39 Basics of Electricity and Electronics for Electrodiagnostic Studies

In the office, hospital, and home, we are surrounded by equipment, appliances, and many other devices powered by electricity. Although knowledge of electricity and electronics is not needed to watch television, talk on the telephone, or use a toaster, these examples are just the tip of the electrical and electronic iceberg in the world we live in as electromyographers.

One might ask, is it really necessary to understand the basics of electricity and electronics in order to perform routine electrodiagnostic (EDX) studies? Although a degree in electrical engineering certainly is not needed, the answer clearly is yes. First, and most important, understanding the basics of electricity is essential to safely perform EDX studies and prevent potential electrical injuries to patients (see Chapter 40). Second, all of the responses recorded during nerve conduction studies and needle electromyography (EMG) are small electrical signals that are amplified, filtered, and then displayed electronically. Knowledge of electricity and electronics allows for a better understanding of what these potentials represent. Finally, and equally as important, knowledge of electricity and electronics is critical to understand and correct the variety of technical problems that frequently arise during EDX studies (see Chapter 8).

Basics of Electricity

All atoms have a nucleus composed of positively (+) charged particles, protons, and particles with no charge, neutrons. Orbiting around the nucleus are negatively (−) charged particles, electrons. Most atoms have the same number of protons and electrons; the electrons remain bound in their orbit by their magnetic attraction to the protons (i.e., in magnetism, opposites attract).

Electricity is formed when electrons are removed from their orbit and flow to adjacent atoms. Materials that allow electrons to move freely are known as conductors. In contrast, materials that inhibit the flow of electrons are known as insulators. Conductors typically are metals, most often copper. Insulators most often are rubber, plastic, or ceramic. To understand basic electrical circuits, one needs first to be acquainted with several important terms:

• Coulomb is the standard unit of electric charge, approximately equal to 6.24 × 10¹⁸ electrons.

• Current, represented by the symbol I, is the actual flow of electrons. The ampere is a measure of current, designated by the letter A. An ampere is defined as 1 coulomb passing a point in a conductor in 1 second. Current can only flow when a complete circuit exists.

• Voltage is the electromotive force required to make electricity flow through a conductor. This electromotive force results from a fundamental property of magnetism that oppositely charged particles attract each other. Any source with an excess of electrons (negatively charged particle) will be drawn to a source with a lack of electrons (positively charged particle). Voltage is designated by the symbol E. Its unit of measurement is volts, which is designated by the letter V.

• Resistance opposes the flow of electrons. Resistance is designated by the symbol R. The unit of measurement for resistance is Ohms, which is designated by the Greek letter Ω. All materials, even conductors, impede the flow of electrical current to some extent. In general, resistance increases with the length of the conductor and decreases as the cross-section of the conductor increases.

Analogy between Electricity and Water

Because current and electrons cannot be seen, it may be difficult to relate to electricity and its basic definitions. One useful way of understanding electricity and its properties is to make an analogy to the flow of water. The analogy to water and plumbing often is easier to grasp and can be extrapolated to the understanding of electricity.

Water can be measured as a specific volume (e.g., a liter or gallon). Thus, a gallon of water is analogous to a coulomb of electricity, an amount of charge. For water to flow, it must have some force that is driving or pushing it. This force can be gravity, in the case of water stored in a water tower, or a pump that mechanically propels the water. In either case, water is put under pressure. Pressure is measured as force per unit area, typically as pounds per square inch (psi). Thus, water pressure is analogous to voltage, the driving electromotive force. Water will flow if there is a pressure difference between two points (i.e., from an area of high pressure to low pressure). Likewise, electrons will flow if there is a difference in voltage between two points. Flow is the actual movement of water, which is measured as volume passing by a point in a specific time period (e.g., gallons per second). Thus, flow of water is analogous to current, the movement of electrons, which is measured in amperes (1 coulomb passing a point in a conductor in 1 second). Lastly, resistance to water flow is determined by the physical characteristics of the pipes it is traveling through. Longer and especially narrow-diameter pipes impede the flow of water. Thus, the mechanical resistance of a water pipe is analogous to the electrical resistance of a circuit.

The flow of water is determined by Poiseuille’s law:

At point D in the figure above, the water pressure is essentially zero. Water is taken up by the pump and pressurized, resulting in a high pressure at point A. Water will now flow because it is under high pressure at point A and low pressure at point D. The water pressure at point B will still be high because the diameter of the pipe is so large that it offers little resistance to flow. However, the marked narrowing of the pipe between points B and C increases the resistance to flow. The higher the resistance, the less the flow. Conversely, the higher the water pressure difference, the more the flow. At point C, the water pressure is now very low. However, it must still be slightly higher than point D so that water will flow from point C to D. If extra water were to somehow get into the system and be a greater amount than the water pump could pump, it could easily be diverted to the reservoir (analogous to the ground, see later).

Ohm’s Law

The most important basic principle of electricity is Ohm’s law, which defines the relationship among current, voltage, and resistance in a circuit. Ohm’s law is directly analogous to Poiseuille’s law for water. For electrical circuits, Ohm’s law states that:

The figure above depicts a simple circuit consisting of a battery (E) (an electromotive source of electrons) connected to one resistor (R). The amount of current (I) flow is determined by Ohm’s law, I = E/R, where E is the voltage from the battery, and R is the resistance. Also note the presence of the ground connection. The ground is ideally a true electrical zero. Most often true grounds are physically connected to the earth (e.g., through a pipe).

One of the confusing aspects of electricity is figuring out the direction that current actually flows. In the conventional flow notation, electric charges move from the positive (surplus) side of the battery to the negative (deficiency) side. However, as electricity comes about by the flow of electrons, which are negatively charged, the actual flow of electrons occurs from the negative to the positive. In the electron flow notation, electric charges moves from the surplus of negative charges at the negative side of the battery to the positive side of the battery which has a deficiency of negative electrical charges. Both notations are correct when used consistently. The conventional flow notation is used by most electrical engineers and found in most electrical engineering textbooks, and will be used in this chapter.

One helpful aid in remembering the relationships in Ohm’s law is the Ohm’s triangle illustration (above). If a triangle is constructed with E at the top and I and R at the bottom as shown, the value of E, I, or R can readily be determined by blocking the variable of interest (shaded in the figure) and looking at the relationship between the other two parameters.

Kirchhoff’s Laws

In addition to Ohm’s law, there are two other important principles, known as Kirchhoff’s laws, with which one must be familiar in order to understand basic electricity.

Kirchhoff’s current law states that the algebraic sum of all the currents meeting at any point in a circuit must be zero. Put another way, the sum of incoming currents must equal the sum of outgoing currents. This law represents the conservation of charge. The number of electric charges that flow toward a point must equal the number of electric charges that flow away from that point.

Kirchhoff’s voltage law states that, in a closed circuit, the algebraic sum of all the voltage (i.e., potential) drops is equal to the electromotive source voltage of the circuit. The figure above shows a battery with a voltage (V_A) connected in series to three resistors (B, C, D). The current running through the three resistors results in a voltage drop across each resistor, V_B, V_C, and V_D, respectively. Kirchhoff’s voltage law requires that the sum of the voltage drops across all three resistors equals the voltage of the battery (i.e., V_B + V_C + V_D = V_A).

Simple Resistive Circuits

Resistors in Series

From Ohm’s and Kirchhoff’s laws, one can predict the behavior of simple resistive circuits.

First, take the example of a simple circuit with a battery (E) connected to three resistors in series. From Kirchhoff’s current law, the current (I) must be the same going through each resistor (i.e., current flowing into any point equals the current flowing out of that point). From Ohm’s law, a voltage drop will be present across each resistor (E = I × R). Thus, the voltage drops for the three resistors must be I × R_1, I × R₂, and I × R₃, respectively. From Kirchhoff’s voltage law, the voltage from the battery (E) must equal the sum of all the voltage drops across the three resistors (V_B + V_C + V_D). With this information, applying simple algebra:

E = V_B + V_C + V_D (Kirchhoff’s voltage law)

E = I × R₁ + I × R₂ + I × R₃ (Ohm’s law)

E = I ×  (R₁ + R₂ + R₃) (Algebra)

E = I × R (Ohm’s law)

R = R₁ + R₂ + R₃ (Algebra, using substitution)

Thus, resistors in a series can be directly added together to calculate a net resistance. Take an example of the same circuit of a battery connected to a series of three resistors, using real values.

The battery has a voltage of 100 V. The resistors have a resistance of 12, 10, and 3 Ω, respectively. Thus, the total resistance of the circuit is the sum of the resistors (12 + 10 + 3)  = 25 Ω. With this information, the current can be easily calculated from Ohm’s law:

Knowing the current, the individual voltage drop across each resistor (48 V, 40 V, 12 V) can be calculated from Ohm’s law (E = I × R).

Resistors in Parallel

When resistors in a circuit are placed in parallel, a net resistance can also be calculated using Ohm’s and Kirchhoff’s laws.

Take an example of a simple circuit with a battery (E) connected to three resistors in parallel. From Kirchhoff’s current law, the total current (I) must be the sum of the individual currents going through each resistor:

From Ohm’ law, the voltage across each resistor can be calculated:

From Kirchhoff’s voltage law, the voltage from the battery must equal the voltage drops along any closed circuit. Thus, the same voltage (E) from the battery must be present across each of the three resistors:

With this information, we can solve the equation for total current:

Now, we can solve for the total resistance:

Thus, resistors in parallel reduce the total resistance, as opposed to resistors in series, which increase the total resistance. For instance, three resistors in series, each 100 Ω, result in a total resistance of 300 Ω. However, three resistors in parallel, each 100 Ω, result in a net resistance of 33 Ω. The analogy to water is as follows. Imagine a bucket full of water. The weight of the water creates a water pressure against the bottom of the bucket. If a hole is drilled through the bottom of the bucket, water will start to flow, based on how large the hole is (i.e., the resistance) and the water pressure in the bucket. If another hole is drilled nearby (i.e., in parallel), there are now two ways for water to escape (under the same pressure), and hence the amount of water leaving the bucket (i.e., the current) will increase. Thus, the two holes in parallel effectively decrease the resistance to water leaving the bucket.

Direct Current and Alternating Current

Direct current (DC) is current that always flows in the same direction. In DC, electrons flow uniformly from the power source through a conductor to a load (i.e., an electrical device) and back to the power source. The most common example of a DC power source is the battery.

However, current also can be supplied as an alternating current (AC). In an AC, electrons follow the path of a sine wave, flowing first in one direction and then reversing. The current reverses polarity many times a second [measured as cycles per second (cps) or Hertz (Hz)]. The most common example of AC is the conventional 60 Hz electricity in wall sockets in houses and offices.

Because DC and voltage are constant, their measurements are straightforward. However, AC measurement is more complicated, because voltage and current are constantly changing values. There are several ways to measure AC, including measuring baseline to peak or peak to peak. A mean would not be useful, because the mean of an AC current is actually zero. However, the most common method of measuring AC is the root mean square (RMS) value. The RMS is calculated by dividing the waveform into many small increments. The value of each increment is squared and a mean of all the squares determined. Finally, the square root of the mean results in the RMS value. The RMS value is the most useful way of measuring AC because power in a circuit is defined as voltage multiplied by current:

Thus, power is proportional to the square of the voltage. Accordingly, for the same resistance, 1 volt RMS of AC delivers the same power as 1 volt DC. For the typical house or office AC, the RMS voltage is approximately 0.707 multiplied by the voltage measured between baseline and the maximum value. Thus, in the United States, 120 V RMS corresponds to approximately 170 V baseline to peak.

One natural question to ask is: why alternating current? Current constantly flowing back and forth in opposite directions many times a second seems confusing and counterintuitive. However, alternating current arises from all the common ways that electricity is generated. Whether the source is a windmill, hydroelectric, nuclear, coal, or natural gas, all ultimately result in a rotational mechanical movement (e.g., wind and hydro directly turning an axis; nuclear, coal, and natural gas heating water to steam which then turns a turbine). Electricity is then created by attaching a coil (a conductor shaped as a loop) to the mechanical rotation with the coil placed in a strong magnetic field. As the conductor rotates in the magnetic field, electricity is generated and flows to an attached load. The angle and direction of the coil in the magnetic field determines the amount and direction of the electricity. When the coil is perpendicular to the magnetic field and moving with the positive side of the coil up, the maximal current is generated (i.e., the top of the sine wave). However, when the coil is perpendicular to the magnetic field and moving with the negative side of the coil up, the maximal current is generated in the other direction (i.e., the bottom of the sine wave). When the coil is parallel to the magnetic field, no current is generated (the zero crossings of the sine wave). It is this rotation of a coil within a magnetic field that creates an alternating current with its characteristic sinusoidal waveform.

Capacitance, Inductance, and Reactance

Beyond simple resistive circuits, one needs to move next to the basics of capacitance, inductance, and reactance. Although these concepts are more complicated, they have direct relevance to EDX studies regarding (1) low- and high-frequency filters, and (2) stray leakage currents that potentially pose a risk of electrical injury to patients undergoing EDX studies (see Chapter 40).

Although capacitance and inductance are present in DC circuits, they are more germane to AC circuits. The concept of reactance is only applicable to AC circuits. As noted in the following, capacitance and inductance share many fundamental properties but also have significant and important differences.

Capacitance

Capacitance, represented by the symbol C, is a property of a circuit that allows it to store an electrical charge. The farad is a measure of capacitance, designated by the letter F. A capacitor is an electronic component made from a pair of conductive plates separated by a thin layer of insulating material (the insulating material is known as a dielectric). When a voltage is applied across the plates of a capacitor, electrons are forced onto one plate and pulled away from the other. The plate with an excess of electrons is negatively charged, whereas the opposite plate with a deficiency of electrons is positively charged. The amount of charge stored in a capacitor is proportional to the voltage across it as described by:

where Q is the charge in coulombs, C is capacitance in Farads, and V is voltage in volts.

Because of the dielectric material between the plates, no actual current (i.e., flow of electrons) moves across the plate; however, there is an “apparent flow,” also known as a capacitive current.

Take the above example of a battery connected to a single capacitor with a simple open and closed switch.

When the switch is moved to the closed position, electrons flow from the power source to the conductive plate of the capacitor. This flow of electrons will create an actual current in the conductor. When the electrons arrive at the negative plate, they do not actually cross the plate.

However, the buildup of electrons at the negative plate results in the electrons at the opposite plate being repelled (in magnetism: opposites attract, but likes repel). Thus, there will be an “apparent current” across the capacitor. This will continue until the voltage across the capacitor equals the voltage from the power source.

At that time, no further apparent current will flow. The capacitor will be fully charged, and an electric field will exist between the two plates.

The rate of accumulation of charge (and the resulting voltage) at a capacitor occurs exponentially, based on the equation:

where t is time

e (natural logarithm base) is 2.718281828459045235

R is resistance of the circuit in Ohms

C = capacitance in Farads

Note that, in the above equation, the time required for voltage to rise to its maximum value in a circuit is dependent on the product of resistance (R) multiplied by capacitance (C). This product (RC) is known as the time constant of a capacitive circuit.

Thus, one time constant (RC) defines the time it takes for the voltage across a capacitor to reach 63.2% of its maximum value. During the second time constant, voltage will rise to 63.2% of the remaining 36.8%, or a total of 86.4%. It takes about five time constants for voltage across the capacitor to reach its maximum value.

Once fully charged, what happens if the power source is then turned off? The opposite occurs. The capacitor will discharge, with the excess electrons now flowing away (i.e., in the opposite direction than during charging) from the negative plate of the capacitor. Again, an apparent capacitive current will occur on the other side of the circuit and continues until the capacitor is fully discharged. The discharge of a capacitor follows a similar exponential fall, described by the equation:

Thus, after one time constant, the voltage across the capacitor will have dropped to 36.8% of its original value. Again, it takes approximately five time constants for a capacitor to completely discharge.

In a DC circuit, when the circuit initially is turned on, current flows. However, after five time constants, the capacitor is fully charged and no further current occurs. At this point, the capacitor effectively acts as an open circuit. Understanding these properties of a capacitor in a simple DC circuit allows one to extrapolate to what occurs in an AC circuit.

Take the example of an AC circuit where the frequency of the current is much faster than the frequency 1/RC. When current is first applied to a capacitive circuit, it flows readily because of the apparent or capacitive current. If the AC then reverses before the capacitor is fully charged, a capacitive or apparent current will flow in the opposite direction. Thus, in essence, a capacitor is effectively a short circuit for high frequencies. Conversely, if the frequency of the current is much slower than the frequency 1/RC, the capacitor can fully charge before the current reverses. Thus, a capacitor can act like an open circuit for low frequencies. These properties can be used to an advantage in designing low and high filters (see following sections).

In an AC circuit, also note that a capacitor constantly charges and discharges. When charge accumulates between the two plates of the capacitor, an electric field develops between the plates. Thus, in an AC circuit, there is a constantly expanding and collapsing electrical field around a capacitor. Other conductors near this changing electrical field may develop capacitive currents. This is of importance in understanding the concept of stray capacitance and the risks of leakage currents (see following sections).

Inductance

The property of an electrical circuit that causes it to oppose any change in current is known as inductance. Inductance is designated by the symbol L and is measured in henries (H). Inductance is somewhat similar to mechanical inertia, which must be overcome to get a mechanical object moving or stopping. Whereas resistance opposes all current flow, inductance only opposes a change in current. If current increases, inductance tries to hold it down; conversely, if current decreases, inductance tries to hold it up.

Inductance occurs as a result of magnetic fields induced by a current. Whenever current flows, a magnetic field develops around the conductor, known as an electromagnetic field. Moving a conductor through a magnetic field will induce a voltage in a conductor. Likewise, having a stationary conductor in a magnetic field that is either expanding or collapsing will also induce a voltage in the conductor. Thus, when current first begins to flow in a conductor, an expanding magnetic field develops. This expanding (i.e., changing) magnetic field induces a voltage in the conductor that opposes the flow of current, known as a counter electromotive force. This counter electromotive force results in a time delay for current to reach a steady value. Once a steady value is reached, the magnetic field around a conductor is static, and no further opposing voltage develops.

Similar to the calculation for capacitance, the resulting current in a circuit with an inductor occurs exponentially and is described by the following equation:

where t is time

e (natural logarithm base) is 2.718281828459045235

L is inductance in Henries

R is resistance of the circuit in Ohms

Note that, in the above equation, the time required for current to rise to its maximum value in a circuit is dependent on the value of inductance divided by resistance. This value (L/R) is known as the time constant of an inductive circuit.

Thus, one time constant (L/R) defines the time it takes for the current to reach 63.2% of its maximum value. During the second time constant, current will rise to 63.2% of the remaining 36.8%, or a total of 86.4%. It takes about five time constants for current to reach its maximum value.

At steady state, what happens if the power source is then turned off? The opposite occurs. The electromagnetic field collapses and induces a counter electromotive force in the conductor, opposing the flow of current. The current flow follows a similar exponential fall, described by the equation:

Thus, after one time constant, the current will have dropped to 36.8% of its original value. Again, it takes approximately five time constants for current to completely dissipate. Once the current has reached a steady state (in this case zero), there will be no changing magnetic field, and no further opposing voltage will be induced.

In a DC circuit, when the circuit is turned on, current flows but is initially impeded by inductance. However, after five time constants, the current reaches steady state and no further inductive voltage occurs. At this point, an inductor effectively acts as a short circuit. From understanding these properties of inductance in a simple DC circuit, one can extrapolate what happens in an AC circuit. Take an AC circuit where the frequency of the current is much slower than the frequency 1/(L/R). When current is first applied to the circuit, it is impeded due to inductance. However, after five time constants, the current has reached steady state and no further inductance occurs. Thus, for low frequencies, inductors allow current to flow and reach their maximum. However, in AC circuits with frequencies higher than 1/(L/R), the AC reverses before the current can reach its steady state. In this case, the inductor effectively attenuates high-frequency currents from flowing.

Thus, as a capacitor stores energy as charge in an electrical field, an inductor stores energy in the form of a magnetic field. Just like capacitance, inductance is dependent on the frequency. If the frequency is low, the current has more time to reach its maximal value, before the polarity of the sine wave reverses. Conversely, if the frequency is very high, the current has less time to reach its maximal value. Thus, inductance attenuates high frequencies much more than low frequencies; this is exactly the opposite of capacitance. Taken to the limit, an inductor is essentially a short circuit at low frequencies and an open circuit at high frequencies.

In an AC circuit, current will be constantly flowing and then reversing, resulting in an expanding and collapsing magnetic field around any conductor. This can induce voltages in other conductors near this changing magnetic field, which is important to understanding the concept of stray inductance and the risks of leakage currents (see following sections).

Reactance and Impedance

In a purely resistive circuit, either DC or AC, opposition to current flow is termed resistance. However, in an AC circuit, current can also be opposed by inductance, capacitance, or both. Opposition to current flow from capacitance is the capacitive reactance, termed XC. The larger the capacitor, the smaller the capacitive reactance. Opposition to current flow from inductance is the inductive reactance, termed XL. The larger the inductor, the larger the inductive reactance. Similar to resistance, reactance is measured in Ohms (Ω). Thus, total reactance in an AC circuit depends on both inductive and capacitive reactances. Clearly, from the earlier discussion, inductive and capacitive reactances depend on frequency. In the case of inductance, reactance is much higher for high frequencies. Conversely, in the case of capacitance, reactance is much lower for high frequencies.

Capacitive and inductive reactance can be calculated by the following equations:

where f is frequency, and C is capacitance.

where f is frequency, and L is inductance.

Lastly, impedance, designated by the letter Z, is also measured in Ohms (Ω). Impedance incorporates the total opposition to current flow in an AC circuit, including resistance, capacitive reactance, and inductive reactance. Impedance is calculated using the following equation:

Thus, from the above equation, one can appreciate several facts about impedance:

• Impedance = Resistance, in circuits with no inductance or capacitance

• Impedance = Resistance, in circuits where inductive reactance equals capacitive reactance

• Inductive and capacitive reactances directly oppose each other.

Waveforms, Frequency Analysis, and Filtering

During nerve conduction studies and needle EMG, every displayed waveform represents a small bioelectrical potential (i.e., voltage) that is recorded, amplified, and then filtered. The last process, filtering, improves the quality of the recorded potential by preventing a wandering baseline and eliminating much unwanted electrical noise. To understand the process of filtering, one must first appreciate the frequency spectrum of any recorded waveform.

The Fourier analysis is a mathematical construct that states that any waveform can be derived by adding a series of sine waves. The sine waves may vary by amplitude, frequency, or phase. One of the most illustrative examples is that of a square wave, which also can be constructed by adding a series of sine waves.

Take the above example of a square wave with a frequency of 3 Hz.

The square wave can first be approximated by a 3 Hz sine wave.

If a smaller-amplitude 9 Hz sine wave is added to the 3 Hz sine wave, the following waveform results. This is now starting to look somewhat like a square wave.

If now an even smaller-amplitude 15 Hz sine wave is added to the two earlier sine waves, the resultant waveform is generated. If one continues this analysis, the actual Fourier analysis for a square wave with a frequency (x) can be derived from the following equation:

The above waveform represents the Fourier reconstruction of ten separate sine waves. Thus, as more waveforms with higher frequencies and smaller amplitudes are added, the reconstructed waveform continues to more closely approximate that of a true square wave. Thus, a 3 Hz square wave contains the following frequencies: 3, 9, 15, 21, and 27 Hz, in addition to other higher frequencies.

A similar analysis can be performed for all waveforms recorded during routine EDX studies. The figure above shows the relative frequency components of a compound muscle action potential (CMAP) compared to that of a sensory nerve action potential (SNAP) (from Gitter and Stolov, 1995). Note that the SNAP has higher-frequency components compared to the CMAP.

Ideally, one would like an EMG machine to display the amplified bioelectric signal of interest exactly. However, if a signal is contaminated with electrical noise, it can be difficult to properly record and interpret it. In general, very low frequencies will contaminate the signal of interest by causing the baseline to wander and very high frequencies can easily obscure many small waveforms (e.g., SNAPs, fibrillation potentials). Thus, it is desirable to filter out unwanted low and high frequencies while retaining the frequency spectrum of the actual waveform as much as possible.

Low-Frequency (High-Pass) Filters

Low-frequency filters remove undesirable low frequencies while allowing high frequencies to pass. Analog low-frequency filters can be constructed with a capacitor followed by a resistor. In the illustration above and those that follow, the Signal Source will be modeled to generate either a low frequency, high frequency, or square wave input to the circuit. The input to the circuit is measured from point A (to a reference or ground), and the output of the circuit is measured from point B (to a reference or ground).

Recall from earlier discussions that for an AC with a high frequency, the capacitor effectively acts like a short circuit, allowing the current to pass. If the AC changes direction before the capacitor has charged, the apparent or capacitive current will continue unaltered.

Conversely, for an AC with a very low frequency, the capacitor effectively acts like an open circuit. In this case, there will be ample time for the capacitor to fully charge before any change in current direction occurs. Once the capacitor is fully charged, no current, real or apparent, will flow. At this point, the capacitor will act as an effective open circuit, not allowing the waveform to pass from point A to the output at point B.

Of course, most waveforms have a combination of low and high frequencies. If a square wave is put through a low-frequency filter, the high frequencies will pass, but the lower frequencies will be filtered out.

High-Frequency (Low-Pass) Filters

High-frequency filters remove undesirable high frequencies while allowing low frequencies to pass. Analog high-frequency filters can be constructed with a resistor followed by a capacitor.

In the case of an AC with a high frequency, the capacitor effectively acts like a short circuit and shunts the signal to ground.

Conversely, for a very low-frequency AC, the capacitor effectively acts like an open circuit. In this case, there will be ample time for the capacitor to fully charge before any change in current direction occurs. Once the capacitor is fully charged, no current, real or apparent, will flow. At this point, the capacitor will act as an effective open circuit, allowing the waveform to be present at the output at point B.

Of course, most waveforms have a combination of low and high frequencies. If a square wave is put through a high-frequency filter, the low frequencies will pass, but the higher frequencies will be filtered out.

Putting low- and high-frequency filters in tandem allows for a passband, whereby frequencies above and below the cutoff values are filtered out. However, no passband removes frequencies above or below a cutoff value with perfect precision. There is a normal roll-off of the frequencies that pass through. In general, cutoff frequency values for both high and low filters are defined as the point where the power of the signal is reduced by 50% [i.e., approximately 0.707 of its voltage. Remember that power is proportional to the square of the voltage and that (0.707)² = 0.50.]

Practical Implications for Electrodiagnostic Studies

Congratulations. You have almost reached the end of this chapter, but you still may be asking whether basic knowledge of electricity and electronics really is needed to perform EDX studies. The answer clearly is yes, because there are many practical implications for performing EDX studies based on the principles learned in this chapter. Most important among them are the following:

• Filters. Understanding that all waveforms, including those recorded during EDX studies, have their own unique frequency spectrum allows for the use of electronic filters to remove unwanted low- and high-frequency noise while permitting the principal frequencies of the waveform to pass unaffected (i.e., passband). Although filters remove unwanted electrical noise, they also impact the waveform of interest and can alter certain characteristics of the waveform (especially amplitude for high-frequency filters and duration for low-frequency filters).

• Tissue acting as a filter: nerve conduction studies. Skin and subcutaneous tissue act as a high-frequency filter. Accordingly, if surface electrodes are not optimally placed directly over a nerve or muscle, much of the waveform’s higher frequencies will be filtered out. Amplitude is predominantly a high-frequency response. SNAPs contain more high frequencies than CMAPs. Thus, if the surface electrodes are not optimally placed, amplitudes on nerve conduction studies will be reduced, more so for SNAPs than for CMAPs. If a patient has limb edema, then even if the surface electrodes are optimally placed, the increased tissue and edema between the nerve or muscle and the recording electrode will result in an artificially low amplitude.

• Tissue acting as a filter: needle EMG. During the needle EMG examination, tissue between the motor unit action potentials and the needle electrode also acts as a high-frequency filter. Again, as amplitude is predominantly a high-frequency response, MUAP amplitude can be markedly influenced by the distance between the needle and the motor unit. During needle EMG, the proper location to analyze an MUAP is reached when the major spike (i.e., the highest frequency component of the MUAP) is very short, less than 500 µs. This ensures that the needle is very close to the motor unit. Likewise, this property of tissue acting as a filter also explains why duration is a much better determinate of motor unit size than is amplitude. Duration is predominantly a low-frequency function. Thus, tissue, which acts as a high-frequency (low-pass) filter, allows the low-frequency components from distant muscle fibers of the same motor unit to be recorded.

• Inductive electrical noise from the environment. How does a nearby radio or coffee maker result in electrical interference during EDX studies? Every power cord contains a 60 Hz AC signal. Around that power cord is a continuously expanding and collapsing magnetic field. If a conductor (e.g., a recording electrode) is near that magnetic field, an inductive voltage can be generated on that lead, which then can be amplified, often saturating the amplifier and obscuring the signal of interest.

The photo above is a real example of this problem from one of our laboratories. Note the ophthalmoscope hanging on the wall adjacent to the EMG table and the power cord next to it. Even in the off position, AC is present in the power cord, resulting in an unseen expanding and collapsing magnetic field. When recording electrodes were placed near the magnetic field, an induced current was generated in the leads. Sensory responses could not be recorded without excessive electrical noise unless the power cord plug was physically pulled out of the socket.

• The stimulator cable and the recording electrodes should not cross or be near each other. When the stimulator is discharged, a brief current flows through the stimulator, creating an expanding and then collapsing magnetic field around the stimulator cable. If the recording electrodes or their leads are near that field (especially if the cables are crossed and touching), an inductive voltage can easily be generated in the recording leads, resulting in a large stimulus artifact.

• Importance of eliminating electrode impedance mismatch. Despite one’s best efforts, there will always be some electrical noise in every EMG laboratory, usually 60 Hz AC from nearby electrical equipment. However, if the impedances (which include resistance, capacitive reactance, and inductive reactance) of the active and reference electrodes are identical, then any current resulting from electrical noise contaminating the recording electrodes will create the same extraneous voltage on each lead (from Ohm’s law: Voltage = Current_Noise × Impedance). Because all signals are amplified by way of a differential amplifier, the extraneous voltage will be canceled out. Several important techniques help ensure that the recording electrodes have the same impedance, among them, the use of a coaxial cable, good skin preparation, and an ample amount of conductive paste between each electrode and the skin.

• Importance of the ground electrode. One might assume at first glance that there is no difference between the reference and the ground lead, both being at electrical zero. However, all voltages are relative potentials, determined by the difference between two points in a circuit. Thus, one can measure a potential of 10 V between a point on a circuit that is 10 V higher than the ground (which is at electrical zero). However, 10 V also can be measured in a circuit between a point that is 20 V above ground and another point that is 10 V above ground. Thus, in most electronic applications, there is usually a potential difference (i.e., a voltage) between the neutral or reference electrode, and the ground electrode.

Whenever a waveform is recorded, current flows from the active to the reference lead. Even though the reference electrode is a conductor, there is a small amount of resistance in all materials, including conductors. Thus, a small voltage will be present on the reference lead, as determined by Ohm’s law (E = I × R_Reference). Accordingly, the ground potential is actually at a lower potential than the reference electrode. If a stray current develops on the patient, the ground allows a safe pathway to dissipate the current, thereby protecting the patient from possible electrical injury (see Chapter 40). In addition, because the ground is at a lower potential than the reference electrode, any stray current will be preferentially shunted to the ground electrode rather than the reference electrode (electricity follows the path of least resistance). Thus, the electrical noise will not contaminate the reference electrode and obscure the potential of interest.

This is easily demonstrated in the EMG laboratory. In the example above, a routine radial sensory response is recorded from a normal individual, first with the ground electrode attached and then with the ground electrode disconnected. Note that with the ground electrode disconnected, there is a large superimposed 60 Hz electrical signal, making the sensory response barely visible.

• Leakage currents: stray capacitance and inductance. Although EMG machines are designed to minimize leakage currents, there will always be some leakage current on the machine chassis from stray capacitance and inductance. This is because any circuitry with ACs containing capacitors will have expanding and collapsing electrical fields. Likewise, any circuitry with ACs will have expanding and collapsing magnetic fields. If any part of the machine chassis is metal (i.e., a conductor) and near enough to electrical or magnetic fields from internal circuitry, stray capacitive or inductive currents potentially can be produced. These small leakage currents pose a potential electrical risk to certain vulnerable patient groups (see Chapter 40). With preventative maintenance of the machinery and by closely following specific protocols these possible hazards can be eliminated (see Chapter 40).