fed at corner of stub and radiator, the gain drops to 6.87 dBi and impedance is around 55 ohms.

So the difference might be too small or trivial for some, it might be important when the effect is used in multielement arrays of loaded and stub matched elements. (Multiple wrong values of current and its distribution get magnified.) But the point is that there IS a difference, contrary to some claiming that it IS NOT.

The net result is that Beta or hairpin match can be used to find the match of antenna to the feedline at the expense of some loss of efficiency. Slightly better way is to use coil inductor in place of the hairpin stub, which would have the current along the coil in line with the element wire and adding its small portion.

Yet better way is to tap the 50 or 75 ohm point along the full size antenna element as has been promoted by Ken Glanzer, K7GCO. This requires feed point off center with proper balun while using full size element.

Feb. 7, 2007

EZNEC file Dipole w. hairpin