EE101L: Introduction to Electronic Circuits Laboratory. Lab-3: Transient Response of RC/RL Circuits

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EE101L: Introduction to Electronic Circuits Laboratory Lab-3: Transient Response of RC/RL Circuits EE101L-F13, Lab-3 Introduction: This experiment is the first that deals with signals

Read through chapter II of the introductory handout which contains a description of some of the main features of these instruments. This should be helpful in getting started.

1 EE101L: Introduction to Electronic Circuits Laboratory Lab-3: Transient Response of RC/RL Circuits EE101L-F13, Lab-3 Introduction: This experiment is the first that deals with signals (voltages and currents) that change over time. In order to generate and analyze such signals, you will use two more pieces of equipment, the oscilloscope and the function generator. Read through chapter II of the introductory handout which contains a description of some of the main features of these instruments. This should be helpful in getting started. Capacitors come in different forms, here is how they look in real life: It is important to note that some capacitors are polarized and others are not. Below is an example for the polarized capacitor: 1

2 In the experiment, you will use both one-time perturbations of a DC circuit (transients as induced by a switch) and continuously varying signals. As goals of this experiment, at the end of the lab, you will be able to: 1. Understand RC and RL circuits 2. Measure the time dependent response of an RC circuit 3. Measure time dependent signals on the oscilloscope 4. Design an RC transient circuit with desired properties Topics from lecture you need to be familiar with: 1. Capacitors and inductors as energy storing circuit elements 2. Transients in RC/RL circuits 3. RC time constant 4. Simple exponential functions, steady-state values Pre-lab questions (hand in before lab starts): 1. In what form do capacitors and inductors store energy? 2. For a discharging capacitor, what percent of it s original value will it have after 1 time constant ( )? What about 2 time constants ( )? 5 time constants ( )? 3. How do you get a short/long time constant in an RC/RL circuit? 4. How does a capacitor respond to DC voltages? What about an inductor? 5. How does a capacitor respond to AC voltages at an infinite frequency? What about an inductor? 2

3 MainLab-3: Transient Response of RC/RL Circuits First and Last Name: Group (if any): Section Time and Day: 1. Introduction (a paragraph, 10pts) 2. Part-1: RC Circuit Basics 2.1. Basic RC circuit Build the capacitor charging/discharging circuit below. Use a source voltage of 10V. CAUTION: Make sure you connect the capacitor correctly (polarity!). Note: There is a jumper wire that connects A to either point-1 or point-2. We are essentially using it as a switch, so it is drawn on the diagram as such. (a) We want to measure the voltage across the capacitor over time as it charges, so pick a time constant =RC such that we will be able to observe the charge/discharge (around ten second is measurable). You will need to pick a combination of R and C that can be constructed with the parts in your lab kit. Electrolytic (polarized) capacitors work well for this. What combination of R and C can you build? (b) What inductor would you use to obtain the same in an RL circuit? (c) Connect a wire (switch) from A to position-1 and use a watch to record the capacitor voltage VC as a function of time. Use the DMM to read off VC. Then throw the wire (switch) to position-2 and record VC versus t as the capacitor discharges. Designate the moment when you switch to the position-2 as t = 0 for this cycle. Record your values in a table. Plot your data using your favorite spreadsheet (Excel, google docs, openoffice, etc). Include the graph in the report. 3

4 (d) Find the time constant from via the two different graphs (by interpolating t and VC from the 63% of your max voltage. (i) For the charging cycle the capacitor voltage is given by ( ) ( ), and for the discharging cycle it is given by ( ). At t=, ( ) ( ) for the charging cycle, and ( ) ( ) for the discharging cycle. Determine the RC time constant of the circuit which is equal to the time after which the voltage has dropped to 37% of its original value (discharging cycle) or risen to 63% of its final value (charging cycle). (ii) Another way to determine the time constant for the discharging cycle is to plot the same data on a semi-log scale, i.e., plot { ( )} (natural log) versus t, because we can rewrite the equation for the capacitor voltage as { ( )} { }. This is the equation for a straight line and its slope can be found easily and accurately. Find the from this graph. Can you find the for the charging cycle in a similar way? (e) Compare your measured value for the time constant with your initial calculation. Discuss possible reasons for discrepancies. (f) One main reason for inaccuracies is the finite internal resistance of the DMM, RD. With an introduction of the RD, your circuit actually looks more like this: Calculate the time constant of this modified circuit. Can you determine the internal resistance of the DMM from your measured data? Consider how the circuit behaves in steady state after charging. 4

5 (g) In order to minimize the effect of RD, do you have to increase or decrease the series resistor R? (h) Try replacing your DMM with the oscilloscope. Use the oscilloscope to view a graph of the charging and discharging of the capacitor. This may be easier if you make your time constant smaller. (i) Try out different values for R and C and observe the effects on how fast the circuit charges or discharges. You do not have to plot your results, but describe qualitatively what you observe Transient response on the oscilloscope Please study the Oscilloscope guided tour provided on pages 7-9 before starting this part. (a) Replace your circuit elements with R=22K and C=1 F. Calculate the new time constant. (b) You will no longer be able to use a watch and need to use the oscilloscope instead. The scope replaces the DMM in your circuit. (c) Replace the DMM with the scope. Use channel-1 across points-a and -B and channel-2 for VC. Start with a sweep rate of 20 ms/div on the scope. Set the input coupling to DC and triggering to AUTO. Throw the switch (wire) back and forth and describe what you see on the scope. (d) Replace the circuit to the left of A and B with the function generator. Set the generator to output a square wave with a period of 6. Set the scope s trigger to channel-1 and the triggering slope to positive. Observe the signal voltage V from the function generator on channel-1 and VC on channel-2. Determine the time constant from the scope image. (e) Increase the frequency of the square wave signal. Adjust the time scale on the scope such that you see 2-3 periods of the applied signal on the screen. Observe VC for each frequency and compare VC and V. What happens as the frequency increases? Why? 5

6 3. Part-2: Design of an RC circuit In this part of the lab, you will design an RC circuit with a given time constant. Your design does not have to hit the target time constant exactly (even though that is possible), but the closer you get, the better. (a) Using one of your light bulbs (rating: 1.5V), a 10 V DC source, a capacitor, and other resistors if necessary, design an RC circuit which has the following properties: With the switch closed, the power dissipation in the bulb is 30 mw. Assume a light bulb resistance of RL = 30. As the switch is opened, the capacitor voltage decreases with a time constant of = 30ms. (Hint: These properties give you two conditions from which you can determine your required circuit element values C and R.) Your circuit diagram should look somewhat like this: (b) Draw the circuit diagram for your design and explain your reasoning for the choice of circuit elements. (c) Build the circuit and verify it operates as desired. Specifically: Determine the bulb power with the switch closed. Measure the time constant by monitoring the capacitor voltage on the oscilloscope. Plot VC versus t. Measure the time constant by monitoring the light bulb voltage VL. Plot VL versus t. Why is there a difference in the time constants for VL(t) and VC(t)? Think back to the Part-1. What happens to the light bulb brightness immediately after the switch is opened? Explain. 4. Conclusion (10pts) 6

7 Oscilloscope Guide: EE101L-F13, Lab-3 7

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UC Berkeley, EECS Department

UC Berkeley, EECS Department B. Boser EECS 4 Lab LAB5: Boost Voltage Supply UID: Boost Converters We have tried to use resistors (voltage dividers) to transform voltages but found that these solutions