Moxon Antenna Calculator

Design and optimize your Moxon Rectangle Antenna with precision.

Moxon Antenna Design Parameters

What is a Moxon Antenna?

The Moxon antenna is a popular two-element wire directive antenna that offers a compromise between the simplicity of a dipole and the gain and directivity of more complex multi-element beams. It is particularly favored by radio amateurs (hams) operating on the HF (High Frequency) bands due to its relatively compact size, ease of construction, and respectable performance. Unlike a standard Yagi-Uda antenna, the Moxon antenna uses a driven element and a parasitic “reflector” element that is placed very close to the driven element, forming a characteristic “rectangle” or “trapezoid” shape when viewed from the front. This close spacing is key to its unique characteristics.

Who should use it?
Radio amateurs looking for a directional antenna with more gain and front-to-back ratio than a simple dipole, but without the complexity, weight, or size of a full-sized Yagi. It’s an excellent choice for rooftop mounting, portable operations, or situations where space is limited. DXers (long-distance communicators) often find the directivity helpful.

Common misconceptions:
A common misconception is that the Moxon antenna is simply a “folded dipole” or a “lazy- H”. While it shares some similarities, its design principles and performance characteristics are distinct. The close spacing of the parasitic element is not just for compactness but fundamentally alters the electromagnetic behavior compared to a standard dipole or a typical Yagi reflector. Another misconception is that it’s a low-gain antenna; while its gain isn’t as high as a multi-element Yagi, it typically offers 1-2 dB more gain over a dipole, along with significant front-to-back ratio improvement.

Moxon Antenna Formula and Mathematical Explanation

Designing a Moxon antenna involves calculating specific dimensions based on the desired operating frequency, feedline impedance, and physical construction constraints. The core idea is to create a compact, directional antenna by placing a parasitic element very close to a driven dipole element. The formulas are derived from antenna theory, particularly focusing on mutual impedance and the behavior of closely spaced resonant conductors.

Step-by-step derivation:

1. Determine the Free-Space Wavelength (λ): The fundamental unit of measure is the wavelength of the radio wave in free space. This is calculated using the speed of light (c) and the operating frequency (f).
   
   Formula: λ = c / f
   
   Where:
   c = approximately 299,792,458 meters per second (speed of light)
   f = operating frequency in Hertz (Hz)
2. Calculate the Ideal Free-Space Half-Wave Dipole Length: A standard dipole’s resonant length is approximately half a wavelength.
   
   Formula: L_free_space = λ / 2
3. Account for Velocity Factor (VF) and Wire Diameter: In practice, the physical length of the antenna wire is shorter than the calculated free-space length due to the effects of the wire’s velocity factor (influenced by insulation and diameter) and the end effects of the conductor. The velocity factor (VF) is a multiplier (typically < 1.0) that accounts for these effects.
   Formula: L_resonant_dipole = (λ / 2) * VF
   
   Note: The calculator uses the VF input directly.
4. Determine the Moxon Spacing Factor (K): This is the most unique part of the Moxon design. The parasitic element is placed very close to the driven element. The distance between them, expressed as a fraction of a wavelength, is critical. This distance is often denoted by ‘K’ (or sometimes ‘d/λ’). The value of K is influenced by the desired feedpoint impedance. For a target impedance of 50 Ohms, K is typically around 0.160 to 0.170. For higher impedances (like 100 or 200 Ohms), K increases. The calculator determines this based on the impedance input.
   
   Conceptual Relationship: K is related to the ratio of the parasitic element’s length to the driven element’s length and the spacing, affecting mutual impedance.
5. Calculate the Side Element Length (A): Each of the two identical side elements of the Moxon rectangle is essentially a quarter-wavelength element, adjusted by the velocity factor.
   
   Formula: A = L_resonant_dipole / 2 = (λ / 2) * VF / 2
6. Calculate the Connecting Element Length (B): This is the element that connects the two side elements, forming the characteristic shape. Its length is determined by the spacing factor K and the wavelength, also adjusted by VF.
   
   Formula: B = K * λ * VF
7. Calculate Total Wire Length: This is the sum of the lengths of the two side elements and the connecting element.
   
   Formula: Total Wire Length = 2 * A + B
8. Calculate Boom Length (C): The boom provides structural support. A common approximation for the boom length is the length of one side element plus the connecting element.
   
   Formula: C ≈ A + B
9. Approximate Height Above Ground: While not strictly part of the dimension calculation, a recommended height is provided. For lower bands (like 40m or 20m), an approximate height of around 0.1 to 0.2 wavelengths above average ground is often suggested for good performance and low takeoff angle. For example, on 7 MHz (approx. 42m wavelength), 0.15 * 42m ≈ 6.3 meters. This provides a general guideline.

Variable Explanations Table:

Moxon Antenna Design Variables

Variable	Meaning	Unit	Typical Range / Notes
f	Operating Frequency	MHz	1.8 – 30 MHz (Common HF bands)
c	Speed of Light	m/s	299,792,458
λ (Lambda)	Wavelength in Free Space	meters	Calculated from f
VF	Velocity Factor	Unitless	0.90 – 0.98 (Higher for bare wire, lower for insulated)
K	Moxon Spacing Factor	Unitless	Approx. 0.16 (for 50Ω) to 0.20+ (for 200Ω)
A	Side Element Length	meters	Calculated
B	Connecting Element Length	meters	Calculated
C	Boom Length	meters	Approx. A + B
Wire Diameter	Diameter of the conductive wire	mm	1.0 – 5.0 mm (Typical antenna wire)
Impedance	Desired Feedpoint Impedance	Ohms	50, 75, 100, 200 Ω (Affects K)

Practical Examples (Real-World Use Cases)

Let’s explore two practical scenarios for using the Moxon antenna calculator. These examples illustrate how to input values and interpret the results for different amateur radio operating bands.

Example 1: Building a 20-Meter Band Moxon Antenna

A radio amateur wants to build a directional antenna for the 20-meter band (approximately 14.200 MHz). They plan to use standard insulated copper wire (VF ≈ 0.95) and feed it with a 50 Ohm coaxial cable.

Inputs:

• Operating Frequency: 14.200 MHz
• Desired Impedance: 50 Ohms
• Wire Diameter: 2.0 mm
• Velocity Factor (VF): 0.95

Calculated Results:

• Target Frequency: 14.200 MHz
• Spacing Factor (K): ~0.165 (for 50 Ohms)
• Side Element Length (A): ~2.48 meters
• Connecting Element Length (B): ~3.66 meters
• Total Wire Length: ~8.62 meters
• Boom Length (C): ~6.14 meters
• Approx. Height above Ground (for 7MHz): ~6.3 meters (This is a general guide, not specific to 20m)

Interpretation:

This Moxon antenna will require approximately 8.62 meters of wire in total. The physical structure will span about 6.14 meters on the boom. This is a manageable size for many installations, offering directivity and gain over a dipole. The 50 Ohm feedpoint is convenient for direct connection to standard coaxial cable. The calculated dimensions allow for precise tuning to the 14.200 MHz frequency.

For more insights into antenna design, check out HF antenna basics.

Example 2: Designing a Low-Band Moxon for 40 Meters

Another ham operator is interested in a Moxon antenna for the 40-meter band (around 7.150 MHz) and prefers a slightly higher impedance feedpoint, aiming for around 100 Ohms, which might be easier to match using a balun or alternative feed methods. They are using bare wire, so the VF is higher (e.g., 0.97).

Inputs:

• Operating Frequency: 7.150 MHz
• Desired Impedance: 100 Ohms
• Wire Diameter: 2.5 mm
• Velocity Factor (VF): 0.97

Calculated Results:

• Target Frequency: 7.150 MHz
• Spacing Factor (K): ~0.180 (for 100 Ohms)
• Side Element Length (A): ~4.85 meters
• Connecting Element Length (B): ~7.76 meters
• Total Wire Length: ~17.46 meters
• Boom Length (C): ~12.61 meters
• Approx. Height above Ground (for 7MHz): ~6.3 meters

Interpretation:

Building a 40-meter Moxon requires significantly more wire (17.46 meters) and a longer boom (12.61 meters) compared to the 20-meter version, primarily due to the lower frequency. The higher target impedance of 100 Ohms results in a larger spacing factor (K), making the connecting element (B) longer relative to the side elements (A). This design might require a balun to match the 100 Ohm feedpoint to a standard 50 Ohm coax. The approximate height guidance suggests mounting it at least 6-7 meters high for optimal low-angle radiation. Understanding these factors is crucial for successful antenna construction.

Learn more about impedance matching in our guide on Baluns and Antenna Matching.

How to Use This Moxon Antenna Calculator

Our Moxon antenna calculator is designed for simplicity and accuracy, empowering radio amateurs to quickly determine the optimal dimensions for their custom antenna projects. Follow these steps to get started:

Step-by-step instructions:

1. Select Your Target Frequency: In the “Operating Frequency” field, enter the specific frequency in Megahertz (MHz) you wish your antenna to be resonant on. For example, for the 20-meter band, you might enter 14.200 MHz. For the 40-meter band, perhaps 7.150 MHz.
2. Choose Your Desired Impedance: Use the dropdown menu for “Desired Impedance” to select the target feedpoint impedance. Common choices are 50 Ohms (for direct coax feed) or 100 Ohms (which might be easier to match with a balun). The calculator adjusts its internal spacing factor (K) based on this selection.
3. Input Wire Characteristics:
   • Wire Diameter: Enter the diameter of the wire you plan to use in millimeters (mm). This has a minor effect on the calculations.
   • Velocity Factor (VF): This is a crucial parameter. Enter a value between 0.50 and 1.00. A good starting point for insulated wire is 0.95. For bare wire, 0.97 or 0.98 is more typical. Consult wire manufacturer specifications if available, or use these common values.
4. Calculate: Click the “Calculate Dimensions” button. The calculator will instantly process your inputs and display the results.

How to read results:

• Main Result (Highlighted): This typically shows the most critical dimension, often the Total Wire Length required for the antenna.
• Intermediate Values:
  • Side Element Length (A): The length of each of the two main radiating wires.
  • Connecting Element Length (B): The length of the wire connecting the two side elements.
  • Boom Length (C): The approximate physical length of the support structure (boom) needed to hold the elements in place.
  • Approx. Height above Ground: A general recommendation for mounting height relative to the frequency, crucial for performance and radiation angle.
  • Element Spacing Factor (K): An important design parameter indicating the ratio of spacing to wavelength, derived from your impedance choice.
  • Resonant Frequency Target: Confirms the frequency the calculations are based on.
• Formula Basis: Provides a plain-language explanation of the underlying antenna theory and formulas used.

Decision-making guidance:

Use the calculated dimensions as a starting point. Always allow for slight tuning adjustments (trimming or adding wire) once the antenna is erected, as environmental factors (proximity to ground, nearby objects, specific insulation properties) can slightly alter the resonant frequency. The Boom Length (C) is an approximation; you might need a slightly longer or shorter boom depending on your chosen mounting method and materials. For higher impedance targets, consider using a balun to match to your 50 Ohm coax.

For building your antenna, refer to our guide on Antenna Construction Techniques.

Key Factors That Affect Moxon Antenna Results

While the Moxon antenna calculator provides precise dimensions based on input parameters, several real-world factors can influence the antenna’s actual performance and tuning. Understanding these factors is crucial for successful construction and operation.

• Velocity Factor (VF) Accuracy: The VF is an approximation. The exact VF depends heavily on the type and thickness of the wire’s insulation, its material, and even environmental conditions (humidity, temperature). Using a VF that’s too high or too low will shift the antenna’s resonant frequency. It’s always best to start with the calculated dimensions and then fine-tune by adjusting the wire length.
• Height Above Ground: The height at which the antenna is mounted significantly impacts its radiation pattern, impedance, and resonant frequency. Lower heights tend to lower the impedance and raise the angle of radiation, making it better for shorter-distance communication (NVIS – Near Vertical Incidence Skywave). Higher heights generally lower the radiation angle, favoring DX (long-distance) contacts. The calculator provides a general guideline, but optimal height varies by band and desired performance.
• Proximity to Conductive Objects: Nearby metal structures (gutters, fences, metal poles, other antennas) can detune the antenna, altering its impedance and resonant frequency. They can also affect the front-to-back ratio. It’s best to mount the Moxon antenna as clear of such objects as possible.
• Environmental Conditions: Moisture (rain, dew, snow) on the antenna elements can effectively change the diameter of the wire and alter the velocity factor, lowering the resonant frequency. Temperature fluctuations can also cause minor changes in dimensions and resonance.
• Wire Sag and Tension: The exact physical configuration of the wire elements affects the antenna’s performance. Significant sag can change the effective electrical length. Ensure elements are reasonably taut and uniformly shaped according to the design. Uneven tension can lead to asymmetrical electrical performance.
• Feedline and Balun Effects: The type of feedline used and the presence (or absence) of a balun can influence the impedance match at the transmitter. A poorly chosen or non-existent balun can lead to RF in the shack or poor SWR. The calculator targets a specific impedance, but the final match depends on the entire system. A 1:1 current balun is often recommended for 50 Ohm Moxons to ensure clean current distribution and prevent feedline radiation.
• Construction Precision: While the Moxon is forgiving, precise measurements are still important, especially for the spacing factor (K) and the overall geometry. Errors in constructing the “rectangle” can lead to suboptimal performance and detuning.

For more on understanding antenna performance, read about Antenna Radiation Patterns.

Frequently Asked Questions (FAQ)

Q1: What is the main advantage of a Moxon antenna over a dipole?

The primary advantages are its directivity and front-to-back ratio. A Moxon antenna typically offers 1-2 dB more gain than a dipole and significantly better rejection of signals from the rear, making it effective for reducing interference and focusing transmitted power in a specific direction. Its compact size for its performance is also a major plus.

Q2: Can I use any wire for a Moxon antenna?

Yes, you can use various types of wire (e.g., copper-clad steel, insulated copper wire, bare copper wire). However, the insulation type and thickness will affect the Velocity Factor (VF). Using the correct VF in the calculator is important for accurate initial dimensions. Always be prepared to tune the antenna after installation.

Q3: What is the typical feedpoint impedance of a Moxon antenna?

The impedance varies depending on the spacing factor (K) and the height above ground. For typical designs (K around 0.16-0.17), the impedance is often in the range of 50 to 150 Ohms. The calculator allows you to target specific impedances like 50 Ohms or 100 Ohms, which influences the K value and dimensions.

Q4: Do I need a balun with a Moxon antenna?

It is highly recommended, especially if your coax feedline impedance (usually 50 Ohms) doesn’t match the antenna’s feedpoint impedance. A 1:1 current balun is commonly used to ensure balanced current feed, prevent RF from getting onto the coax shield (reducing interference and improving pattern), and provide a clean match to the coax. If your calculator target impedance is 50 Ohms and you use a 1:1 balun, it simplifies matching.

Q5: How critical is the height above ground for a Moxon antenna?

Height is critical for both impedance and radiation pattern. Lower heights (e.g., 10-20 feet) favor NVIS and closer contacts, while higher heights (e.g., 30-60 feet or more) favor DX contacts by lowering the radiation angle. The calculator provides a general suggestion, but experimentation with height is often needed to optimize for your specific location and desired communication range.

Q6: Can the Moxon antenna be mounted vertically?

Yes, the Moxon antenna can be mounted in either a horizontal or vertical polarization. Horizontal polarization is more common for DX. Vertical polarization tends to have a higher angle of radiation, which can be beneficial for regional contacts or certain ionospheric conditions. The dimensions calculated remain the same regardless of mounting orientation.

Q7: What does the “Element Spacing Factor (K)” mean in the results?

The Element Spacing Factor (K) is a key design parameter representing the ratio of the spacing between the driven and parasitic elements to the wavelength (d/λ). It’s influenced by the desired feedpoint impedance. A higher K value generally corresponds to a higher impedance. The calculator derives K based on your selected impedance target.

Q8: How do I tune the Moxon antenna after building it?

After constructing the antenna to the calculated dimensions, use an SWR meter or antenna analyzer. If the resonant frequency is too low (SWR minimum is below your target frequency), shorten the elements slightly (usually by trimming the ends of the side elements symmetrically). If the resonant frequency is too high, lengthen the elements (by adding wire or adjusting solder joints). Fine adjustments are key. Ensure the connecting element (B) maintains its proportion relative to A.

Related Tools and Internal Resources

• Dipole Antenna Calculator: Design a simple half-wave or full-wave dipole antenna.
• Yagi Antenna Calculator: Calculate dimensions for multi-element Yagi antennas.
• Antenna Tuner Guide: Learn about antenna tuners and impedance matching.
• Understanding SWR: A comprehensive guide to Standing Wave Ratio.
• Choosing Feedlines: Factors to consider when selecting coaxial cable.