CHAPTER 21
Antenna Noise Temperature

Radio reception is essentially a matter of signal-to-noise ratio (SNR). Signals must be at or above some amplitude relative to the noise floor of the system in order to be detected properly for their intended use. All electronic systems (receivers and antennas included) generate noise internally, even if there is no power flowing in them. While we normally think in terms of the antenna designer maximizing signal strength to overcome noise, often a second goal is to minimize the noise from some or all of the various sources.

In general, at HF and below, the external signals and noise sources detected by the antennas described in this book (including even the very low efficiency antennas of Chap. 14) are strong enough to swamp any noise generated within a well-designed receiver. Thus, we typically have to take special measures to override internally generated receiver noise only at VHF and above, and the balance of this chapter is primarily for the benefit of those who are concerned with weak signal reception above 30 MHz or so.

One of the basic forms of noise seen in systems is thermal noise. Even if the amplifiers in the receiver add no additional noise (they will!), there is thermal noise at the input. In fact, if we replace the antenna attached to the receiver input with a totally shielded resistor matched to the system impedance, some noise will still be present. This noise is produced by the random motion of electrons inside the resistor. At all temperatures above absolute zero (about –273.16°C), the electrons in the resistor material are in random motion. In the absence of an external bias voltage creating a uniform field acting on the resistor body, the short-term random motions of the electrons cancel each other out to the extent that no discernable current can be observed.

Thermal noise in a resistor can be modeled as a voltage source, , in series with a noise-free resistor R, where is the root mean square (rms) value of the fluctuating, thermally generated noise voltage. If R—in ohms—is constant over the frequency range of interest, is proportional to , whose components are defined below. When the resistor is connected across a matched load, the noise power transferred to that load is given by Eq. (21.1). Note that the noise power delivered to a matched load is independent of the value of the resistor.

Degrees kelvin (K) is the international way of defining all temperatures relative to absolute zero. (No degree symbol is used with K.) To express temperature in degrees kelvin (K) we add 273.16 to a temperature expressed in Celsius. The formula is

Of course, temperatures expressed in Fahrenheit (°F) are related to Celsius by

so we also have

Thus, water turns to ice at 32°F, 0°C, or 273.16 K. Water boils at 212°F, 100°C, or 373.15 K. Absolute zero corresponds to –459.67°F, –273.16°C, or 0 K.

Another important point on the various temperature scales is room temperature, typically taken to be 27°C (or about 80°F) by some scientific and engineering specialties. This may be higher than what you or I would want our room to be, but it has the advantage of corresponding to 300 K—a nice round number for doing calculations!

Finally, by international agreement, T for terrestrial components and system elements is assumed to be 290 K (about 17°C, or 62°F) unless otherwise stated. To improve weak-signal detection at microwave frequencies and above, however, receiver input stages are often cooled by liquid nitrogen. The markedly lower T of those stages results in their contributing a substantially reduced noise power to the overall system noise figure.

Example 21.1 A terrestrial receiver with a 1-MHz bandwidth and a 50-Ω input impedance is connected to a 50-Ω resistor. The noise power delivered to the receiver input stage is (1.38 × 10^–23 J/K) × (290 K) × (1,000,000 Hz) = 4 × 10^–15 W. This noise is called thermal noise, thermal agitation noise, or Johnson noise.

Noise Factor, Noise Figure, and Noise Temperature

The noise performance of a receiving system can be defined in three different, but related, ways: noise factor F_n, noise figure (NF), and equivalent noise temperature T_e; these properties are definable as a simple ratio, decibel ratio, or kelvin temperature, respectively.

Noise Factor (F_n)

For components such as resistors, the noise factor is the ratio of the noise produced by a real resistor to the simple thermal noise of an ideal resistor. The noise factor of a radio receiver (or any system) is the ratio of output noise power P_no to input noise power P_ni:

In order to make comparisons easier, the noise factor is usually measured at the standard temperature (T₀) of 290 K, although in some countries 299 K or 300 K is commonly used (the differences are generally negligible).

It is also possible to define noise factor F_n in terms of input and output signal-to-noise ratios:

Noise Figure (NF)

The noise figure is a frequently used measure of a receiver’s “goodness”, or its departure from “idealness”. Thus, it is a figure of merit. The noise figure is the noise factor converted to decibel notation:

“log” refers to the system of base-10 logarithms. (See App. A for an explanation of logarithms.)

Noise Temperature (T_e)

Noise temperature is a means for specifying noise in terms of an equivalent temperature. Examination of Eq. (21.1) shows that the noise power is directly proportional to temperature in kelvins, and also that noise power collapses to zero at the temperature of absolute zero (0 K).

NOTE The equivalent noise temperature T_e is not the physical temperature of the amplifier but, rather, a theoretical construct that is an equivalent temperature that would produce the same amount of noise power in a resistor at that temperature.

Noise temperature is related to the noise factor by

and to noise figure by

Noise temperature is often specified for receivers and amplifiers in combination with, or in lieu of, the noise figure. Applied to antennas, the noise temperature concept relates the amount of thermal noise generated to the resistive loss components of the antenna feedpoint impedance.

The antenna/receiver system will be afflicted by three different noise sources external to the receiver:

• The thermal noise temperature (T_R) of the resistive loss portion of the feedpoint impedance

• A sky noise temperature (T_SKY) that depends on where the antenna main lobe is pointed

• A ground noise temperature (T_GND) that consists of components reflected from the sky as well as components caused by internal thermal agitation of the ground

In a typical system (Fig. 21.1) the main lobe will be pointed toward the sky noise source, while the sidelobes will pick up noise from the ground. The total noise temperature of the antenna is thus

FIGURE 21.1 Contributors to antenna noise temperature.