- Overshoot - the maximum amount a signal (usually a voltage) exceeds its steady state value as the circuit transitions to equilibrium. For example, if the maximum voltage is V
_{m}and the steady-state voltage is V_{0}, the percentage overshoot is:OS = (V _{m}/V_{0}- 1) * 100%. - Ringing - the oscillation phenonena that occurs in an underdamped circuit as it approaches equilibrium.

and the homogeneous roots are

s

The current through the capacitor is:

- Make certain that you discharge the capacitors in all series RC & RLC circuits.
- Recall that you will be using the oscilloscope in single-shot mode. The autoscale button eill not be of any use and you will need to select the trigger parameters carefully.
- Remember to discharge capacitors between "shots" in any circuit that doesn;t naturally have a discharge path for the capacitor (e.g. series circuits).
- Switch bouncing, which you learned about during some of the digital labs, can also cause a problems. If ...
- To help with the PSpice simulations (with old version) of the transient circuits, you can download a PSpice example called "lab15.sch". The example has an RC circuit that is deiven lby a 5V battery which is connected to the circuit by a switch (sw_tClose) that closes ar t = 0. The capacitor is shortyed for t < 0 by a 1 W resistor that is disconnected by a switch(sw_tOpen) at t = 0. This is not really necessary for the simulation, but you may nmeed to discharge capacitors between successive attempt during the lab. The simulation is set up to do a transient analysis. Take a careful look at the setup menus to see how this analysis shoud be run. Additional information can be found in the 204 book and in the PSpice references. If when you click on the link you see a text file, you can copy the text file and save it on your computer as "lab15.sch", or you can go back and click on the link with the rigfht mouse button and select "save link as" from the menu.

Lab | R1 | R2 | C1 | C2 | C3 |
---|---|---|---|---|---|

15a | 51 W | 220 W | 4.7 mF | 22 mF | 220 mF |

15b | 220 W | 470 W | 100 nF | 22 mF | 220 mF |

15c | 470 W | 1 kW | 100 nF | 1.0 mF | 220 mF |

15d | 1 kW | 2 kW | 100 nF | 1.0 mF | 4.7 mF |

15e | 33 W | 220 W | 470 pF | 1.8 nF | 10 mF |

15f | 3.3 kW | 4.7 kW | 68 nF | 3.3 mF | 22 mF |

- Draw the wiring diagram for a switched RL circuit powered by a 5 V battery.
- Draw wiring diagrams for a switched RC circuit poweered by a 5 V battery.
- Simulate the circuit in the previous step for R
_{1}and C_{1}. Plot the voltage across the capacitor as a function of time.*Part II - Second-order RLC circuits* - Draw the wiring diagram for a switched RLC circuit powered by a 5V battery. Given the available components, find RLC combinations that are overdamped, underdampped, and critically-damped (1 each).
- Simulate the circuit in the previous step for the underdamped case. Plot the voltage across the capacitor as a function of time.
- Draw the wiring diagram for a switched LC parallel circuit with a series resistance R) powered by a 5 V battery. Given the available components find an RLC combination that is neaerly critically-damped.
- Simulate the circuit in the previous step. Plot the voltae across the the capacitor as a function of time.
that is nearly critically damped.
*Part III - Second-order two-capacitor circuits* - simulate the circuit shown in Fig. 15.8(a) for V
_{1}= 5cos(12pt). Plot the voltages across C_{1}and C_{2}as a function of time. Be certain that initial conditions are correct. What is the maximum voltage on eaxch capacitor and what is the peak voltage in steady-state (on each capaciror)?*Part IV - Resonant charging circuit* - Simulate the circuit in Fig. 15.8(b) assuming that L = 50 mH, C = 22 mF, and the Quality factor (Q) of the inductor is 5 at the circuit's resonant frequency. Plot the voltage on the capacitor as a function of time. Short the diode and repeat the simulation and plot.

During this experiment, be certain that you:*Experimental Procedure:*- Ask the TA questions regarding any procedures about which you are uncertain.
- Turn off all power supplies any time that you make any change to the circuit.
- Arrange your circuit components neatly and in a logical order.
- Compare your breadboards carefully with your circuit diagrams before applying power to the circuit.
- Complete the following tasks:

- Measure the dc resistances of all resistors and inductors to be used in the circuits.
- Measure the inductances and capacitances with the LC meter.
*Part II - First-order circuits* - Construct the switched RL circuit with a 51 W resistor and the 4.7 mH inductor.
- Operate the oscilloscope in triggered mode and plot the voltage across the resistor as a function of time.
- Measure the time constant for the circuit.
- Repeat the previous measurement with the 10 mH, 20 mH and 50 mH incuctors (but do not make additional plots).
- Construct the switched RC circuit with a R
_{2}resistor and the C_{1}capacitor. - Plot the voltage across the capacitor as a function of time.
- Measure the time condtant for the circuit.
- Repeat the prevoius measurement with the C
_{2}and C_{3}capacitors (but don't make more plots).*Part III - Second-order RLC circuits* - Construct the switched RLC series circuit with the values you selected for the underdamped circuit.
- Plot the voltage across the capacitor with time. (Make sure that you choose a time interval greater than the period of the oscillation so that hyou can attempt to measure the oscillation frequency.)
- Repeat the above plot for the overdamped and critically-damped circuits.
- Construct the switched RLC parallel circuit.
- Plot the voltage across the capacitor with time.
*Part IV - Second-order two-capacitor circuit*

*Part V - Resonant-charge circuit*

*Part I - Preliminary measurements*

Generate a lab report following the sample report available in Appendix A. Mention any difficulties encountered during the lab. Describe any results that were unexpected and try to account for the origin of these results(i.e. explain what happened). In ADDITION, answer the following questions/instructions:*Post-lab analysis:*

*Part III - Second-order RLC circuits*

*Part IV - Second-order two-capacitor circuit*

*Part V - Resonant-charge circuit*

*Part II - First-order circuits*