Selecting the right op amp can be a serious challenge when you take all of the possible parameters into consideration. Choosing a low- noise amplifier is particularly daunting. Both internal and external sources of noise, including many that designers ignore or don't recognize, affect the op amp's and overall system's noise performance. Different types of op amps—CMOS, JFET, and bipolar—exhibit various noise characteristics about which you can make some dangerous generalizations. However, an important tool, namely using low noise figure (NF) for given source resistance, does exist to help take some of the guesswork out of choosing a low-noise amplifier.
Unfortunately, many designers aren't even aware that they need such a tool, and they think all the information they need is on the data sheet. They usually just look at the voltage noise (en) numbers on the data sheet and use the "if it's lower, it's better" method. The problem with this method is that it ignores the current-noise (in) half of the equation (see box, "Internal and external op-amp noise sources." By ignoring the effects of current noise, you ignore the effect of the source resistance on the amplifier's noise performance. The total noise voltage, ent, at the input of an amplifier is
This number is absolutely necessary for determining the noise performance of a system. Just looking at en alone can be very misleading. For example, compare the performance of two popular op amps, the LMC662 and the OP-07, when amplifying a signal from two source resistances. At first, the OP-07 with a typical 1-kHz noise voltage of 9.6 nV/[sqrroot]Hz would appear an easy winner over the LMC662 with a typical 1-kHz noise voltage of 22 nV/[sqrroot]Hz. But when you look at the noise currents, you find the opposite is true: 120 fA/[sqrroot]Hz for the OP-07 vs 0.113 fA/[sqrroot]Hz for the LMC662.
To illustrate the effects of these differences, compare signals coming from a 10-k(ohm) and a 10-M(ohm) source. Determining the noise contribution of the amplifier requires only an rms addition of the effects of the noise current and noise voltage. In the case of the OP-07, using Eq 1,
As you can see, the OP-07 noise current makes no real difference at this source resistance. The much lower noise current of the LMC662 has even less effect, so the 22 nV/[sqrroot]Hz is the total noise contribution. In this case, the OP-07 is the easy low-noise winner.
If you perform the same calculations for the OP-07 with a 10-M(ohm), the result is
At this source resistance, the ent of 1200 nV/Hz makes the "quiet" OP-07 a very noisy choice. However, for the LMC662,
In this case, the OP-07's total noise voltage is 55 times higher than the LMC662, making the LMC662 the low-noise choice. From these extreme examples, it is obvious that selecting a low-noise op amp requires more than just looking at en.
Justifying the use of NF
NF is a convenient way to describe the ratio between the total system noise and the theoretical source-resistance noise. An RMS addition of the noise contributed by the amplifier with that of the source results in the noise present at the input of the amplifier. Twenty times the log of the ratio of this sum to just the noise from the signal source equals the NF.
NF is a common parameter for comparing RF amplifiers or ac circuits, which allows you to transform the signal resistance to match the amplifier. Over the years, op-amp experts have implied that because you can't adjust the source resistance of a dc circuit (adding resistance to a source because it is lower than optimum only results in more noise and less signal), then knowing the NF at other resistances is useless information.
This viewpoint may have been true when there wasn't such a wide variety of op-amp choices, but the situation is quite different today. Because several op amps may meet the basic requirements of bandwidth, slew rate, and drift, selecting the one with the lowest for the existing source resistance is practical.
Another argument against using NF is based on the premise that, because any source resistance causes the noise current to add to the noise voltage, the lowest system noise is obtained when the source resistance is zero. Calculating the NF for a system with zero source resistance always gives an infinitely high NF (the denominator of Eq 5 is zero). Therefore, if the source resistance is zero, selecting for lowest NF does not give the lowest system noise.
These statements are also true but irrelevant. In the real world, zero source resistance would require infinite signal power, and if you had infinite signal power, you wouldn't need an amplifier.
Note that there is also the case of the purely reactive source. A signal from a lossless capacitor or inductor has no thermal noise, and the selection process would be quite different from that of resistive sources. For more discussion on reactive sources, see Ref 1.
Calculating NF
Although almost no op-amp manufacturer provides NF curves, most data sheets do include the information (namely, en and in) necessary to plot these curves. Using these voltage- and current-noise numbers and performing a few calculations, you can determine the NF for any amplifier at the resistance of interest. To make the process even easier, a Basic program automatically calculates NF over a wide range of resistance values and generates an ASCII file of NF numbers (see EDN's computer bulletin-board system (BBS).
Figs 1 and 
2 show the plotted NF results using data from the OP-07 and LMC662 data sheets. The log dB scale of the NF graphs shows how close to zero the NF will go but still provides detail at the higher noise levels. To make comparisons easier, the horizontal and vertical scales of all the plots are identical. The curves owe their shape to the large contribution of amplifier-noise voltage on the left and descending side and to the noise-current contribution, which causes the NF to begin rising to the right.
Internal and external op-amp noise sources
The easiest way to represent the noise parameters of an op amp is to assume there are two separate, uncorrelated noise generators at the inputs of an ideal noiseless op amp: a noise voltage source in series with an input and a noise-current generator connected between each of the inputs of the amplifier and ground (Fig A).The value of the source resistance has no effect on the internal noise-voltage source because the source resistance is in series with the input. However, because the current-noise sources are between the two inputs and ground, the contribution due to these sources is directly related to the source resistance. This noise current flows through the source and anything else connected to the inputs, such as the feedback resistance. This current produces a noise voltage proportional to the total impedance seen from the inputs. As a result, this contribution depends upon the value of the source resistance. These two noises add at the amplifier input and appear as the amplifier's contribution to the total system noise (Eq 1).
Recognize other noise sources Noise can corrupt a signal in more ways than through these voltage- and current-noise sources, and many contributors to noise go unrecognized. For example, air currents flowing over a pc board generate low-frequency signals. These air currents produce small fluctuations in temperature at the thermocouple junctions produced where the IC is soldered into the board. Most system designers are not aware that the common IC lead frame material, Kovar, and the copper board traces produce effective thermocouples, which produce about 35 mV/8C. A low-noise bipolar op amp, such as the OP-07, has a typical 0.1- to 10-Hz noise of 0.35 mV p-p. If the lead frame were made of Kovar, the soldered connection on the board would need to wander around only 0.018 to produce a "noise" signal equal to that of the op amp. Because of the thermal mass of the board, this noise appears as 1/f noise starting below 2 or 3 Hz. This air-current "zephyr" noise may in fact be the 1/f noise shown on many low-noise op-amp data sheets. There are two ways to eliminate this noise source. One is to prevent temperature fluctuations from occurring at all connections between the low-level signal source and amplifier's input by embedding a portion of the circuit in foam or enclosing it in a small, separate, closed box. Using amplifiers built on copper- lead frames, such as the OP-07, also eliminates this source of noise. However, internal connections of silicon and other metals, such as gold or aluminum, create thermocouples with outputs as much as 10 times higher than those produced by Kovar-copper connections. Thus, even copper lead frames are not a complete answer. Reducing thermal gradients is still necessary for the lowest system noise. Excessive bandwidth is another source of noise that op-amp users often overlook. The bandwidth itself doesn't cause extra noise. However, most of the types of noise generated in the amplifier or inherent in the signal source are broadband generators, which the op amp then amplifies over its full bandwidth. Many signals do not require extremely wide bandwidths. To pass a 1-kHz square wave and maintain sharp edges requires an amplifier with a 10- to 20-kHz bandwidth. If the objective is to restore this signal when its amplitude is as small as the amplifier noise, you must first limit the maximum bandwidth of the incoming signal and the amplifier to around 1 to 3 kHz. This limit reduces the amount of noise being amplified with the signal. Limiting the low-frequency response of the system with a bandpass filter reduces the noise even further. In addition to the voltage and current noise of the op amp itself, one other fixed noise source, external to the op amp, is significant: the signal source. Designers tend to assume that a signal source is noiseless, but, in reality, all resistive sources generate thermal noise proportional to the square root of the source's resistance. Using the formula
 where K is Boltzman's constant (1.38310-23 joules/kelvin), T is the temperature in kelvin, BW is the bandwidth in hertz, and Rs is the source resistance, you can calculate this noise voltage. For example, at 258C (298K) a 1-kV source produces a minimum noise of 4 nV/[sqrroot]Hz. This noise is always present, along with the signal, and determines the optimum SN ratio of the signal source.
|
The curves clearly point out that at 10 k(ohm), the NF for the OP-07 is 4 dB. At this source resistance, the LMC662 has an NF of 11 dB, making the OP-07 the easy winner. However, at 10 M(ohm), the situation is reversed. The OP-07 now has an NF of 19.08 dB, compared with 0.025 dB for the LMC662. Thus, at 10 M(ohm), the LMC662 is the low-noise winner.
The curve in 
Fig 3 shows that the LF156A is a good example of an amplifier suitable for high source impedances. 
Fig 4shows that the OP-27 exhibits its lowest noise performance with low-resistance sources.
Even if a data sheet doesn't provide the in numbers, in some cases, you can still arrive at an approximate NF, which is theoretically the best NF. Specifically, if the input stage of the op amp doesn't use bias-current cancellation, you can use the input bias current to estimate a best possible case. To calculate the lowest possible noise current, you can use the formula for shot noise (noise that results from current flowing across a pn junction), which is
where Q is the electron charge (1.6×10-19), BW is the bandwidth, and Ib is the bias current in amps. Don't forget that the input current of JFET op amps doubles for each 10°C increase in junction temperature. Thus, the resulting noise current increases by [sqrroot]2 with each 10°C rise. A conservative approach is to use the input current specified on the data sheet at the highest temperature.
If you question the usefulness of this number, you should know that the data sheet's in number for most CMOS and some JFET amplifiers is the result of this very calculation. The calculated 113 aA (10-18 amps) (700 electrons/sec rms)/[sqrroot]Hz for the LMC662 is much too small to measure in the real world. This noise current reduces the S/N ratio of a 1000-M(ohm) source by only 0.024 dB.
These calculated numbers are most useful when the source resistance is less than 1 GV. At higher source resistances, the number becomes more theoretical than practical. At the level of 113 aA/[sqrroot]Hz, the current has no real effect in almost all cases. For noise currents to have a meaningful effect, you must consider the true value of the source resistance. Resistors with values of 1012 V or more are available, but just 1 pF of shunt capacitance reduces the impedance at 100 Hz by a factor of over 600. For this reason, noise currents, such as those of the LMC660 family, normally have no effect. At high resistances, the noise voltage of the source is so much higher than the op amp that the resulting NF is nearly zero.
As you can see from the figures, the en of many op amps is not the limiting factor of low-noise performance. However, by selecting an amplifier with a low NF for the source resistance, you can design a low-noise system. An NF of 1 dB or less provides nearly ideal noise performance.
BiFET and CMOS op amps usually have higher noise voltages than do op amps with bipolar input stages. Contrary to popular opinion, using CMOS op amps with high-resistance signal sources can result in a low system NF. At lower source resistances, many bipolar op amps can provide good low-noise performance because of their low en. A quick look at the NF graphs can simplify selection.
Finally, remember that for many applications, the noise contributed by the amplifier may be insignificant compared with that of other parts of the system. Many of today's low-noise amplifiers have much lower noise than do most signal sources. Also, if the NF curves you generate show only minor differences between amplifiers—a 0.2-dB difference, for example—other, possibly more important, parameters such as power consumption, bandwidth, offset voltage drift, and price, may make more of a difference in your op-amp choice.
John W Christensen is a principal applications engineer at National Semiconductor and has been with the company for over 6 years. His hobbies include sailing and scuba diving.