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.net barcode reader library Transmission lines in Software
84 Transmission lines Reading Data Matrix 2d Barcode In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Data Matrix 2d Barcode Maker In None Using Barcode drawer for Software Control to generate, create Data Matrix image in Software applications. In Example 35 we discovered that the impedance looking into a lossless (or very low loss) halfwavelength transmission line is the load impedance: Z = ZL [330] Scan Data Matrix In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. Making DataMatrix In C# Using Barcode creation for Visual Studio .NET Control to generate, create Data Matrix 2d barcode image in Visual Studio .NET applications. The fact that line input impedance equals load impedance, is very useful in certain practical situations For example, a resistive impedance is not changed by the line length Therefore, when an impedance is inaccessible for measurement purposes, the impedance can be measured through a transmission line that is an integer multiple of a half wavelength Our next special case involves a quarterwavelength transmission line, and those that are odd integer multiples of quarterwavelengths (of course, even integer multiples of a quarter wavelength obey the halfwavelength criteria) 4 Quarterwavelength lossy lines: Z = (Zo) and 5 Quarterwavelength lossless or very low loss lines: (Zo)2 Z= Z L [332] ZL + Zo coth (al) Zo + ZL coth (al) [331] Data Matrix ECC200 Encoder In .NET Using Barcode drawer for ASP.NET Control to generate, create Data Matrix image in ASP.NET applications. Data Matrix ECC200 Generator In .NET Framework Using Barcode encoder for .NET Control to generate, create Data Matrix ECC200 image in .NET applications. From Eq 332, you can discover an interesting property of the quarterwavelength transmission line First, divide each side of the equation by Zo: [Zo]2 Z = Z Z Zo L o = Zo ZL [333] Create ECC200 In VB.NET Using Barcode generator for .NET framework Control to generate, create DataMatrix image in .NET applications. Making DataMatrix In None Using Barcode printer for Software Control to generate, create ECC200 image in Software applications. [334] Printing GS1  13 In None Using Barcode drawer for Software Control to generate, create EAN 13 image in Software applications. Printing Barcode In None Using Barcode encoder for Software Control to generate, create barcode image in Software applications. Transmission line responses 85 The ratio Z/Zo shows an inversion of the load impedance ratio ZL/Zo, or, stated another way, Z 1 = Zo ZL/Zo [335] Barcode Maker In None Using Barcode maker for Software Control to generate, create bar code image in Software applications. Create UCC  12 In None Using Barcode creation for Software Control to generate, create USS128 image in Software applications. Again, from Eq 332, you can deduce another truth about quarterwavelength transmission lines: If Z= then ZZL = which means Zo = ZZL [338] Zo [337] Zo ZL [336] ISSN  13 Drawer In None Using Barcode generation for Software Control to generate, create ISSN  13 image in Software applications. Printing EAN 13 In None Using Barcode maker for Office Excel Control to generate, create EAN13 Supplement 5 image in Office Excel applications. Equation 338 shows that a quarterwavelength transmission line can be used as an impedance matching network Called a Q section, the quarterwavelength transmission line used for impedance matching requires a characteristic impedance Zo if Z is the source impedance and ZL is the load impedance Example 36 A 50 source must be matched to a load impedance of 36 Find the characteristic impedance required of a Q section matching network Solution: Z= = = ZZL (50 ) (36 ) 1800 2 = 42 EAN13 Encoder In Visual Studio .NET Using Barcode encoder for Reporting Service Control to generate, create GTIN  13 image in Reporting Service applications. UPC A Generation In VS .NET Using Barcode creator for Reporting Service Control to generate, create UPCA image in Reporting Service applications. 6 Transmission line as a reactance: Reconsider Eq 328, which related impedance looking in to load impedance and line length: Z = (Zo) ZL + jZo tan (Bl) Zo + jZL tan (Bl) [339] GS1  13 Maker In ObjectiveC Using Barcode maker for iPhone Control to generate, create EAN / UCC  13 image in iPhone applications. Encode Bar Code In VS .NET Using Barcode drawer for Reporting Service Control to generate, create bar code image in Reporting Service applications. Now, for the case of a shorted line (ie, ZL = 0), the solution is Z = (Zo) (0) + jZo tan (B l) Zo + j(0) tan (B l) [340] Painting Barcode In None Using Barcode printer for Font Control to generate, create barcode image in Font applications. Data Matrix 2d Barcode Reader In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. 86 Transmission lines jZo tan (Bl) Zo
Z = (Zo) [341] [342] Z = j Zo tan (Bl) Recall from Eq 325 that B = WZoC Substituting Eq 343 into Eq 342 produces Z = j Zo tan ( ZoCl) or Z = j Zo tan (2 FZoCl) [343] [344] [345] Because the solutions to Eqs 344 and 345 are multiplied by the j operator, the impedance is actually a reactance (Z = 0 + jX) It is possible to achieve almost any possible reactance (within certain practical limitations) by adjusting the length of the transmission line and shorting the load end This fact leads us to a practical method for impedance matching Figure 310A shows a circuit in which an unmatched load is connected to a transmission line with characteristic impedance Zo The load impedance ZL is of the form Z = R jX, and, in this case, it is equal to 50 j20 A complex impedance load can be matched to its source by interposing the complex conjugate of the impedance For example, in the case where Z = 50 j20, the matching impedance network will require an impedance of 50 + j20 The two impedances combine to produce a result of 50 The situation of Fig 310A shows a matching stub with a reactance equal in magnitude, but opposite in sign, with respect to the reactive component of the load impedance In this case, the stub has a reactance of +j20 to cancel a reactance of j20 in the load A quarterwavelength shorted stub is a special case of the stub concept that finds particular application in microwave circuits Waveguides (Chap 19) are based on the properties of the quarterwavelength shorted stub Figure 310B shows a quarterwave stub and its current distribution The current is maximum across the short, but wave cancellation forces it to zero at the terminals Because Z = V/I, when I goes to zero, the impedance becomes infinite Thus, a quarterwavelength stub has an infinite impedance at its resonant frequency, and redundant acts as an insulator This concept may be hard to swallow, but the stub is a metal insulator

