LinearandNonlinearNetworks(handouts).pdf

# LinearandNonlinearNetworks(handouts).pdf - ECE 403...

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1 ECE403 - Fundamentals to Electronics Engineering Spring 2018 - © Morteza Abbasi ECE403 Spring 2018 - © Morteza Abbasi ECE 403 Fundamentals to Electronics Engineering L INEAR AND N ONLINEAR N ETWORKS ECE403 Spring 2018 - © Morteza Abbasi So far we learned that networks can be mathematically modeled by their ports’ current and voltages This description is independent of what is connected to the ports, i.e. the source and the load networks P REVIOUSLY Lecture 2 - Linear and Nonlinear Networks V 1 I 1 V 2 I 2 I 1 = f (V 1 ,V 2 ) I 2 = g (V 1 ,V 2 )

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2 ECE403 - Fundamentals to Electronics Engineering Spring 2018 - © Morteza Abbasi ECE403 Spring 2018 - © Morteza Abbasi E XAMPLE Lecture 2 - Linear and Nonlinear Networks { I 2 = -0.4V 1 + 0.001 V 2 I 1 = (1E-17) e 40xV 1 I 2 I 1 V 1 1k (1E-17) xe 40xV 1 0.4V 1 V 2 ECE403 Spring 2018 - © Morteza Abbasi ECE 403 Fundamentals to Electronics Engineering L INEAR AND N ONLINEAR N ETWORKS Solving Electrical Networks
3 ECE403 - Fundamentals to Electronics Engineering Spring 2018 - © Morteza Abbasi ECE403 Spring 2018 - © Morteza Abbasi A complex electronic circuit may be represented as interconnection of several simpler networks With this arrangement, output current of one network becomes the input current to several other networks C ONNECTING T HINGS T OGETHER Lecture 2 - Linear and Nonlinear Networks V α V β V V Mathematical models of all networks become related! ECE403 Spring 2018 - © Morteza Abbasi V I 50 40 60 0.2A V 2 I 2 V 1 I 1 V I 50 1V E XAMPLE Lecture 2 - Linear and Nonlinear Networks I = 0.02 (V-1) { I 1 = 0.01 (V 1 -V 2 )+0.08 I 2 = 0.01 (V 1 -V 2 )-0.12 I = 0.02 V -I 1 = 0.02 (V 1 -1) V=V 1 I=-I 1 I 2 = 0.02 V 2 V=V 2 I=I 2 I 1 = 0.095 A I 2 = -0.105 A

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4 ECE403 - Fundamentals to Electronics Engineering Spring 2018 - © Morteza Abbasi ECE403 Spring 2018 - © Morteza Abbasi ECE 403 Fundamentals to Electronics Engineering L INEAR AND N ONLINEAR N ETWORKS Solving Electrical Networks Linear and Nonlinear Networks ECE403 Spring 2018 - © Morteza Abbasi A NOTHER E XAMPLE V 1 I 1 50 V 1 I e 40xV 1 1V 1 1E-7x I 1 = 1E-17 x e 40xV 1 I 1 = 0.02 (1-V 1 ) V 1 =V 1 I 1 =I 1 I 1 = -0.02 (V 1 -1) 0.02 (V 1 -1)+ 1E-17 x e =0 40xV 1 How to Solve for V1? Lecture 2 - Linear and Nonlinear Networks