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Pulse Response - First Order Circuits

Pulse Response - First Order Circuits. Unit Step functions, Pulse Sources, and SPICE. The 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.

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Pulse Response - First Order Circuits

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  1. Pulse Response - First Order Circuits Unit Step functions, Pulse Sources, and SPICE Kevin D. Donohue, University of Kentucky

  2. The 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. • 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 Kentucky

  3. Example Determine the unit step response for io(t) the circuit below with input vs(t) = u(t): Show: Kevin D. Donohue, University of Kentucky

  4. The Unit Pulse Function The unit pulse function is defined as : It can be expressed in terms of a combination of unit step functions: Kevin D. Donohue, University of Kentucky

  5. The Unit Ramp Function The unit ramp function is defined as : It can be expressed as the integral of the unit step: Kevin D. Donohue, University of Kentucky

  6. The Unit Impulse Function The unit impulse function is defined as : It can be expressed as the derivative of the unit step: Note that: Kevin D. Donohue, University of Kentucky

  7. Example Determine the pulse response for io(t) the circuit below with input vs(t) = 40v(t) V, where pulse duration T is 2 ms: Show: Kevin D. Donohue, University of Kentucky

  8. SPICE Simulation with Step Source Do 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. tranex-Transient-14-Table TIME 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 +396.630u tranex-Transient-14 Time (s) +0.000e+000 +2.000m +4.000m +6.000m +8.000m (Amp) +500.000m +0.000e+000 I(VAM) Kevin D. Donohue, University of Kentucky

  9. SPICE Simulation with Switch Do 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) Kevin D. Donohue, University of Kentucky

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