Antenna Parameters and Field Strength Formulas
The table summarizes key parameters for common antenna types used in EMC testing and RF engineering, including directivity, effective antenna length, radiation resistance, and field strength formulas.
Field strength values are given for power levels in watts (W) and kilowatts (kW). All formulas assume far-field conditions and loss-free antennas unless noted otherwise.
| Antenna Type | Parameters1,2 |
|---|---|
| Isotropic radiator |
Directivity: 1 ≙ 0 dB Field (P/W): √30 · √(P/W) / (r/km) Field (P/kW): 173 · √(P/kW) / (r/km) |
| Hertz dipole with end capacitance3 |
Directivity: 1.5 ≙ 1.8 dB Effective length: l Radiation resistance: 80π² · (l/λ)² Field (P/W): 3 · √5 · √(P/W) / (r/km) Field (P/kW): 212 · √(P/kW) / (r/km) |
| Short antenna on infinitely conducting ground with top capacitance4 |
Directivity: 3 ≙ 4.8 dB Effective length: h Radiation resistance: 160π² · (h/λ)² Field (P/W): 3 · √10 · √(P/W) / (r/km) Field (P/kW): 300 · √(P/kW) / (r/km) |
| Short dipole without end capacitance3 |
Directivity: 1.5 ≙ 1.8 dB Effective length: l/2 Radiation resistance: 20π² · (l/λ)² Field (P/W): 3 · √5 · √(P/W) / (r/km) Field (P/kW): 212 · √(P/kW) / (r/km) |
| Short antenna on infinitely conducting ground without top capacitance4 |
Directivity: 3 ≙ 4.8 dB Effective length: h/2 Radiation resistance: 40π² · (h/λ)² Field (P/W): 3 · √10 · √(P/W) / (r/km) Field (P/kW): 300 · √(P/kW) / (r/km) |
| Half-wave dipole |
Directivity: 1.64 ≙ 2.15 dB Effective length: λ/π Radiation resistance: 73.2 Ω Field (P/W): 7 · √(P/W) / (r/km) Field (P/kW): 221 · √(P/kW) / (r/km) |
| Quarter-wave antenna on infinitely conducting ground |
Directivity: 3.28 ≙ 5.2 dB Effective length: λ/(2π) Radiation resistance: 36.6 Ω Field (P/W): 10 · √(P/W) / (r/km) Field (P/kW): 316 · √(P/kW) / (r/km) |
| Small single-turn loop in free space |
Directivity: 1.5 ≙ 1.8 dB Effective length: 2πA/λ Radiation resistance: 80π² · (4π²A²/λ⁴) Field (P/W): 3 · √5 · √(P/W) / (r/km) Field (P/kW): 212 · √(P/kW) / (r/km) |
| Full-wave dipole |
Directivity: 2.4 ≙ 3.8 dB Effective length: ≫ λ Radiation resistance: 200 Ω Field (P/W): 6 · √2 · √(P/W) / (r/km) Field (P/kW): 268 · √(P/kW) / (r/km) |
| Folded half-wave dipole |
Directivity: 1.64 ≙ 2.15 dB Effective length: 2λ/π Radiation resistance: 4 · 73.2 ≙ 280 Ω Field (P/W): 7 · √(P/W) / (r/km) Field (P/kW): 221 · √(P/kW) / (r/km) |
| Turnstile antenna (Hertz dipole) radiating in horizontal plane |
Directivity: 0.75 ≙ 1.2 dB Effective length: l Radiation resistance: 40π² · (l/λ)² Field (P/W): (3/2) · √10 · √(P/W) / (r/km) Field (P/kW): 150 · √(P/kW) / (r/km) |
| Broadside array (Hertz dipoles) (L ≫ λ) |
Directivity: ∼ (8/3) · (L/λ) Field (P/W): 2 · √30 · √(L/λ) · √(P/W) / (r/km) Field (P/kW): 346 · √(L/λ) · √(P/kW) / (r/km) |
| Collinear array (Hertz dipoles) (L ≫ λ) |
Directivity: ∼ (4/3) · (L/λ) Field (P/W): 2 · √15 · √(L/λ) · √(P/W) / (r/km) Field (P/kW): 245 · √(L/λ) · √(P/kW) / (r/km) |
| Antenna with directivity D |
Directivity: D Field (P/W): √30 · √D · √(P/W) / (r/km) Field (P/kW): 173 · √D · √(P/kW) / (r/km) |
1 Directivity values correspond to antenna gain for a loss-free antenna.
2 Field strength formulas assume a loss-free antenna and surroundings.
3 Valid for short antennas with l < 0.2 λ.
4 Valid for short monopoles with h < 0.2 λ on an infinite ground plane.
Example Calculations
1. Field Strength at Distance
Scenario: A half-wave dipole transmits 100 W. What is the electric field strength at 5 km distance?
Formula: E = 7 · √(P/W) / (r/km)
Calculation: E = 7 · √100 / 5 = 7 · 10 / 5 = 14 mV/m
Result: At 5 km distance, the field strength is 14 mV/m.
2. Comparing Antenna Types
Scenario: Two 1 kW transmitters at 2 km distance. Station A uses an isotropic radiator, Station B uses a quarter-wave antenna on ideal ground. How do field strengths compare?
Station A (Isotropic): E = 173 · √1 / 2 = 86.5 mV/m
Station B (λ/4): E = 316 · √1 / 2 = 158 mV/m
Result: The quarter-wave antenna delivers nearly twice the field strength (158 / 86.5 ≈ 1.83) due to directivity and ground plane reflection.
3. Radiation Resistance of Short Antenna
Scenario: A 1-meter monopole on a vehicle roof operates at 30 MHz (λ = 10 m, so h/λ = 0.1). No top capacitance. What is the radiation resistance?
Formula: R = 40π² · (h/λ)²
Calculation: R = 40 · 9.87 · (0.1)² = 394.8 · 0.01 = 3.95 Ω
Result: The radiation resistance is only 3.95 Ω, making it difficult to match to standard 50 Ω systems and resulting in poor efficiency—a common challenge with electrically short antennas.
Calculate Field Strength for These Antenna Types
Use our interactive calculator to compute electric field strength based on your transmit power and distance.
→ Antenna Field Strength Calculator
Select from isotropic, half-wave dipole, quarter-wave monopole, or full-wave dipole antennas. Enter your parameters and get instant results in mV/m.