DOC PREVIEW
UK EE 211 - Pulse Response - First Order Circuits

This preview shows page 1-2-3 out of 9 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 9 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 9 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 9 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 9 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Pulse Response - First Order CircuitsThe Unit Step FunctionExampleThe Unit Pulse FunctionThe Unit Ramp FunctionThe Unit Impulse FunctionSlide 7SPICE Simulation with Step SourceSPICE Simulation with SwitchKevin D. Donohue, University of Kentucky1Pulse Response - First Order CircuitsUnit Step functions, Pulse Sources, and SPICEKevin D. Donohue, University of Kentucky2The Unit Step Function The unit step function models the behavior of a switch (i.e. off-on) and can be used to describe more complex circuit sources.0for 10for 0)(tttuMultiplying u(t) by a constant changes the value of u(t) for t > 0.Subtracting a positive number from the argument of u(t) shifts the step in the positive t direction.Adding step functions together results in piece-wise steps with the resultant values equal to the sum of step values in each t interval.Kevin D. Donohue, University of Kentucky3ExampleDetermine the unit step response for io(t) the circuit below with input vs(t) = u(t):Show: 0.1 mF10 40 io(t)vs(t) amps40)()1250exp(8.08.0)(steptuttio0 1 2 3 402468101214161820msmaStep ResponseKevin D. Donohue, University of Kentucky4The Unit Pulse FunctionThe unit pulse function is defined as :It can be expressed in terms of a combination of unit step functions:  for 00for 1 0for 0);(TtTttTtv    Ttututv )(-10 -5 0 5 10 1500.20.40.60.811.21.4Pulse Function for T = 5TimeVoltsKevin D. Donohue, University of Kentucky5The Unit Ramp FunctionThe unit ramp function is defined as :It can be expressed as the integral of the unit step: 0for 0for 0)(ttttrtdutr)()(Kevin D. Donohue, University of Kentucky6The Unit Impulse FunctionThe unit impulse function is defined as :It can be expressed as the derivative of the unit step: 0for 00for 0for 0)(ttttdttdut)()( 00)(1 dttNote that:Kevin D. Donohue, University of Kentucky7ExampleDetermine the pulse response for io(t) the circuit below with input vs(t) = 40v(t) V, where pulse duration T is 2 ms:Show: 0.1 mF10 40 io(t)vs(t)    amps)m2())m20(125exp(8.08.0)()0125exp(8.08.0)(pulse tuttuttio   amps)m2(1825.12)()1250exp(8.0)m2()(8.0)(pulse tututtututio0 1 2 3 4 5 6 7 800.10.20.30.40.50.60.70.8Pulse ResponsemsmaKevin D. Donohue, University of Kentucky8SPICE Simulation with Step SourceDo a SPICE Simulation to determine the pulse response for io(t) the Previous circuit with input vs(t) = 40v(t) V, where pulse duration T is 2 ms:To solve you must do a transient analysis, define the voltage source as piece-wise linear, and describe its transient properties. V0R 10 R0 40 C0.0001VAmtranex-Transient-14-TableTIME I(VAM)(s) (Amp)+0.000e+000 +0.000e+000+10.000n +99.999n+10.840n +109.104n: :: :: :+7.285m +972.534u+7.445m +795.710u+7.605m +651.035u+7.765m +532.665u+7.925m +435.817u+8.000m +396.630uI(VAM)Time (s)tranex-Transient-14(Amp)+0.000e+000+500.000m+0.000e+000 +2.000m +4.000m +6.000m +8.000mKevin D. Donohue, University of Kentucky9SPICE Simulation with SwitchDo a SPICE Simulation to determine the pulse response for io(t) the circuit below with input vs(t) = 40 V, where pulse duration T is 2 ms:To solve you must do a transient analysis, define auxiliary circuits for voltage sources and meters that control the opening and closing of the switches.(Amp)V40R040C0.0001R 10 VAmSwitchV1SwitchV0IVmV00V10IVm0I(VAM)Time (s)tranexsw-Transient-0(Amp)+0.000e+000+200.000m+400.000m+600.000m+0.000e+000 +2.000m +4.000m +6.000m


View Full Document

UK EE 211 - Pulse Response - First Order Circuits

Download Pulse Response - First Order Circuits
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Pulse Response - First Order Circuits and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Pulse Response - First Order Circuits 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?