Lab #6
Transients in First Order Reactive Systems

Purpose
To become familiar with transient behavior of first order circuits. This response is discussed in Section 8.3 of your textbook.

Pre-Lab
1. Calculate τ, V_o @ t = τ, 5τ, and frequency for 1/(10τ), for Circuit 1, Circuit 2, Circuit 3, and  Circuit 4. (V_o is the voltage across C₁ or L₁ depending on the circuit.) Section 7.5 & 7.6 (in  the text) discusses the Natural and Forced Response that you are looking for here. Once the current is found, V_o can be determined by Ohms Law (V_o = V_L = V_S - I_L*R_TH). We will be using a 2V_PP square wave input signal, so use a 2V step input  for V_S when calculating V_o in the second column below. Section 8.9 discusses how PSpice can be used to predict the response of the circuits.

Above f is the frequency for the square wave signal you will use in the lab.

2. Sketch what you would expect V_o to look like for 1-2 and 2-1. Remember, we are looking at the voltages across the inductor and capacitor.

3. Calculate the steady state input resistance (eg. what the generator "sees") of Circuit 5 (assuming L₁ has a DC resistance of 0Ω).

4. Print  Gradicules.pdf for sketching the waveforms in the lab.

Equipment
Proto Board
Short pieces of wire
Resistors (two - 100kΩ, three - 220Ω, one - 68Ω) (resistor color code)
Capacitors (two - 0.01µF)
Inductors (one - 25mH)
Multimeter
Function Generator
Oscilloscope

Note: In order to study the transient response of reactive systems, we will be exciting the circuits with a square wave (eg. a repetitive step voltage). The frequency of the square wave will be chosen to be low enough as to give the circuit being tested long enough to reach 99.3% of its steady state value, which is a time duration equal to 5τ where τ is the time constant of the circuit.

Procedure

1. Transients in R-C Circuits
1-1. Construct the RC circuit labeled Circuit 1. Show me 
Apply a 2Vpp (2V peak to peak) square wave with the frequency calculated in the Pre-Lab. Show me Connect the output from the function generator to both the circuit and channel 1 (CH1) on the oscilloscope. Connect the output from the circuit (the voltage across the capacitor C₁) to channel 2 (CH2) on the oscilloscope.

1-2. Using the oscilloscope, observe the applied voltage on channel 1 and the voltage across the capacitor C₁ on channel 2. Carefully sketch the waveforms (using Gradicules.doc that you printed in the Pre-Lab) and measure τ. Show me

1-3. Add C₂ to the circuit as shown in Circuit 2, adjust the frequency to that calculated in the Pre-Lab and reset the function generator to 2Vpp. Carefully sketch the new waveforms and measure τ. 

1-4. Add R₂ to the circuit as shown in Circuit 3, adjust the frequency to that calculated in the Pre-Lab and reset the function generator to 2Vpp. Carefully sketch the new  waveforms and measure τ. 

2. Transients in R-L Circuits
2-1. Construct the RL circuit labeled Circuit 4. Show me 
Note: R₄ is needed in the circuit because the function generator does not like to drive an inductive load. The 68Ω resistor allows the function generator to "see" a (mostly) resistive load.
Apply a 2Vpp (2V peak to peak) square wave with the frequency calculated in the Pre-Lab. Connect the output from the function generator to both the circuit and channel 1 (CH1) on the oscilloscope. Connect the output from the circuit (the voltage across the inductor L₁) to channel 2 (CH2) on the oscilloscope. Observe the applied voltage and the voltage across the inductor. Carefully sketch the waveforms and measure τ. Show me

2-2. Add R₃ to the circuit as shown in Circuit 5, adjust the frequency to 1/2 that used for Circuit 4 and reset the function generator output to 2Vpp. Carefully sketch the new waveforms and measure τ.

2-3. Disconnect the generator and measure the input resistance of the circuit shown in Circuit 5 using a multimeter. Show me how

Analysis
1. Carefully sketch the observed waveforms and indicate horizontal and vertical scales.

2. Indicate the time constants (τ's) on the response curves above.

3. Compare the calculated values of τ with the experimental values of τ.

4. Why was 1/(10τ) used and not 1/(5τ), since after 5τ the voltage has reached 99.3% of the steady state value?

5. How does the calculated input resistance of Circuit 5 compare with the measured resistance of 2-3? The output impedance (R_TH)of the function generator is about 50Ω. What could you say about how the circuit in Circuit 5 is loading the generator (power transfer wise)?

6. Were the sketched waveforms similar to what you sketched in the Pre-Lab? Explain.

7. Use PSpice to simulate the step response of the voltage across the inductor Circuit 5. In PSpice, you can simulate a repetitive step response with a VPULSE with the attributes in Figure 1. Figure 2 describes what the attributes of the VPULSE are. Print the response of V_RL and V_SRC. (Note: V_RL is the voltage at the Net Alias RL in Circuit 5. To add a Net Alias press the icon (located on the right had side of Orcad Capture) and follow the menus.

To see simulated response seen in Photo 3:

• In Orcad Capture, choose PSpice/New Simulation ProfileIn
• Under Analysis Type choose TimeDomain(Transient)
• In Run To Time put 2.4ms to have the simulation last for 3 cycles (3 * 0.8 ms)
• Click OK
• Choose PSpice/Run or click  (the Run Icon)
• The PSpice window should now open with the blank black display area in Photo 4
• Choose Trace/Add Trace... and then click on V(RL) and V(SRC) to choose these voltages to display. (These Net Aliases ware added, to the circuit, to make it much easier to find the nodes we want to display.)
• Use the File/Print... menu option in PSpice to print the response instead of using the <PrntScr> key to capture the image for the report as  it uses way too much black ink.