Theory of the DK7ZBMatch (new)  The "classic" DK7ZBMatch  Full symmetrical 28OhmMatch by DF9IC  "Sperrtopf" by DF7DJ 
Bandwidth of some
Amateurbands
Band 
Frequency Range 
Bandwidth
in % 
70cm 
430440MHz 
2,3% 
2m 
144146MHz 
1,38% 
6m 
50,050,3MHz 
0,6% 
10m broad 
28,029,7MHz 
5,9% 
10m narrow 
28,028,8MHz 
2,81% 
15m 
21,021,45MHz 
2,1% 
20m 
14,014,35MHz 
2,5% 
For a 3El.Yagi the following parameters are interesting: 1. Gain: High gain means narrow bandwidth, bad F/Bratio and low impedance 2. F/B: High F/B means lower gain 3. Bandwidth/SWR: Great bandwidth means low gain and high impedance 4. Impedance:  High impedance means great bandwidth, but low gain (50 Ohm)  Low impedance means narrow bandwidth, but high gain (12,5 Ohm)  Medium Impedance means medium bandwidth and medium gain (28 Ohm) 

50 Ohm 
28 Ohm 
12,5 Ohm 

SWR
<1,5 6,7% 
SWR
<1,5 2,9% 
SWR
<1,5 1% 

Gain
5,0 dBd, V/R 20 dB 
Gain
5,6 dBd, V/R 24 dB 
Gain
6,25dB, V/R 26dB 

Pos. 
Length 
Diff. 
Pos. 
Length 
Diff. 
Pos. 
Length 
Diff. 

Ref 
0 mm 
1041 mm 
+4,8% 
0 mm 
1026 mm 
+4,6% 
0 mm 
1022 mm 
+4,5% 
Rad 
350 mm 

 
275 mm 
981 mm 
 
220 mm 
978 mm 
 
Dir 
600 mm 
890 mm 
10,4% 
600 mm 
900 mm 
8,25% 
600 mm 
923 mm 
5,6% 
SWR 50OhmType 
SWR 28OhmType 
SWR 12,5OhmType 
As you see ist the best impedance for the bandwidth of the most bands 2530 Ohm and gives you a good balance of gain and F/B. This is the reason for the 28Ohmconstructions. But what is with long Yagis? To understand that we look at the pictures below. A very good indicator for a Yagi structure is the element current profile. 
For the 2mYagis above and two further Yagigroups with 0,2 and 0,41lambdaboom I have calculated the data, here you can download the EZNECFiles for your own modifications and comparsisons: 
Element currents in a 5El.28Ohm2mYagi with 2,00mBoom
The highest current is in the radiator, from the center the currents in the wave structure of the yagi are falling to the end slightly. If you have elements with lower currents in the structure, there is a failure in the contruction! This is the case for many older designs and the reason for bad patterns. Now we try to change the design to an impedance of 50 Ohm. Therefore we need an additional "matchelement" very close to the radiator. This element is not working as a classic director, it is an "opensleeveelement", which has now the highest current in the yagi system. We have replaced the one radiator (2) by two new elements ( 2 and 3). This system is very critical for the impedance trend and the pattern of the yagi. Why do that? My conclusion is the 28Ohmprinciple. All highgainlong yagis with 50Ohmimpedance have a significant lower bandwidth with slighly less or equal gain in comparison with the 28OhmYagis. 
Element currents in a comparable (good designed!) 6El.50Ohm2mYagi with 2,00mBoom
A lot of 50OhmYagis have a bad element current profile!
One of the best yagi designs for 2m I know is the 12El.28OhmYagi. Please look for the extrem clear pattern (no big backlobe and good sidelobes), gain 14,28dBd, bandwidth for SWR < 1,5 is 2 MHz! You will not find any comparable yagi with the same boomlength, gain, pattern and bandwidth. It is impossible to match the antenna with the described matchelement for a 50Ohmdirect feed. This is the reason why a lot of contest groups, EMEamateurs and severe DXers use homemade DK7ZByagis. 
Horizontal pattern of the 12Element28OhmYagi at 144,3 MHz You can earn a box with 20 bottles of good German beer if you reach that aim to construct any comparable 50OhmYagi with 8mboom, 14,28dBd gain, 2MHz bandwidth and such a clean pattern! 
Here are some arguments and questions you can hear about Yagis and my answers: 1.
Medium impedance Yagis (28 Ohm) have losses We
had these arguments here in DL years ago, when I introduced my
28OhmYagis. People said, an antenna has to have 50 Ohm impedance (Why?
Because the cable has 50 Ohm?). It took 5 years until the amateurs
believed that it must not. In
the last ten years more and more “homebrewers” built thousands of
that Yagis and in DL, SP, OM and OK the most contest crews with homemade
antennas are running DK7ZB28OhmYagis. And believe me, there are a lot
of experienced hams who know what they do. When
you optimize a Yagi you must set the parameters for the optimizing
conditions: Gain, bandwidth, pattern and impedance. I normally do not
start with the impedance! A good compromize between the first three
arguments does not lead to 50Ohmimpedances automatically, in much
cases an impedance around 30 Ohm is better. Why
no impedance match? Why should a short piece of two paralled 75Ohmcoax
cables cause more losses than a normal piece of coax as used in a
halfwavebalun? When you construct a stacking harness for a Hframe
with four 50OhmYagis you use quarterwave transformation lengths to
points of 25Ohmimpedance. Do you believe in any mystic losses in that
case? I do not. 2.
OWAYagis are a better choice If
you prefer a wide bandwidth and lower gain, why not? But in most cases
you do not need that. If you have a lot of
metal around the antenna your OWAYagi shows only a little
influence to the SWR indeed. Great! But what you do not see is the
distortion of your pattern and the reduced gain. Better is a clean
surrounding of your antenna….. and then you can use a design with
higher gain and better performance. Real
OWAYagis have a lot of elements on a smaller boom and can have 50 Ohm,
but must not. 3.
50Ohmdirect feed is better than a lower impedance Do
not believe that 50Ohmfeed in a Longyagi means greater bandwidth! If
you compare the magnitudes and phases of the currents in the radiator
and the D 1 in a 50Ohmdesign you will see the cause for many problems:
The close spaced first director is no real director, it has a much
higher current than the radiator itself and that coupled system with
“opensleeveprinciples” has severe influence to the pattern and the
impedance across a greater part of the band (and losses, if you use a
FlexaYagi with thin steel rods). There are some new developments, which claim "50Ohmdirectfeed", e.g. the LFAYagis by G0KSC. But these Yagis are lowimpedanceYagis, where the loop is the match from 12,5 to 50 Ohm. This has some advantage, because the impedance matching acts similar as with a horizontal folded dipole with a greater distance between the two parts. An other way for a 50Ohmfeed is a OWLYagi with 12,5 Ohm impedance and a folded dipole, which gives an impedance ratio of 1:4 and 50 Ohm. So, what is "lowimpedance"? Anay match device can transform to an impedance of 50 Ohm. This can be the quartewavecoaxcable solution, a folded dipole or a LFAloop. 