Example designs

Designer files (<name>.design.json, format in The designer). The *_867 designs are the sources of the app's 867 MHz examples: the desktop app installs them, read-only, in the workspace's models folder, and Open as new design… on one of those examples makes an editable copy under Start › Your designs. In a checkout, copy one under a new file name into python/models/ to edit it (the *_867 names are reserved for the examples). They also run from the command line like any model:

fairbeam run examples/designs/wideband_dipole_867.design.json --engine gpu --out /tmp/wideband

python/tests/test_example_designs.py checks that every design here builds and passes the design checks.

Slotted wideband planar dipole, 867 MHz (wideband_dipole_867.design.json)

A telemetry antenna for a UAV with a composite (non-metal) fuselage, where there is no metal skin to act as the ground plane of a monopole. It is a balanced printed dipole that fits a blade radome, for the 863–870 MHz SRD / LoRa band. It is vertically polarised and omnidirectional in azimuth. The arms are wide ("fat") for bandwidth and slotted ("kesikli") for height.

Model. A vertical FR-4 strip (εr 4.3, tan δ 0.02 at f0, 1.6 mm, in the xz plane; x is the flight axis, z points up) carries two copper arms (PEC sheets) on its y = 0 face, above and below a center feed gap g. A 50 Ω lumped port bridges the gap. Each arm widens from a feed tab wf wide at the gap to the full width w_arm over the flare height ht, and runs on to the tip, h_arm from the gap edge. Four pairs of transverse slots, l_s long and w_s wide, are cut in from both outer edges of each arm (the designer's part cuts, so they follow the parameters). The first pair is z_s from the gap edge, the next ones every p_s. The top arm is drawn and cut once and mirrored across z = 0 to make the bottom arm. There is no ground plane. The open boundaries are PML (8 cells), with a quarter wavelength at 0.7 GHz (107 mm) of air on every side. The mesh is automatic, 30 cells per wavelength at 1.05 GHz (about 270 000 cells), with 2 cells across each 2 mm slot and 4 through the board.

Facing slots leave a solid spine w_arm − 2 l_s = 6 mm wide down the middle of each arm. A wide arm carries most of its current along its outer edges. The slots cut that path, so the current detours around every slot and crowds through the spine and the slot ends, which the surface-current map at f0 shows. The electrical length grows, so the resonance moves down for the same height. Because the slots come in facing pairs, their horizontal currents cancel, and the pattern stays vertically polarised.

Band 0.7–1.05 GHz, end criterion −60 dB, far field and surface current at f0, radiation efficiency at 21 frequencies across the band. The slot count is fixed at four pairs per arm, one cut per slot in the file. h_arm should stay above slot_top; below it the last cuts remove nothing, and the checks say so.

Tuning (GPU engine, about 7 s per run). The first guess (h_arm 60, wf 3, l_s 14) matched from 0.758 to 0.897 GHz, too low, and only to −16.5 dB. Shortening the arm moved the band up, by about 1.3 % per mm of h_arm. A wider feed tab lowers the inductance of the feed. At h_arm = 56, widening wf from 3 to 10 mm improved the best |S11| from −16.8 to −19.3 dB and the band from 18.2 to 19.9 %. At 58 mm, going from 10 to 18 mm improved them from −19.1 to −22.3 dB and from 19.2 to 20.6 % (band 0.797–0.976 GHz at l_s = 14). Longer slots (l_s 17) then lowered the resonance by 5 %, and 4 mm less of each arm brought it back, at 17.8 % bandwidth.

Results (defaults: PML 8, 30 cells per wavelength; GPU engine, 6.6 s solver time):

The design was first tuned with MUR boundaries at 20 cells per wavelength. That gave 2.21 dBi Dmax against 2.01 dBi from the pattern alone and 41.8 + j6.4 Ω: with only a quarter wavelength of air, MUR reflects enough to bias the power balance (the sleeve dipole below measured the same). PML at 30 cells per wavelength brings the two Dmax estimates within 0.02 dB and is the default now; the match barely moved.

Slots against no slots. The same arms without the slots (the cuts removed, the same wf, ht and w_arm) reach the same resonance at h_arm = 67 mm: X = 0 at 0.847 GHz and a band of 0.769–1.000 GHz. The slots take the tip-to-tip height from 136 mm to 110 mm, 19 % shorter at the same 40 mm width. They cost bandwidth: the unslotted dipole matches over 27 %, with −27 dB at 867 MHz. It also has 0.2 dB more directivity (2.43 / 2.19 dBi from the pattern) and twice the azimuth ripple (0.27 dB).

Against theory.

At 0.32 λ tip to tip, the dipole is shorter than a resonant λ/2 dipole. Its directivity lies between that of a short dipole (1.76 dBi) and that of a λ/2 dipole. The wide arms keep its resistance near 40 Ω, where a thin dipole this short would have about 25 Ω, and give it two to three times the bandwidth of a thin dipole.

Caveats.

• Balun. The port is balanced. A coax connected straight to the gap puts current on the outer conductor of the cable, which radiates, tilts the pattern and moves the match. In practice, run the coax along the center of the lower arm to the gap and add a sleeve choke (a λ/4 sleeve, about 86 mm in air at 867 MHz, or ferrite beads) where it leaves the arm, or print a balun (a tapered microstrip or a Marchand balun) on the back of the board. The model has none of these.
• Radome and FR-4 tolerance. The radome, the paint and the mount are not modeled. A thin glass-fiber shell lowers the frequency by a few per cent, and FR-4's εr varies from about 4.2 to 4.7 between suppliers and with frequency. Both mostly lower the band. The band reaches 11 % above 870 MHz and 6 % below 863 MHz, so a downward shift of up to about 10 % keeps 863–870 MHz inside it. If the fitted radome shifts the band by more, shorten h_arm: 1 mm moves the band by about 1.3 %.
• Mounting. The dipole needs its composite surroundings. Carbon-fiber parts, cables, the battery and metal hardware within about λ/4 (86 mm) change the match and the pattern. Route the feed coax away from the arms, perpendicular to them where possible.
• Losses. The copper is lossless (PEC). Real copper costs a few tenths of a per cent. The FR-4 loss is modeled. It costs about 1 %, because most of the field is in the air.

Printed meander dipole for non-metal airframes, 867 MHz (meander_dipole_867.design.json)

An airframe-mounted monopole needs a suitable ground plane. A composite or foam fuselage (glass fiber, foam, 3D-printed plastic) has no such skin, so a monopole on it has nothing to work against: the coax shield becomes the other half of the antenna and the match and the pattern depend on how the cable runs. A dipole carries both halves itself. This design is a vertical printed dipole for 863–870 MHz that fits a blade radome of about 110 × 35 mm.

Model. A 1.6 mm FR-4 board (εr 4.3, tan δ 0.02) stands in the xz plane: x is the flight axis (+x aft), z points up. Its outline is blade-like, 34 mm wide at the root and 22 mm at the tip, with the forward edge swept back by sweep. The copper is on one face (y = 0), drawn 35 µm thick and built as a sheet (the designer's thin-metal default). Each arm starts at the center gap as a straight strip l_feed long and ends in a meander of n turns (turn width a, pitch p: two rungs per turn) and a short straight end section l_end. The lower arm is the mirror image of the upper one (a mirror transform on each arm part), so the horizontal currents in the rungs of the two arms flow in opposite directions and cancel in the far field. A balanced 50 Ω lumped port, w wide, bridges the gap g at the center. There is no ground plane: the open boundaries are PML (8 cells), with a quarter wavelength at 0.75 GHz (100 mm) of air between the board and the PML on every side.

The arms are bricks per segment (rungs, the links between them, the feed strip and the tip), with translate copies that follow n, so every value stays editable and the optimizer can vary them. The board is two polygons that meet at z = 0. The joint puts a mesh line in the middle of the feed gap, so the port gets two cells instead of one.

Why straight arms with meandered tips. The current on a short dipole is largest at the feed and falls to zero at the tips. The part near the feed does most of the radiating and sets the radiation resistance. A meander there would carry opposing currents in its rungs, which radiate almost nothing. So the arms are straight where the current is high, and the meander sits at the tips, where it adds electrical length (it loads the arm like a coil) at a small cost in resistance. The first try used 3 turns and a 25 mm straight section (112 mm tall). It resonated at 767 MHz with only 29 Ω. Two turns and a 30 mm straight section give 40 Ω at 101 mm.

Derived: copper height H = 101 mm tip to tip (0.29 λ at 867 MHz), board 107 × 34 mm (H_board, W_board), trace length of one arm L_arm ≈ 114 mm. A straight printed λ/2 dipole would be about 140–150 mm tall.

Band 0.75–1.0 GHz, end criterion −50 dB, far field and surface current at f0, radiation efficiency at 21 frequencies across the band. The automatic mesh (20 cells per wavelength at 1 GHz) has 966 000 cells. The smallest cell is 0.26 mm: 6 cells across the 2 mm trace, 6 across the 2 mm gaps between the rungs and 2 across the feed gap. A run takes 18 500 timesteps, 10 s of solver time on the GPU engine.

Boundaries. With MUR the fields decayed too slowly (−37 dB after 60 000 timesteps) and the far field came out at 2.5 dBi, more than a dipole this short can have. The first-order MUR boundary reflects part of the wave that a small, low-gain antenna sends towards it at grazing angles. PML absorbs it: the run reaches −50 dB in 18 500 timesteps, and 1.97 dBi is between a short dipole (1.76 dBi) and a λ/2 dipole (2.15 dBi).

Tuning. GPU engine, 14 cells per wavelength and −40 dB while tuning, then the final run at the design's 20 cells per wavelength and −50 dB:

The mesh change from run 3 to run 4 moved the resonance by 0.3 MHz. Run 6 gives the tuning slope: −7.5 MHz per mm of l_end (each tip), about −0.9 % per mm. Run 5 shows that FR-4 matters little here, because most of the field is in the air: +0.2 in εr moves the band by −0.4 %.

Results (final run, defaults):

Margins in the −10 dB band: the band can move down by 5.0 % (the upper edge reaching 870 MHz) or up by 2.2 % (the lower edge reaching 863 MHz) before 863–870 MHz leaves it. A radome, which lowers the frequency, has the larger side.

Compared with the others.

The meander dipole gives up 0.2 dB of directivity against a full λ/2 dipole for a third less height. It needs no ground plane, and its pattern peaks on the horizon, where the ground station is for most of a flight.

Build notes and caveats.

• Balun. The port is balanced; the coax is not modeled. A coax soldered straight onto the arms carries current on its shield, which radiates, tilts the pattern and moves the match with the cable route. Use a balun or a common-mode choke at the feed: a λ/4 sleeve (bazooka) balun on the cable where it leaves the feed (about 80 mm), clip-on ferrite beads rated for UHF on the cable within 2–3 cm of the feed, or a printed balun on the board. Measure S11 with the choke fitted. Run the cable away from the feed at right angles to the dipole (along the x axis) for at least λ/4 (86 mm) before it turns.
• Match. 40 Ω gives |S11| of −19 dB at best, with no matching network. A 50 Ω match needs a higher resistance, which a longer straight section l_feed with fewer or narrower turns (a smaller a) gives, at the cost of height. A wider trace w widens the band a little.
• Radome and FR-4. The radome is not modeled; a glass-fiber shell a few millimeters thick lowers the frequency by a few per cent, inside the 5 % margin. FR-4 varies (εr 4.2–4.7, tan δ 0.015–0.025 from batch to batch and with frequency); that moves the band by under 1 %. Real copper (the model's sheets are lossless) costs roughly another 1 % on the 2 mm trace. After building, measure S11 inside the radome and trim l_end (−7.5 MHz per mm, the same on both tips).
• Airframe. A non-metal airframe is assumed. Carbon fiber conducts: keep the antenna away from carbon tubes and skins, batteries, servo and power wiring (ideally λ/4, 86 mm), or model them.
• Feed. The feed is a 2 mm lumped port, not a connector.

Other bands. Scale every length by k = 0.867 / f_new (FR-4 thickness excepted), set f0 and the simulated band (about 0.85 × and 1.15 × f0), and re-tune l_end, or l_feed for larger steps. Only 867 MHz has been simulated. The −10 dB band of the 867 MHz dipole ends at 916 MHz, so it does not cover the 902–928 MHz ISM band: that needs its own tuning.

Printed sleeve dipole, 867 MHz (sleeve_dipole_867.design.json)

A coax-fed telemetry dipole for a UAV with a composite (non-metal) fuselage, where there is no metal skin to act as a monopole's ground plane. It is a half-wave dipole printed on a slim FR-4 strip that fits a blade radome, for the 863–870 MHz SRD / LoRa band. It is vertically polarised and omnidirectional in azimuth. The lower arm is a sleeve around the feed coax, so the coax reaches the center feed along the antenna itself and leaves at its bottom end, with no separate balun.

Model. A vertical FR-4 strip (εr 4.3, tan δ 0.02 at f0, t = 1.6 mm, in the xz plane; x is the flight axis, z points up) carries all the copper (PEC sheets) on its y = 0 face:

• the upper arm, w_up wide and l_up long, above the feed gap g;
• the sleeve (the lower arm), w_sl wide and l_sl long below the gap. It is a pair of strips (each ws wide) either side of the coax, with a slot s between each strip and the coax. A bridge hb tall across the full sleeve width joins the strips and the coax braid at the top;
• the coax, modeled as its outer conductor: a strip w_f wide on the center line, from the bridge down to the bottom edge of the board, where the cable leaves.

A 50 Ω lumped port, w_f wide, bridges the gap from the bridge to the upper arm. It stands for the coax inner conductor, which jumps the gap from the end of the cable to the base of the upper arm. Because the braid touches the sleeve only at the bridge, the coax and the sleeve strips form a short-circuited coplanar stub (about 66 mm, roughly 0.3 λ in the board's effective medium at 867 MHz). This is the choke of a sleeve dipole: it presents a high impedance between the braid and the sleeve at the open lower end, which keeps the antenna current off the outside of the cable. The board extends m beyond the copper at both ends. There is no ground plane. The open boundaries are PML (8 cells) behind a quarter wavelength at 0.75 GHz (100 mm) of air on every side. The mesh is automatic, 30 cells per wavelength at 1.0 GHz (about 443 000 cells), with 3 cells across each 1 mm slot, 3 across the 2 mm feed gap and 4 through the board.

Where the coax goes. Use a thin coax (RG-178, RG-316, or 2.2 mm semi-rigid for a stiff build) laid on the center strip. Solder its braid to the bridge pad and, if you like, along the strip. The braid must not touch the sleeve strips anywhere else: the two 1 mm slots keep them apart. Solder the inner conductor across the 2 mm gap to the base of the upper arm. The cable runs down the axis and leaves the board at its bottom edge (z = −73.8 mm), through the radome base.

The dipole is L = 139.6 mm from tip to end (0.40 λ at 867 MHz); the board is H = 147.6 × 20 × 1.6 mm. Band 0.75–1.0 GHz, end criterion −60 dB (timestep limit 150 000), far field and surface current at f0, radiation efficiency at 21 frequencies across the band.

Tuning (GPU engine, 11 runs, 7–61 s each):

The first run decayed slowly: the coax-and-sleeve stub resonates near 0.7 GHz, below the band, with a Q set mostly by the FR-4 loss, and the excitation for a narrow band is long (9 900 steps). With 150 000 steps allowed, runs converge at about 98 000 (20 cells/λ) or 137 000 steps (30 cells/λ). The boundaries matter here. With MUR, openEMS' Dmax (2.72 dBi) and the Dmax integrated from the pattern (2.10 dBi) disagreed by 0.6 dB, and the match was about 1.4 % low in frequency. With PML 8, the two agree within 0.03 dB and more air changes nothing. The 20-cell mesh put the match 1.4 % low, while 30 and 40 cells agree within 0.1 %, so the file uses 30. One millimeter of both lengths moves the match by about 11 MHz (1.3 %).

Results (defaults, GPU engine, 442 800 cells, 137 448 timesteps, 32.5 s solver time):

Against theory and the wideband dipole.

The sleeve dipole behaves like a λ/2 dipole: the same pattern (78° beamwidth, 0.05 dB less directivity) and a resonant resistance of 65 Ω, close to a thin dipole's 70 Ω. The FR-4 under the copper shortens it: it resonates (X = 0) at 0.42 λ instead of 0.48 λ. The 10–16 mm wide strips give it about twice a wire's bandwidth, but the match stays at −19 dB: its resistance rises through the band (51 Ω at 0.85 GHz, 67 Ω at 0.90 GHz). It is the narrowest of the three in width (a 20 mm board) and the only one fed by coax without a balun. It is 30 mm taller than the slotted wideband dipole.

Caveats.

• The cable. The model ends the coax at the bottom edge of the board. A real cable continues from there, and whatever current reaches the braid's outside at the sleeve end flows on down the cable, radiates, tilts the pattern and moves the match. In the model, the coax strip carries up to about 15 % of the peak arm current near its lower end. The stub is 0.3 λ long, not the ideal λ/4, so its choking is good but not perfect. Keep the cable on the antenna axis for at least λ/4 (86 mm) below the board. If it must turn, add a ferrite bead or a clip-on ferrite at the board edge. To see the effect, add a wire of the cable's radius that continues the coax strip down from the board edge, and compare.
• Radome. The radome, the paint and the mount are not modeled. A thin glass-fiber shell lowers the frequency by a few per cent. The best match sits 1.1 % high, and the band reaches 5.3 % below 863 MHz and 9.6 % above 870 MHz, so a shift of up to about 5 % down keeps 863–870 MHz inside the −10 dB band. If the fitted radome shifts it by more, shorten l_up and l_sl together: 1 mm moves the band by about 1.3 %.
• FR-4 tolerance. FR-4's εr varies from about 4.2 to 4.7 between suppliers and with frequency, and the thickness by ±10 %. Most of the field is in the air, so the band moves by roughly a fifth of the relative change in εr (about 2 % down at εr 4.7; an estimate from how much the board shortens the dipole, not simulated). Measure S11 on the first boards and trim both lengths together.
• Mounting. Carbon-fiber parts, cables, the battery and metal hardware within about λ/4 (86 mm) of the antenna change the match and the pattern.
• Losses. The copper is lossless (PEC); real copper costs a few tenths of a per cent. The FR-4 loss is modeled and costs about 1 %.

Printed 2-element collinear, 867 MHz (collinear_867.design.json)

A higher-gain telemetry antenna for a UAV with a composite (non-metal) fuselage. It is the sleeve dipole above with a second half-wave element stacked on top and fed in phase. It is vertically polarised and omnidirectional in azimuth for 863–870 MHz, and needs no ground plane and no balun. It answers one question: how much more gain on the horizon than a λ/2 dipole is possible, and what that costs in elevation beamwidth and length. The answer is 2.0 dB more on the horizon (4.1 dBi against 2.1 dBi). The elevation beam narrows from 78° to 39°, and the antenna is 352 mm long instead of 140 mm.

Model. A vertical FR-4 strip (εr 4.3, tan δ 0.02 at f0, t = 1.6 mm, 30 mm wide, in the xz plane; x is the flight axis, z points up). All the radiating copper (PEC sheets) is on its y = 0 face:

• the lower element, the sleeve dipole of sleeve_dipole_867. This is an arm l_up long above the feed gap g, and a sleeve l_sl long below it. The sleeve is two strips either side of the braid strip w_f, with a slot s on each side, joined to the braid strip by a bridge hb at the top. As in that design, the braid strip and the sleeve form the choke that keeps the current off the cable;
• the phasing meander, n_m = 6 turns of a w_m = 2 mm trace, 2 a_m = 26 mm wide, with pitch p_m, from the top of the arm to the bottom of the upper element (74 mm tall);
• the upper element, l_top long and w_top wide, fed at its lower end by the meander.

The feed point is about 200 Ω, which a 50 Ω cable cannot feed directly: the upper element is fed through the dipole arm, so its radiation resistance adds to the dipole's. So the feed is a quarter-wave line. A w_t = 1.2 mm trace on the back face (y = −t) runs up behind the 1.2 mm braid strip, from z = −l_t to the feed gap, where a via joins it to the base of the arm. The trace and the braid strip form a broadside strip pair across the board, about 116 Ω. It is l_t = 58 mm long, about a quarter of the guided wavelength once the via and the ends are counted. The 50 Ω lumped port bridges the board at the lower end of the line, where the coax ends. There, the braid is soldered to the braid strip and the inner conductor goes through a via to the back trace.

There is no ground plane. The open boundaries are PML (8 cells) behind a quarter wavelength at 0.75 GHz (100 mm) of air on every side. The mesh is automatic, 30 cells per wavelength at 1.0 GHz (3.46 million cells). It has 3 cells across each 1 mm slot, 4 across the feed gap, 6 across the 1.2 mm feed trace, 10 in the 4 mm gaps between the meander rungs and 12 through the board.

Why this variant. Three kinds of collinear were considered:

• a center-fed pair of in-phase dipoles with a corporate feed, which needs a balanced divider and a balun on a 30 mm strip;
• a Franklin (two λ/2 strips joined by a phase-reversing stub), fed at the center of one element. With a balanced port it needs a balun, like the plain printed dipoles above;
• a sleeve-dipole base with a stub and a second element (this one).

The sleeve base is the most practical to build. The coax arrives along the axis through its own choke, and the rest is a single-sided etch plus one line on the back and two vias. All of it is thin copper on FR-4 with a lumped port, which Fairbeam models faithfully (only the copper is idealised, as lossless). The stub must reverse the current between the two elements. With a plain gap the two elements would radiate in antiphase, and a λ/2 of straight wire would add an antiphase radiator between them. So the stub is folded into a meander, whose rungs carry opposite currents that cancel.

The spacing sets the gain. Two ideal collinear λ/2 dipoles have 3.8 dBi at 0.5 λ between centers, 4.4 dBi at 0.6 λ and 5.0 dBi at 0.75 λ (half-power beamwidth 48°, 42° and 35°). On FR-4 each element is only about 0.41 λ long, so an in-line stub is also the only way to get the spacing. The 74 mm meander puts the centers 211 mm (0.61 λ) apart. The 5 dBi of the 0.75 λ case needs about 50 mm more length, about 400 mm in total, which is beyond the 350 mm budget.

Derived: meander height H_m = 74 mm and trace length L_m ≈ 384 mm. The tightly coupled rungs make that trace much longer than a λ/2. Element spacing d_el = 211 mm (0.61 λ). Antenna length L = 351.6 mm from the sleeve end to the tip; the board is H = 359.6 × 30 × 1.6 mm. Band 0.75–1.0 GHz, end criterion −60 dB (timestep limit 250 000). Far field and surface current at f0, radiation efficiency at 21 frequencies across the band.

Tuning (GPU engine, 12 runs. Runs 1–7 at 30 cells/λ and −50 dB, 8–9 at 30 cells/λ and −40 dB, 10 at 20 cells/λ and −40 dB, 11–12 at the defaults):

The zig-zag stub (runs 1–5) set the phase: near the right height, each mm moved the beam by 1.3–3°. But its links are not mirror-symmetric. At the right height they left a horizontal current that put 2.1 dB of ripple into the azimuth pattern. A meander whose rungs span the full width cancels that current (0.2 dB ripple). More turns or wider rungs add phase: one more turn lifted the beam by about 15° (runs 7–8), and 0.7 mm more of a_m by 2° (runs 8–9). With the port at the gap, the variants that pointed the beam near the horizon had 150–300 Ω at the feed. The strip-pair transformer brings that down to 50 Ω. Runs 11 and 12 differ only in its length (48 and 58 mm): the longer line widened the band and moved it up. The runs slowed down as the model grew. The meander's fine cells took the grid from 1.1 to 3.5 million cells, and the choke and the feed line ring down slowly (227 000 timesteps to −60 dB).

Results (defaults, GPU engine, 3.46 million cells, 227 360 timesteps, 420 s solver time):

The surface current at f0 has two maxima, one on the dipole arm and one on the upper element, in phase within 15°. Between them, the meander rungs carry large opposite currents that cancel. The meander is not a perfect phase shifter, though. Its links carry a net vertical current in antiphase, comparable to the upper element's, and that costs some gain. So the antenna has 4.1 dBi on the horizon, 0.3 dB less than two ideal dipoles at the same 0.61 λ. The bundle stores the total directivity only, so the cross-polarisation is not separated. The rungs are symmetric about the axis, and the azimuth ripple is 0.2 dB.

Against the sleeve dipole and the ideal collinear.

What the narrow beam means in flight. The 2 dB is gained only near the horizon. At range, a ground station is usually within a few degrees of the horizon, so long, level flight gets the full gain. The table gives the gain (mean over azimuth) against the angle below the horizon, with the antenna vertical:

The collinear is better out to about 20° from the horizon and worse beyond. The difference is large past 30°:

• Banking. A 30° bank tilts the beam by 30°: down on the low-wing side, up on the high-wing side. A ground station on the horizon, out to the side, is then 30° off the beam peak. The collinear gives −4.9 dBi on the low-wing side and −2.7 dBi on the high-wing side, where the λ/2 dipole still gives 0.3 dBi. That is 3–5 dB worse than the dipole, instead of 2 dB better. A station 10–20° below the horizon gets 0.4 to 3.1 dBi on the low-wing side, and −10 to −25 dBi on the high-wing side. Only along the flight direction does the bank leave the beam alone. For turns, budget the link with about −5 dBi for the collinear and 0 dBi for the dipole.
• Overhead passes. Within about 45° of the vertical (above the station, on a climb-out, or close to the field), the collinear has −15 to −18 dBi, against −2 to −12 dBi for the dipole. Both have a null straight down, but the collinear's cone of weak signal is much wider. A UAV that flies over or near the ground station needs the link margin for that, or a second antenna with diversity (for example a dipole, or a patch looking down).

The collinear pays off for long-range, mostly level flight. For short-range work with steep banks or overflights, the sleeve dipole's 78° beam is the more robust choice.

Build notes and caveats.

• Feed and cable. Lay a thin coax (RG-178 or RG-316) on the braid strip, from the bottom edge of the board to the lower end of the feed line (z = −58 mm). Solder its braid to the strip there, and take the inner conductor through a plated via to the back-face trace. The trace ends in a second via into the base of the arm, 1.5 mm above the gap. The braid must not touch the sleeve strips: the two 1 mm slots keep them apart, so strip only a short length. As in the sleeve dipole, the cable beyond the board is not modeled. Keep it on the axis for at least λ/4 (86 mm) below the board, or fit a ferrite on it at the board edge.
• Match. The match across 863–870 MHz is −12 dB, not the −19 dB of the sleeve dipole. The band is wide (15.7 %), but it has two minima, with −11.5 dB at about 880 MHz between them. Its center sits 3 % above 867 MHz, not the 1 % aimed for. No further tuning runs were made. The next steps are a slightly wider trace w_t (a lower line impedance), or re-tuning l_t by a millimeter or two around 58 mm. The mismatch costs 0.28 dB of realized gain.
• Radome. A thin glass-fiber shell lowers the frequency by a few per cent. The band reaches 4.8 % below 863 MHz, so a shift of up to about 4 % keeps 863–870 MHz inside it. The phase is more sensitive: if the radome slows the meander more than the elements, the beam tilts. Check the pattern (or the signal strength at the horizon) with the radome fitted, and trim a_m (about 3° of tilt per mm) or the upper element.
• Length. At 360 mm, the board is long for a UAV. It needs a stiff radome or a mast. A board that flexes in flight tilts the beam, just as a bank does. The lower 150 mm (the sleeve dipole) can sit inside the fuselage, if the skin is glass fiber and not carbon.
• Losses. The radiation efficiency is 87.6 %, against 98.8 % for the sleeve dipole. The extra loss is most likely in the FR-4 under the feed line and the meander rungs, where the current density is high (an estimate: the model does not separate it). A low-loss laminate (tan δ about 0.004) would recover most of it, but it changes εr, so re-tune l_t and a_m. The copper is lossless (PEC); real copper costs a few tenths of a per cent more.
• FR-4 tolerance. An εr anywhere from 4.2 to 4.7 moves the band and, through the meander, the tilt. Measure S11 and the pattern on the first boards before fixing the design.

Ground-station 5-element Yagi, 867 MHz (yagi_867.design.json)

A directional antenna for the ground station of a UAV telemetry link in the 863–870 MHz SRD / LoRa band. The UAV keeps an omnidirectional antenna (sleeve_dipole_867), and the extra gain for range comes from the station. It is a five-element Yagi-Uda on a 283 mm boom: a reflector, a driven dipole with a hairpin match, and three directors. It has 10.4 dBi of gain and an 18.6 dB front-to-back ratio. Mount it with the elements vertical, to match the vertical polarisation of the UAV's dipole.

Model. All the metal is aluminum, modeled as PEC sheets in the xz plane (y = 0). x is the boom axis (+x forward, towards the UAV), and z points up along the elements. There is no board and no dielectric. Each element is a 4 mm rod (d), modeled as a flat strip w = 2 d = 8 mm wide. A flat strip of width w has the equivalent radius w/4 of a round wire, so the strip and the rod have about the same current distribution and resonance. Sheets need no mesh through a volume, which keeps the timestep reasonable. The automatic mesh puts 6 cells (1.33 mm) across each strip, and two cells of that size either side of the sheet plane. The parts are:

• the reflector, L_r long, at x = −s_r;
• the driven element, the two halves of a straight dipole, L_de from tip to tip, with a feed gap g = 6 mm between them at the origin;
• the hairpin (a beta match). Two rails, as wide as the elements, run back from the two halves towards the reflector, along the edges of the feed gap. A bar shorts them l_hp = 23 mm behind the rear edge of the driven element, 35 mm from its axis (x_hp). The hairpin is a shorted strip-pair stub in parallel with the feed: a shunt inductance of about 7–9 nH;
• directors 1–3, L_d1, L_d2 and L_d3 long, at x = s_1, s_1 + s_2 and s_1 + s_2 + s_3.

A 50 Ω lumped port, 8 mm wide, bridges the feed gap. The feed is balanced: in practice the coax needs a 1:1 balun at the gap (see the build notes). The boom is taken to be non-metal (glass fiber, PVC or wood) and is left out. The open boundaries are PML (8 cells) behind a quarter wavelength at 0.8 GHz (94 mm) of air on every side. The mesh is automatic, 30 cells per wavelength at 0.95 GHz (715 000 cells). The smallest cell is 0.37 mm, where the hairpin rails meet the short.

Why this variant. Three kinds of driven element were considered:

• a folded dipole (about 200–300 Ω in a Yagi). It needs a 4:1 balun, and a 50 Ω port would see a 4–6:1 mismatch unless the balun is modeled too;
• a printed quasi-Yagi on FR-4. It is compact, but the FR-4 costs efficiency (the collinear above loses 12 %), its εr tolerance moves the band, and 10 dBi needs a board about 0.8 λ (280 mm) long;
• a straight dipole with a hairpin match (this one). A Yagi with about 10 dBi of gain has a low feed-point resistance (25 Ω in the first run below). The driven element is set slightly short (capacitive), and the hairpin's shunt inductance transforms the result to 50 Ω.

The hairpin variant is the easiest of the three to build from rod or strip, and it needs only a 1:1 balun. It is all metal strips in the air with a lumped port across the gap, which Fairbeam models faithfully. The hairpin's short is a voltage null, so it can be bonded to the boom or the mast as a DC ground.

The dimensions start from the NBS 5-element design (NBS Technical Note 688: a 0.8 λ boom, 0.2 λ spacings, a 0.482 λ reflector and 0.428/0.420/0.428 λ directors, for d/λ = 0.0085). The NBS design is optimized for gain alone. A thin-wire method-of-moments (MoM) model with the 4 mm rods gave it 11.3 dBi but only 12.9 dB front-to-back at 867 MHz, and 11.7 dB at 870 MHz. (The MoM model is a small Python script, not part of fairbeam.) The lengths and spacings were re-optimized in that model for 10.3–10.8 dBi, with at least 20 dB front-to-back over 863–870 MHz. This moved the reflector further back and the last director further forward, giving a 0.82 λ boom. The FDTD runs then corrected the lengths for the strip model (see Tuning below).

Derived: the boom length boom is 283 mm (0.82 λ) from the reflector to director 3. The hairpin length x_hp is 35 mm, from the driven element's axis to the back of the short. The antenna is 283 × 162 mm, plus 8 mm in x for the strip widths. Band 0.8–0.95 GHz, end criterion −60 dB (timestep limit 200 000). Far field and surface current at f0, radiation efficiency at 21 frequencies across the band.

Tuning (GPU engine, 6 runs: 1–5 at 20 cells/λ and −40 dB, 6 at the defaults):

Run 1 showed the strips behaving about 2.5 % longer than the MoM rods: to match it, the MoM model needed every length scaled up by 2.5–3 %. Its front-to-back ratio (15.8 dB) and gain matched the MoM model at about 882 MHz instead of 867 MHz. Run 2 shortened the parasitic elements by 2.5 %, which gave 18 dB front-to-back across the band. After that the pattern hardly changed: Dmax stayed within 0.05 dB and the front-to-back ratio within 0.7 dB in the remaining runs. The hairpin and the driven element were tuned together. After each run, a fit of the runs so far picked the next values; the fit models the hairpin as a shorted stub in parallel with a driven element whose impedance is linear in L_de. One millimeter of L_de changes the reactance at the feed by about 6–8 Ω. The final run's match sits within about 0.3 % of where the coarse runs put it for 156 mm.

Results (defaults, GPU engine, 714 840 cells, 79 206 timesteps, 38.0 s solver time):

The beamwidths are interpolated from the pattern (3° steps in θ, 5° in φ). For the band-edge values, the final run used a copy of the file with far fields at 863, 867 and 870 MHz; the file itself records the far field at f0 only. The surface current at f0 peaks on the driven element. Relative to that peak, the directors carry 59 %, 76 % and 52 % (directors 1 to 3), the reflector 51 %, and the hairpin's short 60 % (its circulating current).

Against theory and the sleeve dipole.

A 0.8 λ Yagi has about 10–11 dBi (the NBS table gives about 9.2 dBd, 11.3 dBi, for its gain-optimized version). Trading 0.9 dB of that for a clean rear hemisphere is the usual choice for a ground station, where the back lobe mostly picks up interference and ground reflections. The FDTD front-to-back ratio is 2.3 dB below the MoM one, most likely because the strips couple a little differently from round rods. It stays within 0.5 dB of 18.6 dB across 863–870 MHz.

Link budget: the extra range. In free space, the range at a fixed link margin grows with the square root of the product of the two antenna gains. So a gain difference ΔG (in dB) at one end multiplies the range by 10^(ΔG/20). With the Yagi (10.39 dBi realized) in place of the sleeve dipole (1.99 dBi realized) at the station:

The factor applies to the uplink and the downlink alike, since the antenna is reciprocal. It is a free-space figure. On a real path, the ground reflection, the Fresnel-zone clearance and the earth's curvature limit the range first, so the antenna heights and the terrain matter as much as the gain. The SRD band's power limit (typically 25 mW ERP, 14 dBm, over most of 863–870 MHz) counts the antenna gain. So a transmitting station with the Yagi must lower its transmitter power by the Yagi's gain over a dipole (8.2 dB) to stay within it. The receive direction keeps the full 8.4 dB.

Build notes and caveats.

• Pointing. The station Yagi must point at the UAV. The azimuth beamwidth is 70°: the gain drops by 3 dB at ±35° off the boom and by about 12 dB at ±60°. For a UAV that flies all around the field, a tracker helps: a pan servo driven from the UAV's GPS position in the telemetry. A tilt axis helps on close, high passes, where the UAV is more than about 25° above the horizon. A fixed Yagi suits a mission flown in one sector.
• Polarisation. Mount the elements vertically, to match the UAV's vertical dipole. A horizontal Yagi would lose 20 dB or more to cross-polarisation against it.
• Balun. The feed is balanced, so the coax needs a 1:1 current balun at the gap. Ferrite beads over the last 50 mm of the cable work (for example 3–5 type 43 or 61 beads on RG-316, or a clip-on core on RG-58), and so does a λ/4 sleeve (bazooka) balun, about 86 mm long. Without a balun, current on the outside of the coax distorts the pattern and costs front-to-back ratio. Take the coax away along the boom, not parallel to the elements.
• Boom and mast. The model has no boom. With a non-metal boom, fit the elements as they are. With a metal boom and the elements bonded through it, lengthen each element by the boom correction: roughly 0.5–0.7 times the boom diameter for a small round boom, following DL6WU's chart (not simulated here). With the elements insulated and at least one boom diameter above the boom, the correction is almost zero. The driven element must be insulated from a metal boom, apart from the center of the hairpin's short, which may be bonded. A metal mast close to and parallel with the vertical elements degrades the pattern. Mount the boom on the mast behind the reflector, or use a non-metal mast section for the top half meter.
• Rods or strips. The model is a flat strip 8 mm wide. Flat aluminum strip of that width (1–2 mm thick) builds exactly what was simulated. Round 4 mm rods are equivalent in theory; expect the match to move by up to about 1 %. Trim L_de or l_hp on the finished antenna: 1 mm of L_de moves the match by about 5 MHz.
• Hairpin. Build the rails from the same rod or strip, 6 mm apart edge to edge, level with the edges of the feed gap. The slot length l_hp and L_de set the match together; a longer slot adds inductance. The geometry keeps the short behind the driven element for any l_hp > 0. The design checks would not flag a short that crossed the feed gap (a sheet across the port shorts it), so keep that in mind when editing the hairpin.
• Band. The −10 dB band is 4.5 % wide, narrower than the printed dipoles', so the length tolerance is about ±1 % (±2 mm on L_de). The pattern has a wider band: the front-to-back ratio stays above 18 dB over 863–870 MHz.
• Losses. The metal is lossless (PEC). Aluminum costs a few tenths of a per cent at 867 MHz.
• Surroundings. Buildings, vehicles and people within a few wavelengths in front of the antenna change the pattern and reflect the signal. Mount it high and clear.