This article originally appeared in Cabling Business Magazine 
Inductance: from Electric Motors to Characteristic ImpedanceBy David HerresWhat electricians and cabling technicians have to know about inductance and characteristic impedance Inductance, one of the three electrical operatives (the other two are capacitance and resistance), plays an enormous role in how we are able to use energy to perform work and to process and transmit data. Without inductance, we might be able to generate small amounts of electricity by chemical means and distribute DC power limited distances at low voltage for strictly resistive loads like light and heat. But it is inductance that makes electric motors, relays and transformers posssible and in cabling it's at the heart of characteristic impedance which makes data transmission a reality for us. In 1824 Hans Christian Oersted found that electricity flowing through a conductor measurably altered the surrounding space by creating a magnetic field. A few years later, Michael Faraday and Joseph Henry, working independently, discovered an incredible corollary. They found that if the magnetic field moved relative to a nearby conductor, current would flow in that second wire. Almost immediately, it was noticed that instead of relative motion between the magnetic field and the nearby conductor, current flow would also be induced if the polarity and/or intensity of the magnetic field could be made to vary by varying the current flow in the first conductor. Soon after Faraday and Henry published their findings, Heinrich Lenz added greatly to this new body of knowledge. He found that an induced current flows in the direction such that the resulting magnetic flow opposes the magnetic field that induced current in the first place. Leaving the historical perspective, let's take a look at the physical phenomena and some very simple formulas that quantify them. If electrons flow through a conductor, a magnetic field is established around that donductor, diminishing with distance from it. If the conductor is formed into a coil, the magnetic field is intensified in proportion to the number of turns because the individual fields merge to form a single more intense field. If half the windings went in one direction and half in the other direction, they would canceol and there would be no magnetic field. If an iron core is placed inside the coil, the field becomes more intense since iron has a higher magnetic permeability than airl One of the important things to remember is that a straight conductor going through pace with either AC or DC flowing through it creates a magnetic field. It is just not as intense as that produced by the coil with an iron core. What happens if we place another conductor parallel to the one producing the magnetic field? If we connectg a load to the second conductor and if the two are moving with respect to one another or if the current is AC or pulsating DC so that the magnetic field is moving, current will flow through the second conductor and the load will receive power. In the case of DC, current will only be induced at the moment that it is switched on or off. If instead of the first conductor a permanent magnet is placed near the second wire, there will be current flow as well, but only if there is relative motion. No relative motion or current fluctuation in the first conductor means no current in the second conductor. It is not the magnetic field that makes the induced current, it is the change in the magnetic field that makes the induced current. There are no free rides in the world of classical physics. If a static magnetic field could induce current, we would not have an energy crisis in the world today. If both conductors are formed into coils wound around the same iron core, the effect becomes much more pronounced. The property of one conductor to induce current flow in a second is called inductance. Like in capacitance, the effect is frequency dependent. At higher frequencies, inductance becomes more important. There are two types of inductance. Ine type is mutual inductance, where current is induced in a second conductor without voltage being applied to it. This forms the basis for the transformer and also for inductive coupling resulting in attenuation and crosstalk in communication and data cabling. The other type of inductance is selfinductance, where a single conductor induces current flow in itself, forming the bais for inductive reactance. This is the phenomenon described by Heinrich Lenz. Selfinductance is usually simply called inductance. If we examine a sine wavek we see the greatest rate of change in voltage occurs near zero, where the voltage level is least. If applied voltage and induced current in a singole conductor are plotted on the same X and Y coordinates, the reason for inductive current lag becomes clear. The greatest current flow occurs when the voltage is least and there is actually zero induced current flow when the applied voltage is highest. As a convention, we say a complete cycle is 360 degrees, so in a purely inductive load, the current flow is out of phase and is said to lag behind the applied voltage by 90 degreesl With a purely capacitive loadm the current flow leads the applied voltage by 90 degrees. This is the phase angle. In the case of a purely resistive load, the applied voltage and resulting current are in phase. An inductor's opposition to current flow is called inductive reactance and the quantity is given by the following formula:
XsubL = 2(pi)fLwhere XsubL = inductive reactance in ohms f = frequency in cycles per second L = inductance in henrys
The term 2(pi)f is the number of radians per second at which the alternating current is turning, assuming one AC cycle to be a full circle. A radian is a unit of angular motion. 2(pi) radians comprise a complete circle. A twopole alternator makes one AC cycle for every complete shaft rotation, in other words every 2(pi) radians. The product of 2(pi) and f, the frequency in cycles per second, is the angular velocity. 2(pi)f, the angular velofcity, may be condensed as lowercase omega, giving rise to:
XsubL = lowercase omega(L)Thus the circular motion of an alternator shaft is the origin of the sine wave, a pure AC with no harmonics. Early electronic (nonrotary) inverters could only produce a square wave, which had a problem with harmonics and tended to make motors overheat. Today it is possible to produce a good sine wave output by purely electronic means. A capacitor also offers opposition to current flow. The higher the frequency and/or the greater the capacitance, the less capacitive reactance. Capacitive reactance is measured in ohms and conforms to the following formula:
XsubC = 1/2(pi)fCwhere XsubC = capacitive reactance in ohms f = frequency in cycles per second C = capacitance in farads.
Capacitive reactance is expressed in ohms and circuits having this attribute conform to Ohm's law, the only difference being that the quantity is frequency dependent. Notice that the formulas for capacitive and inductive reactance have a reciprocal relationship. The higher the frequency, the more reactance or opposition to current flow in an inductive circuit. Capacitive reactance is greater (meaning that there is more opposition to current flow) at lower frequencies. Frequency has no effect on resistive circuits except insofar as they have unintended capacitive and inductive properties, which become more pronounced at higher frequencies. For example,the two terminals of a resister comprise plates of a capacitor with the resistive element being the dielectric. And since the resister is a conductor, current flow establishes a magnetic field so a high frequencies it becomes an inductor as well and exhibits inductive reactance. Unwanted ("parasitic") capacitance and inductance can appear anywhere, inside solid state components, in the traces of a printed circuit board and in long transmission or telephone lines. Careful engineering is required to prevent harmful effects from occurring. Circuits that have both inductive and capacitive reactance have the smaller subtracted from the larger so that there will be a net capacitive or inductive reactance. This quantity is added to any resistive element, but since these values are out of phase, they must be added vectorially. The formula is:
Z = Square Root of (X squared) + (R squared)where Z = impedance in ohms X = capacitive or inductive reactance in ohms R = resistance in ohms
It is as if two oxen were hitched to a log and they were pulling in somewhat different directions. There would be a resultant force pulling the log but it would not be equal to the sum of the efforts of the two creatures. A capacitor and unductor can be connected to create a resonant circuit. If they are in series, they pass the resonant frequency and block all others. If they are in parallel, they block the resonant frequency and pass all others. Accordingly, these combinations can be used to filter and separate different frequencies or to tune in a single frequency as in radio transmission and reception. As a matter of terminology, reactance is made up of capacitive and inductive reactance, which are added when they are in the same circuit, but the actual calculation is one of subtraction since they are 180 degrees out of phase. When resistance is added to the mix, the aggregate is called impedance. The algebraic symbol for impedance is Z. It is measured in ohms and obeys Ohm's law, but varies with frequency as given in the formulas for capacitive and inductive reactance. Capacitance and inductance figure prominently in the field of cabling, especially where the frequencies are high or the distances long. Voltage drop, as a function of resistance to the flow of current, is familiar in DC and low frequency power and light circuits, but in high frequency applications such as data cabling, that concept is eclipsed by characteristic impedance, a phenomenon that is a little bit counterintuitive. it is represented by the expression: Zsubo. We speak of 50 ohm and 75 ohm coaxial cable. What does that mean? Does it mean thaqt we can connect an ohmmeter to the end of a specified length of cable and, with the two conductors at the far end either shunted together or open, expect to read that resistance? Definitely not! Characteristic impedance is a whole different concept. You do not measure it with an ohmmeter. It is ascertained by referring to the manufacturer's specifications. The length of the cable, when it approaches 1/10 the wavelength of the signal that it is carrying, has nothing to do with its impedance. Characteristic impedance is a function of the diameter of the conductors and the type of dielectric between them. The calculations are complex, but we are not called upon to calculate characteristic impedance. It is in specifications supplied by the manufacturer and remains constant for any length of cable. To understand the concept of characteristic impedance, it is helpful sto participate in a hypothetical mental exercise. Imagine a coaxial or UTP cable of infinite length connected to a high frequency signal source. The cable may be thought of as an infinite series of parallel connected capacitors since the two conductors are like plates of aa capacitgor separated by dielectric material. the capacitive reactance, accordingly, would approach zero and the signal would be shorted out. But between each parallel connected capacitor in both conductors is a segment of wire that has a certain inductance and its inductive reactance limits the current flow, so that th applied signal is not shorted out after all. As the frequency rises, the parallel connected capacitive reactance decreases, tending to lower the impedance. But this tendency is balanced by a rise in the series connected inductive impedances so that a stable resultant is achieved. Its valued depends on cable characteristics which conform to the manufacturer's design intent. You may wonder how it is possible that an infinite length of cable would be relevant to anything in the real world. The answer is that when the cable is terminated at both ends to matching impedances, there is maximum power transfer and it behaves exactly like an infinitely long cable. In the case of high frequency data transmission, typically at low current levelsm traditional resistance with heat dissipation is largely replaced by characteristic impedance. If the cable characteristic impedance is the same as the signal source internal impedance and the final load impedance, there will be maximum power transfer, If these items are not matched, there will be partial reflection of the signal back toward the source, resulting in signal distortion and loss of data. It is of great importance that Zsubo remains constant at all points along the transmission line. Therefore, quality control in cable manufacture is critical. In coax, if the distance between the center conductor and outer shielding varies at all, harmful reflections and incomplete power transfer result. Also, conductor thickness cannot vary or the inductance and therefor characteristic impedance will vary. Moreover, proper methods and workmanshiip are necessary in making field terminations, Any kinking or abrading of cable is equally harmful. To verify cable integrity by measuring characteristic impedance of a finite length, a TDR (Time Domain Reflectometer) is needed. For a threefoot data cable, it completes the impedance measurement in less than three nsec, and holds the result. The instrument is a lot more expensive than an ohmeter, but it is one of the tools you need to enter the recessionproof world of cable certification.

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