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PART 1REAL VERSUS IDEAL COMPONENTSMajor Edwin Armstrong, who was undoubtedly the most prolific and downtoearth of the radio " pioneers, " was fond of repeating a saying which went something like this: It ain't the things you don't know that get you into trouble; it's the things you know for surethat ain't so. Armstrong went on to prove the wisdom of that proverb by singlehandedly inventing FM radio, even though the theoretical experts already "knew for sure" that FM radio wouldn’t work. Electronics technicians today often get into trouble because there are too many things that they "know for sure" about electronic components that in reality "ain’t so." Ideally, for example, hookup wire has zero resistance, and a coil whose inductance is measured as 10 uH at 1 MHz will also be 10 uH at 10 MHz. Such idealizations are commonly applied in the practice of electronics, and indeed a good case could be made that the practice of the art as we know it would be impossible without such simplifying assumptions. Eventually, however, the technician is bound to run afoul of his assumptions and he will have to recall that his initial analysis was based on an idealized mathematical model of a certain device which cannot possibly reflect all the properties of the actual physical component. Then he will have to ask himself: "What are the real properties of this component? How are they different from the mathematical model? Under what conditions is the model essentially valid, and when must I discard the model and look for the nonideal effects?" He may find that the nearzero resistance of hookup wire is not nearzero enough in the case of 5A current pulses, and that the distributed capacitance in the windings of a 10uH coil cancels out the majority of the coil's reactance at 10 MHz, even though it was negligible at 1 MHz. The purpose of this unit is to give the technician some awareness of the nonideal effects in common electronic components. In many cases, these concepts will not be needed, as the behavior of the real component will be close enough to the ideal to make the idealized model valid. However, when an "impossible" situation comes up in troubleshootingsay a substantial voltage drop across a supposedly zeroresistance wire, or a transistor that refuses to saturate even though the beta formula says that it has morethanenough base divethen it will be time to remember the difference between the ideal and the real. PROPERTIES OF REAL WIRE AND CABLE1.1 CONDUCTIVITY OF WIRE The actual dc resistance of various sizes of solid copper wire is given in Fig. 11. For resistance to ac, be sure to read Section 1.4 on skin effect. Stranded wire is sized to have a similar crosssectional area, and hence equivalent dc resistance, as equivalentsized solid wire. For example, 10 strands of No. 30 wire would have an area of 1000 circular mils, and would be called No. 20 stranded wire, since No. 20 wire has about the same area (1020 circular mils, to be exact). Other Metals: The resistance of other metals relative to copper is given in Fig. 13. Notice, for example, that a length of aluminum wire has 1.64 times the resistance of a copper wire of the same length and diameter.
Circular Mils: The crosssectional areas of the wires in Fig. 11 are given in circular mils. One circular mil is the area of a circle 1 mil in diameter. As illustrated in Fig. 12, circularmil area is then simply the square of wire diameter in mils (thousandths of an inch). (11) Calculating Wire Resistance: If necessary, the resistance of a length of wire can be found directly from the following formula: (12) where R is the wire resistance in ohms, p the resistivity of the wire material in ohmscmil/ft (Fig. 13), / the length of the wire in feet, and A the crosssectional area in circular mils (square of diameter in mils, or from Fig. 11). EXAMPLE 11 What is the dc resistance of 5280 ft of No. 26 stranded copper wire at 25°C? Solution From Fig. 11, each foot has 0.0418 ohm: R = 5280 ft x 0.0418 i/ft = 220.7 ohm EXAMPLE 12 What is the resistance of 10 ft of No. 22 Nichrome wire? Solution From Fig. 11, 10 ft of No. 22 copper wire has a resistance of 0.165 0. From Fig. 13, Nichrome wire has 65.09 times the resistance of copper, so R = 0.165 Q x 65.09 = 10.7 EXAMPLE 13 The diameter of a solid steel conductor measures 0.25 in. What is the resistance of 500 ft of this conductor? Solution […] 1.2 TEMPERATURE EFFECTS AND CURRENT CAPACITY OF WIRE Figure 13 shows that the resistance of metal conductors increases at higher temperatures. Copper wire, for example, undergoes an increase of 0.393% for each degree Celsius rise in temperature. For a 100°C rise (the rise from freezing to boiling of water) this would amount to a resistance increase of 39%. TemperatureStable Alloys: For applications where highly temperaturestable resistances are required, special alloys (usually of copper with nickel) are available which have temperature coefficients below 0.00002 per ° C. For such metals, resistances can be held stable to better than 0.1% over the normal range of humanenvironment temperatures. Semiconductor Temperature Coefficients: Nonmetals, such as carbon, generally have a negative temperature coefficient of resistance, meaning that their resistance goes down as temperature goes up. The semiconductor materials, "doped" silicon and germanium, have temperature coefficients which are large and negative, but are otherwise difficult to predict because of their extreme dependence on very small impurity contents. The resistance versus temperature curve for a typical slab of silicon semiconductor is given in Fig. 14. The rapid change of resistance with temperature is exploited in the manufacture of thermistors for temperature measurement and control. Maximum Current versus Wire Size: The recommended maximum currents for various sizes of copper wire may be obtained from Fig. 15. The lowest line (10° C rise) should be used for systems that must run cool. The center (35° C) should be thought of as the maximum for most common types of insulated wire, since it represents operating temperatures in the neighborhood of 150° F. The top (140°C rise) line represents final wire temperatures of about 320°F, and should be used only for bare wire suspended by hightemperature insulating supports. The basic chart is for two or three insulated wires in a bundle, and the allowable currents should be reduced by the factors given in the table accompanying Fig. 15 for larger bundles. 1.3 INSULATION AND VOLTAGE RATING OF WIRE Any insulating material can be made to conduct if enough voltage is applied across it to rip the normally wellbound electrons loose from their atoms. If a fairly large current is allowed to flow through such an insulation breakdown, enough heat may be generated to permanently destroy the insulator. Figure 16 shows that not all materials are alike in their ability to resist voltage breakdown, and that just about any solid insulator is better than air. The values given do not include a safety factor, so the wise designer will assume the worstcase insulating strength to be onefifth to onetenth of the value given. In choosing an insulating material, it is well to consider the possibility of environmental deterioration as well as the original insulating ability. Rubber can become cracked and brittle with age, oil can become contaminated, polyvinyl chloride materials can embrittle under exposure to sunlight, and air can be laden with salt spray and humidity. Arcing from a Sharp Point: Electric charge accumulates at a sharp point, but spreads evenly over a smooth surface. The results of this are depicted in Fig. 17. Four different conductors were held 2 mm from a metal plate, and the voltage required to arc the air between them was measured. When the conductor was a smooth sphere, a voltage of 8 kV was required. When a 90° bend in a No. 24 wire was used, 5 kV caused an arc. But when a sharply pointed No. 24 wire was used, arcing started at only 2.5 kV. A piece of insulating sleeving on the wire stopped all arcing. Therefore, when constructing highvoltage systems, the technician should: 1. Cut or file off all sharp metal and wire points. 2. Leave smooth, rounded solder joints with no sharp protruding solder "tails." 3. Use insulating sleeving on any bare highvoltage conductors. 4. Cover, coat, or paint surfaces where arcing is likely to be a problem. Special "corona dope" compounds are available for this purpose. 1.4 SKIN EFFECT AND STRAY INDUCTANCE OF WIRE At high frequencies, the magnetic fields within a wire become such as to force all charge carriers to flow at the surface of the wire, leaving the center of the wire useless as a conductor. This phenomenon, known as the skin effect, means that the resistance of a wire conductor increases at high frequencies. At dc and low ac frequencies the conductivity of a wire is proportional to its circularmil area (diameter squared), and heavier wire really does have much better conductivity. However, at radio frequencies conductivity is proportional to surface area (which is directly proportional to diameter), and the advantage of heavier wire is less pronounced. Largersized wire begins to suffer from the skin effect at a lower frequency because its central core is farther removed from the skin. Calculating Skin Effect: Although the current density under the skin effect actually drops off exponentially from the surface toward the center of the wire, the effect is the same as if a uniform current density were confined to a conductive surface with a thickness 5, called the skin depth. This is illustrated in Fig. 18(a). Actually, the current density is 38% of its full value at the skin depth. For round copper conductors, skin depth can be calculated by V? where S is in centimeters and / is in hertz. For other metals, the depth can be determined by multiplying by the square root of the relative resistivity from the table of Fig. 13. Aluminum, for example, has a skin depth of Vl.64 = 1.28 times that of copper. Skin depth is important because it determines the heaviest solid wire that can be effectively employed at a given frequency. If the wire has a diameter greater than 25, the center of the wire is relatively useless.
EXAMPLE 14 What is the maximum effective diameter of a copper wire for 60Hz power transmission? Solution (13) The actual resistance of a copper wire under skin effect can be determined from Vf… (14) where R is in ohms, / is in hertz, and t and / are thickness and length, respectively, in any commensurate units (both inches, both centimeters, or whatever). For other conductors, multiply by the square root of the relativeresistance value in Fig. 13. Silver, for example, has a skineffect resistance of V0.945 or 0.972 times that of copper. Figure l8(b) shows the ratio of skineffect resistance to dc resistance as a function of wire size and frequency, and may be used in place of Equation 14 for obtaining rough estimates. EXAMPLE 15 What is the voltage loss across a 200ft length of RG58 coax feeding a 500 load at 30 MHz? Solution Assuming the loss to be primarily in the 0.033in. diameter center conductor, we find its skineffect resistance. This situation was set up in the laboratory where a V„/Vin ratio of 0.58 was measured at 30 MHz. Proximity Effect: The skineffect formulas are accurate only for round conductors running in a straight line. When the wire is wound into coils, additional magnetic fields cause further increases in wire resistance. This proximity effect is difficult to predict, but it is by no means negligible. The following factors will serve as a rough guide to the proximity effect to be expected. pretty (actual) Coil Configuration /{ (calculated) Singlelayer, spaced 5 to 20 1.5 to 3 diameters between windings Singlelayer, closewound 5 to 15 Multilayer winding 15 to 100 A summary of the most common situations may be helpful. At 60 Hz, skin effect does not become evident even in transformer coils except in wire sizes larger than about AWG 4. In audio transformers up to 10 kHz, skin effect is negligible for wire sizes smaller than about AWG 24. Such large wire sizes are quite uncommon, making dc resistance satisfactory for most power and audio trans former calculations. For most common wire sizes skin effect or proximity effect is evident by 100 kHz, and there are few practical situations above 1 MHz where skineffect resistance is not many times dc resistance. Combating Skin Effect: Stranded wire suffers from skin effect to about the same degree as does equivalentsized solid wire. (The advantage of stranding is the ability of the wire to flex without breaking.) However, if each strand is separately insulated from the others, with the strands tied together at each end, some relief from skin effect is obtained. Such wire is called litz wire and is effective for winding highQ coils in the 0.1 to 2MHz range. Below 0.1 MHz, stray capacitance between the strands washes out the benefits of litz wire. Where energy loss is critical and strength is important, copperclad steel wire is often employed. The copper coating, one or two skin depths thick, provides conductivity while the steel provides strength. For largediameter conductors, hollow tubing is lighter, cheaper, and just as conductive, provided that its thickness is two skin depths or more. Flat copper strap also provides greater surface area with less volume of metal. At high radio frequencies a very thin silver plating on a metal or plastic support provides as much conductivity as possible, if the plating is several times the skin depth. Stray Inductance of Wire: In practice, skin effect in hookup wire is usually masked by the stray inductance of the wire, which may be anticipated to be about 0.04 uH/cm or 1 uH/25 cm. Skineffect resistance in hookup wire is typically an order of magnitude (factor of 10) less than the reactance caused by stray inductance. Figure 18(c) shows measured values of total impedance for three sizes of solid copper wire from low audio to high radio frequencies. Notice that a simple 1meter test lead of No. 22 wire has an impedance in the vicinity of 60 ohm at 10 MHz. Any two conductors separated by an insulator form a capacitor, and adjacent lengths of hookup wire fill this requirement in every respect. The following list will be helpful in estimating the stray capacitance between various types of conductors.  Two No. 22 solid PVCinsulated wires 40 pF/m adjacent in a bundle Two No. 22 wires twisted 1 turn/cm 46 pF/m One No. 22 wire held flat against a 65 pF/m metal chassis Two No. 22 wires held 2 cm apart 12 pF/m Two conductors of No. 18 lamp cord 50 pF/m Shielded wire; No. 22 stranded center 300 pF/m conductor to braid RG58/U coax cable (7 mm diameter) 88 pF/m 300 U TV twin lead 20 pF/m Tubular capacitor, 2 cm diameter, 5 cm long; 1020 pF outside foil to metal chassis  HighFrequency Loss on a Microphone Line: Cable capacitances may prove far from negligible in many practical cases. For example, at 5 kHz, 20 m of heavy shielded wire may present a reactance to ground of 5 k ohm. The popular lowcost crystal microphones typically have an internal impedance of 50 k ohm. Figure 19(a) illustrates how the loading effect of the cable capacitance may cause the higher audio frequencies to be attenuated (by a factor of about 10 in this case) before they reach the amplifier input. Of course, the problem can be readily solved in a number of waysuse a lowimpedance microphone; use a stepdown transformer at the "mic" and a stepup transformer at the amp; put an emitter follower or FET amplifier stage in the mic case; use special hiZ shielded cable; and so on. But the first step in solving any problem must be to identify its cause. Selfoscillation in an Amplifier: Figure 19(b) illustrates another common problem caused by stray capacitance. The input and output leads of the highfrequency amplifier depicted pass within a few centimeters of each other for a short distance, resulting in a feedback capacitance of 0.5 pF. At about 300 kHz this capacitance has a reactance of 1 Mohm and the voltage division of Xc with provides a feedback voltage equal to the input voltage. If the phase shift within the amplifier is right, the result will be selfoscillation. To avoid this problem, the input and output wires of any amplifier should be kept completely away from each other and the components on the circuit board should be laid out to implement this. Vertical shield plates can be mounted across a transistor and soldered directly to the chassis to screen the input from the output. Keeping the amplifier input impedance low reduces the feedback ratio and thus helps prevent oscillation. Coupling between Shielded Cables: Shielded wire and coaxial cable can greatly reduce unwanted coupling between wire runs, but you should guard against the feeling that nothing can get into or out of a shielded cable. Figure 110 shows the results ol some laboratory tests using RG59/U coax cables. In Fig. 110(a) an unshielded length of hookup wire run along the outside of the coax cable picks up as much as 25% of the cable' s signal at certain frequencies. In Fig. 110(b), two lengths of coax couple as much as 3% of the signal from one to the other at high frequencies when held close together.

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