as the series-to-parallel transformation.

Decode QR Code JIS X 0510 In NoneUsing Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.

QR Code JIS X 0510 Maker In NoneUsing Barcode encoder for Software Control to generate, create QR Code ISO/IEC18004 image in Software applications.

FREQUENCY RESPONSE, FILTERS, AND RESONANCE

Read QR Code JIS X 0510 In NoneUsing Barcode recognizer for Software Control to read, scan read, scan image in Software applications.

Encoding QR Code JIS X 0510 In Visual C#Using Barcode creation for .NET framework Control to generate, create Quick Response Code image in .NET applications.

[CHAP. 12

QR Code ISO/IEC18004 Generation In .NET FrameworkUsing Barcode encoder for ASP.NET Control to generate, create Quick Response Code image in ASP.NET applications.

QR-Code Generator In .NET FrameworkUsing Barcode generation for Visual Studio .NET Control to generate, create QR Code 2d barcode image in Visual Studio .NET applications.

LOCUS DIAGRAMS

Encode Quick Response Code In VB.NETUsing Barcode creator for .NET framework Control to generate, create Denso QR Bar Code image in .NET applications.

Creating Barcode In NoneUsing Barcode drawer for Software Control to generate, create bar code image in Software applications.

Heretofore, the frequency response of a network has been exhibited by plotting separately the magnitude and the angle of a suitable network function against frequency !. This same information can be presented in a single plot: one nds the curve (locus diagram) in the complex plane traced by the point representing the network function as ! varies from 0 to 1. In this section we shall discuss locus diagrams for the input impedance or the input admittance; in some cases the variable will not be !, but another parameter (such as resistance R). For the series RL circuit, Fig. 12-28(a) shows the Z-locus when !L is xed and R is variable; Fig. 1228(b) shows the Z-locus when R is xed and L or ! is variable; and Fig. 12-28(c) shows the Y-locus when R is xed and L or ! is variable. This last locus is obtained from Y 1 1 q tan 1 !L=R R j!L R2 !L 2

Create Bar Code In NoneUsing Barcode generation for Software Control to generate, create bar code image in Software applications.

Generate UCC-128 In NoneUsing Barcode printer for Software Control to generate, create GS1 128 image in Software applications.

Fig. 12-28

GTIN - 12 Generation In NoneUsing Barcode drawer for Software Control to generate, create Universal Product Code version A image in Software applications.

Data Matrix ECC200 Generator In NoneUsing Barcode drawer for Software Control to generate, create Data Matrix image in Software applications.

Note that for !L 0, Y 1=R 08; and for !L ! 1, Y ! 0 908. When !L R, 1 Y p 458 R 2 A few other points will con rm the semicircular locus, with the center at 1/2R and the radius 1/2R. Either Fig. 12-28(b) or 12-28(c) gives the frequency response of the circuit. A parallel RC circuit has the Y- and Z-loci shown in Fig. 12-29; these are derived from Y 1 j!C R and R Z q tan 1 !CR 1 !CR 2

Code 93 Extended Generation In NoneUsing Barcode generator for Software Control to generate, create Code 9/3 image in Software applications.

Decoding UPC-A Supplement 2 In Visual C#.NETUsing Barcode reader for VS .NET Control to read, scan read, scan image in .NET applications.

Fig. 12-29

Creating GS1 - 13 In .NET FrameworkUsing Barcode generation for ASP.NET Control to generate, create EAN / UCC - 13 image in ASP.NET applications.

Encoding Linear 1D Barcode In C#Using Barcode creation for VS .NET Control to generate, create Linear 1D Barcode image in .NET applications.

CHAP. 12]

UCC-128 Printer In NoneUsing Barcode generator for Font Control to generate, create UCC - 12 image in Font applications.

Draw EAN / UCC - 13 In .NET FrameworkUsing Barcode drawer for Visual Studio .NET Control to generate, create European Article Number 13 image in Visual Studio .NET applications.

FREQUENCY RESPONSE, FILTERS, AND RESONANCE

Bar Code Maker In NoneUsing Barcode creation for Word Control to generate, create bar code image in Microsoft Word applications.

Barcode Recognizer In Visual Basic .NETUsing Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET applications.

For the RLC series circuit, the Y-locus, with ! as the variable, may be determined by writing Y G jB whence G R R2 X 2 1 R jX R jX R2 X 2 X B 2 R X2

Both G and B depend on ! via X. Eliminating X between the two expressions yields the equation of the locus in the form 2 G 1 2 2 1 G2 B2 or G B R 2R 2R which is the circle shown in Fig. 12-30. and ! !h . Note the points on the locus corresponding to ! !l , ! !0 ,

Fig. 12-30

For the practical tank circuit examined in Section 12.14, the Y-locus may be constructed by combining the C-branch locus and the RL-branch locus. To illustrate the addition, the points corresponding to frequencies !1 < !2 < !3 are marked on the individual loci and on the sum, shown in Fig. 12-31(c). It is seen that jYjmin occurs at a frequency greater than !a ; that is, the resonance is highimpedance but not maximum-impedance. This comes about because G varies with ! (see Section 12.14), and varies in such a way that forcing B 0 does not automatically minimize G2 B2 . The separation of

Fig. 12-31

FREQUENCY RESPONSE, FILTERS, AND RESONANCE

[CHAP. 12

the resonance and minimum-admittance frequencies is governed by the Q of the coil. Higher Qind corresponds to lower values of R. It is seen from Fig. 12-31(b) that low R results in a larger semicircle, which when combined with the YC -locus, gives a higher !a and a lower minimum-admittance frequency. When Qind ! 10, the two frequencies may be taken as coincident. The case of the two-branch RC and RL circuit shown in Fig. 12-32(a) can be examined by adding the admittance loci of the two branches. For xed V V 08, this amounts to adding the loci of the two branch currents. Consider C variable without limit, and R1 , R2 , L, and ! constant. Then current IL is xed as shown in Fig. 12-32(b). The semicircular locus of IC is added to IL to result in the locus of IT . Resonance of the circuit corresponds to T 0. This may occur for two values of the real, positive parameter C [the case illustrated in Fig. 12.32(b)], for one value, or for no value depending on the number of real positive roots of the equation Im YT C 0.

Fig. 12-32