⚠ WORK IN PROGRESS — Some features are under development. Verify all output against known reference designs before use in a real installation.
An Excel-based engineering calculator for designing non-resonant long-wire (end-fed random wire) HF antennas with impedance-matching networks. Supports multi-band optimization from 160 m through 6 m, with resonance avoidance scoring, VSWR estimation (resistive and complex), counterpoise impedance correction modelling, UnUn ratio sweep, core saturation analysis, counterpoise recommendations, and alternative air-core antenna tuner design.
- Background & Theory
- Features of this Calculator
- Workbook Structure
- How to Use the Calculator
- Mathematical Model
- Practical Construction Guidance
- Supported HF Bands
- Limitations and Caveats
- Glossary
- References and Further Reading
- License
In strict technical terms, a long wire antenna is a traveling-wave antenna many wavelengths long, with directivity that increases with length. However, in everyday amateur radio usage the term "long wire" refers to any end-fed random-length wire — typically between 10 m and 60 m of bare or insulated copper wire, fed at one end against a counterpoise.
This is also called:
- EFRW — End-Fed Random Wire
- Non-resonant end-fed wire
- Random wire antenna
The wire is suspended as high as possible and as horizontally as practical, exiting the shack or transmitter location and running to a convenient support (tree, mast, fence post). On transmission it radiates in all directions; on reception it collects signals from all directions. The great advantages are simplicity, low cost, and the ability to operate on multiple HF bands with a single wire and a single matching device.
Modern HF transceivers and receivers present a 50 Ω unbalanced (coaxial) port. The feedpoint impedance of an end-fed wire, however, fluctuates dramatically with frequency and wire length — varying from roughly 20–50 Ω (near a quarter-wave resonance, very low) up to several thousand ohms (near a half-wave resonance, very high). Without matching, this mismatch causes:
- High Reflected Power and standing-wave ratio (SWR) on the feedline
- Possible damage to the transmitter's output stage
- Efficiency loss due to reflected waves on lossy coaxial cable
- Erratic ATU (Antenna Tuner Unit) behaviour or inability to tune
A broadband impedance transformer placed at the antenna feedpoint pre-matches the wire's impedance to a value within the tuning range of the transceiver or of an auxiliary ATU, dramatically reducing these problems.
A UnUn (from Unbalanced-to-Unbalanced) is a broadband RF transformer where both the primary (feedline side) and the secondary (antenna side) are unbalanced with respect to ground. This distinguishes it from a BalUn (Balanced-to-Unbalanced), which is appropriate for balanced antenna systems such as dipoles.
A long-wire end-fed antenna is inherently unbalanced: one side of the feedpoint goes to the radiating wire, the other to the counterpoise (or ground). The 50 Ω coaxial feedline is also unbalanced: the center conductor carries the signal and the shield is the return path. Therefore, a UnUn is the correct choice for this application — using a BalUn here would be technically incorrect, even though many commercial products are mislabeled.
How the UnUn transforms impedance:
The most common ratio used with long-wire antennas is 9:1, meaning the impedance at the antenna side is 9× that at the coaxial side. So:
Z_antenna ≈ 9 × Z_feedline = 9 × 50 Ω = 450 Ω
This means the antenna wire should ideally present approximately 450 Ω at the feedpoint for a direct 9:1 match, which happens at wire lengths that are roughly 3/8 λ or 5/8 λ — the midpoints between quarter-wave (low-impedance) and half-wave (high-impedance) resonances.
Measured vs. Theoretical Impedance (2024–2025 Research):
Recent field measurements from multiple sources have demonstrated that the actual antenna feedpoint impedance is often significantly less than the theoretical 450 Ω assumption on each band. This challenges decades of conventional wisdom. The "450 Ω rule of thumb" is a gross oversimplification that depends heavily on:
- Wire length and geometry
- Height above ground
- Counterpoise configuration and length
- Environmental factors (proximity to structures, ground conductivity)
Evidence: A 2024 study by "Ham Radio Outside the Box" measured a specific 84-foot random wire and found impedances were well below 450 Ω across all tested bands. This invalidates the assumption that a 9:1 transformer is optimal for all installations.
Implications for UnUn Selection:
- A 9:1 transformer may be overmatched for many installations
- Some wire lengths work better with 4:1, 6:1, 7:1, 16:1, 25:1, or 49:1 ratios
- Best practice: Measure actual antenna impedance with a VNA or antenna analyzer BEFORE construction
- This calculator provides the theoretical foundation, but real-world impedance must be validated experimentally
The feedpoint impedance of a wire antenna depends on:
- Length relative to wavelength: Quarter-wave (λ/4) presents very low impedance (~20–50 Ω); half-wave (λ/2) presents very high impedance (several thousand ohms)
- Height above ground: Higher antennas radiate more efficiently but may have different impedance
- Wire diameter: Thicker conductors have slightly lower impedance
- Nearby objects: Metal structures, buildings, and terrain affect impedance
- Frequency: The same wire has different impedance at different frequencies
For a non-resonant (random) wire of length between 10–60 m operating on HF (1.8–54 MHz), the impedance typically varies:
- Magnitude: 50 Ω to 2000+ Ω depending on frequency
- Reactance: Capacitive or inductive depending on proximity to quarter-wave and half-wave multiples
- Pattern: Usually a mix of resistive and reactive components
The central design challenge with random-wire antennas is avoiding resonances where the impedance becomes unacceptably high or low.
Why resonances are problematic:
- At half-wave resonance (λ/2): Impedance becomes several thousand ohms; most tuners cannot match this
- At quarter-wave resonance (λ/4): Impedance becomes very low; little power is radiated
- Between these points (3/8 λ, 5/8 λ, etc.): Impedance is moderate and tunable
The solution: Choose a wire length that avoids half-wave and quarter-wave multiples of all bands you want to operate on. The avoidance score in this calculator measures how far your chosen length is from these "forbidden" resonance points. Scores range from 0 (on resonance) to 0.25 (maximum distance from all resonances — the wire sits exactly at the midpoint between λ/4 and λ/2).
Key reference: J.C. Sprott's research (revised 2022) identified that 74 feet (22.6 m) has the largest gap (376 kHz) between quarter-wave resonances, making it the single best length for 80–10 m multi-band coverage.
The speed at which an electromagnetic wave travels through a conductor is less than the speed of light in free space (300,000 km/s). The velocity factor (VF) is the ratio of this reduced speed to the speed of light.
Typical values:
- Bare copper wire in free air: 0.95–0.98 (wire's electrical length is 95–98% of physical length)
- Insulated wire (PVC/polyethylene): 0.92–0.96 (insulation slows the wave further)
- Coaxial cable (solid PE dielectric): 0.66
- Open-wire transmission line: 0.95–0.97
Why it matters: When calculating resonant lengths, you must multiply the theoretical wavelength by the VF. A dipole cut for 14 MHz in free space using VF=1.0 would be electrically too long and resonant at a slightly lower frequency.
Default in this calculator: VF = 0.95, which accounts for both the wire's inherent VF and "end effect" (capacitance at wire ends). This is appropriate for insulated copper wire with typical end effects.
A counterpoise is a wire or set of wires that acts as a reference return path (ground plane substitute) for the antenna. It is electrically and RF-wise "in parallel" with the antenna feedline and carries the return RF current.
Why it's needed:
- The antenna circuit must be complete (outgoing current must have a return path)
- In a balanced antenna (like a dipole), the return path is symmetrical
- In an unbalanced antenna (like a long wire), the return path is the counterpoise
- Without a counterpoise, RF current flows on the coax shield → RFI in the shack
Counterpoise design (Updated 2025):
The traditional formula is λ/4 of the lowest operating frequency, which is the value the Calculator sheet displays and pre-fills.
However, recent research (PA9X 2025, RF.Guru 2025) provides a more practical guideline for the minimum effective length:
Minimum practical length: 0.05 × longest wavelength you plan to transmit on
Example: For 80–10 m operation (80 m is longest), λ = 80 m, so 0.05 × 80 = 4 meters is sufficient. This length:
- Provides adequate return current path
- Doesn't radiate as a co-radiator
- Is much easier to implement than λ/4 (which would be ~20 m for 80m)
Number of radials:
- Single radial: 1–2 meters minimum; works for QRP
- Multiple radials (preferred): 2–4 radials each ~1.5–2 m → Impedance halves with each additional parallel radial
- Ground system: Buried radials more effective than elevated wires
This workbook provides a comprehensive toolkit for long-wire antenna design:
- ✅ Resonance avoidance algorithm — Identifies wire lengths that avoid problematic resonances on all selected bands
- ✅ Top-10 ranking — Recommends best wire lengths ranked by avoidance score
- ✅ Feedpoint impedance modeling — Empirical estimation of antenna impedance at each frequency
- ✅ VSWR prediction — Estimates standing-wave ratio across bands for chosen wire length
- ✅ Counterpoise design — Recommends counterpoise length and configuration
- ✅ UnUn ratio optimization — Tests multiple transformer ratios and recommends the best
- ✅ UnUn transformer design — Calculates ferrite toroid windings and specifications
- ✅ Air-core antenna tuner design — Alternative approach using tapped air-core coil
- ✅ NEC2 export — Generates ready-to-paste NEC2 input deck for full-wave simulation validation (EZNEC, 4NEC2, MMANA-GAL)
- ✅ Core saturation awareness — Notes power limits and saturation risk (see Limitations)
- ✅ Comprehensive references — Links to research papers, standards, and practical guides
This workbook contains eight interconnected sheets for designing and optimizing long-wire antennas:
Purpose: Main user interface and dashboard for wire length selection and band optimization
What It Does:
- Select which HF bands you'll operate on (160m–6m with YES/NO dropdowns)
- Automatically calculates optimal wire lengths using resonance-avoidance algorithm
- Recommends Top-10 wire lengths ranked by "avoidance score"
- Suggests counterpoise length for selected bands
- Provides installation guidance for common-mode chokes (CMC) and baluns
Key Inputs (Blue cells):
- Velocity Factor: Default 0.95 (insulated wire + end-effect); adjustable for bare copper (0.97–0.98)
- Band Selection: Set to YES for bands you want to use (ACTIVE column)
Key Outputs:
- Top 10 Recommended Wire Lengths: Ordered by avoidance score (EXCELLENT ★★★ to AVOID ✗)
- Recommended Counterpoise Length: λ/4 of the lowest active band (see Section 5.5 for the practical 0.05λ alternative)
- Choke/Balun Installation Guidance: Placement, impedance targets, core recommendations
Typical Workflow: Start here, select your bands, note Top-1 or Top-3 wire length, then verify with VSWR Calculator.
Purpose: Estimate feedpoint impedance and predict VSWR for your chosen wire length
What It Does:
- Predicts antenna feedpoint impedance (R + jX) at each HF frequency using empirical model
- Models counterpoise impedance and its effect on feedpoint
- Calculates VSWR across bands for specified wire length
- Accounts for counterpoise height, length, and number of radials
- Provides impedance vs. frequency analysis
Key Inputs:
- Wire length (m): Select from Top-10 list or enter custom value
- UnUn Ratio (N:1): Enter any integer ratio (e.g. 9:1, 16:1, 25:1, 30:1, 49:1); the sheet accepts any value — use the UnUn Ratio Optimizer (Sheet 7) to find the best ratio for your wire length
- Counterpoise configuration: Height, length, number of radials
Key Outputs:
- Impedance per band: R and X components (resistance & reactance)
- Feedpoint impedance magnitude: |Z| = √(R² + X²)
- Phase angle: Direction of impedance in complex plane
- VSWR: Voltage Standing Wave Ratio with color coding
- Return loss: Reflection coefficient in dB
- Model is empirical, not NEC2-based
- Accuracy: ±20–30%
- Real antenna impedance depends on: height, ground type, environment, weather
- Always validate with antenna analyzer or VNA before connecting to transmitter
Typical Workflow: After selecting wire length, check VSWR on each band here. If SWR >3:1 on all bands, consider alternative wire length.
Purpose: Design a ferrite-based wideband UnUn transformer (impedance matching)
What It Does:
- Calculates ferrite toroid specifications for your UnUn
- Designs windings: Number of turns, wire gauge, connections
- Predicts impedance matching performance across 1.8–30 MHz
- Provides step-by-step construction instructions
Key Inputs (Blue cells):
- UnUn Ratio (N:1): Enter any integer ratio — 9:1 (most common), 16:1, 25:1, 49:1, or any custom value; the sheet accepts any primary turns count and computes the resulting impedance ratio
- Wire diameter: AWG or mm (for coil winding)
- Core type & size: FT-114, FT-140, FT-240 (from Toroid Database)
- Turns: Default calculated; can adjust for experimentation
Key Outputs:
- Winding design: Primary turns, secondary turns, impedance ratio confirmed
- RF Performance (per frequency): Impedance transformation, phase shift
- Construction Notes: How to connect, polarity, box specifications
- Max Turns Warning: The sheet displays a per-core maximum turns limit beside the "Actual Secondary Turns (Rounded)" cell. For example, the T-200-2 core shows a max of 40 turns. If your calculated secondary turns exceed this limit, select a larger core or reduce the impedance ratio.
- Counterpoise Impedance Analysis: Corrected feedpoint Z with counterpoise effect
- Core Saturation & Max Power Handling: Saturation voltage and power limits
- Multi-Band Reactive Compensation Analysis: VSWR with/without series L or C
-
Do NOT use Mix 31 ferrite for UnUn; use Mix 43, 52, or 61 only
- Mix 31 (MnZn) is for 1:1 chokes ONLY
- Mix 43, 52, 61 (NiZn) are for impedance transformers
- See Section 6.3 for detailed ferrite selection
-
Core power limits (1.8–30 MHz, 9:1 ratio):
- FT-114 (mix 43): 100–150 W max
- FT-140 (mix 43): 300–400 W max
- FT-240 (mix 43): 1000–1500 W max
-
Saturation not fully modeled — Keep actual power ≤50% of rated for safety margin
Typical Workflow:
- Get recommended ratio from UnUn Ratio Optimizer (Sheet 7)
- Select core size from Toroid Database (Sheet 8)
- Input core type & ratio here
- Note turn counts and construction details
- Build & test with VNA/analyzer
Purpose: Design an air-core antenna tuning network (impedance matching coil with multiple taps)
| Aspect | UnUn (Sheet 3 — design; Sheet 7 — ratio optimizer) | Transmatch (Sheet 4) |
|---|---|---|
| What it is | Fixed-ratio ferrite wideband transformer | Air-core tapped coil tuner |
| Matching | Same impedance ratio all bands (9:1, 16:1, etc.) | Different tap optimized per band |
| Setup | Plug-and-play; broadband | Manual tap switching (or relays) |
| Efficiency | 95%+ (ferrite losses) | 98%+ (air-core, minimal loss) |
| Complexity | Simple build (1–2 hours) | Moderate (3–4 hours); requires tap switching |
| Cost | Low-moderate | Low |
| Best for | QRP portable, multiband easy operation | Home station, optimization, experimentation |
| Power handling | Limited by core size (50W–1500W) | Essentially unlimited (wire gauge limited) |
| Optimization | Fixed by transformer ratio | Can optimize each band separately |
- Designs an air-core coil with multiple taps for different bands
- Calculates tap positions — Each tap optimized for a specific frequency/band
- Predicts SWR for each tap — Shows which tap is best for each band
- Provides construction details — Turns per section, wire length needed, winding geometry
- Accounts for actual antenna impedance — Links to impedance model in VSWR Calculator
- Antenna length (m): Entered independently in the Transmatch Calculator sheet (cell C5); it is not automatically inherited from the VSWR Calculator — you must enter your chosen wire length here manually. Check that this matches your selection on Sheet 1.
- Coil dimensions: Diameter (mm), wire gauge (AWG or mm)
- Target output impedance: Always 50 Ω (coax)
- Active bands: Inherited from Calculator sheet
- Tap summary: Which tap for which band, required turns ratio, impedance
- Winding details: Cumulative turns, delta turns per section, wire length
- RF performance: Two SWR columns are shown per tap/band:
- SWR (unmatched) — the raw impedance magnitude referenced to 50 Ω before the autotransformer step; typically very high (>10:1) and informational only. This column reflects the antenna impedance Z_in directly, without any turns-ratio transformation.
- SWR with 5% comp Serial — the matched SWR after the autotransformer transformation plus a 5% series compensation component; this is the working value to evaluate (green SWR ≤1.5, red SWR >3.0)
- Return loss and reflected power per tap (based on matched SWR)
- Construction guide: Color-coded interpretation (green SWR <1.5, red SWR >3.0)
-
Wind the coil on air-core form (PVC pipe, cardboard tube, etc.)
- Diameter: Specified in C11 (typically 50 mm)
- Wire: AWG #18–#12 enamel copper (typically 1 mm ≈ AWG #18)
- Spacing: ~1 mm between turns (allows air cooling and better coupling)
-
Mark tap points at cumulative turn counts from calculator
- Use small PCB pads, solder pads, or banana jacks
- Label each tap clearly with band (80m, 40m, 20m, 10m, etc.)
-
Connect to antenna:
- Bottom tap (lowest turn count) → Hot lead to antenna wire
- Reference point (middle turns) → Counterpoise connection
- Switching mechanism → Select tap for desired band
-
Add switching method:
- Manual: Alligator clip on desired tap (portable, field use)
- Relay: Motorized relay per band (home station, automatic)
- Plug: Banana jack at each tap (convenient, stable)
-
Test with antenna analyzer or VNA:
- Measure actual impedance at each band
- Compare to calculator predictions (should be ±10%)
- Fine-tune tap spacing if needed
✅ Very high efficiency (no ferrite losses; air-core ~2% max)
✅ Can be optimized for any impedance (not fixed)
✅ Low cost (wire + coil form)
✅ Fully reversible (no ferrite saturation)
✅ Can be rebuilt if needs change
✅ Unlimited power handling (only wire gauge limited)
❌ Requires tap switching (manual or automatic)
❌ Each tap is optimal only at one frequency
❌ More complex design than broadband UnUn
❌ Requires antenna analyzer for validation
❌ Not ideal for QRP portable (many taps)
- Select wire length on Calculator (Sheet 1)
- Use Transmatch Calculator (Sheet 4) to design air-core coil
- Build coil with marked tap points
- Test with antenna analyzer; fine-tune tap positions if needed
- Use manual alligator clip or relay to switch taps per band
Purpose: Generate ready-to-use NEC2 simulation input files for your antenna design
What It Does:
- Produces a complete NEC2 input deck (
.necfile content) from your antenna parameters - Supports two counterpoise geometries: horizontal in-line and vertical drop from feedpoint
- Automatically calculates the correct number of wire segments per NEC2 rules (≤ λ/10 at highest frequency)
- Generates a frequency sweep from the lowest to highest active band
- Handles "Real (Sommerfeld-Norton)" ground, perfect ground, and free-space options
- The output can be pasted directly into EZNEC, 4NEC2, MMANA-GAL, or any NEC2-compatible modeler
Key Inputs (Blue cells):
- Rank selector (cell E5): Enter a rank number 1–10; wire length auto-fills from the Calculator Top-10 list
- Counterpoise Length (cell B6): Auto-filled as λ/4 of lowest active band; override manually or set to 0 to omit
- Wire Height above ground (cell B7): Typical 5–15 m for portable, 10–30 m for home station
- Wire Diameter (cell B8): Conductor diameter — 1.0 mm (AWG 20), 2.05 mm (AWG 12), 3.26 mm (AWG 8)
- Wire Conductivity (cell B9): Copper = 5.8×10⁷, aluminium = 3.5×10⁷, steel = 1.0×10⁷
- Ground Type (cell B12): "Real (Sommerfeld-Norton)", "Perfect Ground", or "Free Space"
- Ground Conductivity (cell B13) & Permittivity (cell B14): Typical soil: σ = 0.005 S/m, εr = 13
- Frequency Step (cell B17): Sweep resolution (default 0.5 MHz)
- Source Power (cell B19): Used for field strength calculations in NEC2 output
- Highest/Lowest Sim. Freq. (B15, B16): Auto-filled from active bands in Calculator sheet
Key Outputs:
- Coordinate table: Wire geometry with X/Y/Z endpoints for visual inspection
- NEC2 Input Deck — Horizontal counterpoise: Full deck for inline horizontal counterpoise configuration
- NEC2 Input Deck — Vertical counterpoise: Full deck for vertical drop counterpoise at the feedpoint end
How to Use:
- Set the rank selector to your chosen Top-10 wire length (auto-fills from Calculator sheet)
- Adjust height, diameter, and ground parameters
- Copy all of column A from the dashed separator line to the
ENcard - Paste into a new
.necfile and open in EZNEC, 4NEC2, or MMANA-GAL - Run the frequency sweep and examine feedpoint impedance vs. frequency
- Compare NEC2 impedance results with the VSWR Calculator estimates — they validate each other
NEC2 Deck Structure:
CMlines — comment block with antenna dimensions and simulation parametersCE— end of commentsGWlines — geometry wires (tag 1 = antenna, tag 2 = counterpoise)GE 1— geometry end, ground presentLD 5lines — wire conductivity loads (realistic conductor model)EX 0— voltage excitation source at the antenna feedpoint end (end-fed model)GN 2— ground parameters (Sommerfeld-Norton real ground)FR— linear frequency sweepRP— azimuth radiation pattern at horizon elevationEN— end of input file
Note: The segment count formula used is
MAX(11, 2×INT(L×f/30/2)+1), which enforces both the NEC2 odd-segment rule and the ≤ λ/10 maximum segment length at the highest simulated frequency.
Typical Workflow:
- Select wire length on Calculator (Sheet 1)
- Check VSWR estimates on VSWR Calculator (Sheet 2)
- Export a NEC2 file from this sheet to validate with NEC2 simulation
- Compare NEC2 impedance to the empirical model — large discrepancies indicate unusual geometry
Purpose: Visual analysis of antenna impedance vs. wire length
What It Does:
- Calculates impedance for ALL possible wire lengths (5.0 m to 60.0 m, 0.1 m increments)
- Computes resonance avoidance score for each length
- Creates visual "heatmap" showing good lengths (green) vs. bad lengths (red)
- Ranks all lengths by avoidance score
- Identifies which lengths resonate on which bands
Key Inputs:
- Band selection: Inherited from Calculator — column E, rows 12–22 (the ACTIVE column)
- Velocity factor: Inherited from Calculator (cell D7)
Key Outputs:
- Large data table: Impedance (R, X, |Z|) for every 0.1 m increment
- Avoidance score column: Color-coded (green = good, red = bad)
- Sorted ranking: All lengths ranked by avoidance score
- Visual chart: (if present) Shows impedance vs. length graphically
What "Avoidance Score" Means:
- 0.25 (perfect): Maximum distance from ALL resonances — wire is at 3λ/8 or 5λ/8, the ideal position
- ≥ 0.20 (excellent): ★★★ Score; large gap to any resonance
- ≥ 0.12 (good): ★★ Score; well-positioned, easy to tune
- 0.05–0.12 (fair/marginal): ★/⚠ Score; getting close to a resonance
- 0.0 (worst): ✗ AVOID; on a λ/2 or λ/4 resonance
Typical Workflow:
- Provides data for Top-10 list in Calculator
- Use to understand why certain lengths are better than others
- If you have a specific length in mind, check its score here
Purpose: Suggest the best ferrite UnUn impedance ratio for your chosen antenna
What It Does:
- Tests UnUn ratios from 4:1 through 69:1 for your specific wire length
- Calculates average VSWR for each ratio across all active bands for the top-5 wire lengths simultaneously
- Recommends which ratio provides best broadband performance
- Shows per-band VSWR for every ratio — includes both integer (4:1, 9:1, 16:1, 25:1, 36:1, 49:1, 64:1) and non-integer ratios
- Shows trade-offs between different ratios
Key Inputs:
- Wire lengths: Automatically pulls the Top-5 wire lengths from the Calculator sheet
- Antenna impedance data: Calculated from the same empirical impedance model used in the VSWR Calculator
Key Outputs:
- Feedpoint Impedance Table (Section 1): Resistive part Z_R (Ω) for each top-5 wire length per active band
- Optimal UnUn Ratio Summary (Section 2): Per-band best ratio and best achievable VSWR for each of the 5 wire lengths
- Full VSWR Table (Section 3): Complete sweep 4:1–69:1, showing VSWR for every ratio on every active band for each wire length
- Recommended ratio: Which ratio minimises average VSWR across all active bands
Typical Workflow:
- Select wire length on Calculator (Sheet 1)
- Check impedance on VSWR Calculator (Sheet 2)
- Use this sheet (Sheet 7) to confirm best UnUn ratio
- Go to UnUn Calculator (Sheet 3) to design the transformer
Purpose: Reference table of ferrite core specifications and recommendations
What It Contains:
- Fair-Rite & Micrometals cores: Common part numbers and specifications
- Mix types: 31, 43, 52, 61 (organized by material) and iron powder Mix 2 and 6
- AL values: Inductance per-turn-squared (nH/turn²)
- Dimensions: O.D., I.D., height (mm)
- Effective area (Ae, cm²): Used by the UnUn Calculator for core saturation calculations
- Recommended uses: Which cores for what applications
Note: The sheet tab name in the workbook is
Toroid_Database.
How to Use:
- Decide on impedance ratio — use UnUn Ratio Optimizer (Sheet 7) to find the best ratio for your wire length. Common integer-square ratios are 9:1, 16:1, 25:1, 49:1, 64:1, but any ratio from 4:1 to 69:1 can be built as a tapped autotransformer.
- Choose power level you need (QRP: 5–10W, SSB: 50–100W, AM: 100–400W)
- Look up core size from table matching power & ratio
- Note part number and AL value
- Input into UnUn Calculator (Sheet 3)
- Mix 31 (MnZn) is ONLY for 1:1 chokes, not UnUn transformers
- Never use Mix 31 for impedance transformers — it will have:
- Poor frequency bandwidth
- Higher losses
- Low power handling
- Always use Mix 43, 52, or 61 (NiZn) for UnUn applications
Example:
- Want: 9:1 UnUn for 100 W
- Look in table: FT-140-43 rated ~300–400 W
- Choose FT-140-43 (NiZn Mix 43)
- Use AL value (from spec sheet)
- Input into UnUn Calculator (Sheet 3)
- Open
LongWire_Antenna_Calculator.xlsxin Microsoft Excel or compatible spreadsheet software - You should see the Calculator sheet (Sheet 1) as the default
- Locate the Band Selection table (rows 11–22)
- For each band, set the ACTIVE column to:
- YES — You want to operate on this band
- NO — You don't need coverage on this band
- Default: 40m, 20m, 10m are set to YES
Example:
160m: NO
80m: YES ← You selected 80m
60m: NO
40m: YES ← You selected 40m
20m: YES ← You selected 20m
10m: NO
...
- Cell D7: Default is 0.95 (insulated wire + end-effect)
- For bare copper wire in free air: Use 0.97–0.98
- For heavily insulated wire: Use 0.92–0.94
- See rows 29–38 in the Calculator sheet (row 27 is the section title, row 28 is the column header)
- Each row shows:
- Wire Length (meters)
- Avoidance Score (0.0–0.25; higher is better)
- Quality Rating (★★★ EXCELLENT to ✗ AVOID)
Interpretation:
- #1 (Best) — Longest distance from all resonances on selected bands
- #2–#3 — Also excellent; choose if #1 is inconvenient
- #4–#5 — Good, practical options
- #6–#10 — Acceptable but less optimal
- Cell D25: Automatically calculated as λ/4 of the lowest active band (e.g. ~10 m for 40m as the lowest band)
- Example: For 40–10m bands, counterpoise ≈ 9.97 m (λ/4 at 7.15 MHz)
- A practical alternative supported by 2025 research is 0.05 × longest wavelength (~4 m for 80–10m operation); see Section 5.5 and 6.4 for details
- Copy the length of Top-1 or Top-3 recommendation
- This becomes your antenna wire length
- Go to Sheet 2 (VSWR Calculator)
- Cell C4: Paste your chosen wire length
- Review the VSWR (complex Z) column H (rows 8–18, one per band)
- If SWR >3:1 on most active bands, a tuner will be required; try the next-best length from the Top-10 list if SWR >6:1 on any band
- SWR ≤ 1.5:1 → Excellent (green); 1.5–3.0:1 → Good/Acceptable (white); 3.0–6.0:1 → Marginal (tuner needed); > 6.0:1 → Poor (red)
-
Option A: UnUn Transformer (Fixed Ratio)
- Go to Sheet 7 (UnUn Ratio Optimizer)
- Check recommended ratio (9:1, 16:1, 49:1, etc.)
- Go to Sheet 3 (UnUn Calculator) to design
- Build ferrite-based transformer
-
Option B: Air-Core Transmatch (Switched Taps)
- Go to Sheet 4 (Transmatch Calculator)
- Design air-core coil with multiple taps
- Build and test with antenna analyzer
- Construct your chosen transformer/tuner
- Validate with antenna analyzer or VNA
- Test at low power (5–10W) first
- Measure final SWR at transmitter end
- Check for RFI in shack
The avoidance score measures how far your chosen wire length is from problematic resonances.
⚠️ Important: The maximum possible avoidance score is 0.25 (not 1.0). A score of 0.25 means the wire sits exactly at the mid-point between a quarter-wave and a half-wave resonance — the ideal position. The Length Sweep sheet header confirms: "0.25 = perfect (mid-gap between λ/4 and λ/2), 0.00 = on resonance."
Scale:
- 0.25 (Perfect) — Wire is at maximum distance from ALL quarter-wave and half-wave resonances
- ≥ 0.20 (Excellent) — ★★★ Score; large gap between resonances
- ≥ 0.12 (Good) — ★★ Score; acceptable gap; easy to tune
- 0.05–0.12 (Fair/Marginal) — ★ / ⚠ Score; close to a resonance; careful tuning needed
- 0.0 (Worst) — ✗ AVOID; on a quarter-wave or half-wave resonance
Why it matters:
- Wire at high avoidance score (≥ 0.20): Antenna impedance is moderate and easy to match with UnUn/tuner
- Wire at low avoidance score (< 0.12): Antenna impedance will be very high or very low; difficult to achieve good SWR
Example (with 40m, 20m, 10m active):
53.4 m: Score 0.179 (★★ GOOD) — Recommended Top-1 for default band selection
43.4 m: Score 0.178 (★★ GOOD) — Excellent home station option
5.0 m: Score 0.000 (✗ AVOID) — On quarter-wave resonance of 40m; very low impedance
The VSWR Calculator (Sheet 2) predicts standing-wave ratio for your chosen wire and transformer.
Color Coding (from interpretation guide at bottom of sheet):
- 🟢 Green — SWR ≤ 1.5:1 → Excellent match; <4% reflected power
- ⚪ White — SWR 1.5–3.0:1 → Good; acceptable for most ham radio work (tuner helpful)
- 🟠 Marginal — SWR 3.0–6.0:1 → Marginal match; tuner required
- 🔴 Red — SWR > 6.0:1 → Poor match; high-loss mismatch; consider different wire length
Note: The VSWR sheet uses a 4-tier guide. The threshold ">3:1 → consider different wire length" mentioned in the Quick Start (Step 7) refers to the point where a tuner becomes mandatory, not the absolute worst-case limit.
Reading the Results:
- SWR Column (per band): Voltage Standing Wave Ratio (1.0 = perfect, >6.0 = poor)
- Return Loss (dB): Reflection coefficient (>14 dB = acceptable; >20 dB = excellent)
- Phase (degrees): Reactance angle (0° = purely resistive, ±90° = purely reactive)
What to Do:
- If all bands are green (≤1.5): Your wire length is excellent; proceed to transformer design
- If some bands are white (1.5–3.0): Acceptable; use antenna tuner on those bands
- If any band is marginal (3.0–6.0): Tuner required; consider a different wire length
- If any band is red (>6.0): Try a different wire length from the Top-10 list
Important: These are theoretical predictions based on an empirical model. Always validate with an antenna analyzer before full power.
You have two main options for matching your antenna to 50 Ω coax:
Advantages:
✅ Simple, broadband match
✅ No switching needed
✅ Works on all bands simultaneously
✅ Good efficiency (95%+)
✅ Easy to build (1–2 hours)
✅ Ideal for portable/field use
✅ No tap adjustment needed
Disadvantages:
❌ Fixed impedance ratio (9:1, 16:1, etc.)
❌ May not be optimal for every band
❌ Limited power handling (depends on core size)
❌ Ferrite saturation risk at high power
❌ Ferrite core cost
Best for: QRP portable, multiband operation, set-and-forget approach
How to proceed:
- Go to Sheet 7 (UnUn Ratio Optimizer)
- Note the recommended ratio
- Go to Sheet 3 (UnUn Calculator)
- Select ferrite core from Sheet 8 (Toroid Database)
- Build using winding instructions
Advantages:
✅ Extremely high efficiency (98%+)
✅ No ferrite losses
✅ Unlimited power handling
✅ Can optimize each band separately
✅ Low cost (just wire)
✅ Fully reversible (rebuild if needed)
✅ No saturation risk
Disadvantages:
❌ Requires tap switching (manual or relay)
❌ More complex build (3–4 hours)
❌ Each tap only optimal at one frequency
❌ Requires antenna analyzer for validation
❌ Not ideal for portable (many taps)
❌ More tuning effort needed
Best for: Home station, optimization, experimentation, high-power use
How to proceed:
- Go to Sheet 4 (Transmatch Calculator)
- Note calculated tap positions
- Build air-core coil with marked tap points
- Test with antenna analyzer
- Use manual clips or relay to switch taps
The electrical length of a half-wavelength at frequency f is:
λ/2 = (150 / f_MHz) × VF [meters]
λ/2 = (492 / f_MHz) × VF [feet]
Where:
- f_MHz = Frequency in megahertz
- VF = Velocity factor (0.95 for typical insulated wire)
Example: 80m band center frequency = 3.6 MHz
λ/2 = 150 / 3.6 × 0.95 = 39.6 meters
This means a wire of 39.6 m will resonate (half-wave) at 3.6 MHz.
The avoidance score measures how far your wire is from the nearest resonance. For each active band, the score is computed as the minimum fractional distance from both the nearest λ/2 and λ/4 resonance multiples, then the overall score is the minimum across all active bands:
per_band_score = MIN(
MIN(MOD(L/λ½, 1), 1 − MOD(L/λ½, 1)), ← distance from nearest λ/2
|MOD(L/λ½, 1) − 0.5| ← distance from nearest λ/4
)
avoidance_score = MIN(per_band_score across all active bands)
The maximum possible value is 0.25, which occurs when the wire sits exactly at the midpoint between a λ/4 and a λ/2 resonance (i.e., at 3λ/8 or 5λ/8). Inactive bands return 1.00 and are not counted.
Interpretation:
- Score 0.25: Wire is at maximum distance from ALL resonances (ideal)
- Score close to 0.0: Wire is on a resonance
The calculator computes this for all quarter-wave and half-wave multiples across all selected bands.
The feedpoint impedance is estimated using empirical formulas:
R_est = 50 · 80^(cos²(π·L/λ½))
X_est = 1500 · sin(2π·L/λ½)
Z_antenna = R_est + j·X_est
Where:
- L = Wire length (m)
- λ½ = Half-wavelength at frequency (m)
- j = Complex number operator
Important: This model is empirical, not physics-based. Real impedance depends on height, ground, environment. Accuracy: ±20–30%
Once antenna impedance is known:
Γ = (Z_antenna - Z₀) / (Z_antenna + Z₀) [reflection coefficient, complex]
VSWR = (1 + |Γ|) / (1 - |Γ|)
Return Loss = -20 log₁₀(|Γ|) [dB]
Where:
- Z₀ = 50 Ω (source impedance)
- |Γ| = Magnitude of reflection coefficient
Example: If antenna impedance is 400 Ω (at resonance):
Γ = (400 - 50) / (400 + 50) = 350 / 450 = 0.78
VSWR = (1 + 0.78) / (1 - 0.78) = 1.78 / 0.22 = 8.1:1 (very poor match)
With 9:1 UnUn: Z_antenna transforms to ~45 Ω, giving VSWR ≈ 1.1:1 (excellent).
Formula used in the Calculator sheet (λ/4 of lowest active band, velocity-factor corrected):
L_cp = (75 × VF) / f_low_MHz [meters]
⚠️ Important: The spreadsheet applies the velocity factor (VF) to the counterpoise formula, giving an electrical quarter-wave length. This matches what the Calculator sheet actually computes. The purely physical quarter-wave (without VF) would be75 / f_low_MHz, which is slightly longer.
This is the value displayed on the Calculator sheet and pre-filled in the VSWR Calculator and UnUn Calculator sheets. For example, with VF = 0.95 and 40m (7.15 MHz) as the lowest active band:
L_cp = (75 × 0.95) / 7.15 ≈ 9.97 m (λ/4 at 7.15 MHz, VF-corrected)
Updated practical formula (2025 research — 0.05 × longest wavelength):
L_cp = 0.05 × (300 / f_lowest_MHz) [meters]
Example: For 80–10m operation (80m is lowest frequency):
- λ/4 formula (VF-corrected): (75 × 0.95) / 3.65 ≈ 19.5 m (traditional, conservative)
- 0.05λ formula: 0.05 × (300 / 3.65) ≈ 4.1 m (practical, sufficient per PA9X 2025)
Note: The Calculator sheet uses the VF-corrected λ/4 formula for its displayed counterpoise recommendation. The 0.05λ result is a valid practical alternative supported by recent field measurements — both approaches work. The λ/4 value provides a more conservative (lower-loss) return path, while 0.05λ is the minimum effective length.
For a ferrite UnUn transformer:
n = √(Z_antenna / Z₀) [turns ratio — ratio of total turns to tap turns]
Impedance_ratio = (N_total / N_tap)² [impedance transformation for autotransformer]
For 9:1 UnUn (autotransformer):
n = √9 = 3 → total 9 turns, tap at 3 turns (N_tap = 3, N_total = 9)
Z_out = Z_in × (N_total/N_tap)² → 50 Ω × 9 = 450 Ω (antenna side)
⚠️ Autotransformer vs. Two-Winding Transformer: The UnUn Calculator implements a tapped autotransformer (single winding with a tap), as shown in Section 2.1 of the sheet. In this topology,N_tapis the number of turns from ground to the coax input tap, andN_totalis the full winding. The impedance ratio is(N_total / N_tap)². Do not confuse this with a two-winding transformer where primary and secondary are wound separately.
Common recommended lengths (from W0IPL analysis and Sprott research):
| Length (feet) | Length (meters) | Best Coverage | Notes |
|---|---|---|---|
| 42 | 12.8 | 40m+ | Compact portable |
| 63 | 19.2 | 80–10m | Good all-band compromise |
| 74 | 22.6 | 80–10m | Best gap (376 kHz) — most recommended |
| 84 | 25.6 | 80–10m | Commonly used alternative |
| 111.5 | 34.0 | 160–10m | Extended coverage |
| 135 | 41.1 | 160m+ | For 160m coverage |
For your specific needs:
- Use Calculator sheet to find Top-10 lengths for YOUR selected bands
- All Top-3 recommendations are excellent
- Test with VSWR Calculator to compare performance
A 9:1 autotransformer is the most common and practical design. Here's how to build one:
- 1× FT-240-43 ferrite toroid (or FT-140-43 for lower power)
- ~3 m of 18-20 AWG enamel copper wire (trifilar winding)
- Small enclosure (plastic food container, aluminum box ~4"×4"×2")
- 3× Banana jacks or wire posts (antenna, ground, coax center)
- 2× Coaxial connectors (SO-239 or SMA) OR wire terminals
- Heat shrink tubing
- Silicone seal (weatherproofing)
-
Prepare the wire
- Cut two lengths ~1.5 m each of 18 AWG enamel wire
- The 9:1 UnUn is built as an autotransformer: a single 9-turn winding with a tap at turn 3
- The coax (50 Ω) connects across turns 0–3 (the tap); the antenna connects across the full 0–9 turns
-
Wind the toroid (Bifilar/autotransformer method)
- Wind a single winding of 9 turns total through the toroid
- Mark a solder tap at turn 3 (this is the coax / low-impedance input tap)
- Turns 0–3: primary (coax side, 50 Ω) tap point
- Turns 0–9: full winding (antenna side, ~450 Ω)
- Total: 9 passes through toroid
-
Strip and Identify Leads
- Carefully scrape enamel off all wire ends and the mid-winding tap
- Label them: T0 (start/ground), T3 (input tap), T9 (antenna end)
⚠️ Autotransformer note: A 9:1 autotransformer uses one continuous winding with a tap, not separate primary and secondary windings. The impedance ratio is (N_total/N_tap)² = (9/3)² = 9:1. This is confirmed by Section 2.1 of the UnUn Calculator sheet. Do not wind 3 turns and 9 turns separately — that would give a turns ratio of 3:9 and an impedance ratio of 1:9 (wrong direction). -
Make Connections (autotransformer configuration)
- Coax/input side (50 Ω):
- Coax center conductor → T3 (tap)
- Coax shield → T0 (start/ground)
- Antenna side (high impedance):
- Antenna wire → T9 (full winding end)
- Counterpoise → T0 (same as ground)
- Impedance ratio: (T9/T3)² = (9/3)² = 9:1 — antenna sees 9 × 50 Ω = 450 Ω
- Coax/input side (50 Ω):
-
Mount in Enclosure
- Place toroid in center
- Mount connectors on side
- Keep leads short and direct
- Apply silicone seal for weatherproofing
- Drill small drain hole at bottom for water drainage
-
Validate (before connecting to antenna)
- Use antenna analyzer or VNA
- Measure impedance ratio at various frequencies
- Should see roughly 9:1 across 1.8–30 MHz
- If ratio is wrong, check connections
- FT-114-43: 100–150 W max
- FT-140-43: 300–400 W max
- FT-240-43: 1000–1500 W max
Use 50% margin: If 100W is your target, use FT-140-43 (rated 300–400W).
DO NOT USE Mix 31 for UnUn/Balun impedance transformers. Mix 31 (Manganese-Zinc ferrite) is only suitable for 1:1 common-mode choking applications. According to Palomar Engineers and Fair-Rite specifications:
Ferrite Mix Comparison:
| Mix | Material | Frequency Range | Best Use | Impedance Transformer? | Notes |
|---|---|---|---|---|---|
| 31 | MnZn | 1–10 MHz | 1:1 RF chokes ONLY | ❌ NO | Low frequency; NOT for UnUn |
| 43 | NiZn | 10–250 MHz | UnUn 9:1, 16:1, 25:1 | ✅ YES | BEST for HF UnUn |
| 52 | NiZn | 1–250 MHz | HF/VHF UnUn | ✅ YES | Effective across HF range; more turns needed than Mix 43 |
| 61 | NiZn | 200–2000 MHz | Ultra-wideband | ✅ YES | Very low µ; many turns needed |
Toroid Database availability: The
Toroid_Databasesheet includes FT-114, FT-140, FT-240 variants for Mix 31, 43, 52, 61, plus T-130 and T-200 in iron powder Mix 2 and Mix 6. FT-82 and Mix 75 cores are not listed in the sheet — consult Fair-Rite datasheets directly for these.
For HF Long-Wire UnUn applications (1.8–54 MHz):
- ✅ Best choice: Mix 43 — Ideal balance of permeability, bandwidth, and efficiency
- ✅ Secondary: Mix 52 — If higher frequencies needed (not typical for HF)
- ❌ NEVER Mix 31 — Not suitable for impedance transformers
Core Size and Power Handling (Ferrite):
| Core Size | Max Power (PEP) @ 1.8–30 MHz | Recommended For | Notes |
|---|---|---|---|
| FT-114 (mix 43) | 100–150 W | SSB voice (10–50W sustained) | Compact, moderate power |
| FT-140 (mix 43) | 300–400 W | Linear amp (50–150W sustained) | Larger; good thermal mass |
| FT-240 (mix 43) | 1000–1500 W | High power (100W+ sustained) | Large; excellent thermal performance |
- Ferrite saturation flux density (Bsat) decreases by 20–30% with every 50°C temperature rise
- If core is warm to touch during operation, saturation may be occurring
- Design safety margin: Keep flux density at <50% of Bsat at room temperature
- Never use a core at maximum rated power continuously — leave 30–50% margin for sustained operation
- Small cores (FT-114) heat up and saturate more quickly than larger cores
Stacking Cores for High Power:
- Single FT-240-43: ~1000–1500 W @ 1.8–30 MHz
- Two FT-240-43 stacked: ~2000–3000 W @ 1.8–30 MHz
- Stacking reduces saturation risk and extends bandwidth
A counterpoise is a wire or set of wires that acts as a reference return path (ground plane substitute) for the antenna. It is electrically and RF-wise "in parallel" with the antenna feedline and carries the return RF current.
Counterpoise Length Formula (Updated 2025):
The traditional rule of thumb is: λ/4 of the lowest operating frequency — this is what the Calculator sheet computes and displays.
However, recent research (PA9X 2025, RF.Guru 2025) provides more nuanced guidance:
- Minimum effective length: 0.05 × longest wavelength you plan to transmit on
- Example: For 80–10m operation (80m is longest), λ = 80 m, so 0.05 × 80 = 4 meters is sufficient
- This length:
- Provides return current path without radiating as co-radiator
- Much more practical than λ/4 (~20m for 80m)
- Verified effective by multiple 2025 studies
Number of Radials:
- Single radial: 1–2 meters minimum; works well for QRP
- Multiple radials (preferred): 2–4 radials each ~1.5–2 m → Impedance halves with each additional radial in parallel
- Ground system: Buried radials more effective than elevated wires
Configuration Options:
-
Separate counterpoise wire (preferred)
- Run dedicated wire from UnUn ground to suitable point
- Can be elevated or buried
- Completely isolated from feedline
-
Coax braid as counterpoise (practical but less ideal)
- Section of coax between UnUn and first CMC acts as return path
- Length: Use 0.05λ formula
- Note: Part of coax does carry RF; this is intentional and necessary
-
Combination (good compromise)
- Dedicated counterpoise wire + coax section
- Provides low-impedance return path
- Reduces reliance on coax alone
Long-wire antennas can be mounted in several configurations:
-
Horizontal (far field favored)
- Wire runs horizontally, suspended as high as possible
- Radiates best in horizontal plane
- Ideal for DX (distant) communications
- Requires high supports (trees, towers)
-
Sloper (favored for NVIS)
- Wire angles downward from one high support to lower point
- Radiates at higher angles (up toward sky)
- Good for NVIS (Near Vertical Incidence Skywave) on low bands
- Works with single support
-
Inverted-L
- Vertical section + horizontal section forming an "L"
- Combines vertical and horizontal radiation
- Can provide good low-angle radiation for DX
- Requires single tall support
-
End-fed (antenna only)
- Fed at one end, other end open or terminated
- Can be any of above configurations
- Feed point impedance varies with configuration
- Most common for this calculator
-
Center-fed (dipole-like, for comparison)
- Fed at center; requires parallel feedline or balanced line
- Not primary focus of this calculator
- Would require BalUn (Balanced-to-Unbalanced), not UnUn
Recommendation: Horizontal or sloper configuration at maximum practical height gives best overall performance.
A common-mode choke (also called 1:1 balun or 1:1 UnUn) suppresses RF current flowing on the outside of the coaxial shield. This prevents the feedline from radiating and causing RFI.
The CMC placement is critical and often done incorrectly. Here is the correct 2025 guidance:
INCORRECT (often mistakenly recommended): CMC immediately at the UnUn feedpoint
CORRECT (2025 best practice): CMC at the radio end of the feedline, before it enters the shack
Why the difference:
- With a CMC at the feedpoint, it blocks the coax braid from acting as the counterpoise
- The antenna requires the coax to carry some return current — this is intentional and necessary for impedance matching
- A CMC at the feedpoint destabilizes the impedance transformation
- The CMC should allow the coax to act as counterpoise near the antenna, then suppress common-mode current before it reaches sensitive equipment
Recommended Installation (Correct Order):
- UnUn at antenna feedpoint (no CMC here!)
- Coaxial feedline (typically 1–50 feet)
- Outer braid carries return RF current (necessary for impedance matching)
- This is intentional; don't block it
- Optional: 1:1 ferrite choke at 16–50 feet from UnUn (if additional isolation needed)
- Provides extra isolation on low bands
- FT-240-31 or similar
- 10–12 bifilar turns
- Coaxial feedline continues to shack
- Can be bundled with other cables
- CMC / 1:1 balun BEFORE ENTERING HOUSE/RADIO ROOM ← Critical placement!
- This is where common-mode current is suppressed
- Prevents RF in shack
- Shields radio and AC mains from antenna currents
Exception: For EFHW (end-fed half-wave) with separate dedicated counterpoise wire, place CMC as close as possible to the UnUn (30–50 cm acceptable). This prevents the coax from acting as an unintended counterpoise.
CMC Core Selection & Design:
- Mix 31 (MnZn): Best for 1.8–10 MHz (≥ 1000 Ω at 1.8 MHz)
- Mix 43 (NiZn): 10–250 MHz broadband choking
- Recommended: FT-240-31 or FT-240-43 with 10–12 bifilar turns
- Provides 1000+ Ω from 1.8–30 MHz
- For maximum performance: Two FT-240-31 stacked with 12 bifilar turns each
- Target choking impedance: ≥1000 Ω at lowest operating frequency
Coax Braid Current (Expected):
- Small amount of RF current on coax shield is NORMAL and EXPECTED
- This shields the inner conductor from field coupling
- Only suppress it with a CMC when it becomes excessive (causing RFI)
- Don't block this current at the antenna; allow it to return via coax, then suppress at shack
This calculator supports all amateur radio HF bands from 160 meters to 6 meters:
| Band | Frequency Range | Wavelength (m) | λ/4 (m) | λ/2 (m) |
|---|---|---|---|---|
| 160m | 1.8–2.0 MHz | 167–150 m | 42–37.5 m | 83–75 m |
| 80m | 3.5–3.8 MHz | 86–79 m | 21–20 m | 43–39 m |
| 60m | 5.35–5.37 MHz | 56 m | 14 m | 28 m |
| 40m | 7.0–7.3 MHz | 43–41 m | 10.7–10.3 m | 21.4–20.5 m |
| 30m | 10.1–10.15 MHz | 30–29.5 m | 7.5–7.4 m | 15–14.8 m |
| 20m | 14–14.35 MHz | 21.4–20.9 m | 5.4–5.2 m | 10.7–10.4 m |
| 17m | 18.068–18.168 MHz | 16.6–16.5 m | 4.1–4.1 m | 8.3–8.2 m |
| 15m | 21–21.45 MHz | 14.3–14.0 m | 3.6–3.5 m | 7.1–7.0 m |
| 12m | 24.89–24.99 MHz | 12.0–12.0 m | 3.0–3.0 m | 6.0–6.0 m |
| 10m | 28–29.7 MHz | 10.7–10.1 m | 2.7–2.5 m | 5.4–5.0 m |
| 6m | 50–54 MHz | 6.0–5.6 m | 1.5–1.4 m | 3.0–2.8 m |
The calculator automatically finds wire lengths that avoid half-wave and quarter-wave resonances on all selected bands.
Model Accuracy:
- The feedpoint impedance model (R_est and X_est) used in the VSWR Calculator is empirical, NOT based on NEC2 full-wave antenna modeling
- Real antenna impedance depends on: height, ground type, nearby objects, weather conditions (humidity/rain), exact geometry
- For NEC2 validation: Use the NEC2 Export sheet (Sheet 5) to generate a simulation file and compare against these empirical estimates
- Always validate with a VNA or antenna analyzer before connecting to a transmitter at full power
450 Ω Assumption (CORRECTED 2024):
⚠️ This calculator assumes the "standard" 450 Ω for 9:1 matching, but measured data shows impedance varies widely- A 9:1 UnUn may not be optimal for your specific wire length and installation
- Use the VSWR Calculator sheet to estimate actual impedance and select appropriate UnUn ratio
- Consider alternative ratios (4:1, 6:1, 7:1, 16:1, 49:1) if your measured impedance differs significantly from 450 Ω
- Key source: Ham Radio Outside the Box (Sept 2024) measured an 84-foot wire showing impedance LESS than 450 Ω on all bands
Core Saturation Not Modeled:
- The UnUn Calculator sheet does NOT account for ferrite core saturation in detail
- At high power (>100 W on HF), small cores heat up and lose permeability
- Check the "Toroid Core Selection" section for power ratings; do not exceed 50% of rated power for sustained operation
- FT-114-43 is the smallest core in the Toroid Database — avoid sustained high-power operation on this core
Counterpoise Impedance Model (Empirical):
- The counterpoise impedance model in the VSWR Calculator is based on heuristic formulas, not NEC2 simulation
- Real counterpoise impedance depends on: length, height, number of radials, ground conductivity, soil type
- Use as a rough guide; actual values may vary ±30%
- Validation: Measure with antenna analyzer to confirm
Ferrite Mix 31 Warning (Critical):
⚠️ Do NOT use Mix 31 for UnUn transformers; use ONLY for 1:1 chokes- Use Mix 43, 52, or 61 (NiZn) for all multi-ratio UnUn designs
- Mix 31 will have poor bandwidth, higher losses, and low power handling on HF
Common-Mode Choke Placement (UPDATED):
- CMC should be placed at the radio end of the feedline, NOT at the antenna feedpoint
- Placing CMC immediately at the UnUn can degrade impedance matching by blocking the counterpoise effect
- Correct placement: Before feedline enters house/radio room
Temperature Effects:
- Ferrite saturation flux density decreases 20–30% per 50°C temperature rise
- Design with 30–50% margin from rated saturation
- If core is warm to touch, you may be approaching saturation
- Stacking cores reduces saturation risk
Empirical Model Accuracy:
- This model is NOT validated against NEC2 or measured data across all conditions
- Predicted impedance is accurate to approximately ±20–30%
- Results may vary significantly with installation geometry, height, and environment
- Always verify with measurement equipment before full-power operation
| Term | Definition |
|---|---|
| Antenna tuner | Device that matches antenna impedance to transmitter impedance; also called ATU or transmatch |
| Avoidance score | Metric (0–0.25) indicating distance from resonance; 0.25 = wire at maximum distance from all resonances (3λ/8 or 5λ/8), 0.0 = wire is on a resonance (λ/4 or λ/2) |
| BalUn | Balanced-to-Unbalanced transformer; used for balanced antennas like dipoles |
| Bandwidth | Range of frequencies over which a component operates effectively |
| Characteristic impedance | Reference impedance of a transmission line (typically 50 Ω for coax) |
| Common-mode choke | RF choke that suppresses current flowing on cable shields (1:1 transformer function) |
| Counterpoise | Ground-plane substitute; return path for antenna current, running in parallel with feedline |
| dB (decibel) | Logarithmic ratio; 10 dB = 10× power, 20 dB = 10× voltage |
| End-fed | Antenna fed at one end; opposite of center-fed (dipole) |
| EFRW | End-Fed Random Wire; another name for long-wire antenna |
| Feedpoint impedance | Complex impedance presented at the feed terminals of an antenna; combination of radiation resistance, loss resistance, and reactance |
| Ferrite | Magnetic ceramic material; used in cores for transformers and chokes |
| HF | High Frequency — 3–30 MHz, encompassing the major amateur radio bands |
| Impedance | Opposition to AC current flow; combination of resistance (R) and reactance (X); Z = R + jX |
| Inverted-L | Antenna configuration with a vertical section and a horizontal section forming an L-shape |
| λ/2 | Half-wavelength — the wire length at which a resonant maximum of feedpoint impedance occurs |
| λ/4 | Quarter-wavelength — the wire length at which a resonant minimum of feedpoint impedance occurs |
| NEC | Numerical Electromagnetics Code — the standard electromagnetic simulation engine for antenna modeling |
| QRP | Low-power amateur radio operation (typically < 5 W) |
| Radial | A single wire in a ground/counterpoise system, extending radially from the antenna feed point |
| RF choke | Common-mode inductance placed on a feedline to suppress current flow on the coax shield exterior |
| SWR / VSWR | (Voltage) Standing Wave Ratio — ratio of forward to reflected voltage on a feedline; 1:1 = perfect match |
| Toroid | Donut-shaped ferrite or powdered-iron magnetic core used to wind transformers and chokes |
| Transmatch | Antenna tuning network; can be air-core (tapped coil) or ferrite-based (transformer) |
| Turns ratio | The ratio of the number of turns on the primary to secondary winding of a transformer; impedance ratio = turns ratio² |
| UnUn | Unbalanced-to-Unbalanced transformer — used where both feedline and antenna are unbalanced |
| VF / Velocity Factor | The ratio of wave propagation speed in a conductor to the speed of light in vacuum (0 < VF ≤ 1) |
| VNA | Vector Network Analyzer — instrument for measuring antenna impedance, SWR, and complex S-parameters |
| VSWR | See SWR |
| X_est | Estimated feedpoint reactance (Ω) — the imaginary part of the complex feedpoint impedance |
| Zcp | Counterpoise impedance — the RF impedance of the counterpoise wire, which appears in series with the antenna load at the UnUn primary |
| Z0 | Characteristic impedance; typically 50 Ω for coaxial cable |
- ARRL Antenna Book (24th edition and later) — comprehensive coverage of end-fed antennas, impedance matching, and feedline theory
- Lewallen, R., W7EL — NEC-based Antenna Modeling Software, EZNEC documentation (http://www.eznec.com)
- Moxon, L.A., G6XN — HF Antennas for All Locations, RSGB, 1982 — classic reference for practical HF wire antennas
- Sprott, J.C. — "Optimal Length of a Random Wire Antenna", technical note (April 2012, revised May 2022), University of Wisconsin, https://sprott.physics.wisc.edu/technote/randwire.htm — algorithmic approach to finding lengths that avoid all amateur band half-wave resonances simultaneously. Key result: 74 feet (≈ 22.6 m) is identified as the length with the widest gap (376 kHz) between resonances, making it one of the most robust choices for 80–10 m multi-band coverage without a balun of large turns ratio.
- W0IPL — "Optimal Non-Resonant Wire Lengths for HF Operation" — table of odd quarter-wave multiples versus amateur band resonances; origin of the widely-cited 74-foot non-resonant recommendation; referenced in ARRL Antenna Book and the Wikipedia Random wire antenna article
- AA5TB — "End-Fed Half-Wave Antenna", https://www.aa5tb.com/efha.html — detailed analysis of EFHW impedance and transformer design
- W8JI — "Long Wire Antenna", https://www.w8ji.com/long_wire_antenna.htm — authoritative practical analysis including counterpoise design and the argument for a 1:1 current balun rather than a UnUn
- G3TXQ (Steve Hunt, SK 2015) — "Wideband Transformers" and "Common Mode Chokes", http://www.karinya.net/g3txq/ — extensive research on ferrite vs. powdered iron core performance for UnUn applications (site archived; content remains an authoritative reference)
- Fair-Rite Products — Material Data Sheets for Mix 31, 43, 52, 61, https://fair-rite.com/product-category/toroid-cores/ — primary source for AL values, permeability curves, and frequency range data
| Resource | URL | Content |
|---|---|---|
| Ham Radio Outside the Box — Random Wire Antennas Challenge | https://hamradiooutsidethebox.ca/2024/09/04/random-wire-antennas-a-challenge-to-common-knowledge/ | CRITICAL 2024 STUDY — Measured 84-foot wire impedance is LESS than 450 Ω on all bands, directly contradicting conventional wisdom. Questions the optimality of 9:1 UnUns. |
| W8JI — Long Wire Antenna | https://www.w8ji.com/long_wire_antenna.htm | Authoritative practical analysis of long-wire systems including counterpoise design |
| Bob Cromwell, AC6V — 9:1 UnUn Build | https://cromwell-intl.com/radio/9-1-unun/ | Detailed construction guide with NanoVNA measurements and core material comparison |
| M0UKD — 9:1 Magnetic Longwire Balun | https://m0ukd.com/homebrew/baluns-and-ununs/91-magnetic-longwire-balun-unun/ | Step-by-step with photos |
| KB6NU — End-Fed Wire and 9:1 UnUn | https://www.kb6nu.com/playing-end-fed-wire-antennas-91-ununs/ | Discussion of core selection and practical results, including G3TXQ core comparisons |
| HFkits — Manual 1:9 UnUn | https://www.hfkits.com/manual-19-unun-600-watts-for-long-wire-antennas/ | Commercial kit instructions with winding details |
| Electronics Notes — End-Fed Wire | https://www.electronics-notes.com/articles/antennas-propagation/end-fed-wire-antenna/ | Beginner-friendly theoretical overview |
| PA9X — Common Mode Choke | https://www.pa9x.com/the-broadband-common-mode-choke/ | Core ratings, choke construction, power limits |
| Toroids.info | https://toroids.info | Online calculator for AL values and inductance of ferrite toroids |
| 73QRZ Choke Calculator | https://73qrz.com/choke-calc | Online tool for balun/choke/UnUn core selection |
| Practical Antennas | https://practicalantennas.com/designs/end-fed/ | Comprehensive analysis of end-fed types |
| RF.Guru — Counterpoise Role & CMC Placement | https://shop.rf.guru/pages/understanding-the-role-of-the-counterpoise-in-4-1-and-9-1-antennas/ | August 2025: Detailed counterpoise design; optimal CMC placement guidance |
| PA9X — Proper Counterpoise Design | https://www.pa9x.com/boost-your-end-fed-antenna-with-proper-counterpoise/ | October 2025: Rule of thumb for counterpoise length (0.05λ); RFI prevention |
| PA9X — Why Antennas Need Counterpoises | https://www.pa9x.com/why-does-an-antenna-require-a-counterpoise/ | Complete explanation of counterpoise function |
| K7MEM — End-Fed Wire Calculator | https://k7mem.com/Ant_End_Fed.html | Interactive online calculator for non-resonant end-fed wire lengths; similar avoidance approach to this workbook |
| VU2NSB — EFHW Antenna | https://vu2nsb.com/antenna/wire-antennas/multiband-efhw-antenna/ | Detailed harmonic analysis of EFHW antenna |
| Battery Eliminator Store — EFHW Deep Dive | https://batteryeliminatorstore.com/blogs/ocf-masters-articles/a-deep-dive-into-end-fed-half-wave-antennas-original | Analysis of transformer ratios from 9:1 to 64:1 |
| Wikipedia — Random Wire Antenna | https://en.wikipedia.org/wiki/Random_wire_antenna | Historical context and impedance characteristics |
| Wikipedia — Counterpoise | https://en.wikipedia.org/wiki/Counterpoise_(ground_system) | Ground system theory |
| RF.Guru — Feed Point Impedance | https://shop.rf.guru/pages/feed-point-impedance-vs-height-for-end-fed-antennas | Feedpoint impedance vs. height and geometry analysis |
| KM1NDY — 64:1 UnUn Build | https://km1ndy.com/diy-linked-efhw-64-to-1-antenna/ | DIY construction of 64:1 UnUn for linked EFHW |
| HF Underground — 9:1 vs 49:1 Discussion | https://www.hfunderground.com/board/index.php?topic=59165.0 | Community discussion on UnUn ratio selection |
| dbBear — EFHW Transformer Theory | https://www.dbbear.com/k0emt/kits/2024-efhw/theory/index.html | Transformer theory and capacitor compensation |
| Palomar Engineers — Ferrite Mix Selection | https://palomar-engineers.com/ferrite-cores-for-rfi-emi-noise-suppression-mix-31-43-61-75-palomar-engineers/ | Updated 2025: Mix 31 NOT for UnUn; detailed mix comparison |
| Palomar Engineers — Power Ratings | https://palomar-engineers.com/choke-transformer-power-ratings | Core size power limits; saturation guidance |
💡 Built-in NEC2 Export: This workbook includes a NEC2 Export sheet (Sheet 5) that generates a ready-to-paste
.necinput file for any of the Top-10 wire lengths. Use it to validate the empirical VSWR estimates against a full-wave simulation.
| Tool | Platform | Description |
|---|---|---|
| EZNEC | Windows | Industry-standard NEC-2 antenna modeler by W7EL; recommended for precise feedpoint impedance validation |
| 4NEC2 | Windows (free) | Free NEC-2/NEC-4 GUI with optimizer; excellent for wire antenna design |
| MMANA-GAL | Windows (free) | Simple NEC-based modeler, popular with beginners |
| OpenEMS | Cross-platform (free) | Full-wave FDTD simulator for advanced analysis |
| NanoVNA | Hardware | Low-cost vector network analyzer (50 kHz–1.5 GHz); ideal for validating built UnUn transformers and antenna impedance |
| miniVNA Tiny | Hardware/Software | Another popular portable VNA for antenna measurement |
This spreadsheet calculator is released under the Creative Commons Zero v1.0 Universal (CC0 1.0) license — effectively a public domain dedication.
⚠️ Note: The workbook header and all sheet footers declare CC0 v1.0. CC0 waives all copyright and related rights; no attribution is legally required, although it is always appreciated. An earlier version of this README incorrectly stated CC BY 4.0.
You are free to:
- Share — copy and redistribute in any medium or format
- Adapt — remix, transform, and build upon the material for any purpose, including commercially
Under CC0 there are no conditions. To the extent possible under law, the author has dedicated the work to the public domain.
Full license text: https://creativecommons.org/publicdomain/zero/1.0/
73 de the author — good DX and may your SWR always be low!
Disclaimer: This tool is provided for educational and experimental purposes. The author makes no warranties regarding the accuracy of the impedance models or the suitability of any recommended configuration for any specific installation. Always verify designs with proper measurement equipment (VNA, antenna analyzer) before connecting to a transmitter. Comply with all applicable regulations regarding antenna installations and transmitter power limits. High voltages may be present at the antenna feedpoint during operation — exercise appropriate caution.