Prelab

1. For each of circuit 1 - 3 calculate the equivalent resistance, equivalent capacitance or inductance, time constant τ, & voltage at τ.

   • Assume a 2VPP square wave as the generator input signal.

   • You may use PSpice or Multisim to do the simulation if you would like to attempt to use the time domain analysis functionality.

     • Use the "Pulse" Source with:

       • V1 = 0V

       • V2 = 2V

       • Time Delay = 0

       • Time to Rise = 0.1ns

       • Time to Fall = 0.1ns

       • Pulse Width = your value for 5τ.

       • Period = your value for 10τ.

     • Add "Voltage Probes" where the channels are shown in the circuit diagrams below.

2. Sketch what you would expect the Vo response to look like for each circuit using your input frequency.

   • Remember, we are looking at the voltages across the inductor and capacitor versus the 2VPP input.

   • Include the input waveform superimposed as a reference.

   • You may use the PSpice or Multisim output for this question, but it is worthwhile verify the result by hand to ensure a proper result.

     • Adjust the scale and number of divisions to show only a period or two, and an accurate value for τ.

3. Use these results to complete the chart below, create a duplicate chart for the experimental results.

4. Be sure to bring a USB key to the lab.

Purpose

To learn how energy storage elements behave in real circuits, and to model their time dependent behavior.

Theory

    Circuits containing capacitors, inductors, and other components with energy storage capability behave differently than simple DC circuits. The behavior of these circuits changes over time, as the conditions present in the elements change. Capacitors accumulate an electric charge, and inductors build a magnetic field. As these processes are occurring energy is absorbed and stored. This will affect the voltage and current that these elements and the others in the circuit experience. As the amount of energy stored changes from none, to some maximum value, the way the element behaves changes as well. 

• Capacitors initially behave as a short circuit, and as charge builds, eventually act as an open circuit when VC = VApplied.

  • Capacitors are measured in Farads, and abbreviated as "C" in schematics. 

• Inductors initially behave as an open circuit, and as the magnetic field builds, eventually act as a short circuit when VL = VApplied.

  • Inductors are measured in Henrys, and are abbreviated as "L" in schematics.

 These effects result in the time dependent behavior of circuits containing capacitors and inductors. The time constant, often represented by tau (τ) offers a way to predict the behavior of these elements over time. In all circuits, the voltage across the element changes by ~63.2% of the VPP after one time constant has elapsed. After 5τ, the voltage across the element changes by over 99% and can be said to be at steady-state relative to the current state.

• For capacitors, τ= Req*CT, where Req is the equivalent Thevenin resistance, and CT is the total capacitance.

  • Capacitors are summed opposite to resistors in circuit:

  • In parallel CT = C1 + C2 ... + ... CN.

  • Capacitors are generally only connected in parallel.

• For inductors τ=   LT/Req  where Req is the equivalent Thevenin resistance, and LT is the total inductance.

  • Inductors are summed similar to resistors in circuit:

  • In series LT = L1 + L2 ... + ... LN.

  • Inductors are generally only connected in series.

• In both cases (L or C) a resistor in parallel with the source element does not alter the Thevenin Resistance or time constant. 

  • Deactivate the source to check this for yourself.

• They WILL change the circuit behavior however.

  • In 6.3 Since both resistors are 1k, you may treat that circuit as though it contains a voltage divider.

    The following lab will use a square wave as the voltage source. The analysis is simplified by considering the square wave a 2-state source, one state ON, and the other OFF. The behavior is simpler than one involving a continuously variable AC source. By calculating the time constants, and setting an appropriate driving frequency (several time constants long), you can compare the voltage in the element under study to the square wave signal. 

Results

1. Include your 3 oscilloscope images and a description of each:

   1. • Which circuit is being analyzed.

      • The frequency of the generator.

      • The Vo at  τ, indicate this point on the image.

      • The Vmax at 5τ, you may estimate, find by inspection, or reference your results here, you don't have to have an oscilloscope image for this.

      • Compare the printout waveforms to the prelab predicted sketch.

2. Calculate the percent that Vo and Vmax reach relative to the 2VPP.

• • Are the percents reasonable compared to the expected ?

  • In the case with the inductors, why does the inductor voltage appear to exceed the voltage supplied? Where does the extra energy come from?

Questions

1. What unit is the result of a: Farad*Ohm, or Henry/Ohm calculation in?

2. How many time constants are required before the voltage across the capacitor or inductor will exactly equal the input voltage ? Explain.