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resistances. At A, sets of series resistors are connected in parallel. At B, sets of parallel resistances are connected in series. These examples show symmetrical n-by-n matrices with n = 3.

Problem 4-16

Suppose there are five resistors R1 through R5 in parallel, as shown in Fig. 4-9, all having a value of 4.7K . What is the total resistance, R You can probably guess that the total is a little less than 1K or 1000 . So you can convert the value of the single resistor to 4,700 and divide by 5, getting a total resistance of 940 . This is accurate to two significant figures, the 9 and the 4; engineers won t usually be worried about the semantics, and you can just say 940 .

Linear Predictive Coding (LPC)

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2 = 18 W, for example A 10 10 array of 1-W resistors can dissipate up to 100 W The total powerhandling capacity is multiplied by the total number of resistors in the matrix But this is true only if all the resistors have the same ohmic values, and the same power-dissipation ratings It is unwise to build series-parallel arrays from resistors with different ohmic values or power ratings If the resistors have values and/or ratings that are even a little nonuniform, one of them might be subjected to more current than it can withstand, and it will burn out Then the current distribution in the network can change so a second component fails, and then a third It s hard to predict the current and power distribution in an array when its resistor values are all different.

When combinations of resistances are hooked up to a source of voltage, they will draw current. You can easily figure out how much current they will take by calculating the total resistance of the combination and then considering the network as a single resistor. If the resistances in the network all have the same ohmic value, the power from the source will be evenly distributed among the resistances, whether they are hooked up in series or in parallel. If there are eight identical resistors in series with a battery, the network will consume a certain amount of power, each resistor bearing 1/8 of the load. If you rearrange the circuit so that the resistors are in parallel, the circuit will dissipate a certain amount of power (a lot more than when the resistors were in series), but again, each resistor will handle 1/8 of the total power load. If the resistances in the network do not all have identical ohmic values, they divide up the power unevenly. Situations like this are discussed in the next chapter.

If you need a resistance with a certain power-handling capacity, you must be sure the network can handle at least that much power If a 50-W rating is required, and a certain combination will handle 75 W, that s fine But it isn t good enough to build a circuit that will handle only 48 W Some extra tolerance, say 10 percent over the minimum rating needed, is good, but it s silly to make a 500-W network using far more resistors than necessary, unless that s the only convenient combination given the parts available Nonsymmetrical series-parallel networks, made up from identical resistors, can increase the powerhandling capability over that of a single resistor But in these cases, the total resistance is not the same as the value of the single resistors.

We mention Linear Predictive Coding (LPC) here only because it has carved out a niche for itself in certain voice-related applications such as voice mail systems, automobiles, aviation, and electronic games that speak to children LPC is a complex process, implemented completely in silicon, which enables voice to be encoded at rates as low as 2400 bps The resulting quality is far from toll-quality, but it is certainly intelligible and its low bit rate capability gives it a distinct advantage over other systems LPC relies on the fact that each sound created by the human voice has unique attributes, such as frequency range, resonance, and loudness, among others When voice samples are created in LPC, these attributes are used to generate prediction coefficients These predictive coefficients represent linear combinations of previous samples, hence the name, Linear Predictive Coding.

Sets of resistors, all having identical ohmic values, can be connected together in parallel sets of series networks, or in series sets of parallel networks. By doing this, the total power handling capacity of the resistance can be greatly increased over that of a single resistor.

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