Understanding your amplifier

Bandwidth and digital sampling

When performing nanopore experiments, you measure ionic current through the pore, but there are many steps, with different degree of complexity, involved in getting from the movement of ions to the storage of a signal on your hard drive. This transfer of information presents an issue in that the real-world current is an analog signal (i.e. it is continuous) while the computer relies on digital information (i.e. discreet snapshots of that continuous signal). In order for communication to occur smoothly, an Analog to Digital Converter (ADC) must be used between the current amplifier and the computer, which essentially takes the continuous signal that the pore generates and converts it into a series of snapshots which are then sent to the computer. If the snapshots are short enough in time then the signal the computer receives can be a very good approximation of the real signal. However, things can become a bit more complicated if the snapshots are longer – or, conversely, if you are looking for molecular signals that are very fast relative to your sampling frequency. As an analogy, imagine two TV shows, one with a car moving slowly down a road and the other with a car moving fast down a highway. Then imagine pausing the videos. The car moving slowly will be shown clearly by the paused video while the car moving fast will be a blur. Why? Because the car moving slowly was roughly in one spot for the length of time of one data package while the car moving fast moved significantly during the length of time of one data package.


This is a well studied topic in many fields and we will make no attempt to cover everything here. Rather, we focus only on the subset of understanding that we think is essential to being an effective nanopore researcher. Interested readers can explore a little more detail in dedicated publications on the subject and references therein [1].

One of the most important parameter for a current amplifier is its bandwidth. This is not always an intuitive concept to new entrants to the field. In mathematical terms, bandwidth is the range of frequencies present in a signal. In practical terms, the bandwidth of your amplifier is the range of frequencies, typically between DC and some maximal value that it can faithfully record and sets the speed at which the electronics can respond to a change in the electrical load on the circuit. If your amplifier has very high bandwidth then it can respond and faithfully record very rapid changes in the electrical load; for example, a change in the resistance of the pore caused by a molecule blocking it for a few microseconds. Bandwidth can be set in hardware, by the quality of the design and components being used, or by actively filtering the signal during or after acquisition, either in hardware or in software after the fact. The figure below shows an example of a power spectrum with the bandwidth labelled.


A common misconception revolves around the distinction between sampling rate and bandwidth. Imagine that you are sampling from a pure sine wave. It should be clear that to resolve the shape of the wave, you need to sample many times in a single cycle. Or in other words, if you want to resolve a frequency component completely in your signal, you need to sample at a higher frequency.


Nyquist Theorem states that to fully resolve a signal one must sample at a rate at last twice as high as the bandwidth. In practice, it is usually beneficial to oversample for the sake of having more data to fit when analyzing downstream. Suppose for example that you have a signal that you want to record that is a continuous sine wave with frequency f:

The graph below shows the effect of sampling this signal with various sampling rates k, in which case we now have a discrete signal, as in the equation below for integer values of n.

Note that in some undersampled cases for k<2f, the signal is completely distorted and no longer resembles the underlying signal at all.


In the image above, we have a continuous sine wave with period 1 in blue, sampled at two different sampling frequencies. In grey, we have k/f=0.25 and the sine wave looks like a triangular wave. In yellow, k/f=0.6 and not only is the wave completely distorted, but if you look closely you'll see that it has a period of 3. Undersampling has distorted a 1Hz sine wave into a signal at a lower frequency.


In short, undersampling will distort the frequency components of your signal, and the distortion can completely change the observation, making high frequency signals indistinguishable from lower frequency signals. This is called aliasing.


In practice, your nanopore signal will contain all frequencies up to the bandwidth of the amplifier or filter you are using, and all of them need to be fully resolved in order to accurately reproduce the underlying signal. If you undersample, you will end up distorting part of your power spectrum, which will manifest itself as an increase in noise at lower frequencies and possible artefacts in the events that you measure. Know the bandwidth accessible to your electronics, and sample at least twice that fast. The only downside to oversampling is the increased requirement for hard drive space to store the signal, though hard drives are cheap.


More concretely, an idealized model of a molecule passing through a pore indicates that the molecule should produce an instantaneous step change in the resistance of the pore. Due to bandwidth limitations, however, the current change that is read is not a perfect step, instead rising smoothly between the open and blocked states. The figure below shows a few examples of this. In the image, the black line is the idealized signal, the red line is a denoised representation of the bandwidth limited response of the electronics limited in this case by the resistor-capacitor (RC) network that makes up the system, while the green line is the sampled signal with noise.

When the event is long relative to the response time of the system (as in a and b above), the effect is the distortion is minor. When the length of the even becomes comparable to the response time, as in panel c, the signal is distorted (it appears attenuated, barely reaching the full blockage level). What should be clear here is that the signal you measure is never a perfect representation of the underlying physics, and care must be taken in interpreting the signals you read. Always bear in mind the response time/bandwidth of the electronics you are using when interpreting what you see in your experimental work.


Electrodes

For a detailed dive into electrochemistry and the implications of electrode choice we refer interested readers to these excellent guides on the subject [1,2]. The important point for most nanopore work is to ensure that the electrode you are using is electrochemically matched to the conductive species being used to carry current through the pore. The vast majority of nanopore literature uses Ag/AgCl electrodes and a salt solution containing chloride ions. The benefit is that there is no potential drop involved in exchanging the ionic current through the pore for electronic current in the electrode and gives both improved noise performance and a more faithful electronic reproduction of the iontronic signal in the pore for any voltage change. Should a carrier solution without chloride ions be used, the electrode should be changed to match if possible.


Troubleshooting noise

In my time in the field, I have had noise resulting because someone in the next room made a poorly timed cellphone call, because someone in the next lab over plugged a freezer into the wrong outlet, because a particular type of lightbulb happened to be nearing the end of its life, and a whole host of others for which I never actually found a satisfactory cause and which eventually just went away. Excess noise in your signal is often due to second or third-order interactions between different components of your circuitry and troubleshooting is more art than science. That being said, there are some general rules that can help most of the time.


The first line of defense is your Faraday cage. A good Faraday cage is a contiguous block of conductive material (copper or aluminum are excellent options). While some holes in the cage are unavoidable for cabling and the link, the fewer the better. NNi carries a line of high-quality Faraday cages optimized for most commercial amplifiers built around this design paradigm.


If even our Faraday cages are not enough to save you, the power spectrum is your single most useful tool. If you can isolate the noise you are seeing to a particular frequency band, you can often diagnose it. Below, we summarize the most likely causes that you might see in different spectral bands.


Low-frequency noise:

If your power spectrum looks like the one below, with a large but fairly unfocused bump below 100Hz, the most likely cause of your noise is mechanical resonance. Try moving your setup to a vibration isolation table or put it on a piece of cloth or rubber to break the coupling between your instrument and the surface on which it rests. Try to shorten or fix in place any free-standing sections of electrode wire, or any wires that carry the signal prior to digitization, to avoid the possibility of resonant vibrations.


If you have a lot of low-frequency noise but it is still 1/f-type noise, then it is coming from the pore itself. In that case, see our previous discussion about pore fabrication for mitigation options.


50/60 Hz and harmonics

If you have a clear, narrow spike at 60Hz and integer multiples thereof (or 50Hz if you are in Europe) then you have either a ground loop or a leaky Faraday cage that is picking up noise from the AC power sources surrounding your instrument. Check carefully that your Faraday cage is properly grounded to your amplifier. If it is already, ensure it only has a single path to ground, as a loop in the ground path can amplify noise. Ensure that there are no wires or fluidic lines entering or leaving the Faraday cage. These can act as antennas carrying noise back into your Faraday cage. Ensure that all analog cables are as straight as possible (avoid loops and coils) and route them as far as possible from any equipment that is drawing large amounts of current. In general, keep all analog cables as short as possible. Physically moving the Faraday cage and/or amplifier to a different location, or a different power outlet, can often help as well.


Higher Frequencies

Well-defined noise spikes at higher frequencies are harder to diagnose generally. If they have newly appeared where they were not before, consider carefully what, if anything, has changed in the setup recently. For example, I once encountered 40 kHz noise which I later tracked down to the installation of a new graphics card in the computer that was controlling the setup, and once traced noise in the 10kHz range to a particular malfunctioning nearby lightbulb.


If all else fails, the fallback is to turn off everything. Literally everything, right down to the lights in the lab and the computer itself. Connect an oscilloscope directly to the output of your amplifier and turn things on one at a time, noting carefully when the problematic noise contribution appears. Note that noise is often a nonlinear effect, requiring an interaction between two or more sources to manifest, so consider combinatorics in turning things on as well.


Table of Contents

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References

[1] V. Tabard-Cossa, “Chapter 3: Instrumentation for Low-Noise High-Bandwidth Nanopore Recording,” in Engineered Nanopores for Bioanalytical Applications, J. B. Edel and T. Albrecht, Eds. Ottawa: Elsevier Inc., 2013, pp. 59–88. https://doi.org/10.1016/B978-1-4377-3473-7.00003-0


[2] N. Elgrishi, K. J. Rountree, B. D. McCarthy, E. S. Rountree, T. T. Eisenhart, and J. L. Dempsey, “A Practical Beginner’s Guide to Cyclic Voltammetry,” J. Chem. Educ., vol. 95, no. 2, pp. 197–206, Feb. 2018. https://doi.org/10.1021/acs.jchemed.7b00361.


Last Updated: 2021-05-11