 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
ssrs barcodelib SINUSOIDAL STEADYSTATE CIRCUIT ANALYSIS in Software
SINUSOIDAL STEADYSTATE CIRCUIT ANALYSIS QR Code JIS X 0510 Scanner In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Encode Quick Response Code In None Using Barcode creation for Software Control to generate, create QR Code 2d barcode image in Software applications. Z11 4 Z21 Z31
Reading QR Code In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Print QR In Visual C# Using Barcode printer for Visual Studio .NET Control to generate, create QR image in Visual Studio .NET applications. Z12 Z22 Z32
QR Code 2d Barcode Generator In .NET Framework Using Barcode generation for ASP.NET Control to generate, create QR image in ASP.NET applications. Generate QR Code In .NET Framework Using Barcode maker for Visual Studio .NET Control to generate, create QR Code ISO/IEC18004 image in .NET framework applications. 32 3 2 3 Z13 I1 V1 Z23 54 I2 5 4 V2 5 Z33 I3 V3
Making QR Code In Visual Basic .NET Using Barcode maker for VS .NET Control to generate, create Denso QR Bar Code image in .NET framework applications. GS1  12 Encoder In None Using Barcode creation for Software Control to generate, create UPC Symbol image in Software applications. for the unknown mesh currents I1 ; I2 ; I3 . Here, Z11 ZA ZB , the selfimpedance of mesh 1, is the sum of all impedances through which I1 passes. Similarly, Z22 ZB ZC ZD and Z33 ZD ZE are the selfimpedances of meshes 2 and 3. Code 39 Printer In None Using Barcode creator for Software Control to generate, create Code39 image in Software applications. EAN128 Drawer In None Using Barcode generation for Software Control to generate, create UCC.EAN  128 image in Software applications. Fig. 912 Generating Bar Code In None Using Barcode generator for Software Control to generate, create bar code image in Software applications. Painting EAN13 Supplement 5 In None Using Barcode generation for Software Control to generate, create European Article Number 13 image in Software applications. The 1,2element of the Zmatrix is de ned as: X Z12 (impedance common to I1 and I2 where a summand takes the plus sign if the two currents pass through the impedance in the same direction, and takes the minus sign in the opposite case. It follows that, invariably, Z12 Z21 . In Fig. 912, I1 and I2 thread ZB in opposite directions, whence Z12 Z21 ZB Similarly, Z13 Z31 Z23 Z23 X X (impedance common to I1 and I3 0 (impedance common to I2 and I3 ZD International Standard Serial Number Creation In None Using Barcode printer for Software Control to generate, create International Standard Serial Number image in Software applications. EAN / UCC  13 Creator In VS .NET Using Barcode drawer for .NET framework Control to generate, create GTIN  128 image in .NET framework applications. The Zmatrix is symmetric. In the Vcolumn on the righthand side of the equation, the entries Vk (k 1; 2; 3) are de ned exactly as in Section 4.3: X (driving voltage in mesh k Vk where a summand takes the plus sign if the voltage drives in the direction of Ik , and takes the minus sign in the opposite case. For the network of Fig. 912, V1 Va V2 0 V3 Vb Code 39 Extended Maker In ObjectiveC Using Barcode generation for iPhone Control to generate, create Code 3/9 image in iPhone applications. Print GS1 DataBar Expanded In Visual Studio .NET Using Barcode encoder for .NET framework Control to generate, create GS1 DataBar14 image in Visual Studio .NET applications. Instead of using the meshes, or windows of the (planar) network, it is sometimes expedient to choose an appropriate set of loops, each containing one or more meshes in its interior. It is easy to see that two loop currents might have the same direction in one impedance and opposite directions in another. Nevertheless, the preceding rules for writing the Zmatrix and the Vcolumn have been formulated in such a way as to apply either to meshes or to loops. These rules are, of course, identical to those used in Section 4.3 to write the Rmatrix and Vcolumn. Printing Code 3 Of 9 In ObjectiveC Using Barcode encoder for iPad Control to generate, create Code 3/9 image in iPad applications. Drawing ANSI/AIM Code 128 In Java Using Barcode printer for Java Control to generate, create Code 128C image in Java applications. EXAMPLE 9.6 Suppose that the phasor voltage across ZB , with polarity as indicated in Fig. 913 is sought. Choosing meshes as in Fig. 912 would entail solving for both I1 and I2 , then obtaining the voltage as VB I2 I1 ZB . In Fig. 913 three loops (two of which are meshes) are chosen so as to make I1 the only current in ZB . Furthermore, the direction of I1 is chosen such that VB I1 ZB . Setting up the matrix equation: Data Matrix ECC200 Creator In Java Using Barcode printer for Java Control to generate, create DataMatrix image in Java applications. Barcode Decoder In .NET Framework Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. SINUSOIDAL STEADYSTATE CIRCUIT ANALYSIS 2 32 3 2 3 0 I1 Va ZD 54 I2 5 4 Va 5 ZD ZE I3 Vb
[CHAP. 9
ZA ZB 4 ZA 0 from which
ZA ZA ZC ZD ZD
Va ZB V VB ZB I1 z a Vb where z is the determinant of the Zmatrix.
ZA ZA ZB ZC ZD
0 ZD ZD ZE
Fig. 913 Input and Transfer Impedances The notions of input resistance (Section 4.5) and transfer resistance (Section 4.6) have their exact counterparts in the frequency domain. Thus, for the singlesource network of Fig. 914, the input impedance is Zinput;r Vr z Ir rr where rr is the cofactor of Zrr in z ; and the transfer impedance between mesh (or loop) r and mesh (loop) s is Ztransfer;rs where rs is the cofactor of Zrs in z . V r z Is rs Fig. 914 As before, the superposition principle for an arbitrary nmesh or nloop network may be expressed as V1 Ztransfer;1k Vk 1 Ztransfer; k 1 k Vk Zinput;k Vk 1 Ztransfer; k 1 k Vn Ztransfer;nk Ik
CHAP. 9] SINUSOIDAL STEADYSTATE CIRCUIT ANALYSIS
THE NODE VOLTAGE METHOD
The procedure is exactly as in Section 4.4, with admittances replacing reciprocal resistances. A frequencydomain network with n principal nodes, one of them designated as the reference node, requires n 1 node voltage equations. Thus, for n 4, the matrix equation would be 2 32 3 2 3 V1 I1 Y11 Y12 Y13 4 Y21 Y22 Y23 54 V2 5 4 I2 5 Y31 Y32 Y33 V3 I3 in which the unknowns, V1 , V2 , and V3 , are the voltages of principal nodes 1, 2, and 3 with respect to principal node 4, the reference node. Y11 is the selfadmittance of node 1, given by the sum of all admittances connected to node 1. Similarly, Y22 and Y33 are the selfadmittances of nodes 2 and 3. Y12 , the coupling admittance between nodes 1 and 2, is given by minus the sum of all admittances connecting nodes 1 and 2. It follows that Y12 Y21 . Similarly, for the other coupling admittances: Y13 Y31 , Y23 Y32 . The Ymatrix is therefore symmetric. On the righthand side of the equation, the Icolumn is formed just as in Section 4.4; i.e., X (current driving into node k k 1; 2; 3 Ik in which a current driving out of node k is counted as negative. Input and Transfer Admittances The matrix equation of the node voltage method, Y V I is identical in form to the matrix equation of the mesh current method, Z I V Therefore, in theory at least, input and transfer admittances can be de ned by analogy with input and transfer impedances: Yinput;r Ir Y Vr rr Ir Y Vs rs

