Signal-to-noise ratio

Overview

Amplifiers can be evaluated on the basis of signal-to-noise ratio (S/N or SNR), denoted S_n. The goal of the circuit or instrument designer is to enhance the SNR as much as possible. Ultimately, the minimum signal level detectable at the output of an amplifier is the level that appears above the noise floor level. Therefore, the lower the system noise floor, the smaller the minimum allowable signal. Although often thought of as a radio receiver parameter, SNR is applicable in other amplifiers in which signal levels are low and gains are high. This situation occurs in scientific, medical, and engineering instrumentation as well as in other applications.

Noise resulting from thermal agitation of electrons is measured in terms of noise power (P_n) and carries the units of power (watts or watt subunits). Noise power is found from:

where

P_n is the noise power in watts (W)
K is Boltzmann's constant
(1.38 X 10^-23 J/°K)
B is the bandwidth in hertz (Hz)

Notice in Equation 5-13 that there is no center frequency term, only the bandwidth (B). True thermal noise is Gaussian (or near-Gaussian), so frequency content, phase, and amplitudes are equally distributed across the entire spectrum. Thus, in bandwidth limited systems, such as a practical amplifier or network, the total noise power is related to temperature and bandwidth. We can conclude that a 200-Hz bandwidth centered on 1-kHz produces the same thermal noise level as a 200-Hz bandwidth centered on 600 Hz or any other frequency.

Noise sources can be categorized as either internal or external. The internal noise sources are due to thermal currents in the semiconductor material resistances. Internal noise is the noise component contributed by the amplifier under consideration. When noise, or S/N ratio, is measured at both input and output of an amplifier, the output noise is greater. The internal noise of the device is the difference between output noise level and input noise level.

External noise is the noise produced by the signal source, so it is often called source noise. This noise signal is due to thermal agitation currents in
the signal source, and even a simple zero-signal input termination resistance has some amount of thermal agitation noise. In fact, the simple terminated noise level might be higher than V_n because of component construction. For example, the noise signal produced by a carbon composition resistor has an additional noise source modeled as V_na in Figure 5-16. This noise generator is a function of resistor construction and manufacturing defects.

Figure 5-17a shows a circuit model showing that several voltage and current noise sources exist in an operational amplifier (op-amp). The relative strengths of these noise sources, hence their overall contribution, varies with op-amp type. In a field effect transitor FET-input op-amp, for example, the current noise sources are tiny, but voltage noise sources are very large. On bipolar op-amps the exact opposite situation obtains.

All of the noise sources in Figure 5-17a are uncorrelated with respect to each other, so one cannot simply add noise voltages; only noise power can be added. To characterize noise voltages and currents they must be added in the root sum squares (rss) manner.

Models such as the one shown in Figure 5-17a are too complex for most situations, so it is standard practice to combine all of the voltage noise sources into one source and all of the current noise sources into another source. The composite sources have a value equal to the rss voltage (or current) of the individual sources. Figure 5-17b is such a model, in which only a single current source and a single voltage source are used. The equivalent ac noise in Figure 5-17b is the overall noise, given a specified value of source resistance, R_s, and is found from the rss value of V_n and I_n:Purchase Introduction to Biomedical Equipment Technology from Prentice Hall.

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