1 / 24

Sensitivity Analysis by Adjoint Network

CSE 245: Computer Aided Circuit Simulation and Verification. Sensitivity Analysis by Adjoint Network. CK Cheng. Outline. Tellegen’s Theorem Resistive Network Dynamic System. Tellegen’s Theorem . Tellegen’s Theorem: For a vector of branch voltages and branch currents, we have .

bona
Download Presentation

Sensitivity Analysis by Adjoint Network

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CSE 245: Computer Aided Circuit Simulation and Verification Sensitivity Analysis by Adjoint Network CK Cheng

  2. Outline • Tellegen’s Theorem • Resistive Network • Dynamic System

  3. Tellegen’s Theorem Tellegen’s Theorem: For a vector of branch voltages and branch currents, we have

  4. Tellegen’s Theorem I. 1 3 4 2

  5. Tellegen’s Theorem (con’t) I. 1 3 4 2

  6. Tellegen’s Theorem (con’t) II. Example: Two circuits with the same topology 1 (2v) 1 (0v) 3 (3v) 3 (-1v) 1 -2 0 -1 4 (1v) 4 (3v) -1 2 1 -1 0 -1 -1 2 2 (4v) 2 (2v)

  7. Tellegen’s Theorem (con’t) II. Example case: Two circuits with the same topology

  8. Outline • Tellegen’s Theorem • Resistive Network • Dynamic System

  9. Resistive Network • Metric • A: branch voltage • B: branch current • Sensitivity Calculation • D is the set of resistance ib R Vb

  10. Example of Sensitivity Calculation Given circuit i2 v1 R’’’ i3 R’’ + _ R’=R+∆R y=v1 + 2i2 + 4i3

  11. Adjoint Network for Resistive Network original network adjoint network -fk _ + Vk R+∆R R gk ik + _

  12. Adjoint Network for Resistive Network (con’t) For set A (branch voltage), original network adjoint network -fk _ + vk

  13. Adjoint Network for Resistive Network (con’t) For set B (branch current), original network adjoint network gk ik + _

  14. Adjoint Network for Resistive Network (con’t) For set D (resistance), original network adjoint network R+∆R R

  15. Put it together… y

  16. Outline • Tellegen’s Theorem • Resistive Network • Dynamic System

  17. Dynamic System • Metric • A: branch voltage • B: branch current • Sensitivity Calculation • D is the set of resistance • E is the set of capacitance ib(t) R Vb(t) C L We omit L here which is similar to C

  18. Adjoint Network for Dynamic System original network adjoint network -fk(T- t) _ + vk(t) R+∆R R C+ ∆ C C L+ ∆ L L gk(T- t) ik(t) + _

  19. Adjoint Network for Dynamic System (con’t) For set A (branch voltage), original network adjoint network -fk(T- t) _ + vk(t)

  20. Adjoint Network for Dynamic System (con’t) For set B (branch current), original network adjoint network gk(T- t) ik(t) + _

  21. Adjoint Network for Dynamic System (con’t) For set D (resistance), original network adjoint network R+∆R R

  22. Adjoint Network for Dynamic System (con’t) For set E (capacitance), original network adjoint network C+ ∆ C C

  23. Adjoint Network for Dynamic System (con’t) For set E (capacitance), cancellation overall

  24. Put it together… The initial voltage of the capacitor remains fixed when other element parameters vary. Thus, delta vk(0)=0.

More Related