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Noise is a limiting factor is many receivers and other systems. Essentially, it is unwanted energy that sets the sensitivity of a receiver. Noise masks signals of interest at lower levels, preventing the receiver from detecting them. It is almost unavoidable and exists in all electronic systems, from audio and baseband electronic devices through the highest terahertz frequencies and optical electronic systems. While it cannot be eliminated, it can be controlled and managed, enabling receivers to operate effectively with low-level signals.
All components at normal operating temperatures generate some amount of noise when power is applied, due to the random motion of the electrons that account for the flow of current. This is one form of noise, known as thermal noise, associated with the heat that is a byproduct of the applied power. This heat is generated at all temperatures above absolute zero (−273ºC) since, in theory, charge carriers do not move at a temperature of absolute zero.
Thermal noise has a Gaussian distribution, with noise levels spread evenly with frequency. As a result, the amount of noise in a component or circuit increases with bandwidth. For this reason, filters that narrow the bandwidth will also lower the noise. In a 50-Ω system at room temperature (typically +25ºC), the thermal noise power density is −174 dBm/Hz.
The thermal noise power from a noise source, N, can be found from the simple relationship,
N = kTB, where
where
k = Boltzmann’s constant (=1.38 × 10−23 J/K);
T = the temperature (in degrees Kelvin); and
B = the bandwidth in Hz in which the noise is measured.
From this equality, the relationship of noise power to bandwidth is obvious and clear proof of the need for filtering or some other form of bandwidth reduction in order to limit noise in communications systems. Similarly, noise increases with increasing temperature (which is why cryogenic cooling is often used in applications where low noise is essential). (Note: A conversion from ºC to ºK follows from 0ºK = −273ºC, so that +273ºK = 0ºC and so on.)
One of the most essential of electronic components, the resistor, also produces a root mean square (RMS) noise voltage (Vn) as a function of bandwidth and temperature:
Vn = (4kTBR)0.5
where R = the resistance (in Ω) of the resistor.
From this relationship, it is apparent that noise increases with increasing resistance, and resistance should be as low as possible to minimize noise.
Receiver designers and other users of low-noise amplifiers are familiar with a noise parameter known as noise figure (NF) and a related parameter, noise factor. Noise factor is essentially the ratio of the SNR at the output of a device under test (DUT), such as an amplifier, to the SNR at its input, or before it added its own thermal noise to the signal path. The NF is a way of expressing NF in dB, with lower values indicative of less noise.
Measuring Noise
Noise in RF/microwave systems is characterized in various ways, including by excess noise ratio (ENR), carrier-to-noise (C/N) ratio, SNR (in dB), NF (in dB), and noise power density (in dBm/Hz). It can also be measured in a number of ways, using specialized instruments, such as a noise-figure meter, or general-purpose instruments, such as a power meter or a spectrum analyzer.
In all cases, a known source of noise that has been precisely calibrated is an important part of measuring the noise of a DUT since it provides a reference or starting point from which to base the subsequent noise measurements. Noise sources can be simple diode-based components (Fig. 1) with coaxial or waveguide connectors (Fig. 2) or more sophisticated programmable instruments for automated noise measurements (Fig. 3).
Noise sources are typically characterized by their usable frequency ranges and their excess noise ratio (ENR). For a noise diode, the ENR is the difference between the diode’s noise level when it is switched on versus when it is switched off. A switchable noise source can be placed at the input of a DUT and measurements made for the on and off states at the output to determine noise figure.
In addition to measuring the noise characteristics of a DUT, a precision noise source is a form of low-noise test signal generator, since it provides signal energy at all frequencies simultaneously and can be used with a spectrum analyzer to measure such parameters as filter response and amplifier gain for its calibrated bandwidth.
In terms of calculating NF, its relationship to ENR is as follows:
NF (in dB) = ENR – 10log(Y – 1)
where Y = Pon/Poff and where Pon and Poff are the output power levels of the DUT when the noise source at the input of the DUT is biased on and off, respectively.
Calibrated noise sources are used with a spectrum analyzer, an RF power meter, or a noise-figure meter to determine different noise parameters, such as NF. A noise-figure meter essentially subtracts the noise level at the input of the DUT, such as a mixer or amplifier, from the noise level at the output of the DUT to determine the noise added by the DUT.
Thermal noise is one form of noise that haunts RF/microwave components and systems, with other forms of noise, such as shot noise and Johnson noise, often present. One of these other types of noise, for example, is phase noise, which is commonly generated in amplifier and oscillator circuits. As with the instruments for measuring noise figure, specialized phase-noise analyzers have been developed and are available from several manufacturers for precise measurement of phase noise over different frequency ranges.
