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Stacked Log-Periodic - 5GHz

While playing with my milling machine and little microwave PCB Yagi antennas, I wondered about increasing the bandwidth and still getting directional gain.  A Log-Periodic antenna looks almost exactly, but not quite unlike a Yagi...

Practice is the best of all instructors
-- Publius Syrus

On a Log-Periodic, all the elements are driven, but each dipole is reversed by 180 degrees.  To make it on a single sided PCB, will require some links to wire up the dipoles.  I added a BNC connector and thin equilength coax to the feed points of the antennas.

Stacked Log-Periodic 5GHz

To reduce the amount of copper that needs to be milled out, I cut the board close to the radiators.  The bar at the back is for mounting and also serves as a reflective ground plane.  A log-periodic antenna is surprisingly compact and a little 5 dipole antenna will have a gain of about 3 dBi.  

By carefully stacking two of them 0.75 Lambda1 centre to centre (54 mm), one should get another 2 to 3 dB of gain for a total forward gain of 5 to 6 dBi.

The important thing in radios is not the signal strength, but rather the Signal to Noise Ratio (SNR).  A directional antenna reduces multipath reflections and noise from the surroundings and improves the SNR, so that a radio will perform much better with a directional antenna, compared to a simple omni-directional dipole.

Antenna Calculator
Here is a decent log-periodic antenna designer:

Lowest frequency f1 = 4200 MHz
Highest frequency f = 5200 MHz
Diameter of the shortest element ⌀ = 3 mm 
Characteristic input impedance Zc_in = 50 Ω 
Taper τ = 0.901
Optimal relative spacing σo = 0.168 
Chosen relative spacing σ = 0.050

Number of elements ⌊N⌉ = 5 

Dipole element lengths:
dipole l1 = 0.036 m 
dipole l2 = 0.032 m 
dipole l3 = 0.029 m 
dipole l4 = 0.026 m 
dipole l5 = 0.024 m

Sum of all dipole lengths lo = 0.146 m Distances between the element centres and their position along the boom:
d1,2 = 0.004 m, i.e. l2 @ 0.004 m 
d2,3 = 0.003 m, i.e. l3 @ 0.007 m 
d3,4 = 0.003 m, i.e. l4 @ 0.010 m 
d4,5 = 0.003 m, i.e. l5 @ 0.012 m

Boom length L = 0.012 m
Length of the terminating stub l_Zterm = 0.009 m 
Required characteristic impedance of the feeder connecting the elements Zc_feed = 4.8 Ω

Dielectric vs Antenna Size/Frequency
Bear in mind that the permittivity of FR4 (Fire Rating 4, glass and epoxy PCB) is about 4.3 and because the copper is in air on one side, the effective permittivity is less, about 3.3 - this conspires to make your antenna operate at about 20% lower frequency than the above (air dielectric) calculator indicates.  

The effective Dielectric Constant gives the Velocity factor:
  • VF = 1/sqrt(3.257) = 0.555
For this experiment, I will ignore all that, since I want to know whether this kind of antenna is practical and can make a tuned one another day.

Version 1: Single Sided PCB
An antenna this complex, really should be built on double sided board, for best performance, but I managed to get the prototype together with 22 SWG hookup wire and RG316.

Log-Periodic Wired Up

If you look closely, you can see the hookup wire links under the coax.

Performance Graphs
Considering how it was built, this is not too bad.  It needs a balun to clean up the VSWR ripples.

Log-Periodic - Return Loss

Log-Periodic - VSWR

Log-Periodic - Smith Chart

Design Issues
The graphs show that this a viable antenna and the match is a good 53 Ohm at the centre frequency of 4518 MHz.

When I designed this antenna, I spent much time trying to get the elements done right in the KiCAD footprint editor and Flatcam, so it can be cut out successfully with a 0.8 mm end mill.  However, I did not think enough about how to wire it up and the feed point is not designed for hooking up with unbalanced coax.

The unbalanced feeds cause large VSWR variations, which are very visible in the VSWR and Return Loss graphs.  An infinite balun made with ferrite beads will not work well at 5 GHz (Ferrites falter at about 2 GHz), so I need to change the feed points to match with unbalanced feed lines.  I also need to get some thin coax, which will be easier to hook up than RG316.  I think there is some thin WiFi antenna U.FL pigtails somewhere in a dark corner of my Junque Bochs - it will take a day of archeological digging to find it.

Version 2: Single Sided PCB with J Balun for a Coaxial Cable
This test unit is a single sided board design, which requires wire links and there is no way to make microstriplines, since there is no ground plane, so eventually, there are multiple reasons to go double sided.

I would also like to shift the centre frequency up by 200 MHz to about 5700 MHz, therefore the elements need to be 9% smaller, which makes it even more important to find some thin coaxial cable.

For the second version, I added a folded balun on the front dipole, so that it can connect to a coaxial cable directly.  The other dimensions all stayed the same, so that I can compare the results between the two versions.

Log-Periodic with a Half Folded Dipole Balun for a Coaxial Cable

The whole thing was machined with a 0.8 mm end mill and a cut depth of 0.15 mm into the FR4 board.  I take it slow and mill in an oil puddle, to keep the cutter sharp.  I got some burrs at 30 mm/min with 3 in 1 oil.  The process takes about 3 1/2 hours.  The board cut-out is done in multiple passes, each 0.2 mm deep, so it seemingly takes forever, but I don't want to break the mill bit by forcing it and FR4 with glass fibre is very hard on the mill bit.  

I need to cut the four retaining tabs with a knife and do some soldering before I can test it and see whether the VSWR graph now looks any better.

Log-Periodic With RG316 Feed

Log-Periodic with Shoelace Hook-up Wiring

Log-Periodic VSWR is Smooth, but High

Log-Periodic Smith Chart Impedance Mismatch

Log-Periodic Impedance Chart

The graphs above show that the cable match is remarkably much better at the antennas.  Next, I have to improve the power combiner/splitter match at the connector with a tapered microstrip line to improve the VSWR.

Version 3: Double Sided PCB with J Balun and Tapered Power Combiner
To make a good design, I need to use double sided board, install Microcoax SMD connectors (Molex Microcoax 73412-0110 and 73116-0004) with thin coaxial pig tails and a TNC connector (Amphenol RF jumper cable 095-850-221-048).  BNC connectors are nice for quick connect in a lab at UHF, but they are not stable enough for microwave use - the connection comes and goes by several dB.  TNC connectors provide more consistant and stable performance, since one can torque them.  SMA connectors are nice and small, but expensive - double the cost of TNC.

The third version of this antenna costs a few dollars more, due to the connectors and little cables which I have to buy ready made, to get good quality.  The SMD sockets are tiny, but one can solder them down by hand.  The microcoax cables however are well nigh impossible to do by hand; you have to buy them ready made, but they are not expensive (If you want to play with a scalpel under a microscope to trim a 1 mm diameter coax by hand, get a longer ready made cable and cut it up, Molex 73116-0037).  

The J Balun is simply a half folded Dipole feed, which drives the unbalanced co-axial cable with a good impedance match of almost exactly 50 Ohm.

The simplest way to combine/split the power at the connector for the two antennas, is with two tapered microstriplines 50 Ohm on one end; and 100 Ohm on the other end; and about 1/4 Lambda in length.  Where the two 100 Ohm ends come together at the connector, it becomes 50 Ohm again (resistors in parallel). You can design the taper with the Pasternack calculator
  • Taper length: 18 mm
  • Epsilon: 3.7 - FR4 glass-epoxy PCB
  • Height: 1.5 mm - Standard double sided PCB
  • 50 Ohm Width: 3 mm
  • 100 Ohm Width: 0.8 mm
This results in a bowtie stripline, 3 mm at the outer ends and 0.8 mm in the middle at the connector, with an overall length of 36 mm.  More details here

Now, I need to get into KiCAD again, to convert the design into a double sided board with little microcoax sockets at the drive points. This of course, turned out much easier said than done.  See the PCB Mill guide for the gory details of double sided boards...

Double Sided Board with a Milling Error

The double sided design milled a bit messily despite having 25% overlap and one antenna element was cut through in error.  There was a lot of cleanup to do with a carving knife.  I could have milled the under side with a bigger mill, which would have saved some time, but I just didn't think of it. 

Front Side - Microcoax and Tapers

I patched the cut dipole with a piece of solder braid and soldered tinned copper wire into the through holes.

Back Side

VSWR - Wide Bandwidth

It has a hump in the middle that I don't like, so I need to work on the matching some more.

Smith Chart
The power combiner taper and microcoax pads milled out nicely.  The two sides align perfectly well, so it should be easy to complete with microcoax connectors and 1.2 mm cable.


The middle of the band is about 100 Ohm, which explains the VSWR hump.  I should try a high frequency ferrite bead on the little coaxes.

Phase - A Log-Periodic is Complex

The Microcoax and TNC connectors make a big difference.  All the cable connections are stable and the measurements don't change if I touch or move something.

As for that cutting error, I think I will solder a big capacitor onto the controller board, since it could have been caused by a power glitch.

I would like to change to FR2 board and finally got some single sided board ordered from Radio Spares, but I need double sided FR2.  Some suppliers only ship locally, but Radio Spares is international:  

Version 3: Eight Elements on Double Sided FR4
To get the frequency where I want it, always requires a few iterations and I don't like the VSWR hump in the middle of the five element above.  To get a 20% lower frequency, means that I should design for 3.3 GHz or less, on the low end.   

Note that I found a missing through hole link on the 2nd version above.  It actually works much better than the above graphs show.  However, the bandwidth is still not wide enough to my liking.

If I run the Hamwaves design wizard again with 3.0 to 5.2 GHz frequency, I get an 8 element antenna:

  Lowest frequency f₁ = 3000 MHz
  Highest frequency f = 5200 MHz
  Diameter of the shortest element ⌀ = 1 mm
  Characteristic input impedance Zc_in = 50 Ω
  Taper τ = 0.880
  Optimal relative spacing σₒ = 0.163
  Chosen relative spacing σ = 0.060

  Number of elements ⌊N⌉ = 8
  Dipole element lengths:
    dipole ℓ₁ = 0.050 m
    dipole ℓ₂ = 0.044 m
    dipole ℓ₃ = 0.039 m
    dipole ℓ₄ = 0.034 m
    dipole ℓ₅ = 0.030 m
    dipole ℓ₆ = 0.026 m
    dipole ℓ₇ = 0.023 m
    dipole ℓ₈ = 0.020 m
  Sum of all dipole lengths ℓₒ = 0.267 m

  Distances between the element centres
  and their position along the boom:
    d₁,₂ = 0.006 m, i.e. ℓ₂ @ 0.006 m
    d₂,₃ = 0.005 m, i.e. ℓ₃ @ 0.011 m
    d₃,₄ = 0.005 m, i.e. ℓ₄ @ 0.016 m
    d₄,₅ = 0.004 m, i.e. ℓ₅ @ 0.020 m
    d₅,₆ = 0.004 m, i.e. ℓ₆ @ 0.024 m
    d₆,₇ = 0.003 m, i.e. ℓ₇ @ 0.027 m
    d₇,₈ = 0.003 m, i.e. ℓ₈ @ 0.030 m
  Boom length L = 0.030 m

  Length of the terminating stub ℓ_Zterm = 0.012 m
  Required characteristic impedance of the feeder
  connecting the elements Zc_feed = 126.1 Ω

  Position two antennas 54 mm apart centre to centre for improved gain.

A drawback of working with FR4 is that the glass blunts the mill bits very quickly.  I can only mill one little board with a tungsten-carbide bit.  However, if I redo it on a FR2 paper substrate, then the centre frequency will change again and I also cannot find double sided FR2 anywhere (maybe I can glue two back to back).

The measured results of this antenna are simply awful - the VSWR is around 5.  The impedance is more in line with a 75 Ohm cable.

I think I have a better chance to improve the matching of the smaller 5 element antenna, than to fix this 8 element design.  This one is just too complicated to get right and the elements are too close together to make them wider.

Version 4: Two Pieces of FR2, Back to Back
I eventually received a stack of FR2 boards from Radio Spares.  The phenolic paper boards cut much easier than glass fibre FR4.

Dual 5 Element Logperiodic on FR2

These are single sided boards, so maybe I'll glue them back to back, to make a 3.2 mm thick sandwich.  Since the permittivity of phenolic paper FR2 is a little lower than epoxy glass FR4, the operating frequency will be a little higher, but I have no idea what it will be, until I completed it.  

Target Frequency Band: 4.5 to 5.0 GHz

Design target for single sided FR2 PCB: +20% = 5.4 to 6.0 GHz

Widened design BW for parasitics: 5.0 to 6.5 GHz

LPDA — — v20180914

  LPDA design 2020-07-16 14:11


  Lowest frequency f₁ = 5000 MHz

  Highest frequency f = 6500 MHz

  Diameter of the shortest element ⌀ = 1 mm

  Characteristic input impedance Zc_in = 50 Ω

  Taper τ = 0.880

  Optimal relative spacing σ = 0.163

  Chosen relative spacing σ = 0.060


  Number of elements N = 5

  Dipole element lengths:

    dipole ℓ₁ = 0.030 m

    dipole ℓ₂ = 0.026 m

    dipole ℓ₃ = 0.023 m

    dipole ℓ₄ = 0.020 m

    dipole ℓ₅ = 0.018 m

  Sum of all dipole lengths ℓ = 0.118 m

  Distances between the element centres

  and their position along the boom:

    d₁,₂ = 0.004 m, i.e. ℓ₂ @ 0.004 m

    d₂,₃ = 0.003 m, i.e. ℓ₃ @ 0.007 m

    d₃,₄ = 0.003 m, i.e. ℓ₄ @ 0.010 m

    d₄,₅ = 0.002 m, i.e. ℓ₅ @ 0.012 m

  Boom length L = 0.012 m

  Length of the terminating stub ℓ_Zterm = 0.007 m

  Required characteristic impedance of the feeder

  connecting the elements Zc_feed = 144.7 Ω

Now build it on FR2 and see whether it is anywhere near the desired band…

Double Shoelace Hookup

Logperiodic Dipole Array With Half Folded Match

This little array was designed for 5 to 6.5 GHz and ended up working from about 4 to 6 GHz.  The half folded dipole feed makes a kind of balun with a 75 Ohm match, so it should be used with a 75 Ohm cable.  The trouble is that at 5 GHz, one cannot use Ferrites to make a balun - they only work up to maybe 2 or 3 GHz.  I tried some beads and they had no effect.

The VSWR and Impedance are a Mess

It seems to be a little inductive

From what I have seen so far, the VSWR of a log periodic antenna is quite awful and it is hard to improve.  If a VSWR of 3 is OK for your transmitter, then fine.  If not, then it may be useful to solder a tiny capacitor (1 - 5 pF) onto the antenna feed point, to try and improve the matching with a 50 Ohm cable.  I have to go and dig for one and see what happens.

For a wide band receive antenna, it is good, since the VSWR doesn't matter much on receive.

This Log Periodic experiment turned into a mission.  I now have a whole pile of dud little antenna boards and blunt milling bits.  Pretty much the only thing that I can confidently say, is that one should not mill FR4 fibreglass boards - get FR2 Phenolic Paper boards for milling.  

At least it kept me busy during the Covid19 intermission...


This is not a cheap hobby, but this article shows how one can move stepwise from an idea, to a real product, without going bankrupt along the way.

La Voila!



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