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Operational Amplifier Noise

previous Frequency Response— Current Feedback Op amps
This section discusses the noise generated within op amps, not the external noise which they may pick up. External noise is also important, and is discussed in detail in Chapter 7, but in this section we are concerned solely with internal noise.
There are three noise sources in an op amp: a voltage noise which appears differentially across the two inputs, and two current noise sources, one in each input. The simple voltage noise op amp model is shown in Figure 1-64 below. The three noise sources are effectively uncorrelated (independent of each other). There is a slight correlation between the two noise currents, but it is too small to need consideration in practical noise analyses. In addition to these three internal noise sources, it is necessary to consider the Johnson noise of the external gain setting resistors that are used with the op amp.
Input voltage noise
Figure 1-64: Input voltage noise
All resistors have a Johnson noise of √(4kTBR), where k is Boltzmann's Constant (1.38×10–23J/K), T is the absolute temperature, B is the bandwidth, and R is the resistance. Note that this is an intrinsic property— it is not possible to obtain resistors that do not have Johnson noise. The simple model is shown in Figure 1-65 below.
Johnson noise of resistors
Figure 1-65: Johnson noise of resistors
Uncorrelated noise voltages add in a "root-sum-of-squares" manner; i.e., noise voltages V1, V2, V3 give a summed result of √(V12 + V22 + V32). Noise powers, of course, add normally. Thus, any noise voltage that is more than 3 to 5 times any of the others is dominant, and the others may generally be ignored. This simplifies noise assessment.
The voltage noise of different op amps may vary from under 1nV/√Hz to 20nV√Hz, or even more. Bipolar op amps tend to have lower voltage noise than JFET ones, although it is possible to make JFET op amps with low voltage noise (such as the AD743/AD745), at the cost of large input devices, and hence large input capacitance. Voltage noise is specified on the data sheet, and it isn't possible to predict it from other parameters.
Current noise can vary much more widely, dependent upon the input structure. It ranges from around 0.1fA/√Hz (in JFET electrometer op amps) to several pA/√Hz (in high speed bipolar op amps). It isn't always specified on data sheets, but may be calculated in cases like simple BJT or JFETs, where all the bias current flows in the input junction, because in these cases it is simply the Schottky (or shot) noise of the bias current.
Input current noise
Figure 1-66: Input current noise
Shot noise spectral density is simply √(2IBq)/√Hz, where IB is the bias current (in amps) and q is the charge on an electron (1.6 × 10–19 C). It can't be calculated for bias-compensated or current feedback op amps, where the external bias current is the difference of two internal currents. A simple current noise model is shown in Figure 1-66.
Current noise is only important when it flows in an impedance, and thus generates a noise voltage. Maintaining relatively low impedances at the input of an op amp circuit contributes markedly to minimizing the effects of current noise (just as doing the same thing also aids in minimizing offset voltage).
It is logical therefore, that the optimum choice of a low noise op amp depends on the impedances around it. This will be illustrated with the aid of some impedance examples, immediately below.
Consider for example an OP27, an op amp with low voltage noise (3nV/√Hz), but quite high current noise (1pA/√Hz). With zero source impedance, the voltage noise will dominate as shown in Figure 1-67 below (left column). With a source resistance of 3kΩ (center column), the current noise of 1pA/√Hz flowing in 3kΩ will equal the voltage noise, but the Johnson noise of the 3kΩ resistor is 7nV/√Hz and is dominant. With a source resistance of 300kΩ (right column), the current noise portion increases 100× to 300nV/√Hz, voltage noise continues unchanged, and the Johnson noise (which is proportional to the resistance square root) increases tenfold. Current noise dominates.
Different noise sources dominate at different source impedances
Figure 1-67: Different noise sources dominate at different source impedances
The above example shows that the choice of a low noise op amp depends on the source impedance of the signal, and at high impedances, current noise always dominates.
Different amplifiers are best at different source impedances
Figure 1-68: Different amplifiers are best at different source impedances
From Figure 1-68 above, it should be apparent that different amplifiers are best at different source impedances. For low impedance circuits, low voltage noise amplifiers such as the OP27 will be the obvious choice, since they are inexpensive, and their comparatively large current noise will not affect the application. At medium resistances, the Johnson noise of resistors is dominant, while at very high source resistance, we must choose an op amp with the smallest possible current noise, such as the AD549 or AD795.
Until recently, BiFET amplifiers tended to have comparatively high voltage noise (though very low current noise), and were thus more suitable for low noise applications in high rather than low impedance circuitry. The AD795, AD743, and AD745 have very low values of both voltage and current noise. The AD795 specifications at 10kHz are 10nV/√Hz and 0.6fA/√Hz, and the AD743/AD745 specifications at 10kHz are 2.9nV/√Hz and 6.9fA/√Hz. These make possible the design of low-noise amplifier circuits that have low noise over a wide range of source impedances.
The noise figure of an amplifier is the amount (in dB) by which the noise of the amplifier exceeds the noise of a perfect noise-free amplifier in the same environment. The concept is useful in RF and TV applications, where 50Ω and 75Ω transmission lines and terminations are ubiquitous, but is useless for an op amp that is used in a wide range of electronic environments. Noise figure related to communications applications will discussed later in this blog. Voltage noise spectral density and current noise spectral density are generally more useful specifications in most cases.
Frequency characteristic of op amp noise
Figure 1-69: Frequency characteristic of op amp noise
So far, we have assumed that noise is white (i.e., its spectral density does not vary with frequency). This is true over most of an op amp's frequency range, but at low frequencies the noise spectral density rises at 3dB/octave, as shown in Figure 1-69 above. The power spectral density in this region is inversely proportional to frequency, and therefore the voltage noise spectral density is inversely proportional to the square root of the frequency. For this reason, this noise is commonly referred to as 1/f noise. Note however, that some textbooks still use the older term flicker noise.
The frequency at which this noise starts to rise is known as the 1/f corner frequency (FC) and is a figure of merit— the lower it is, the better. The 1/f corner frequencies are not necessarily the same for the voltage noise and the current noise of a particular amplifier, and a current feedback op amp may have three 1/f corners: for its voltage noise, its inverting input current noise, and its non-inverting input current noise.
The general equation which describes the voltage or current noise spectral density in the 1/f region is
where k is the level of the "white" current or voltage noise level, and FC is the 1/f corner frequency.
The best low frequency low noise amplifiers have corner frequencies in the range 1-10Hz, while JFET devices and more general purpose op amps have values in the range to 100Hz. Very fast amplifiers, however, may make compromises in processing to achieve high speed which result in quite poor 1/f corners of several hundred Hz or even 1-2kHz. This is generally unimportant in the wideband applications for which they were intended, but may affect their use at audio frequencies, particularly for equalized circuits.
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