EEL 5245 POWER ELECTRONICS I

Lecture #6: Chapter 3 Refresher on Series/Parallel RLC

w/ Diff. Eq. Solution

EEL 5245 Objectives

•  Provide Students an Understanding of Why Diode Switching with RLC Circuits is Covered in EEL 5245

•  Give Students and Idea of What They Should be Able to Solve After this the Material is Covered

•  Refresh Student’s Memory on Diff. Eq. Solution of RLC Circuits –  First Order Circuits –  Second Order Circuits

•  Parallel RLC •  Series RLC •  Initial and Final Conditions

EEL 5245 Why Cover this Material?

•  Analysis of Basic RLC Circuits with switching devices (diodes and SCRs) provides students with the fundamental concepts and process that go into the analysis of the more complicated converters in power electronics –  Mode by mode analysis –  Energy Transfer/Exchange Concepts

•  Initial Conditions •  Resonance

–  Energy Conservation –  Current Commutation –  Simulation of Switching Functions

EEL 5245 Goals of Ch. 3 Switching Concepts

•  Analyze any 1st or 2nd Order Circuit which includes switches, diodes, SCRs, or any combination of those items –  Follow a step by step process taking each circuit

configuration or “mode” in turn, noting: •  Time interval mode is valid •  Circuit configuration during mode

–  Which switches, diodes, SCRs are on which are off •  Closed form expressions for variables of interest

–  State Variables (inductor current, capacitor voltage or converter parameter derived from these

•  Initial and Final Conditions of State Variables •  Finish with a clear statement regarding when the mode your

working with ends (time), the reason it has ended, and the switch state configuration that will occur when it does

EEL 5245 Form of Lectures 6-9

•  Will be a combination of hand written mathematics, PSPICE and MathCAD results on paper, and live simulation

•  Hand written notes on lecture materials might not be present on scanned, Website versions, so make sure you note any key points

•  Many examples worked in detail •  Due to number of lengthy examples and limited available

time, we may only cover significant detail on some examples, all detail in others

•  Predominately line by line mathematics development, so if you miss a fundamental concept ask for clarification before we get to far ahead

EEL 5245 Parallel RLC Example-Verification

t 0 .0001, .03..:=

Vc t( ) 100− e 200− t⋅⋅ sin 980 t⋅( )⋅:=

0 0.005 0.01 0.015 0.02 0.025 0.03100

50

0

5039.022

74.09−

V c t( )

0.030 t

EEL 5245 Series RLC Example-Verification

EEL 5245 Example: Natural Response of R-L Circuit

EEL 5245 Step Response Of Parallel RLC

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EEL 5245 Series RLC Example – DC Source

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EEL 5245 Example: Step Response of Series RLC

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EEL 5245 Example: Series RLC

EEL 5245 Series RLC Example-Verification

t 0 .0001, .005..:=

Vc t( ) 48 48 e 1400− t⋅⋅ cos 4800 t⋅( )⋅− 14e 1400− t⋅ sin 4800 t⋅( )⋅−:=

0 0.001 0.002 0.003 0.004 0.0050

20

40

60

80

Vc t( )

t

Vc t( ) 48 48 e 1400− t⋅⋅ cos 4800 t⋅( )⋅− 14e 1400− t⋅ sin 4800 t⋅( )⋅−:=

0 0.001 0.002 0.003 0.004 0.0050

20

40

60

8066.725

0

V c t( )

5 10 3−×0 t

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EEL 5245 Example: Series RLC - Current

EEL 5245 Series RLC Example-Verification

t 0 .0001, .005..:=

ic t( ) .1 e 1400− t⋅⋅ sin 4800 t⋅( )⋅:=

0 0.001 0.002 0.003 0.004 0.0050.04

0.02

0

0.02

0.04

0.06

0.08

ic t( )

t

Series RLC ExampleCurrent

ic t( ) .1 e 1400− t⋅⋅ sin 4800 t⋅( )⋅:=

0 0.001 0.002 0.003 0.004 0.0050.04

0.02

0

0.02

0.04

0.06

0.080.065

0.026−

i c t( )

5 10 3−×0 t