Understanding noise optimization in sensor signal-conditioning circuits (Part 1a of 4 parts)

Accurate signal conditioning and high-resolution measurements are no longer limited to industrial or instrumentation applications. Designers of portable consumer- electronic equipment also need to minimize system noise.

This can be quite challenging due to the small signal voltages found in battery-powered devices. The accuracy of a system depends on its noise floor. To attain the lowest noise floor and best performance from signal-conditioning circuitry, designers must understand component-level noise sources and account for them when calculating the overall noise of an analog front-end.

Some designers believe that choosing the lowest-noise components can solve all of their signal-conditioning noise issues. This is a good starting point, but datasheets for most IC amplifiers and voltage references used in signal-conditioning applications specify noise at a limited number of frequencies. Thus, designers have limited information with which to select parts. They do not know where the component noise comes from and what influences it; whether or not noise changes with respect to time, temperature and circuit configuration, or if it is necessary to know about the fabrication process before selecting the lowest noise part.

With today's low-power, cost-conscious designs, many systems cannot afford the most expensive parts or those that trade low noise for higher power consumption. This article explores these topics and provides guidelines for selecting the best components for the design task at hand.

Low-noise designs have become important in today's portable gadgets. Generally speaking, noise is any unwanted signal that affects the quality of the useful information. To understand why low-noise design is critical, look typical signal chain shown in Figure 1.

Figure1: Typical consumer signal chain
(Click on image to enlarge)

Popular sensor-based applications have moved toward lower operating-supply voltages, from ±22 V several years ago to ±0.9 V today, thus shrinking the LSB size while demanding higher precision and accuracy, Figure 2.

Figure 2: LSB size shrinks as full-scale signals are reduced
(Click on image to enlarge)

As an example, the automotive industry has moved from 8-bit systems to 12 bits or higher. This trend has made measurement of the microvolts generated by sensors quite challenging. Imagine a real-world sensor that generates signals of 30 mV max (this is very common). In this case, 1/2 LSB in a 12-bit system is 3.5 μV, so 1 μV of input referred noise from the amplifier used as the analog front end would affect the quality of the measurement.

Equally important is keeping the analog front-end noise down when driving an ADC. This is critical in order to avoid worsening the signal to noise ratio (SNR). The net SNR degradation (in dB) due to the amplifier will be:

(Click on equation to enlarge)

where:
N_ADC is the rms noise of the ADC in microvolts (μV)
f_{-3 dB} is the –3-dB input bandwidth of the ADC in MHz (or the cutoff frequency of the ADC input filter, if used)
N is the noise gain of the amplifier (1 if in unity-gain buffer configuration).
e_n is the equivalent input noise voltage spectral density of the op amp in nV/√Hz.
FSR is the full-scale input span of the ADC (e.g., 5 V for a ±2.5-V range).

A poorly designed signal-conditioning circuit degrades SNR and eliminates the benefits of the system's high-resolution ADC. For example, Table 1 shows the SNR_Loss for an AD7671 16-bit analog-to-digital converter (28-μVrms noise, 9.6-MHz BW, 0 to 5-V input, G=1) when driven with amplifiers having different noise specs.

Table 1: Higher amplifier noise causes more SNR_Loss for ADC
(Click on Table to enlarge)

Making accurate high-resolution measurements depends on the system noise floor. The maximum achievable signal-to-noise ratio is:

The system designer's goal is to process small signals generated by the sensor without distorting them. The following sections will address the noise generated by signal-conditioning circuits and raise awareness for selecting appropriate parts.

Noise can be separated into two distinct categories: extrinsic (interference) and intrinsic (inherent). Electrical and magnetic noise are forms of extrinsic noise. They can be periodic, intermittent, or random. System designers can reduce their effects in a number of ways.

Intrinsic noise can be defined as random processes due to quantum fluctuations inherent in all resistors and semiconductor devices (PN junctions) that create voltages and currents in any application. Noise cannot be completely eliminated. Thermal agitation of electrons and random generation and recombination of electron-hole pairs are examples of inherent noise that IC manufacturers try to reduce with better processes and design techniques.

Noise is usually specified as peak-to-peak (p-p) or rms, and is graphically shown as p-p or spectral noise density, Figure 3. Unlike ac signals, whose power is concentrated at just one frequency, noise power is spread over the entire frequency spectrum. Instantaneous values of noise are unpredictable, but it is possible to predict noise in terms of probabilities. Most noise has a Gaussian distribution.

(Click on image to enlarge)

Figure 3: Typical peak-to-peak and voltage noise density graphs
(Click on image to enlarge)

It is very difficult to read values accurately and consistently from the p-p noise graphs. When noise power density is plotted versus frequency, it provides a visual indication of how power is distributed over frequency. The noise spectral density shows the noise energy at a given frequency, while the rms number gives the rms value over a given bandwidth or time interval.

It is always good to know the p-p noise value. Because noise is random, there is always a probability that the voltage could exceed the peak-to-peak value. Multiplying the rms noise by 6.6 gives a 99.97% confidence that the p-p value will not be exceeded.

In ICs, the two most common forms of power density distributions are 1/f and white noise. The quantities of e_n(f) and i_n(f) are noise spectral densities and are expressed in nV/√Hz and pA/√Hz . It is important to specify the frequency band, since noise depends on the measurement bandwidth.

It is also difficult to mathematically characterize amplifier noise at low frequencies due to 1/f, temperature and aging effects, and possibly even popcorn noise (the topic is covered in Part 1b), but repeated experiments have shown that noise rises at higher temperatures.

Aside from white noise and 1/f noise, other contributors to IC noise are popcorn noise, shot noise, and avalanche noise. In addition to ICs, other components such as the resistors, capacitors, and inductors commonly used in system designs each have their own noise (see sidebar to get a better understanding of each one of these terms).

Because noise is a probability function, designers need to add uncorrelated noise sources in root-sum-square fashion (rss). This means that adding two noise sources having the same energy only increases the overall noise by √2, or 3 dB. For correlated noise sources, an additional term made up of a correlation factor multiplied by the product of the noise sources will be added into the noise calculation equation.

Various amplifier noise sources, as well as sensor and external component noise sources, are shown in Figure 4. Amplifier noise is modeled by zero-impedance voltage generators in series with the inputs and infinite-impedance current sources in parallel with the input. Each of these terms varies with frequency and with amplifier type. Both input voltage noise (en) and input current noise (in) can be treated as uncorrelated noise sources added around an ideal "noiseless" amplifier

Figure 4: Signal-conditioning circuit showing all noise sources (amplifier is assumed to be noiseless)
(Click on image to enlarge)

Total output noise, referred to input (RTI), is comprised of resistor noise, and op amp voltage and current noise as shown in the following equation:

(Click on equation to enlarge)

Note that in both inverting and non-inverting configurations, noise gain (the amount that noise gets gained up by) is the same: 1+R₂/R₁. Capacitors, not shown here but often used in circuits like this, do not generate noise themselves, but the amplifier current noise drops across a capacitor and creates a voltage noise error.

White noise is passed as if the filter were a brick-wall type but with a cutoff freq 1.57 times as large. The number 0.57 accounts for the transmitted noise above f₀ (corner frequency of the filter). In amplifier applications, this gradual roll off is defined as f₀ = β × f_t, where β is the feedback factor and f_t is the unity gain crossing. The amplifier passes white noise with a cutoff freq of 1.57 f₀.

As shown, amplifier voltage noise plays a big role in the output noise. Assume that the circuit above is configured for an inverting gain of 1000, using a variety of 10 MHz amplifiers with different noise specs and resistor values as shown. The result of this test is shown in Figure 5. But the amplifier with the lowest noise specified in its datasheet is not always the best for the application. There are other factors to consider when choosing an amplifier.

Figure 5: Amplifier noise contributes greatly to the output noise of a signal-conditioning circuit
(Click on image to enlarge)

By knowing the sensor, the designer should be able to determine the operating frequency range (broadband, 1/f). The designer should then pick an amplifier with right characteristics. Today's amplifiers have broadband noise in the range of 0.9 nV/√Hz to 60 nV/√Hz.

Understanding the input architecture and the process technology on which the amplifier is manufactured will help in choosing the right amplifier for the job. In the early stages of system design, always think seriously about designing for best noise performance by choosing the right components and limiting the application's bandwidth.

Users can then analyze for non-noise requirement such as input impedance, supply current and gain. If noise requirements are not met, iterate this process. It is always wise to design for low noise rather than trying to reduce noise by shielding, layout and other techniques.

It is important to know that trade-offs had to be made when the amplifier was designed. These might affect the application, so it is important to know how the part was designed and what process is used for fabricating the part. It is not enough to rely on a datasheet specification (x nV/√Hz, for example).

Bipolar op amp noise characteristic is dependent on its quiescent current. What works to minimize en (low rb and high I_c) is the opposite of what is good for low i_n. This represents a fundamental tradeoff in bipolar design. A number of parts include super beta or I_b cancellation circuits. These introduce correlated noise. During noise analysis, a correlation constant needs to be introduced to account for this correlated noise. Bias compensated op amps have higher noise current than can be predicted from their bias currents (I_b).

CMOS noise contributors are different in different regions of operation. Process dependencies or design tweaks can be used to get better noise specs, but each has its implications on the application. Flicker noise (1/f) is inversely proportional to the transistor width and length (W × L), so to reduce noise, designers use large geometry input stage transistors. This creates large input capacitances that might become a limiting factor in final applications. CMOS parts have much better current noise compared to bipolar parts. Current noise density (I_n) can often be neglected at room temperature, but can be a problem over temperature.

Compared to BJTs, JFETS have low g_m, Therefore, FET op amps tend to have a higher voltage noise for similar operating condition. Their voltage noise (e_n) also contains flicker noise, but JFETs have much better current noise than BJTs. Their current noise (I_n) can be neglected at room but might become a problem over temperature, since it will double for every 20°C temperature increase as the bias current (I_B) doubles every 10°C. Many successful commercially available JFET op amps have traded voltage noise for input capacitance. Table 2 can become handy when selecting amplifiers.

Table 2: Noise performance of different processes
(Click on Table to enlarge)

Table 3 shows some popular amplifiers on different processes.

Table 3: Three popular amplifier noise specs on different processes
(Click on Table to enlarge)

Once the sensor and amplifier have been chosen, based on the above guidelines, choose components that go around the amplifier. Small resistors are usually better, as they will reduce the effects of the amplifier's current noise. Resistors introduce their own noise that will raise the system's noise floor.

Additionally, the resistor noise should not dominate the amplifier noise. In fact, op amp simulation models such as those recently released by Analog Devices do not allow large resistors to be used to set the gain of low-noise amplifiers.

Narrowing the measurement bandwidth is another good practice when designing low-noise signal conditioning circuits. This can be done using simple single-pole circuits or more complicated multi-pole active filter (see filter tool design on the ADI web site).

Conclusion
With today's low power, cost conscious designs, many systems cannot afford the most expensive parts nor can they afford the higher power consumption of low-noise parts. To attain the lowest noise floor and best performance from signal conditioning circuitry, designers must understand component level noise sources.

To be continued. . . .

• Part 1b covers the various types of noise: white (broadband); pink (1/f); popcorn (burst); shot; Schottky; and resistor noise; click here
• Part 2a covers op amp selection and passive component selection
• Part 2b covers bandwidth selection and reviews the lessons

References
(note: all from Analog Devices, Inc, except the book)

1. Application Note AN-347, Shielding and Grounding, http://www.analog.com/static/imported-files/application_notes/41727248AN_347.pdf
2. Application Note AN-358, Noise and Operational Amplifier Circuits, http://www.analog.com/static/imported-files/application_notes/5480117281535838576388017880AN358.pdf
3. Application Note AN-202, An IC Amplifier User's Guide to Decoupling, Grounding, and Making Things Go Right for a Change, http://www.analog.com/static/imported-files/application_notes/135208865AN-202.pdf
4. Barrow, J., and A. Paul Brokaw, Grounding for Low- and High-Frequency Circuits, Analog Dialogue, Volume 23, Number 3, 1989
5. Bryant, James Bryant and Lew Counts. 1990. Op Amp Issues -- Noise, Analog Dialogue, Volume 24 Issue 2, 1990
6. Seminar: Noise Optimization in Sensor Signal Conditioning Circuits Part 1: www.analog.com/onlineseminars/noise1.
7. Seminar: Noise Optimization in Sensor Signal Conditioning Circuits Part 2: www.analog.com/onlineseminars/noise2.
8. Freeman, J. J. 1958. Principles of Noise, New York: John Wiley & Sons, Inc.

About the author
Reza Moghimi is an applications engineering manager for the Precision Analog Products group at Analog Devices, Inc. He holds an BSEE and MBA from San Jose State University (SJSU), CA. In addition to Analog Devices, Reza has worked for Raytheon Corp., Siliconix Inc, and Precision Monolithic Inc. (PMI). He enjoys traveling, music and soccer.