Modeling-3

Modeling-3 - Electrical Network Transfer Functions...

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lectrical Network Transfer Functions Example (cont.): Electrical Network Transfer Functions (Step 4) sum voltages around each mesh through which the currents, I 1 (s) and I 2 (s) ,flow: Mesh 1, where I 1 (s) flows Mesh 2, where I 2 (s) flows by combining terms, the above become simultaneous equations: and (Step 5) use Cramer’sruleor any other way to solve for I 2 (s) : here where: 41 (c) 2010 Farrokh Sharifi
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lectrical Network Transfer Functions Example (cont.): Electrical Network Transfer Functions form the transfer function, G(s) , which can be displayed in block diagram format as: 42 (c) 2010 Farrokh Sharifi
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lectrical Network Transfer Functions Example (cont.): Electrical Network Transfer Functions we observe a pattern: we will be utilizing these patterns for other systems in the future 43 (c) 2010 Farrokh Sharifi
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ramer’s Rule for Small Systems Cramer s Rule for Small Systems 44 (c) 2010 Farrokh Sharifi
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ramer’s Rule for Small Systems Cramer s Rule for Small Systems 45 (c) 2010 Farrokh Sharifi
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lectrical Network Transfer Functions Time-Efficient Problem-Solving Technique Electrical Network Transfer Functions e ave oticed peating atterns e revious We have noticed repeating patterns in the previous examples that we can use to our advantage We need not write the equations component by component We can sum impedances around the mesh in the case of mesh equations Solving complex networks by use of this technique can save significant time and effort 46 (c) 2010 Farrokh Sharifi
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lectrical Network Transfer Functions Example : Write, but do not solve, the mesh equations for the network Electrical Network Transfer Functions shown below: 47 (c) 2010 Farrokh Sharifi
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lectrical Network Transfer Functions Example (cont.) Electrical Network Transfer Functions the equations for Mesh 1, Mesh 2, and Mesh 3 will have the follow form, respectively: via Mesh 1 via Mesh 2 2 ia Mesh 3 via Mesh 3 48 (c) 2010 Farrokh Sharifi
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lectrical Network Transfer Functions Example (cont.) Electrical Network Transfer Functions substituting the values from the network into the equations yields: which can be solved simultaneously for any desired transfer function, )/V(s) i.e. I 3 (s)/V(s) 49 (c) 2010 Farrokh Sharifi
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Translational Mechanical System Transfer Functions 50 (Table 2.4 in the book)
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Translational Mechanical System Mechanical systems parallel electrical systems; there exists Transfer Functions many analogies between electrical and mechanical components each of the two systems have three passive, linear components: Mechanical: two energy-storage elements , spring and the mass , and one energy dissipating element, damper Electrical: two energy-storage elements, inductor and capacitor, and one energy issipating ement sistor dissipating element, resistor Capacitor Resistor 51 Inductor
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Translational Mechanical System additional analogies can be observed by comparing Table 2.3 Transfer Functions with Table 2.4: Compare for Analogies 52 Voltage -> force Current -> velocity
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This note was uploaded on 02/20/2011 for the course MEC 709 taught by Professor Sharifi during the Fall '11 term at Ryerson.

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Modeling-3 - Electrical Network Transfer Functions...

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