Modifica di Electromyography (sezione)

===Differential Amplification and CMRR===
[[File:Opamppinouts.png|thumb|'''Figure 2:''' Operational amplifier symbol. The inverting and non-inverting inputs are distinguished by "−" and "+" placed in the amplifier triangle. V<sub>s+</sub> and V<sub>s−</sub> are the power-supply voltages; they are often omitted from the diagram for simplicity but must be present in the actual circuit.]]

As mentioned earlier, the issue of 50 Hz noise is potentially a rather difficult inconvenience to eliminate. The universally adopted technique to address this starts from the concept that such noise should be the same at all points on the body, while the bioelectric signal to be acquired in the same points must be different. Therefore, a differential amplifier is used. This can be thought of as consisting of two identical amplifiers whose output signals are subtracted from each other by an appropriate subtraction module. If the disturbing signal is the same at both inputs, it will be canceled at the output by the subtractor, while the useful signal, which is different at both inputs, will be amplified in a so-called differential manner. The disturbing signal that is the same at both inputs is also called a "common-mode" signal. Any signal generated far from the body has a high chance of being seen as a common-mode signal, while all signals generated near or inside the body will be "differential" signals. Therefore, noise generated by electromagnetic induction from power lines at 50 Hz will be actively canceled from the final recording of the sEMG signal. Clearly, this explanation requires the availability of highly accurate subtractors, since the common-mode signal can be thousands of times larger than the differential signal. In practice, perfect subtraction can never be achieved, only approximated to varying degrees of quality. The accuracy with which the subtractor performs the difference of the signals from the two inputs can be numerically expressed by the CMRR parameter of the amplifier. The CMRR is the "common-mode rejection ratio" and represents the ratio between the amplification of the differential signal and the amplification of the common-mode signal (which is very low and tends to zero due to the subtractor). Therefore, a perfect, ideal subtractor will have a CMRR equal to infinity. In practice, CMRR values range from 90 to 120 dB (the measurement is expressed in dB as 20 times the base-10 logarithm of the above ratio).<ref>Wang Yang. [https://iopscience.iop.org/article/10.1088/1742-6596/1846/1/012034/pdf A New Type of Right-leg-drive Circuit ECG Amplifier Using New Operational Amplifier.] Journal of Physics: Conference Series '''1846''' (2021) 012034 doi:10.1088/1742-6596/1846/1/012034</ref><ref>Bruce B. Winter; John G. Webster. [https://ieeexplore.ieee.org/document/4121504/authors#authors Driven-right-leg circuit design]. Journals & Magazines IEEE Transactions on Biomedic..Volume: BME-30 Issue: 1</ref>

As strange as it may seem, there are at least three reasons why it is not practical to have a very high CMRR: the first is that amplifiers with extremely high CMRR tend to be excessively expensive; the second is that such amplifiers are increasingly less stable and reliable in the long term as the CMRR value increases; and the third is that common-mode signals are not necessarily common-mode in an absolute sense, as they may have small phase or amplitude variations that undermine the best CMRR. In addition, alterations or asymmetries in the electrodes can have dramatic effects in lowering the overall CMRR of an amplifier that is otherwise of good quality. (Fig. 2)

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====Input Impedance====
The impedance of a circuit in which alternating currents flow (i.e., currents that do not always have the same direction and intensity over time) is the equivalent of resistance for direct current circuits. The difference is that impedance varies with the frequency of the currents, and thus a filtering effect is generally obtained, whereby certain signals at a particular frequency may be recorded with higher or lower intensity depending on the impedance of the circuits (typically electrodes and cables) through which they pass.

Specifically, to avoid unwanted attenuation and distortion, the impedance of the skin and electrode must be as low as possible, while the input impedance of the amplifier must be as high as possible, so that the current drawn from the biological generator that flows through the external circuits is minimized. Modern electronic circuits allow the creation of amplifiers with input impedances reaching up to 10<sup>15</sup> ohms, with input capacitance on the order of a few picofarads. Considering that the voltage from the surface sEMG signal is on the order of 10 mV, with an impedance of 10<sup>15</sup> ohms, the current in the electrodes and amplifier is minuscule, amounting to only a few thousand electrons (!) per second. However, it is not just the absolute value of the input current into the amplifier that matters: the balance of the currents in all the electrode circuits is also highly important. This requires not only careful amplifier design but also precise measurement techniques.

====Design and Use of "Active Electrodes"====
The requirement for a very high input impedance of amplifiers introduces a problem known as capacitive coupling at the inputs.

Indeed, with a very high input impedance, even the small capacitance between the electrode cables and the electrical distribution wires of the power grid can no longer be ignored. The solution to this issue involves reducing the length of the electrode cables or moving the amplifier as close as possible to the electrodes. So close, in fact, that it is incorporated into the electrode itself, thus creating an "active electrode." The already pre-amplified signal is then sent to the instrument through low-impedance cables, completely immune to the problem mentioned above.

====Filtering====
Even with the aforementioned considerations and the most scrupulous methods, the sEMG signal can still be contaminated by unwanted signals that can be eliminated using various filtering techniques. These techniques are based on circuits (or software programs in the case of digital filters) that allow the useful signals to pass through almost unchanged while strongly attenuating noise or other unwanted signals. For the sEMG signal, filters can pass signals in the band from 20 to 500 Hz, with out-of-band attenuation decreasing by 12 dB/octave, meaning a 12 dB reduction for every doubling or halving of the frequency beyond the minimum and maximum limits.

''Stability of the Electrodes''

Electrode stability refers to mechanical, electrical, and electrochemical stability. Mechanical stability has already been discussed. Electrical and electrochemical stability are related to the progress of the redox reaction that occurs at the electrode's contact with the skin and the skin's electrical characteristics. Problems can usually arise from abnormal changes in the hydration state of the electrode, such as drying out or excessive moisture due to sweat, for example.<ref>J.V. Basmajian and C.J. De Luca, ''Muscles Alive. Their Functions Revealed by Electromyography'', fifth edition (Williams and Wilkins, Baltimore, 1985).</ref>