Basic Electronics and Electrical Safety

Peter Seaba

Thoru Yamada

Basic Electricity and Electronics

The following is a synopsis of the “basic electricity” concepts that are important for one to know when studying EEG instrumentation. This chapter should be read while studying the figures to understand the concepts being described.

Basic electricity consists of units (volts, amperes, ohms, watts), components (resistors, capacitors, inductors), and formulas (Ohm’s law, power, components in series/parallel). In addition, there are special topics unique to EEG instrumentation. Understanding these basic concepts will ensure the understanding of EEG-related concepts found later in this chapter.

BASIC ELECTRONIC UNITS

Table 3-1 lists the basic electronic units.

OHM’S LAW

Ohm’s law is a formula which is used in many EEG applications. It describes how current, resistance, and voltage are interrelated in a circuit. To understand Ohm’s law, one should know that voltage (E) is the electrical force that moves electrons through wires and electrical devices. Current (I) is the rate of electron flow. Resistance (R) is a property that limits current.

TABLE 3-1 BASIC ELECTRONIC UNITS

Name	Symbol	Units
Charge	Q	Coulomb (6.25 × 10¹⁸ e^–)
Voltage	E	Volt [Requires 0.799 V to remove outer electron from silver (ionization potential). Also listed as EMF]
Current	I	Ampere (or amp) [flow of 6.25 × 10¹⁸ e^– per second (1 C/s)]
Resistance	R	Ohm
Impedance	Z	Ohm
Power	P	Watt

FIGURE 3-1 | Hydraulic analogy of Ohm’s law.

It might also be helpful to use an analogy between hydraulics and electricity. In a hydraulic system, the flow of water will depend on the water pressure and the dimension of the pipe or hose (resistance). The flow of water is proportional to the water pressure. If someone squeezes the hose, increasing its resistance, the flow decreases. Flow is inversely proportional to resistance. We can combine the two relationships as shown in Figure 3-1.

In a similar manner, electromotive force (EMF) will cause current to flow through a wire. The electrical analogy is that electrical current (I) is proportional to voltage (E) but inversely proportional to resistance (R). This can be stated in the following formula, where “I” is current, “E” is voltage, and “R” is resistance.

This is one form of Ohm’s law. By algebraic manipulation (multiply both sides of the equation by R), we have the more familiar form: E = I × R.

The unit of power is watt. Power can be calculated by the following formulas:

Power = E × I
Power = I²R (since E = I × R)
Power = E²/R (since I = E/R)

RESISTORS

Resistors are electronic components in a circuit which are meant to impede current flow. They can be arranged in a series or in parallel, and the total resistance depends on this arrangement.

Resistors in Series

Resistors can be placed in a circuit one after another in a series. When a string of resistors is connected in a series, the
combined resistance is equal to the individual resistances added together. Therefore, an appropriate single resistor can replace several individual resistors in series. The equivalent resistor must equal the sum of all the resistor values. For example, if resistors R₁ and R₂ are connected in series, their combined resistance, R, is given by

FIGURE 3-2 | Equivalent resistance of resistors in series.

Combined resistance in series: R = R₁ + R₂.

This will be true for more resistors: R_series = R₁ + R₂ + R₃ + …

One important point to remember is that the combined resistance in series will always be greater than any of the individual resistances. A derivation of the equivalent resistor is shown in Figure 3-2.

Using the hydraulic analogy, if you add another section of hose to the existing hose, the resistance increases.

Resistors in Parallel

Notice that parallel resistors provide several individual routes for the current to complete the circuit and return to the negative side of the battery (Fig. 3-3). Thus, the resistance will be lowered, and it will be lower than that of any single resistor. The total resistance of resistors in parallel will always be less than the resistance of any single resistor.

FIGURE 3-3 | Equivalent resistance of resistors in parallel.

FIGURE 3-4 | Hydraulic analogy of a capacitor.

What is the equivalent resistance of three resistors in parallel? This time, we do not have a single loop of current, but one path for each resistor. The equivalent resistance of three resistors in parallel is

CAPACITORS

Capacitors are electronic components of a circuit that are designed to store a charge between compartments. A pump can store pressure by pumping water from one side to the other. The hydraulic analogy of a capacitor is a pressure vessel with a diaphragm between compartments (Fig. 3-4). A capacitor is a component that can store electrical energy analogous to the hydraulic pressure storage system. It has a similar design as shown in Figure 3-5.

The voltage-current relationship changes with time. The rules for adding capacitors in series and parallel are reversed from those for adding resistors in series and parallel, respectively. The capacitance of this device is defined by how much charge is moved per volt applied. A capacitor that will store 1 C when 1 V is applied is a 1 F capacitor.

Capacitance is proportional to the area of the plates or conductors (the more area, the more electrons that can be stored). However, it is inversely proportional to the distance between the plates. The closer the plates, the more the attraction between + and – and the more electrons you can store per volt. These factors, plate area and distance between the plates, affect how capacitors behave in series and parallel.

FIGURE 3-5 | Charging the capacitor.

Capacitors in Parallel

When capacitors are in parallel, the plate area increases. Thus, the capacitance increases proportionately (Fig. 3-6):

Capacitors in Series

When capacitors are in series, the distance between the plates increases. Capacitance then decreases. The formula is the same as that for resistors in parallel (Fig. 3-7):

INDUCTANCE

Inductance is the ratio of magnetic flux to the current in a circuit. Inductance opposes any change in current through the conductor.

Capacitors and the effects of capacitance are common in medical instruments. Inductors are seen more often in highfrequency circuits, such as radios. Inductors used for low-frequency applications are physically large.

Current flowing through a wire produces a magnetic field around the wire. Coiling the wire increases the intensity of the magnetic field. As the current flows, a magnetic field expands around the coil of wire. This generates an opposing voltage and opposes the increase in current. If, once the current is flowing, the switch is suddenly opened, the magnetic field will begin to decrease and collapse around the coil. Whenever a magnetic field changes in intensity, the intensity change will induce a current in the coil of wire (Fig. 3-8). In this case, the diminishing magnetic field will induce current flow in the same direction. Inductance also opposes a decrease in current.

FIGURE 3-6 | Equivalent capacitance of capacitors in parallel.

FIGURE 3-7 | Equivalent capacitance of capacitors in series.

The hydraulic analogy of inductance is inertia. Fluid at rest tends to remain at rest and fluid in motion tends to remain in motion. Similar to inertia, inductance opposes any change in current through the inductor. The unit of inductance is the henry. Inductors in series and parallel circuits are combined like resistors in series and parallel, respectively.

Power Transformers

Power transformers are devices that transfer electrical energy from one circuit to another. They are used to “step up” or “step down” the voltage.

If you induce current in a wire, the wire will develop a magnetic field around it (Fig. 3-9, left). If this magnetic field cuts through a nearby coil of wire, the wire will develop a voltage since it is experiencing a change in the magnetic field strength (Fig. 3-9, right). The transformer combines these two phenomena. An AC voltage is applied to the input called the primary coil. The primary coil will generate a varying magnetic field. The magnetic field then cuts the second coil (secondary) and then induces electricity within the second coil.

The ratio of the number of windings on each side of the transformer affects the voltages. If you have the same number of windings on each side, the output voltage will be the same as the input voltage (Fig. 3-10). If a transformer has a turns ratio greater than 1, the output voltage is less than the input voltage.

If the ratio is 10:1, 120 V would produce 12 V at the output (Fig. 3-11). Even though the voltage is reduced, the amount of current available increases by the same factor. A load of 0.4 Ω would draw 30 A. The power consumed by the resistor would be 360 W (30 A × 12 V). The same power would have to be flowing into the transformer. Since the input voltage is 120 V, the current flowing into the transformer is only 3 A (120 V × 3 A = 360 W).

ISOLATION TRANSFORMER

The isolation transformer is a simple 1:1 transformer as shown in Figure 3-10. This eliminated the problem of one side of the outlet (neutral) being grounded. When nearly all of the anesthetics were explosive, personnel were required to be grounded to avoid static sparks. Since they are grounded, they need only come in contact with a faulty drill, saw, or some other device that has a fault. To reduce the chance of the staff being electrocuted, isolated power is provided. Neither side is grounded, so that leakage current will not flow through a person to the nearest ground. Even though flammable anesthetics are rare and people are no longer required to be grounded, the isolation transformer is still required.

FIGURE 3-8 | Expanding magnetic field induces opposing field. Collapsing tries to maintain the field.

FIGURE 3-9 | Current flowing through wire generates magnetic field. Magnetic field cutting wire induces current.

FIGURE 3-10 | Transformer operation.

FIGURE 3-11 | Transformer decreases voltage and increases current.

Isolation transformers are also used on portable systems that have excessive leakage current. If an isolation transformer is used, the leakage current is only that of the input of the transformer.

THE GROUND LOOP

The ground loop may be problematic for patient safety or may introduce interference into the recording. The ground loop is a loop of wire around a room. Its path may go from an electrical outlet to the instrument attached, through patient connections, to another instrument, to an outlet at the far side of the room, and, through the ground wire, back to the first outlet. This can be avoided by plugging all of the patient-connected instrumentation into the same group of outlets.

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