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Unit Step, Pulse, Ramp, and Impulse Functions in Circuits

Explore the characteristics and applications of unit step, pulse, ramp, and impulse functions in circuit analysis. Learn to model switches, describe complex sources, and simulate responses using SPICE software.

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Unit Step, Pulse, Ramp, and Impulse Functions in 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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