Theory of the DK7ZBMatch (new)  The "classic" DK7ZBMatch  Full symmetrical 28OhmMatch by DF9IC  "Sperrtopf" by DF7DJ 
The DK7ZBMatch for Yagis
It is a well known phenomenon, that the radiators resistance in a Yagistructure drops down by adding parasitic elements to a dipole as a radiating element. For the VHFBands (5050.5MHz, 144146MHz, 430440MHz) a radiation resistance of 2535Ohm has the best balance for gain, back and sidelobes, bandwidth and SWR at tenable losses in a Yagi. The classic match for that resistance/impedance is the GammaMatch. The BetaMatch is a good choice as well, but realisation on VHF is difficult for homebrewing. For that reason a new simple, easy to built match was developed in 1995 for Yagis with resistitive loads of 12.5, 18 and 28 Ohm.

The basic principle is a quarterwave line of two coaxcables in parallel. One end of the line ist connected to the radiator, the other to a socket, which is grounded at the metallic boom and has two functions: 1. It transforms the resistance of the radiator to the 50Ohm of the feeding line. With 2x75Ohmcables 28 to 50 Ohm. With 2x50Ohmcables 12.5 to 50 Ohm. With 3x93Ohmcables 18 to 50 Ohm 2. This line is a simplified coaxial sleeve balun to avoid sleevewaves on the braid of the cable running to the station. Very effective! 
Antennas which that match have some advantages:  You do not need a folded dipole or any exotic radiators like loops, the length of a normal dipole can be corrected easier.  The radiation pattern is very clear.  Simple mechanical solution for the match with the coaxcables.  For shortwave and 6m you can wind the cable to a choke with an additional suppression of sleevewaves With usual coax of 50 and 75 Ohm the following cases are interesting: 
Radiation resistance Z of the Yagi 
Lambda/4 Coaxcable 
Impedance of the line 
12.5 Ohm 
2x50 Ohm parallel  25 Ohm 
18 Ohm  50+75 Ohm parallel  30 Ohm 
28 Ohm  2x75 Ohm parallel  37.5 Ohm 
12.5Ohm: Good for highgain yagis with small bandwidth in the 6m and 2mBand, losses tenable 18Ohm: Can be used on 6m and 2m, medium bandwidth 28Ohm: Best balance for all antenna parameters on 2 m and 70 cm 
Update: The 18OhmMatch in
practise
It is possible to use 50 and 75Ohmcable in parallel. The condition is the same VF. That means we can use cable with FullPE (VF=0,67) or FoamPE (VF about 0,82) with the same lengths. I have tested this method in various antennas with excellent results. For example two impedance matches for 50MHz and 70MHzYagis: 


Here two cables RG58 (50 Ohm) and RG6 (75 Ohm) in parallel. The two cables have different diameters, but the same VF of 0,67. The 70MHzYagi has a perfect match from 18 to 50 Ohm. 
This is a 50MHzYagi with cables of VF=0,82. 50 Ohm with Aircell5 (5 mm diameter) and a CATVcable 75 Ohm with 6,5 mm diameter. Perfect match from 18 to 50 Ohm in a 50MHzYagi. 
The 2m28OhmDK7ZBmatch in practise The best suppression of the common wave currents can be get with a cable of V=0,82. Here I have used a 7mmSATVcable with 75 Ohm. The length is 42,5 cm (refered to the braid!). The additional inductivity of the turn leads to a self resonance near 144 MHz and a very good balance of the feeding.

The 28Ohmmatch with 2x75OhmCATV/SATVcable shown above will handle 750 Wtts RF on SSB/CW on 2 m and >1KW on 50 MHz. Do not bend the loop with a to small diameter! The V (Velocity of propagation) with these cables is in the range of 0,80,85, most cables have a V=0,82. Use a good quality, in the last time a lot of inferior cables with a steel braid are on the market. With 2xRG59 (good MILquality!) you can handle 500 Wtts on 2 m and 1 KW on 50 MHz. The given or calculated lengths is related to the shield. Keep the leads as short as possible. 
Another type of an impedance choke for 2m: 2x RG179 PTFEcable parallel wound to a choke. The length is 2x 37 cm (braid). This choke can be loaded with 500 Wtts SSB/CW power 
There is a lot of 75OhmCATVcable with good
electrical data. The only problem is the screen, which is often made in
Aluminium and cannot be soldered.
Here is the solution of Jörg, DG1JC: Use an end sleeve for strands and you have a simple and effective method. 
There are people criticysing the medium (28 Ω) an low (12,5 Ω) impedance Yagis and have speculations about any mystic losses in the match for that feedpoint impedances. But the same people use stacking harnesses and splitters exact with such impedance points of 25 Ω and 12,5 Ω at the connections for matching. Nobody believes that this has any disadvantage. Paul, GW8IZR, has made an independent measuring of the losses in such a match 12,5 Ω to 50 Ω with the following test circuit: 
With two of such transformation sections back to back he measured the losses against a halfwave piece of straight coax. His results for 2x RG58 (a more lossy cable you will not find...) and 40 MHz: 
Upper graph: A piece of 50Ωcoax with the length of lambda/2 Lower graph: Two matching sections parallel back to back The difference is 0,025 dB. Do you think we should talk about that? If you use better cables the difference will be less. If you construct a 50Ωchoke for feeding a 50ΩYagi or a choke with 2x75Ω or 2x50Ωcables in parallel makes no difference in the losses! 
A lot of antennas were built for the 6m, 2m and 70cmBand. The performance of the Yagis is excellent. Meanwhile stations in many countries are using Yagis with the DK7ZBmatch.
Left: The vertical 3ElementYagi is built by Peter, PA4PS for use on a 202,5MHzlink to the FMRadiostation Havenstad FM in the Netherlands. The Yagi is a 28Ohmtype with the DK7ZBmatch. Seems to be the first time that a DK7ZBYagi is used by a commercial station.... 
1. LongYagis for the 2mBand with 28Ohmtechnology got the first price in the technical competition of the German HamMagazine "FUNKAMATEUR" 1996. 2. See the VE7BQHList for 2mYagis, the DK7ZBYagis have good gain and pattern. 3. The DK7ZBMatch got the first price (part "ANTENNAS") in the constructioncompetition at the German VHFConvention in Weinheim 2000. 4. Meanwhile a lot of Yagis with the DK7ZBDesign are used in several countries, reports about the yagis can be found in many HAMMagazines and the internet. Many VHF/UHFcontestcrews are working with stacked arrays of these Yagis. The DK7ZBMatch is working quite well in practice: DO1IR built up the 6Element144MHzYagi and corrected only the length of the radiatorelement. With an HPNetworkanalyzer HP 8713C he tested the antenna. Look for the result: The reflected wave is damped >50dB! Compare that with other commercial built Yagis..... 