overview
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This article explains what 1/f noise is and how it can be reduced or eliminated in precision measurement applications. 1/f noise cannot be filtered out and can be a limiting factor in achieving good performance in precision measurement applications.
overall architecture process
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1/f noise is a low frequency noise whose noise power is inversely proportional to frequency. 1/f noise has been observed not only in electronic devices, but also in music, biology, and even economics. The source of 1/f noise is still highly debated and research is still ongoing.
Explanation of technical terms
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technical details
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In the voltage noise spectral density of the ADA4622-2 op amp shown, we can see that there are two distinct regions. The left side of the figure is the 1/f noise region, and the right side is the broadband noise region. The crossover point between 1/f noise and broadband noise is called the 1/f corner frequency
Comparing the noise density curves of several op amps shows that each product has a different 1/f corner frequency. In order to compare devices, we need to use the same bandwidth when measuring the noise of each device. For low frequency voltage noise, the standard specification is 0.1 Hz to 10 Hz peak-to-peak noise. For an op amp, 0.1 Hz to 10 Hz noise can be measured using the circuit shown.
The op amp is placed in a unity-gain configuration with the non-inverting input connected to ground. The op amp is powered by dual supplies so that the input and output can be at the same potential as ground. The active filter block limits the measured noise bandwidth while providing a gain of 1000 to the noise from the op amp, ensuring that the noise from the device under test is the dominant noise source. The offset of the op amp is not important because the filter input is ac coupled.
The filter output was connected to an oscilloscope and the peak-to-peak voltage was measured for 10 seconds to ensure that the full 0.1 Hz to 10 Hz bandwidth was captured (1/10 second = 0.1 Hz). The result displayed on the oscilloscope is then divided by a gain of 1000 to calculate the 0.1 Hz to 10 Hz noise. Figure 3 shows the 0.1 Hz to 10 Hz noise of the ADA4622-2. The 0.1 Hz to 10 Hz noise of the ADA4622-2 is very low, typically only 0.75 μV pp.
The total noise of the system is the sum of the 1/f noise and the broadband noise of each device in the system. Passive devices have 1/f noise, and current noise also has a 1/f noise component. But for low resistances, 1/f noise and current noise are usually too small to be considered. This article focuses only on voltage noise. To calculate the total system noise, we first calculate the 1/f noise and broadband noise and then combine them. If the 1/f noise is calculated using the 0.1 Hz to 10 Hz noise specification, then we assume the 1/f corner frequency is below 10 Hz. If the 1/f corner frequency is higher than 10 Hz, then we estimate the 1/f noise using:
To estimate the 1/f noise of the ADA4622-2, fh is approximately 60 Hz. We set fl equal to 1/aperture time. The aperture time is the total measurement time. If the aperture time or measurement time is set to 10 seconds, then fl is 0.1 Hz. The noise density en1Hz at 1 Hz is about 55 nV√Hz. Therefore, the noise result from 0.1 Hz to 60 Hz is 139 nVrms. To convert this value to peak-to-peak, multiply by 6.6, so the peak-to-peak noise is approximately 0.92 μV pp. This is about 23% higher than the 0.1 Hz to 10 Hz specification. Broadband noise can be calculated with the following formula:
The noise-equivalent bandwidth takes into account the additional noise beyond the filter cutoff frequency caused by the gradual roll-off of the filter. The noise-equivalent bandwidth depends on the number of filter poles and filter type. For a simple single-pole low-pass Butterworth filter, NEBW is 1.57x the filter cutoff frequency.
Using this equation, we can calculate the total rms noise of 495.4 nVrms with a simple 1 kHz low-pass RC filter at the output of the ADA4622-2. This noise is only 4% higher than the broadband noise. From this example it is clear that 1/f noise only affects systems whose measurement frequencies range from dc to very low bandwidths. Once about 10 times or more above the 1/f corner frequency, the 1/f noise contributes insignificantly to the total noise. The noise is summed as the square root of sum, and if the smaller noise source is lower than about 1/5 of the larger noise source, then we can decide to ignore the smaller noise source, since noise sources below 1/5 contribute only 1/5 to the total noise About 1%.
summary
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1/f noise can limit the performance of precision dc signal chains. However, techniques such as chopping and ac excitation can be used to remove 1/f noise. There are trade-offs with these techniques, but modern amplifiers and sigma-delta converters have addressed these issues, making zero-drift products easier to use and a wider range of end applications.