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Scroll down to find examples of Power Splitters and other Splitter Z Calculator For using this calculator Javascript must be activated In a 50 ohms system any 1/4 λ 2 x splitter line must be of Z = 35.4 ohms; any 4 x splitter of Z = 25.0 ohms For Vacuum use Er = 1.000 For Air use Er = 1.001 For PE use Er = 2.25 For PE Foam use Er = 1.5x For PTFE use Er = 2.01..2.10 For PTFE Foam use Er = 1.4x Electr. Length in wl: 0.25 = λ/4 etc. Vary Line Length until you find 0.25 or multiples ... Note that actual length in wl might be up to approx. 7 percent less when using a plastic dielectricum at VHF/UHF Read Comments & hints below! Image: © Dr. Tanja Kurzenknabe 
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How to link from your website to the "app" The "app" as a link will appear where you have placed it on your site. Clicking it will make your website contact my webserver and open the "app" just similar to doing that from this site. But please keep in mind that Javascript must be activated on the client side for this. Every client i.e. internet user is self responsible for appropriate browser security settings and up to date anti virus checks etc. on his/her PC. No guarantee is given, whatsoever, use these lines at your own risk And here is the set of formulas for computing velocity factor and round and square shields coaxial lines Z Wherein Er is the dielectrical property or Permittivity of the dielectricums material from which we calculate the actual velocity factor. Any Er > 1 will shorten the coaxial line since it decreases the waves velocity in relation to speed of light; Log10 means to base of 10; D is the shields inner Ø or dimension; d is round cores outer Ø. Comments & Hints • Square shield factor: We find hints in literature that the factor of 1.08 expanding the round coax Z formula to square shield is not on spot or limited to Z > 20 ohms and such (see http://oz2oe.dk/radio/combiner/combiner.html). If in doubt I advise a cross check with the professionals tool "AppCad", see below. • Other shapes: Need to determine any other HF line geometrie's Z like stripline etc.? Go to http://www.hp.woodshot.com/ ... and download Agilent Technologies "AppCad" freeware • Line length correction due to Connector Inductances: What may be much more inflicting the Return Loss or actual resonace dips frequency of a real splitter build are the introduced additional inductances of the sum of connector pins.
Find approximated corrected equivalent QW line length in Splitter Calculator below. Of coarse the splitter line impedance i.e. ratio of diameter core to shield and picked dimensions of the pair has an impact here; which is not enclosed in the equivalent QW line length calculation.
Power Splitters in Detail Splitter Calculator 3, 4 and 6 way splitters with λ/4 lines 2, 4, 6 or 8 way splitters with 2 x λ/4 lines Use splitters on 3rd harmonic bands Testing and plotting splitters 2 way splitters for 50, 60 and 75 ohms feed lines How to determine dimensions for a transforming Quarter Wave Line splitter in 3 steps ... (1.) Find resulting impedance on the left (antenna) side. When feeding two lines of Z_x1 and Z_x2 into ports x1 and x2 the resulting impedance may be calculated as shown below For a pair of identical impedance it is simply half the single impedance of course. port x1 port x2 Za 50 ohms 50 ohms 25.0 ohms 60 ohms 60 ohms 30.0 ohms 75 ohms 75 ohms 37.5 ohms(2.) How to determine Z for a Quarter Wave line transforming between Za and Zb Using this formula for calculating Z for a transforming Quarter Wave line we find Za Zb Z coax line 25.0 ohms 50 ohms 35.36 ohms 30.0 ohms 50 ohms 38.73 ohms 37.5 ohms 50 ohms 43.30 ohms Za Zb Z coax line 25.0 ohms 60 ohms 38.73 ohms 30.0 ohms 60 ohms 42.43 ohms 37.5 ohms 60 ohms 47.43 ohms Za Zb Z coax line 25.0 ohms 75 ohms 43.30 ohms 30.0 ohms 75 ohms 47.43 ohms 37.5 ohms 75 ohms 53.03 ohms (3.) When having determined the needed Z of the splitter line proceed finding matching diameter dimensions in the calculator on top of page ... or calculate whatever Z is needed using the form below Power Splitter Line Z Calculator: How to use this calculator: The sketch below shows a transformation line with ports (a) and (b). It may represent the power splitter. Port (a) is the connection end for 2, 3, 4 ,6 antennas and (b) is the point to connect with 50, 60 or 75 ohms feedline. Go to middle field and chose a "Type of Splitter". Next enter frequency and single antennas Z at point (a)  usually 50 ohms  and feedline Z at point (b)  usually 50 ohms too. Finally chose a core diameter for the transformation line or power splitter  the calculator will compute square and round shield (outer tube) dimensions plus informal Z as sum of connected impedances of antennas (Imp .Za) and Z of the transformation line i.e. splitter and finally an equivalent length for the splitters core. There are two factors that influence the actual length of the transformation line: (1) the basic inductivity of connector pins, (2) a Shield to Core (D/d) equivalent length which weights the length of connector pins from outer to inner tube. Here you may opt for a factor or "Ignore all"  which leads to computation of the 'pure' 1/4 λ length This correction is but an estimation, I have enclosed chosing from 0 to 4 nH per pin. 1.0 nH as default seems reasonable for Nbushings but that depends on connectors used of coarse.
See plot of a build with inductance at ports correction applied, here Back up page Back to Splitters Menu How good a Return Loss can my Power Splitter show in an optimistic case? Everbody wants to build a sound splitter. Down the page I show examples reaching down to Return Losses of 38 to 47 dB. Which is equivalent to a VSWR of < 1.02 ... 1.01. What limits the quality of our splitter? First we take a look at the omnipresent basic formula Z = R + j X (1) In correct terminology what I use as Z in text and online calculators is just R alone. In a simplified view (2) The ratio of the tramsformation lines inner to outer diameters makes the R of that line (3) The overall lenght with the sum of connecting bushings pins inductivities added makes the jX Looking at the real part of Z, the R alone we find a limitation to the outcome of the splitters Return Loss at perfect imaginary part of Z, the jX = 0! as follows Z = R at jX = 0 Return Loss 48.0 ohms 33.8 dB 49.0 ohms 39.9 dB 49.5 ohms 45,5 dB 49.8 ohms 54.0 dB 50.0 ohms infinte 50.2 ohms 54.0 dB 50.5 ohms 46.1 dB 51.0 ohms 40.1 dB 52.0 ohms 34.2 dBAn example If now your inner to outer tube ratio gives a Z = 47.2 ohms your splitter can not get any better than producing a Return Loss of 30.8 dB or a VSWR of 1.06. And that is with ideal fitting of connection bushings pins inductivities to lenght of the splitter tube. The other component, the jX is more complex Besides this little play of words here are some parameters at work. For instance the often relatively unknown properties of the to be used connection bushings. And the overall Q of the to be build splitter. Common Errors and a Plastic Spacer Correction (1) If you think it is wise to leave the core tube of the splitter a little longer, you will not be rewarded with best Return Loss. Any excess length beyond the bushing pins will only mix with the jX of that 1/4 respectively 2 x 1/4 λ resonator the splitter actually is. To make this clear: length means distance from pin to pin of the connection bushings. (2) using plastic spacers is a good ides to increase stability and center the core tube However, any plastic put over the core conductor tributes a velocity factor onto that stretch of conductor. Just like in a common coax cable. At an estimated v ~ 0.6 will change the effective electrical length of a 10 mm stretch of core covered in plastic to effectively 16.7 mm. Using the common correction factors for half wave Yagi antenna elements of 5.85 mm (144 MHz), 1.02 mm (432 MHz) per 1 MHz leads to half that for a resonate 1/4 λ line as the splitter. As an example 2 pieces of 10 mm spacers with a vfactor of 0.6 will extend the covered 20 mm x (1 / 0.6) by 13.0 mm. With extends the cores electrical length by 20 + 13.3 = 33.3 mm. Which for a 144 MHz splitter means an decrease in frequency by 2 x (13.3 mm / 5.85 mm/MHz) = 4.55 MHz. Subtracting the excess length of 13 mm from the total length should compensate the effect caused by the 2 spacers. Effective true compensation depends on having a true vfactor or permittivity of the to be used plastic at the designated frequency at hand. Mind that plastics permittivity is frequency depending at VHF/UHF. An EXPERIMENTAL Calculator If this calculator works as it should, you fill in a length per 1/4 λ of Power Splitter core taken from the above 'Power Splitter Line Z Calculator' with best adaption to port bushings inductivities and add your spacers for a final correction of the core tubes length. Take care, this is fully experimental but in theory should help to produce better results than without and correction if you use plastic spacers. Any feedback on what this calculator delivers is apprechiated! Corrected algebraic sign of length influence 20160302 3, 4 and 6 way splitters with λ/4 lines The image is showing a 3 or 4 way splitter. Just imagine 3, 4 or 6 connectors mounted on left side. How to calculate any cumulation of multiple Z's? Here is the generalised formula for not necessarily even single Z's. It is Kirchhoff's law applied to impedances. Index n is equivalent to number of ports per side. For a 4 way splitter n is 4. For any number n of identical impedance it is simply the nth part of the single impedance of course. Single Z's Calc. Za 2 x 50 ohms 50/2 25.0 ohms 4 x 50 ohms 50/4 12.5 ohms 3 x 75 ohms 75/3 25.0 ohms ...From this we can derive that a 2 x 50 ohms to 50 ohms splitter may be used as 3 x 75 ohms to 50 ohms splitter too. 2, 4, 6 or 8 way splitters with 2 x λ/4 lines The image is showing a 4 way splitter. Just imagine 1, 2, 3 or 4 connectors mounted either side. These commonly are called λ/2 splitters. In my oppinon this name giving falsely suggests that we would have a different transformation mechanism here. A power splitter with 2 x λ/4 lines is a precise mirror image either side of what the half numbers of antenna ports λ/4 splitter is. Just that the Z at feed point (x3) must be twice the number since boths sides meeting results in half impedance. Use same calculator as above. Match to Zb = 100 ohms at port x3 instead when feeding with 50 ohms coax ... any feed line Z must be multiplied by two. Any splitters made from λ/4 lines can be used on 3rd harmonic bands Every splitter using λ/4 or 2 x λ/4 lines may be used on tripple frequency too. The transformating lines length is 3 x λ/4 then, which is equivalent to a single λ/4 line followed by a λ/2 line, which does not change any properties. A 144 MHz splitter will work fine on 432 MHz. Any 432 MHz splitter will give fine results on 1296 MHz. I have used a quality 432 MHz λ/4 4 way splitter made by UKWBerichte with success for feeding four Tonna 1296 MHz Yagis in many contests. Back up page Back to Splitters Menu Testing and plotting splitters • An adjustable 432 MHz 4way λ/2 splitter made and tested by John, ZS6JON While the ideal inner diameter of the square outer tube would be 27.08 mm for the given cores diameter here a tube with 28.6 mm is in use. Further with the tuning screws the frequency can be adjusted in a way that a slightly longer tube can be used when the impedance of the splitter line is slightly higher than it should be. For a 12.70 mm core the ideal outer square tubes inner diameter is 27.08 mm. With the available materials of 12.7 mm core and 28.6 mm square tubes diameter the calculated Z is 53.2 ohms. Instead of the 50.0 ohms, that each side of a 1/2 λ 4 way splitter should have. With those 53.2 ohms the splitter coax on its own would not allow a Return Loss better than 32 dB. The length of the core tube without tuning screws and right d/D ratio would be ~ 347 mm when ignoring all corrections for bushing pin inductivities or d/D ratio correction. This tunable splitters core measures 362 mm, that is an excess length o f at least 7.5 mm per 1/4 λ transformation way each side. It is that bit longer because the capacitances introduced shorten it electrically. The result is a 70 cm splitter with an unseen before fabulous input reflection of well beyond 50 dB on spot on 432.1 MHz for EME operation without having to see a mechanical workshop to do diameters and lenghts of parts to the 10th of a millimeter. S11 (input reflection in dB) plotted with an Anritsu MS2000 series VNA and calibrated measurement lines: Return Loss (432.1 MHz) = 54.9 dB Same as Smith Chart: Z(432.1 MHz) = 50.3 + 0.3 ohms And a drawing of that splitter, bushings are 'screwin' type, tuning screws are 5M Attenzione! When building tunable splitters please make sure that (1) the minimum distance between screws and coax core is sufficient for the used output power (2) seal the screw from environmental influences like rain and air moisture Aluminuim and stainless steel in some pairings are not very 'friendly' to one another as far as electrochemical corrosion is concerned. Putting on clear coat paint on the outside seems a good idea. • An adjustable 144 MHz 4way λ/2 splitter made and tested by Stef, F4EZJ Stef built this splitter with a 7/16 DIN bushing at the feed point and 4 N bushings at the antenna ends. The geometry is as follows: Outer square tube 30 x 30 mm on the outside, 26 x 26 mm on the inside, length is 1047 mm Inner core is a copper tube Ø 12 x 1 mm, length is 1019 mm Tuning screws are M 8 and located at 140mm either side of the 7/16 bushing. Later he added more screws. Which now help to trim down to close to 60 dB and in any case better 35 dB with whatever ~ 50 ohm loads / antennas connected. External link to Stef's 'Onedrive' online album with many detailed photos Stef uses the splitter for terrestrial work as contests and aimed for 144.30 MHz and here we are ... Note: Future builders might use M8 screws or maybe 2 screws in a row as for this build the space left between screws and core tube is not much. More screws help to wider tuning abilities. See the photo above. • A 144 MHz 4way λ/2 splitter made and tested by Peter, DJ4TC Calculated with the above online calculator adjusted 'nH/Port' = 1nH and 'D/d >eqv.lgth' = 0.5 computing a length of 509.5 mm. Making the core a 1019 mm (2 x 509.5mm) and the outer square profile a 1060 mm in length he plots a Return Loss = 47 dB and Z = 50.2 ohms at 144.1 MHz. For this build he used a 25 x 25 mm outer dim., 1.5 mm wall thickness i.e. 22 x 22 mm inner size square tube and a Ø 10 mm rod as core and quality Nbushings throughout • A 432 MHz 4way λ/4 splitter made and tested by John, ZS6JON Note the 4 similar termination loads. It is essential to use good loads at each port to get true results ... Freq. 432.14 MHz, RL = 44 dB, Z = 50.1  0.6 ohms, what more can we expect? Very good for EME • A 144 MHz 4way λ/4 splitter made and tested by John, ZS6JON Note the 4 similar termination loads. It is essential to use good loads at each port to get true results ... Freq. 144.161 MHz, RL = 38.1 ohms, Z = 51.0  0.8 ohms, very good for EME For the above λ 1/4 splitters John used square aluminium tubes 25 x 25 mm with 1.6 mm wall thickness. That leaves an inner height of 25  (2 x 1.6) = 21.8 mm. Which suits 15 mm CU tubes as core. This diameters result in 27 ohms for the transformation line. As the 25 x 25 mm tubes wall thickness is not very consistent it worked out better then that as we can see from the plots he took. He uses my online calculator for determinating length and Z. • A 144 MHz 4way λ/2 splitter made and tested by John, ZS6JON Freq. 144.161 MHz, RL = 37.5 ohms Z = 51.1  0.7 ohms, very good for EME For this λ 1/2 splitter John used square aluminium tubes 25 x 25 mm with 1.6 mm wall thickness. That leaves in inner height of 25  (2 x 1.6) = 21.8 mm. Which suits 10 mm CU tubes as core. As he could not supply himself with that he found 9.7 mm tubes from the airconditioning and refrigeration industry. This diameters result in 53 ohms for the transformation line. As the 25 x 25 mm tubes wall thickness is not very consistent it worked out better then that as we can see from the plots he took. He uses my online calculator for determinating length and Z. Back up page Back to Splitters Menu 73, Hartmut, DG7YBN 