What are Antenna Temperature & Effective Height : Definition & Formula

Antenna temperature and effective height are important parameters in antenna theory used to describe noise performance and receiving capability. Antenna temperature represents the equivalent noise temperature received by an antenna from its surrounding environment and radiation sources, measured in kelvin (K); it depends on the antenna radiation pattern and thermal environment. Effective height, also called effective length in receiving applications, indicates how efficiently an antenna converts an incident electric field into an open-circuit voltage.

Antenna Temperature ($T_A$)

Definition : Antenna temperature is not a measure of how physically hot or cold the metal of the antenna is. Instead, it is a theoretical concept used to quantify the amount of noise power the antenna picks up from its surroundings.

Technically, it is defined as the temperature required for a matched, ideal resistor to deliver the exact same amount of noise power to a receiver as the antenna is currently picking up from incident electromagnetic waves in its environment.

Noise Power Relation Formula

$P_r = k \cdot T_A \cdot B$

Where, Pr = Noise power at receiver, K = Boltzmann’s constant ($1.38 \times 10^{-23}$ J/K), TA = Antenna temperature (in kelvin), B = Bandwidth of receiver (in Hz)

Noise Temperature Components Formula

$T_A = T_e + (1 - \eta) T_p$

Where, TA = total antenna temperature, Te = external noise temperature, Tp = physical temperature of antenna structure itself, $\eta$ = Antenna radiation efficiency (ranging from 0 to 1)

• Note : A lower antenna temperature is highly desirable. It indicates that the antenna is picking up less background noise, which results in a better Signal to Noise Ratio (SNR) and higher sensitivity for the receiving system.

Effective Height of an Antenna ($h_e$)

Definition : Similar to antenna temperature, effective height is not the physical length of the antenna structure or how high it is mounted on a tower. It is a metric that describes how effectively an antenna converts an incoming electromagnetic field into a measurable voltage. Specifically, it is defined as the ratio of the open-circuit voltage induced at the antenna’s terminals to the intensity of the incident electric field.

Primary Formula

$h_e = \frac{V_{oc}}{E_i}$

Where, he = Effective height (meters), Voc = Open circuit voltage developed at the terminals (Volts), Ei = Incident electric field intensity (Volts/meter).

Relation to Received Power Formula

$P_r = \frac{|E_i|^2 |h_e|^2}{8R}$

Where, Pr = Power received (Watts), R = Radiation Resistance of antenna (Ohm)

Relation to Effective Area Formula

$A_e = \frac{|h_e|^2}{R}$

Where, Ae = Effective Area in meter^2.

Characteristics of antenna effective height

• It is a vector. Effective height has both magnitude and phase.

• The value is highly dependent on the direction and polarization of the incoming wave. It reaches its maximum value when the incoming electric field is perfectly aligned (parallel) with the antenna’s axis.

• It changes based on the frequency of the operating signal and the type of antenna used.

• Note: A higher effective height is desirable for receiving antennas. It means the antenna is more sensitive and better at harvesting voltage from an incident electromagnetic wave.

Summary

Antenna temperature quantifies the equivalent noise captured by an antenna, while effective height measures its voltage response to an incident electric field. Together, these parameters help analyze antenna noise performance and receiving characteristics.