Design & Technology
Eight myths about analog noise analysis
Noise is a central topic in analog circuit design, directly affecting how much information can be extracted from a measurement as well as the economy in obtaining the required information. Unfortunately, there’s a large amount of confusion and misinformation regarding noise, which has the potential to cause underperformance, costly overdesign, and/or inefficiency of resources. In this article, Scott Hunt, applications engineer, Analog Devices Inc., addresses eight of the most persistent myths about noise analysis in analog design
1. The noise spectral density of all noise sources can be added up and the bandwidth taken into account at the end of the calculation.
It can save time to combine the noise spectral density (nV/√Hz) of multiple noise sources rather than computing the rms noise of each noise source separately. But this simplification is only applicable if the bandwidth seen by each noise source is the same.
It becomes a dangerous trap if the bandwidths seen by each of the noise sources are different. Figure 1 shows the implications in an oversampled system. It would appear from the noise spectral density that the gain amplifier will dominate the total noise of the system. However, once the bandwidth is considered, the rms noise contributed by each stage is very similar.
2. It’s important to include every noise source in hand calculations. It may be tempting to consider every noise source in a design, but a designer’s time is valuable and such scrutiny can be very time-consuming in large designs. Comprehensive noise calculations are best left to simulation software.
Still, how does a designer simplify the hand noise calculations needed during the design process? Ignore minor noise sources below a certain threshold. If a noise source
is 1/5th the rms value of the dominant noise source (or any other noise source referred to the same point), it contributes less than two per cent to the total noise and can reasonably be ignored.
3. Pick an ADC driver with 1/10th the noise of the ADC.
Analog-to-digital converter (ADC) datasheets may suggest driving the analog input with a low-noise ADC driver amplifier that has something like 1/10th the noise of the ADC. However, this isn’t always the best choice. In a system, it’s often worth examining the tradeoff of the ADC driver noise from a system level. Firstly, if the noise sources in the system
preceding the ADC driver are much larger than the ADC driver noise, then choosing a very-low-noise ADC driver will not provide any system benefit. In other words, the ADC driver noise should be commensurate with the rest of the system. Secondly, even in the simple case where
there’s just an ADC and an amplifier to drive it, it may still be advantageous to examine the noise tradeoff and determine its effects on the system.
4. Since the 1/f noise increases at lower frequencies, dc circuits have infinite noise.
Although dc is a useful concept for circuit
considered by the designer. But it’s important not to overlook the current noise as well. Except in special cases such as input-bias-current compensation, the current noise is typically the shot noise of the input bias current: in = √(2 · q · Ib
).
The current noise is converted to a voltage via the source resistance. As a result, when a large resistance is in front of the amplifier input, the current noise can be a larger noise contributor than the voltage noise. Current noise typically becomes a problem when using a low- noise op amp with a large resistance in series with the input.
Figure 1: This illustrates the justification for using RMS noise rather than spectral density for noise calculations
www.cieonline.co.uk
7. All resistor types have the same noise for a given resistance. The Johnson noise of resistors is fundamental, giving rise to a simple equation for the noise of a certain resistor at a certain temperature. However, Johnson noise is the least amount of noise that can be observed in a resistor, and it doesn’t
decimated by n, and some number m decimated samples are returned. Taking n averages moves the effective sampling rate after decimation to fs
/n, reducing the
effective maximum frequency seen by the system by a factor of n and reducing the white noise by √n. However, it also took n times longer to obtain m samples, so the lowest frequency that can be seen by the system is also reduced by a factor of n (remember, there’s no such thing as 0 Hz). The more averages are taken, the lower these maximum and minimum frequencies move on the frequency band. Once the maximum and minimum frequencies are both within the 1/f range, the total noise depends only on the ratio of these frequencies. Therefore, increasing the number of averages provides no further benefit to the noise. The same logic holds for long integration times for an integrating ADC such as multi-slope.
www.analog.com Components in Electronics May 2017 15
analysis, the truth is that if dc is defined as operation at 0 Hz, then there really is no such thing. As the frequency gets lower, approaching 0 Hz, the period gets longer, approaching infinity. The implication is that a minimum frequency can be seen, even in a circuit that theoretically responds to dc.
5. The Noise Equivalent Bandwidth is a multiplier for the noise.
The Noise Equivalent Bandwidth (NEB) is a useful simplification for noise calculations. Some noise from beyond the bandwidth of the circuit can get into the circuit because the gain above the cutoff frequency is not zero. The NEB is the cutoff frequency of a calculated, ideal brick-wall filter that would let in the same amount of noise as would the actual circuit. The NEB is larger than the –3-dB bandwidth and has been calculated for common filter types and orders.
6. The amplifier with the lowest voltage noise is the best choice. When choosing an op amp, the voltage noise is often the only noise specification
mean that all resistor types are created equal with respect to noise. There’s also excess noise, which is a
source of 1/f noise in resistors that’s highly dependent on the resistor type. Excess noise, somewhat confusingly also called current noise, is associated with the way current flows in a discontinuous medium. It’s specified as a noise index (NI) in dB, referred to 1 µV rms/VDC
per decade. This
means that if there’s 1 V dc across a resistor with a 0 dB NI, the excess noise in a given frequency decade is 1 µV rms.
8. Given enough acquisitions, averaging reduces the noise indefinitely. Averaging is recognised as a way to
reduce the noise by the square root of the number of averages. This is conditionally true when NSD is flat. However, this relationship breaks in the 1/f range as well as in a few other cases.
Consider the case of averaging in a system sampling at a constant frequency (fs
), whereby n samples are averaged and
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