# Circuit noise analysis and optimization, Part 3a

The word “noise” suggests a range of electrical disturbances. The source of some of these disturbances is inherent to analog circuit components. such as amplifiers and converters. To know the lowest signal level a circuit can reliably process, a designer has to calculate the circuit noise.

This can be complex, as it involves deriving and solving many equations. Before writing equations, one has to identify and account for uncorrelated and correlated noise sources. This article will examine special situation where both correlated and uncorrelated noise exist, and offer optimization suggestions for the circuit. In this way, a designer can build circuits that function effectively with optimum noise performance.

My noise articles published at Planet Analog in October 2008 (links below, at the end) covered many of the basic concepts, but left room for many questions about noise calculation and noise optimization of various circuits. This article responds to these issues. It may be helpful to review the previous articles as they are the basis for this new article, and many references will be made to the previous material.

Beginning the analysis
To obtain the best noise performance, one has to limit the bandwidth and calculate noise over the noise effective bandwidth (NEB). One bandwidth-limiting scheme uses a simple low-pass filter in, or after, the signal-conditioning stage.

Noise bandwidth is wider than the signal bandwidth regardless of filter order of the system. A signal has fallen to 0.707 times of its original value at its –3 dB frequency (f0 ), but noise bandwidth for a first-order filter extends to 1.57 f0 . This means that white noise is passed as if the filter were a brick-wall type with a cutoff frequency 1.57 times as large. Multiplication factor for higher-order (N) low-pass filters are shown in Table 1 .

Table 1. Multiplication factors give noise equivalent bandwidth for filters of order N

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To calculate the noise equivalent bandwidth of an arbitrary circuit, such as the band-pass filter shown in Figure 1 , a designer could use Equation 1 , which integrates the magnitude of the signal gain over frequency, and divides it by maximum signal gain.

Figure 1: Band-pass filter

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(Equation 1)

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An easier way to calculate the circuit noise is to use simulation software such as PSpice. This band-pass filter has cut-off frequencies of (1/2π ×R3 ×C1 ) and (1/2π ×R1 ×C21 ). It is important to have an accurate op amp model that models the voltage and current noise densities. The process of noise calculation is the same as hand calculation, but the software does the data crunching.

To find NEB, select “AC sweep” from the “analysis setup” popup menu and click on the “noise enabled” button. The first step is to find the maximum gain, Figure 2 .

Figure 2: Maximum gain of circuit shown in Figure 1.

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Next, the summation operators can be used to find NEB, Figure 3 . The NEB is where the upper part of the graph flattens out, roughly 170 kHz in this example.

Figure 3: Noise equivalent bandwidth (NEB) of circuit shown in Figure 1

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Pspice also calculates other pieces of information that a designer needs to study. For example, it has already gathered the necessary data to display the input and output noise graphs for the circuit shown in Figure 1. This is done by selecting “enable noise” in the setup menu. The output noise result is shown in Figure 4 .

Figure 4. Output noise of circuit shown in Figure 1.

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Knowing the noise bandwidth allows a designer to find the noise over this bandwidth by using probe and the s operator, Figure 5 . Place one cursor at low frequency (e.g., 1 Hz). Right click and place a second cursor at 170 kHz circuit's noise bandwidth). The noise over this bandwidth can be read from “dif” in probe cursor.

Figure 5: Total output noise of circuit shown in Figure 1 integrated over NEB.

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The above approach assumes that all of the circuit's noise sources are correctly identified and are configured for optimum noise performance. Pspice does not know the correct configuration and component values, which must be optimized by the circuit designer. Is the above circuit optimized for noise? Are all noise sources identified and accounted for?

(End of Part 3a ; Part 3b will look at an actual circuit example, with calculations.)

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.

Previous parts of “Understanding Noise Optimization in Sensor Signal-Conditioning Circuits”:

## 1 comment on “Circuit noise analysis and optimization, Part 3a”

1. oijsoifjdsoifj
September 28, 2015

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