Absolute-value impedance

Chapter Absolute-value impedance

Teach Yourself Electricity and Electronics Third Edition Book
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Teach Yourself Electricity and Electronics Third Edition Book

  • Absolute-value impedanceThere will be times when you’ll hear that the “impedance” of some device or componentis a certain number of ohms. For example, in audio electronics, there are “8-Ω” speak-ers and “600-Ω” amplifier inputs. How can manufacturers quote a single number for aquantity that is two-dimensional, and needs two numbers to be completely expressed?There are two answers to this. First, figures like this generally refer to devices thathave purely resistive impedances. Thus, the “8-Ω” speaker really has a complex imped-ance of 8 j0, and the “600-Ω” input circuit is designed to operate with a complex im-pedance at, or near, 600 j0.Second, you can sometimes talk about the length of the impedance vector, callingthis a certain number of ohms. If you talk about “impedance” this way, you are beingambiguous, because you can have an infinite number of different vectors of a givenlength in the RX plane.Sometimes, the capital letter Z is used in place of the word “impedance” in generaldiscussions. This is what engineers mean when they say things like “Z50Ω” or “Z300Ω nonreactive.”“Z8Ω” in this context, if no specific complex impedance is given, can refer to thecomplex value 8j0, or 0j8, or 0 j8, or any value on a half circle of points in theRX plane that are at distance 8 units away from 0 j0. This is shown in Fig. 15-7. Thereexist an infinite number of different complex impedances with Z8Ω.Problems 15-1, 15-2, and 15-3 can be considered as problems in finding absolute-value impedance from complex impedance numbers.Problem 15-4Name seven different complex impedances having an absolute value of Z10.It’s easy name three: 0j10, 10j0, and 0j10. These are pure inductance, pureresistance, and pure capacitance, respectively.A right triangle can exist having sides in a ratio of 6:8:10 units. This is true because6282 = 102. (Check it and see!) Therefore, you might have 6j8, 6 j8, 8j6 and8 j6, all complex impedances whose absolute value is 10 ohms. Obviously, the valueZ10 was chosen for this problem because such a whole-number right-triangle exists.It becomes quite a lot messier to do this problem (but by no means impossible) if Z11 instead.If you’re not specifically told what complex impedance is meant when a single-number ohmic figure is quoted, it’s best to assume that the engineers are talking aboutnonreactive impedances. That means they are pure resistances, and that the imagi-nary, or reactive, factor is zero. Engineers will often speak of nonreactive impedances,or of complex impedance vectors, as “low-Z or high-Z.” For instance, a speaker might becalled “low-Z” and a microphone “high-Z.”Characteristic impedanceThere is one property of electronic components that you’ll sometimes hear called im-pedance, that really isn’t “impedance” at all. This is characteristic impedance orsurge272 Impedance and admittance