Understanding Antenna Factor (AF) and Isotropic Gain Conversion
Antenna Factor (AF) is a fundamental parameter used in Electromagnetic Compatibility (EMC) testing, spectrum monitoring, and RF field intensity measurements. It establishes the mathematical relationship between the incident Electric Field strength ($E$, measured in $\text{V/m}$ or $\text{dB}\mu\text{V/m}$) striking an antenna and the resulting output voltage ($V$, measured in $\text{V}$ or $\text{dB}\mu\text{V}$) delivered to a matched $50\ \Omega$ load receiver.
The Core Formula: Antenna Factor to dBi Gain
Under far-field conditions in a $50\ \Omega$ system, Antenna Factor in decibels per meter ($\text{dB/m}$) is derived directly from free-space wave velocity and isotropic power gain ($G_{\text{dBi}}$):
- $$\text{AF}\ (\text{dB/m}) = 20 \log_{10}(f_{\text{MHz}}) – G_{\text{dBi}} – 29.79$$
- $$G_{\text{dBi}} = 20 \log_{10}(f_{\text{MHz}}) – \text{AF}\ (\text{dB/m}) – 29.79$$
Where $f_{\text{MHz}}$ represents the operating carrier frequency in Megahertz, and $G_{\text{dBi}}$ is the absolute directive gain relative to an isotropic radiator.
Measuring Electric Field Strength ($E$-Field)
During compliance testing or wireless channel propagation analysis, spectrum analyzers record voltage at their input terminals ($V_{\text{rec}}$). To determine the actual ambient Electric Field strength ($E$) present in free space, the calibrated Antenna Factor is added to the measured voltage:
- $$E\ (\text{dB}\mu\text{V/m}) = V_{\text{rec}}\ (\text{dB}\mu\text{V}) + \text{AF}\ (\text{dB/m}) + L_{\text{cable}}\ (\text{dB})$$
Where $L_{\text{cable}}$ accounts for insertion loss in transmission coaxial cables connecting the antenna port to the measurement receiver.