Log Periodic Antenna Design Guide | Frequency Range, Gain, Structure

Design a log-periodic dipole array by defining the required band and radiation performance, calculating an initial scaled geometry, then optimizing and measuring the complete antenna. Element lengths alone cannot guarantee gain, impedance match or power handling. The feed, supports, termination and mounting structure belong in the design model.

1. Set measurable requirements

Specify the lowest and highest operating frequencies before choosing element dimensions. The bandwidth ratio is f_high/f_low: 200–800 MHz is 4:1, while 700–6000 MHz is about 8.57:1. “Broadband” by itself does not define an acceptance limit.

Requirement	What the specification should state
Frequency coverage	Both endpoints, continuous or separate bands, and any rejection band.
Gain	Minimum gain or realized gain in dBi across the band; distinguish a minimum from a peak or average.
Pattern	Beam direction, beamwidth, front-to-back ratio and required polarization.
Impedance	System impedance, connector, reference plane and maximum VSWR.
Mechanical limits	Maximum span, boom length, mass, mounting position and transport envelope.
Transmit operation	Average and peak power, duty cycle, temperature, altitude and allowable mismatch.

For a receiving antenna, include the cable loss and receiver noise requirements in the system budget. For an EMC test antenna, identify the calibration and field-uniformity requirements of the actual test method. A generic LPDA geometry does not establish compliance.

2. Calculate a starting geometry

Let L_n be a dipole’s full tip-to-tip length, numbered from longest to shortest. Let d_n be the boom-axis spacing from that dipole to the next shorter one. The conventional geometric definitions are:

• L_n+1 = τL_n, where 0 < τ < 1.
• d_n = 2σL_n.
• α = arctan[(1 − τ)/(4σ)], where α is the half-apex angle and 2α is the full included angle.

These relations define the taper and spacing. The feeder impedance and coupling among the dipoles must also be included when predicting input impedance and radiation patterns.^[1]

A free-space half-wave estimate is L ≈ 150/f, with L in metres and f in MHz. At 14 MHz it is about 10.71 m across the whole dipole, not each arm. At 30 MHz it is about 5.00 m. End effects, element diameter and coupling require adjustment; there is no universal shortening percentage for every LPDA.

3. Work through a dimensioned example

Consider an initial geometry for investigating a 200–800 MHz design. Choose L₁ = 750 mm, τ = 0.85 and σ = 0.15. These are illustrative inputs, not an optimized design or a Dolph product specification.

The resulting half-apex angle is about 14.04°. Ten scaled elements take the shortest length below the 187.5 mm half-wave estimate at 800 MHz. Coordinates below start at the longest element and run toward the shortest.

Element	Full length (mm)	Boom position (mm)
1	750.0	0.0
2	637.5	225.0
3	541.9	416.3
4	460.6	578.8
5	391.5	717.0
6	332.8	834.4
7	282.9	934.3
8	240.4	1019.1
9	204.4	1091.3
10	173.7	1152.6

Calculate with unrounded values and round only the displayed dimensions. The 1152.6 mm span excludes feed hardware, termination and mounting allowances. It also provides no proof that the band edges meet the required gain or VSWR.

The active region needs surrounding elements to maintain its behavior near a band edge. Extend or adjust the geometry when analysis shows edge degradation; do not assume that adding a fixed 15% or 20% margin guarantees a specified VSWR. The LPDA working-principle explanation shows how that active region moves with frequency.

4. Design the feed as part of the antenna

The twin booms may serve as both supports and a balanced transmission line. Their unloaded characteristic impedance is different from the antenna’s final input impedance, because the connected dipoles load the line.

For two identical round conductors in air, a low-loss line estimate is Z₀ ≈ 120 arcosh(D/d) Ω, where D is center-to-center spacing and d is conductor diameter. This follows from the parallel-wire inductance and capacitance expressions; the simpler logarithmic approximation assumes D is much larger than d.^[2]

For d = 25.4 mm and D = 43.6 mm, that model gives approximately 136 Ω. A 150 Ω unloaded line would require D ≈ 48.0 mm under the same assumptions. Neither result establishes a 50 Ω antenna input. Square booms, dielectric supports and nearby metal need their own model.

Alternating element connections form part of the LPDA feed arrangement. Show those connections explicitly in the assembly drawing and inspect continuity before RF testing. Include the connector launch, exposed conductors and any coaxial routing in the electromagnetic model.

A shorted rear stub is reactive: it changes impedance and phase rather than acting as a resistive absorber. Choose its dimensions with the complete antenna model. A fixed fraction of wavelength cannot guarantee a full-band match for every geometry.

Feed symmetry can also affect radiation behavior. In a published printed-LPDA study, Casula and colleagues used a second coaxial cable to mirror the driven cable and improve pattern and phase-center behavior. That specific arrangement illustrates why feed details matter; it is not a mandatory construction method for all LPDAs.^[3]

5. Optimize performance and manufacturing limits together

Sweep frequency and compare VSWR, realized gain, front-to-back ratio and polarization. Refine the frequency steps near abrupt changes. A design can meet its VSWR target while missing its gain or pattern target.

Vary element lengths, diameters, spacing, boom separation and termination within manufacturable bounds. Then repeat the analysis with tolerance extremes and the intended mast, bracket, cable route and radome. Use the sensitivity results to assign tolerances; do not impose one universal millimetre or percentage limit on every dimension.

If ordinary tube sizes replace ideally scaled diameters, model the actual sizes. Specify alloys, joints and corrosion protection separately. A material trade name does not define its RF loss, mechanical strength or suitability at every temperature.

Set wind and ice requirements for the installation site and mounting system. Calculate loads and deflection using the selected structure and applicable design requirements. Adding elements does not imply a fixed percentage increase in wind load, and low VSWR does not establish a 500 W power rating.

6. Validate the prototype before releasing the drawing

1. Measure critical dimensions and record the built configuration.
2. Calibrate the network analyzer to the specified reference plane and measure full-band input reflection.
3. Measure realized gain and principal-plane patterns with suitable calibration, separation and cable correction.
4. Check polarization and pattern changes at band edges and near simulated anomalies.
5. Repeat relevant measurements with the final mount, cable routing and environmental protection installed.
6. For transmitting service, verify thermal and electrical limits under the specified operating conditions.

A standard gain horn is a possible microwave reference only when its band, polarization and calibration fit the measurement. A product’s nominal gain label is not a substitute for the calibration data required by the test.

Release the final drawing with the measured frequency coverage, minimum performance limits, test setup and permitted manufacturing tolerances. Keep the calculated starting geometry separate from the accepted production configuration.