12-Non-Linear Circuits

12-Non-Linear Circuits - Nonlinear Circuit Issues &...

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Nonlinear Circuit Issues & Examples I © Fred L. Terry, Jr. all, 2008 Fall, 2008 1
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ome Aspects of Nonlinear Circuits Some Aspects of Nonlinear Circuits KVL & KCL Still Apply pp y – Nonlinear Element Constraints Coupled with Network Constraints Require More Complex Solution Methods ometimes Piecewise Linear Approaches Work • Sometimes Piecewise Linear Approaches Work – Notion of Small Signal Model: Linearization Around an Operating Point (to be discussed in transistor aterial) material) • Possibilities for Multiple Valued Solutions (multiple stable or metastable solutions / non- monotonic I-V relationships) • Negative Feedback Can Improve Linearity armonic eneration Frequency ixing 2 Harmonic Generation & Frequency Mixing
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Example: Finite Gain Op Amp with Non-Linearity Function Chosen to V -,in + - v d V o Yield Linearity for small v d and limit to V CC at high v d Physically Appropriate Model or Bipolar Op- mps V +,in - + f (v d ) For Bipolar Op amps Open Loop V out vs. V d A=10 tanh d C C Av f vV ⎛⎞ = 5 10 out ( ) () , dC CC CC dd d V V If v f v Av A ⎜⎟ ⎝⎠ ± -10 -5 0 V 3 100 15 CC Example A V == -20 -10 0 10 20 V d
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Example: Finite Gain Op Amp with Non-Linearity R 2 Can Still Do KCL Here - + - v d f (v d ) V o +- v in R 1 V - + 4
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Example: Finite Gain Op Amp with Non-Linearity 1 1 R 1 R 2 12 2 1 11 in o d V V V KCL RR R R vV ⎡⎤ + +− = ⎢⎥ ⎣⎦ =− - + + - v d f (v d ) V o +- v in V - () 2 1 1 in V Vf V R R or −− ++
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This note was uploaded on 01/31/2011 for the course EECS 215 taught by Professor Phillips during the Spring '08 term at University of Michigan.

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12-Non-Linear Circuits - Nonlinear Circuit Issues &...

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