Theory of the Quadlongs  4/6mQuadlongs  2mQuadlong  2m4xQuadlong  2m4xOblong  The Hentenna (2 m, 4m, 6 m) 
Theory of the DK7ZBQuadlongAntennas
The main advantage of a 2Element Quad is the great 3dBazimuthangle. This advantage disappears, if you mount director elements in front of the antenna. The additional gain comes mainly from the reduced azimuthangle and the antenna parameters become similar to a Yagi antenna. Therefore it makes absolutely no sense to build Quads for one band with more than two elements. Friends of Quads do not like to hear that, but in reality a Yagi with the same number of elements as a multi element Quad has the same gain and bandwidth and you waste material and windload with such constructions! Of cause a 3ElementQuad for shortwave is a good choice, because the spreaders can carry the wires for more than one band and you get an interesting multibandDXantenna for homebrewers. 
But how
can we get the advantages of the 2ElementQuad and can increase the gain? Let
us take a look to the classic Quad (pic. 1). If you prefer a good
F/B and greater bandwidth, the gain is 4,7 dBd and F/B is 2530 dB with a high
impedance of 110 Ω.
Increasing the gain to 5,7 dBd means very low bandwidth, a bad F/B of 68 dB and
a lower impedance of 40 Ω .
With a good compromize we do not reach more than 5 dBd gain. 
The first step is a simple modification. The original single loop with a circumference of 1 λ and a side length of 0,25 λ has only a gain of 1,3 dBd and an impedance of 130 Ω. The Quad element is a stacked system, but the distance between the two parts is to low and the current maxima are to close together. We can increase the gain by changing the Quad to an “Oblong”. The stacking distance will be greater, but the radiating horizontal parts of the loop become smaller. The best compromize between the two influences and the bandwidth is a relation of 0,15 : 0,4 λ (pic. 2). The gain of this loop is now 2,6 dBd and the radiation resistance drops down to 35 Ω. This is the reason why the elements should not be wires with too much loss. See table 1.
Table
1: Data of 2mOblongs with 6mmElements, lengths in lambda

In a
second step we replace the reflector loop by two streched tubing elements. Gain
and pattern are better than with a loop and the mechanical problems for
building the antenna are much easier to solve. So we come to the
“DK7ZB Quadlong” (pic. 3). The gain is 1 dB above the
classical Quad and with 6,45 dBd as high as with a 3ElementQuad, but all other
data are better (see table 1) and the construction is much easier.
The impedance is now 28 +/ j 0 Ω and a simple feeding with the “DK7ZBImpedanceChoke” is possible. We need
only 2x 75Ωcoax
in parallel with an electrical length of λ/4
(pic 4). 
It is possible to add a second loop and a third reflector element. So we come to the DoubleQuadlong (Pic. 5). The gain is 7,5 dBd and the impedance is 28 Ω, too. A very good antenna is the 4xQuadlong in Pic. 6 with 5 reflectors. The gain increased to 9,3 dBd the azimuthangle is still 72° and an impedance of 50 Ω is easy to feed. These constructions are to high for the shortwave bands or 50 MHz, but for 2m you get excellent antennas. The distance of the reflector element in all cases is 0,15  0,16 λ. A comparison of all antenna parameters is listed in the table below. A description of the two antennas is on the page with the 2mQuadlongs 
Type  Gain  F/B  3dBangle Az.  3dBangle El.  Impedance 
Single Quad  1,3 dBd  0 dB  84,2°  131,8°  130 Ω 
Single Oblong  2,6 dBd  0 dB  87,8°  80,1°  35 Ω 
2El.Quad  5,3 dBd  12 dB  70,6°  88,9°  50 Ω 
3El.Quad  6,3 dBd  12 dB  65,2°  79°  50 Ω 
DK7ZBQuadlong  6,4 dBd  21 dB  71,8°  70,0°  28 Ω 
Stacked DK7ZBQuadlong  9,5 dBd  23 dB  72,4°  30,0°  2x25 Ω 
DK7ZBDoubleQuadlong  7,5 dBd  19 dB  71,6°  54,8°  28 Ω 
DK7ZB4xQuadlong  9,3 dBd  17 dB  71,8°  36,7°  50 Ω 