You can scale any antenna made for one particular frequency or band to work on a completely different frequency or band by using very simple calculations. The double quad article posted above was for an antenna designed for 2.4Ghz (the 12.5cm band). The dimensions given are not spot on for 2400Ghz, they for a frequency a bit higher in the band as the calculated length of the sides of each quad loop should be longer than he used for exactly 2400Ghz. Not only that but the designer seems to have been unaware that actual antenna dimensions are always shorter than a calculated antenna in "freespace", usually by a factor of about 0.95x.
You did not mention what frequency you want to convert the design to, but lets assume its for the 70cm amateur band 430-438mhz. The length of the sides of a quad loop, irrespective of the frequency, are always 1/4 wave long at the frequency of choice multiplied by 0.95. So to find the length of the sides of a quad loop made for the middle of the 70cm band, for example, simply divide 300 by the frequency in Mhz (435Mhz), then divide that figure by 4 and multiply it by 0.95. This gives a figure of 16.37cm (163.7mm)...For convenience we can round this up 164mm. So that is the length of each side of a quad loop made for that design frequency. The article states that the reflector should extend at least 1/4 wave larger on each side than the Bi-Quad driven element...So for 435mhz that would make it 164mm x2 (328mm) taller and wider and than the driven element.
The spacing between the driven element and the reflector is about 1/8 wave...That's 164mm divided by 2 (about 82mm for 435mhz).
The bandwidth that the driven element (the Bi-Quad in this case) will cover (where it has a low SWR either side of the design frequency) is determined by the ratio of the diameter of the wire or tube used to actually construct the driven element to the frequency the driven element loop is designed for. The golden rule for conductors used to make driven elements in antennas is the bigger the diameter the conductor has, the greater the bandwidth it will cover.
Obviously, wire has a very small diameter to frequency ratio for low frequencies like HF but as the frequency goes up the ratio changes until at UHF frequencies or higher, a driven element made of wire can be appreciably large in diameter in relation to the frequency and therefore it can still have a relatively large bandwidth. In the UK, the 70cm band covers at least 10Mhz...In order to cover a band that wide, wire is normally replaced with small diameter Copper tube. The 23cm band is a lot wider than the 70cm band (1240-1300Mhz...60Mhz wide!) and in order to maximise the bandwidth of 23cm antennas Copper tubing of around 15mm OD is often used. The advantage of using the latter is that broadband Quad driven elements for 23cm can be easily constructed with off the shelf Copper plumbing parts, like 90 degree elbows etc. Alf, G7VGG.