Delta Loop Calculator

The Delta Loop Calculator calculates optimal triangular loop dimensions and resonant frequency from wavelength, feedpoint choice, and conductor properties.

About the Delta Loop Calculator

The calculator focuses on the dimensions and electrical behavior of an equilateral delta loop made from wire. It computes loop circumference, side length, height, enclosed area, and approximate feed point impedance. You can choose feed location and polarization to see how the impedance and expected pattern shift.

Behind the scenes, it uses wavelength relationships, an empirical sizing constant, and simple current distribution models. It also adjusts for insulation and wire thickness using a velocity factor. These effects slightly change the resonant length and bandwidth, which are captured in the result summary.

It is designed for builders and learners. The outputs include units in metric and imperial where practical. You will also see short notes that explain the derivation, so you can check the math or adapt it to special cases.

The Mechanics Behind Delta Loop

A delta loop is a full‑wave loop shaped as an equilateral triangle. At resonance its circumference is close to one wavelength. Current flows around the loop, creating a broadside radiation pattern. Height, feed point, and orientation control polarization and tuning.

• Resonant condition: the loop circumference is approximately one free‑space wavelength, slightly reduced by end and wire effects.
• Polarization: feed at a lower corner and orient the plane vertically for vertical polarization; feed at the midpoint of a side for horizontal polarization.
• Impedance: corner‑fed delta loops often present near 50–70 Ω; side‑center feeds often present around 100–120 Ω.
• Height above ground: changing height shifts resonance and pattern, especially within 0.5 λ of the earth.
• Wire diameter and insulation: thicker or insulated wire lowers the required circumference due to a reduced effective wavelength.

These principles guide the calculator’s sizing and impedance estimates. While terrain and nearby structures matter, the core physics remains consistent across bands.

Delta Loop Formulas & Derivations

At the heart of the delta loop is the wavelength–frequency link. We combine that with triangle geometry and standard antenna assumptions. Where practice differs from a simple model, an empirical factor captures the difference. Each item below notes the derivation logic.

• Wavelength: λ = c / f. Here c ≈ 299,792,458 m/s and f is frequency in hertz. This directly sets the scale of any resonant antenna.
• Resonant circumference: C ≈ kλ. For typical bare wire loops, k ≈ 1.00–1.02. A widely used empirical form is C ≈ 1005 / f(MHz) feet ≈ 306.5 / f(MHz) meters. Derivation: start with C ≈ λ, then add a small correction from end and conductor effects.
• Velocity factor for insulation: C_adjusted = VF × C, where VF ≈ 0.95–0.98 for common insulated hookup wire. Derivation: the dielectric slows the wave along the conductor, shortening resonant length.
• Triangle geometry: for an equilateral loop, side length s = C / 3. Height h = (√3 / 2) × s. Area A = (√3 / 4) × s². Derivation: standard equilateral triangle relations.
• Feed‑point impedance (approximate): Z_corner ≈ 50–70 Ω for a vertically polarized, corner‑fed loop; Z_side ≈ 100–120 Ω for a horizontally polarized, side‑midpoint feed. Derivation: current distribution and radiation resistance estimates from loop antenna theory and measurements.
• Bandwidth and quality factor: Q ≈ f0 / BW, with BW measured between SWR = 2:1 points. Derivation: standard resonator definition; thicker wire lowers Q, increasing bandwidth.

These formulas produce the baseline result. The calculator combines the empirical circumference relation with your selected VF, then applies triangle geometry for build dimensions. Impedance estimates use feed location and orientation rules of thumb validated in practice.

What You Need to Use the Delta Loop Calculator

Before you start, gather a few design choices and environmental details. These inputs produce a more reliable result and avoid re‑cuts during the build. If unsure, you can start with defaults and refine later.

• Target frequency f in MHz (for example, 14.2 for the 20‑meter band).
• Wire type and insulation (velocity factor VF, typical 0.95–1.00).
• Conductor diameter or AWG (affects bandwidth and small length corrections).
• Feed location and planned polarization (corner vs side‑center).
• Estimated height above ground in meters (affects tuning and takeoff angle).
• Feed line impedance in ohms (50 Ω, 75 Ω, or a matching method).

Most HF designs accept a small trimming step because surroundings vary. Expect resonance to shift down if the loop is close to the ground or nearby metal. For wide bandwidth or wet climates, choose slightly thicker wire. The calculator flags edge cases at very low heights (below 0.1 λ) and very thin wire where derivation assumptions break down.

Using the Delta Loop Calculator: A Walkthrough

Here’s a concise overview before we dive into the key points:

1. Enter your target frequency in MHz.
2. Select wire insulation or set a custom velocity factor.
3. Choose the feed location and desired polarization.
4. Provide an estimated height above ground.
5. Choose your feed line impedance or matching plan.
6. Review the computed circumference, side length, and height.

These points provide quick orientation—use them alongside the full explanations in this page.

Case Studies

Portable 20‑meter vertical delta loop at 14.2 MHz: We use C ≈ 306.5 / 14.2 = 21.6 m for bare wire (VF = 1.00). Side length s = C / 3 ≈ 7.19 m, height h = 0.866 × s ≈ 6.23 m. Corner feed near the bottom yields vertical polarization and Z ≈ 50–70 Ω, suitable for a 50 Ω feed line with minimal matching. Expect a low takeoff angle and broad azimuth coverage for DX at modest heights. What this means: Cut three pieces near 7.2 m each, hang the apex at about 6.2 m, and trim for lowest SWR around 14.2 MHz.

Backyard 10‑meter horizontal delta loop at 28.5 MHz: C ≈ 306.5 / 28.5 = 10.8 m. Then s ≈ 3.60 m and h ≈ 3.12 m. Feed at the midpoint of a side for horizontal polarization; Z ≈ 100–120 Ω is common, so use a 2:1 balun or a short matching section to reach 50 Ω. The pattern shows a high‑angle lobe at low heights, useful for regional contacts. What this means: Build three 3.60 m sides, mount the loop apex at roughly 3 m, and plan a simple transformer to match a 50 Ω rig.

Accuracy & Limitations

The calculator applies accepted loop antenna theory plus simple, proven empirical constants. It is accurate for freestanding loops in open areas. However, antennas are sensitive to their surroundings, and practical installations vary.

• Nearby metal, siding, or trees detune resonance and change impedance.
• Heights below 0.15 λ can shift resonance downward more than predicted.
• Wet insulation or ice increases dielectric loading and narrows bandwidth.
• Feed line routing and a poor balun can introduce common‑mode current and pattern distortion.

Use the results as a starting cut and plan for on‑site trimming. If you need precision, model the exact geometry in NEC software, then iterate with an analyzer at the build site.

Units and Symbols

Clear units make the build predictable and reduce mistakes. The calculator outputs SI values by default, and shows imperial where useful. Symbols are standard in antenna physics, so you can compare the derivation with textbooks and papers.

Read λ from f using λ = c / f, then compute C and s. If you switch units, apply the conversion 1 m ≈ 3.281 ft. Impedance Z is a calculated estimate in ohms; gain G is given in dBi for easy comparison with other antennas.

Troubleshooting

If your on‑air measurements differ from the calculator’s result, check installation details first. Small layout changes create measurable shifts, especially at lower heights or near structures.

• Resonant frequency too low: shorten each side a little, or raise the loop higher.
• Resonant frequency too high: lengthen the loop, or add a short wire pigtail at the feed.
• High SWR across the band: verify feed location, use a current balun, and re‑route the coax away from the loop.
• Pattern not as expected: confirm polarization and loop orientation; avoid slanted supports that skew the triangle.

Make one change at a time and re‑measure. A handheld analyzer helps you see the trend as you trim toward the target frequency. Record each step so you can repeat a successful build.

FAQ about Delta Loop Calculator

How does a delta loop compare to a dipole at the same frequency?

A full‑wave loop usually has a slightly higher free‑space gain than a half‑wave dipole and a smoother pattern. It can offer lower noise pickup in some environments.

Can I build a non‑equilateral delta loop?

Yes. It will still work, but impedance and pattern shift. The calculator assumes an equilateral triangle, so model odd shapes or plan extra tuning.

Do I need a balun with a delta loop?

A current balun is recommended. It reduces common‑mode currents on the feed line and stabilizes the pattern and SWR across the band.

How does insulated wire change the dimensions?

Insulation lowers the resonant length. Use a velocity factor between 0.95 and 0.98 in the calculator to shorten the computed circumference appropriately.

Delta Loop Terms & Definitions

Delta Loop

A full‑wave loop antenna shaped as a triangle, often equilateral, used for HF and VHF communications with flexible polarization.

Wavelength

The physical length of one cycle of a radio wave, equal to the speed of light divided by frequency.

Circumference

The total wire length around the loop. At resonance it is approximately one wavelength with minor corrections.

Feed Point Impedance

The complex ratio of voltage to current at the feed location. For delta loops, typical resistive values range from 50 Ω to about 120 Ω.

Polarization

The orientation of the electric field. Corner‑fed vertical loops radiate vertical polarization; side‑fed loops often radiate horizontal polarization.

Velocity Factor

The ratio of wave speed on a conductor to free‑space speed. Insulation lowers the factor, reducing resonant length.

Quality Factor (Q)

A measure of resonator sharpness equal to center frequency divided by bandwidth. Lower Q means wider bandwidth.

Takeoff Angle

The elevation angle of strongest radiation. It depends on polarization and height above ground in wavelengths.

Sources & Further Reading

Here’s a concise overview before we dive into the key points:

• Wikipedia: Loop antenna overview and theory
• AntennaTheory.com: Loop Antennas fundamentals
• ARRL Antenna Book: Comprehensive reference on antenna design
• 4NEC2: Antenna modeling software for detailed analysis
• Wikipedia: Velocity factor and dielectric effects
• HamUniverse: Practical 20‑meter delta loop projects

These points provide quick orientation—use them alongside the full explanations in this page.