Tools
Handy calculators for everyday use in the shack.
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Grid square and distance
Convert coordinates to a Maidenhead grid square and work out the distance and bearing between two stations.
Power and dB
Watts, dBm, dBW and decibel ratios.
Open-wire line
Impedance of a parallel-wire line (ladder line, window line or twin-lead) from the wire diameter and the center-to-center spacing, and the spacing you need for a given impedance.
The center-to-center spacing must be larger than the wire diameter, otherwise the wires touch.
The spacing exceeds 1% of a wavelength: the line starts to radiate and pick up noise.
Z₀ = 120·VF·acosh(D/d), the exact formula for two round wires. Losses are copper only, with skin and proximity effect; dielectric loss and dirty or wet spacers add to them.
Inductance
Single-layer coils on an air tube, a ferrite rod or a toroid: from turns to µH, or from µH to the turns you need.
The coil's self-resonance is too close to the working frequency, where it no longer behaves as a clean inductance. Use fewer turns on a larger form, or space the turns out.
With this wire, that many turns won't fit in a single layer: use a bigger toroid or thinner wire.
The coil is longer than the rod: the part that sticks out is an air coil and the result is less accurate.
Enameled (magnet) copper wire in a single layer. The calculation uses the exact Nagaoka coefficient with Rosa's round-wire correction. The wire length doesn't include the leads: leave a couple of inches extra.
Toroids use Amidon's published AL values (±10% for iron powder, ±25% for ferrite). The rod is calculated with the coil centered and matches published AL values to within 7%, but ferrite varies from batch to batch: always measure the finished coil.
Pi output filter
For the output of a power stage: the low-pass filter that removes harmonics, or the Pi network that matches the tube or transistor to the antenna. It gives you the capacitors, the air-wound or toroidal coils, and the voltage and current each part has to handle at the power you choose.
| Part | Value | Standard value | Peak voltage | RMS current | Coil |
|---|
A toroid exceeds the recommended flux density at this frequency and will heat up in high-duty-cycle modes (FT8, RTTY, AM): use a bigger one, stack two, or make the coil air-wound.
The turns won't fit in one layer on a toroid: use a bigger one or thinner wire.
An air coil has its self-resonance too close to the operating frequency: use a larger diameter and fewer turns.
Use silver mica or NP0/C0G ceramic capacitors rated for at least twice the peak voltage. Toroid turns must be whole: adjust each coil by squeezing or spreading the turns, and check the finished filter with an antenna analyzer.
Tube: R ≈ Va/(K·Ia), with K = 1.3 (A), 1.5 (AB1), 1.7 (AB2), 1.8 (B) or 2 (C). Transistor: R ≈ Vcc²/(2·P). The plate-side capacitor sees the RF voltage; the blocking capacitor also sees the DC.
Band-pass filter
Grounded LC resonators, top-coupled through capacitors, with identical coils: for a receiver front end, to keep two stations at the same site from interfering, or to clean up a QRP transmitter.
| Part | Value | Standard value | Peak voltage | RMS current | Coil |
|---|
With this inductance a resonator capacitor comes out negative: use a smaller coil or leave it automatic.
A toroid exceeds the recommended flux density at this frequency and will heat up in high-duty-cycle modes (FT8, RTTY, AM): use a bigger one, stack two, or make the coil air-wound.
The turns won't fit in one layer on a toroid: use a bigger one or thinner wire.
An air coil has its self-resonance too close to the operating frequency: use a larger diameter and fewer turns.
The coupling capacitors are small: use exact values or trimmers, and tune each resonator on its own to the center frequency. Top coupling makes the response a little steeper below the passband than above it; the chart already shows this, coil loss included.
Baluns and ununs
Baluns (unbalanced ↔ balanced) at 1:1, 2:1, 3:1, 4:1, 6:1, 9:1, 49:1 and 64:1 and ununs (unbalanced ↔ unbalanced) at 1:1, 2:1, 3:1, 6:1, 9:1, 49:1 and 64:1, also with the Reisert crossover, on ferrite toroids: the turns, the impedance on each band and, for transformers, the core loss and temperature rise at your power level.
Below 500 Ω anywhere in the band, the choke barely stops common-mode current: add turns, use a bigger core or type 31 material, or stack two cores.
Between 500 and 1,000 Ω the choke helps, but below 1 kΩ some RF can still flow on the shield. If you can, stack another core.
The primary doesn't reach 4 times 50 Ω at the lowest frequency: the SWR will rise and the core will heat up. Add turns or use a bigger core.
These turns won't fit in a single layer inside the hole: choose a bigger core, thinner coax or wire, or fewer turns.
The flux density exceeds the recommended limit for ferrite at this frequency: the core will heat up in continuous-carrier modes. Stack another core, add primary turns or reduce power.
The core has to dissipate too much heat for its size: it can get hot enough to lose permeability (and crack). Stack another core or choose a larger one.
Iron powder has low permeability, so a choke would need a huge number of turns. For chokes, type 31 or 43 ferrite works much better.
A choke needs a high impedance that is mostly resistive: the solid curve is |Z| and the dashed one is the resistive part. Wind the coax in a single layer and keep the input and output ends apart (use a Reisert cross-over halfway if needed). Too many turns raise the winding capacitance and the choke falls off on the higher bands, which is why the automatic setting doesn't always use as many turns as will fit.
Sevick's rule: the primary reactance should be at least 4 times the impedance it sees (50 Ω) on the lowest band. On the higher bands, 49:1 and 64:1 ununs usually need a 100 to 150 pF capacitor (silver mica, 1 kV or more) across the primary to compensate for leakage inductance: adjust it while watching the SWR on 10 m. The flux limit is Amidon's guideline for ferrite (about 150/√f gauss); heating is based on the average power of the mode.
Model: each ferrite's complex permeability (µ' and µ'') comes from Fair-Rite's measured curves, the winding capacitance is fitted to VNA measurements (the Reisert crossover lowers it by 26%) and the temperature rise is worked out from the core's surface area. Ferrite tolerance is ±20%, so always measure the finished balun with an antenna analyzer (or a NanoVNA) before applying power.
AWG copper wire table
Diameter, cross-section and resistance for every AWG (American Wire Gauge) size, plus the resistance at 14 MHz, which is what matters in an antenna, and the closest metric size.
| AWG | Dia. (mm) | Dia. (in) | Area (mm²) | Ω/km | Ω/1000 ft | Ω/m at 14 MHz | Closest metric mm² |
|---|---|---|---|---|---|---|---|
| 0000 | 11.68 | 0.4600 | 107.2 | 0.161 | 0.049 | 0.027 | 120 |
| 000 | 10.40 | 0.4096 | 85.0 | 0.203 | 0.062 | 0.030 | 95 |
| 00 | 9.27 | 0.3648 | 67.4 | 0.256 | 0.078 | 0.034 | 70 |
| 0 | 8.25 | 0.3249 | 53.5 | 0.322 | 0.098 | 0.038 | 50 |
| 1 | 7.35 | 0.2893 | 42.4 | 0.407 | 0.124 | 0.042 | 50 |
| 2 | 6.54 | 0.2576 | 33.6 | 0.513 | 0.156 | 0.048 | 35 |
| 3 | 5.83 | 0.2294 | 26.7 | 0.646 | 0.197 | 0.053 | 25 |
| 4 | 5.19 | 0.2043 | 21.2 | 0.815 | 0.248 | 0.060 | 25 |
| 5 | 4.62 | 0.1819 | 16.8 | 1.03 | 0.313 | 0.067 | 16 |
| 6 | 4.12 | 0.1620 | 13.3 | 1.30 | 0.395 | 0.076 | 16 |
| 7 | 3.66 | 0.1443 | 10.5 | 1.63 | 0.498 | 0.085 | 10 |
| 8 | 3.26 | 0.1285 | 8.366 | 2.06 | 0.628 | 0.096 | 10 |
| 9 | 2.91 | 0.1144 | 6.634 | 2.60 | 0.792 | 0.108 | 6 |
| 10 | 2.59 | 0.1019 | 5.261 | 3.28 | 0.999 | 0.121 | 6 |
| 11 | 2.30 | 0.0907 | 4.172 | 4.13 | 1.26 | 0.136 | 4 |
| 12 | 2.05 | 0.0808 | 3.309 | 5.21 | 1.59 | 0.153 | 4 |
| 13 | 1.83 | 0.0720 | 2.624 | 6.57 | 2.00 | 0.172 | 2.5 |
| 14 | 1.63 | 0.0641 | 2.081 | 8.28 | 2.53 | 0.193 | 2.5 |
| 15 | 1.45 | 0.0571 | 1.650 | 10.45 | 3.18 | 0.217 | 1.5 |
| 16 | 1.29 | 0.0508 | 1.309 | 13.17 | 4.02 | 0.244 | 1.5 |
| 17 | 1.15 | 0.0453 | 1.038 | 16.61 | 5.06 | 0.275 | 1 |
| 18 | 1.02 | 0.0403 | 0.823 | 20.95 | 6.38 | 0.309 | 0.75 |
| 19 | 0.912 | 0.0359 | 0.653 | 26.41 | 8.05 | 0.348 | 0.75 |
| 20 | 0.812 | 0.0320 | 0.518 | 33.31 | 10.15 | 0.391 | 0.50 |
| 21 | 0.723 | 0.0285 | 0.410 | 42.00 | 12.80 | 0.441 | 0.34 |
| 22 | 0.644 | 0.0253 | 0.326 | 52.96 | 16.14 | 0.496 | 0.34 |
| 23 | 0.573 | 0.0226 | 0.258 | 66.78 | 20.35 | 0.559 | 0.25 |
| 24 | 0.511 | 0.0201 | 0.205 | 84.21 | 25.67 | 0.630 | 0.25 |
| 25 | 0.455 | 0.0179 | 0.162 | 106 | 32.37 | 0.711 | 0.14 |
| 26 | 0.405 | 0.0159 | 0.129 | 134 | 40.81 | 0.802 | 0.14 |
| 27 | 0.361 | 0.0142 | 0.102 | 169 | 51.46 | 0.906 | 0.08 |
| 28 | 0.321 | 0.0126 | 0.0810 | 213 | 64.89 | 1.02 | 0.08 |
| 29 | 0.286 | 0.0113 | 0.0642 | 268 | 81.83 | 1.16 | 0.08 |
| 30 | 0.255 | 0.0100 | 0.0509 | 339 | 103 | 1.31 | 0.05 |
| 31 | 0.227 | 0.0089 | 0.0404 | 427 | 130 | 1.49 | 0.05 |
| 32 | 0.202 | 0.0080 | 0.0320 | 538 | 164 | 1.69 | — |
| 33 | 0.180 | 0.0071 | 0.0254 | 679 | 207 | 1.92 | — |
| 34 | 0.160 | 0.0063 | 0.0201 | 856 | 261 | 2.18 | — |
| 35 | 0.143 | 0.0056 | 0.0160 | 1,079 | 329 | 2.49 | — |
| 36 | 0.127 | 0.0050 | 0.0127 | 1,361 | 415 | 2.84 | — |
| 37 | 0.113 | 0.0045 | 0.0100 | 1,716 | 523 | 3.26 | — |
| 38 | 0.101 | 0.0040 | 0.0080 | 2,164 | 660 | 3.74 | — |
| 39 | 0.090 | 0.0035 | 0.0063 | 2,729 | 832 | 4.31 | — |
| 40 | 0.080 | 0.0031 | 0.0050 | 3,441 | 1,049 | 4.99 | — |
Solid annealed copper at 20 °C (68 °F). At 14 MHz the current only flows in the outer 18 µm or so of the wire (skin effect), so the RF resistance is far higher than the DC resistance, and 14 AWG is more than enough for an HF dipole. AWG 10 to 18, the sizes most used in antennas, are highlighted. Every 3 AWG sizes the area halves; every 6, the diameter.
Band plan
IARU Region 1 HF segments with the usual modes.
| Band | Segment | Mode | Wavelength | Half-wave dipole | |
|---|---|---|---|---|---|
| 160 m | 1,810 – 1,838 kHz | CW | 164.36 m | 78.89 m | Calculate an antenna |
| 1,838 – 1,843 kHz | Digital | 162.89 m | 78.19 m | Calculate an antenna | |
| 1,843 – 2,000 kHz | SSB | 156.02 m | 74.89 m | Calculate an antenna | |
| 80 m | 3,500 – 3,570 kHz | CW | 84.81 m | 40.71 m | Calculate an antenna |
| 3,570 – 3,600 kHz | Digital | 83.62 m | 40.14 m | Calculate an antenna | |
| 3,600 – 3,800 kHz | SSB | 81.02 m | 38.89 m | Calculate an antenna | |
| 60 m | 5,351.5 – 5,354 kHz | CW | 56.01 m | 26.88 m | Calculate an antenna |
| 5,354 – 5,366 kHz | SSB | 55.93 m | 26.85 m | Calculate an antenna | |
| 40 m | 7,000 – 7,040 kHz | CW | 42.71 m | 20.50 m | Calculate an antenna |
| 7,040 – 7,060 kHz | Digital | 42.52 m | 20.41 m | Calculate an antenna | |
| 7,060 – 7,200 kHz | SSB | 42.05 m | 20.18 m | Calculate an antenna | |
| 30 m | 10,100 – 10,130 kHz | CW | 29.64 m | 14.23 m | Calculate an antenna |
| 10,130 – 10,150 kHz | Digital | 29.57 m | 14.19 m | Calculate an antenna | |
| 20 m | 14,000 – 14,070 kHz | CW | 21.36 m | 10.25 m | Calculate an antenna |
| 14,070 – 14,099 kHz | Digital | 21.29 m | 10.22 m | Calculate an antenna | |
| 14,101 – 14,350 kHz | SSB | 21.07 m | 10.12 m | Calculate an antenna | |
| 17 m | 18,068 – 18,095 kHz | CW | 16.58 m | 7.96 m | Calculate an antenna |
| 18,095 – 18,109 kHz | Digital | 16.56 m | 7.95 m | Calculate an antenna | |
| 18,111 – 18,168 kHz | SSB | 16.53 m | 7.93 m | Calculate an antenna | |
| 15 m | 21,000 – 21,070 kHz | CW | 14.25 m | 6.84 m | Calculate an antenna |
| 21,070 – 21,110 kHz | Digital | 14.21 m | 6.82 m | Calculate an antenna | |
| 21,151 – 21,450 kHz | SSB | 14.07 m | 6.76 m | Calculate an antenna | |
| 12 m | 24,890 – 24,915 kHz | CW | 12.04 m | 5.78 m | Calculate an antenna |
| 24,915 – 24,929 kHz | Digital | 12.03 m | 5.77 m | Calculate an antenna | |
| 24,931 – 24,990 kHz | SSB | 12.01 m | 5.77 m | Calculate an antenna | |
| 10 m | 28,000 – 28,070 kHz | CW | 10.69 m | 5.13 m | Calculate an antenna |
| 28,070 – 28,190 kHz | Digital | 10.66 m | 5.12 m | Calculate an antenna | |
| 28,225 – 29,700 kHz | SSB | 10.35 m | 4.97 m | Calculate an antenna | |
| 6 m | 50,000 – 50,100 kHz | CW | 5.99 m | 2.88 m | Calculate an antenna |
| 50,100 – 50,300 kHz | SSB | 5.97 m | 2.87 m | Calculate an antenna | |
| 50,300 – 50,400 kHz | Digital | 5.95 m | 2.86 m | Calculate an antenna |
These results are a good starting point for cutting wire. Real ground, nearby objects and the feedline always shift the resonance a little: cut it a few inches long and trim while measuring with an antenna analyzer.