EE

215 - Laboratory 4 - First Order Circuits

Introduction The objectives the objectives of the first part of this lab are to confirm the steady state model of capacitors and inductors and determine time constants from observed data. For the second part of this lab, you are able to use an op amp as a comparator and determine inductance from time response. The objectives of the third procedure of this lab are to design, construct a time delay circuits using RC time constants. New Part for This Lab The only new part used in this lab is the Single Pole Double Throw (SPDT) switch. Single Pole means that there is only one moving switch arm. Double Throw means that the arm can connect to two different nodes. Figure 1 shows the circuit symbol for an SPDT switch. The switch is a black rectangular slide switch with three prongs. The prongs fit into breadboard holes. When the slide knob is at one end of the switch, the center prong is connected to the prong at that end, and the prong at the other end is unconnected (an open circuit). Comments See Laboratory 1 for information on obtaining a laboratory parts kit and multimeter, and for identifying many of the parts used in Laboratory. (New part for this lab is introduced later.) For each procedure set up the circuits and record your data and the answers to questions on a separate sheet(s) of paper and hand it in at recitation section when the lab is due. For procedure 3, you will also have to bring your breadboard with designated circuits on it to your recitation section the week the lab is due. Note: If you do not show your TA your circuit from part 3, your grade for this procedure is zero.

Figure 1 - SPDT Switch Circuit Symbol

Procedure 1: RC Circuit (30 points) Comment Check that the electrolytic capacitor in this circuit is connected with the correct polarity. The negative lead is the short one, marked "-" on the side of the capacitor package.

1.a (2 points) Set-up Construct the circuit of Figure P1-1. Have the switch in the position (1) for the long time. Measurements and calculations Compute the value of capacitor voltage vc . Measure vc. Compare your measured and calculated values of vc. 1.b (3 points) More set-up Construct the circuit of Figure P1-1. Have the switch in the position (2) for the long time.

Measurements and calculations Compute the value of capacitor voltage vc . Measure vc. Compare your measured and calculated values of vc. How long is "a long time" for this circuit? 1.c (15 points) Comment Prepare to write down the value of vc every 15 seconds. This is easiest using alligator clips and monitoring voltage continuously. More set-up Construct the circuit of Figure P1-1. Have the switch in position (1) for a long time. Switch it to the down position (2) and simultaneously start timing.

Measurements and calculations Record the value of vc every 15 seconds for three minutes. (For example, throw the switch when the second hand on a watch is at zero seconds, or at the same time as the stopwatch feature on a digital watch is started.) Time (Sec) vc 0 15 30 45 60 75 90 105 120 135 150 165 180

 Graph the voltage values. Characterize the graph - is it linear, quadratic, or exponential? Determine the circuit time constant from the graph. (Refer to the hint below for more information.) Calculate the ideal time constant using nominal component values. Find the % error between the ideal and measured values.

1.d (10 points) More Set-up Construct the circuit of Figure P1-1. Have the switch in position (2) for a long time. Switch it to the down position (1) and simultaneously start timing.

Measurements and calculations Record the value of vc every 15 seconds for three minutes. Time (Sec) vc 0 15 30 45 60 75 90 105 120 135 150 165 180

Hint: Graph the voltage values. Characterize the graph - is it linear, quadratic, or exponential? Determine the circuit time constant from the graph. (Refer to the hint below for more information.) Calculate the ideal time constant using nominal component values. Find the % error between the ideal and measured values.

There are a variety of methods for determining the time constant from a graph of time response. These include: Drawing a tangent to the response at t = 0. This intersects the final steady state value at the time constant . While fine for ideal circuits, the rapid change at t = 0 can produce a lot of error in the calculation for actual circuits. Solving the equation of the response using two points from the response curve. Suppose the response is of the form . Choose two points where v and t are known, and solve for A and . The points can be chosen to minimize error, typically at 90% and 10% of total response. For example, if the initial voltage was 10V and the final voltage was 0, points with voltages near 9V and 1V would be used. Note that A can be eliminated by dividing the equations for the two points

 Procedure 2: RC Circuit (30 points) 2.a (5 points) Set-up Use 100 mH inductor provided in your lab kit. Have your multimeter for measurements. Measurements and calculations Measure the DC resistance of the inductor. Draw a model for the real inductor that includes this resistance. Compute the maximum time constant for this component. Do you think you could see the change of current with time with your multimeter? 2.b(25 points) Simulated inductor circuit: An inductor time constant that is long enough to see with a multimeter requires a very large, heavy and expensive inductor. The problem of inductor size also challenges integrated circuit designers. It is very difficult to put an inductor into an integrated circuit. Fortunately, there is an op amp circuit called a simulated inductor, which uses an op amp, two resistors, and a capacitor to produce a branch relationship similar to an inductor. The circuit is shown in figure P2-1. Don't worry too much about how it works, just build it! (Although you should have the tools to figure out how it works. Think of this, as a challenge.)

 Comment Simulated inductors have some limitations. First, one terminal has to be at the neutral, (the - terminal in figure P2-2) which limits the types of circuits that can be created (but is fine for us). Second, op amp saturation limits the range of response. Third, there can be initialization issues. Also, problems getting the simulated inductor to work are often due to the op amp power supply. Remember that the +9V and 9V supplies are with reference to the neutral, or ground, node, so the 9V batteries must be connected at one end to the ground node. See Lab 3 for a circuit diagram showing specific power supply connections. Set-up Build the circuit of Figure P2-2 using the simulated inductor you built in step 2a. Note that the battery in P2-2 is also the +9V supply for the op amp. (You may want to use an extra +9V battery.) Have your multimeter for measurements.

Measurements and calculations Comment Measure the current, either directly with your multimeter or by observing the voltage across the 1 resistor. (Use the measured resistance value of the 1 resistor for current calculations.) After the switch has been in the down position (2) long enough (until it is less than 7 mA), move the switch to the up position (1). Measure the inductor current iL and voltage vL. After the switch has been in the up position (1) long enough for inductor current to stabilize (be constant), measure and record the inductor current iL and voltage vL. Now move the switch to the down position and record the value of iL every 15 seconds for three minutes. Time 0 15 30 45 60 75 90 105 120 135 150 165 180 (Sec) iL

Graph the current values. Characterize the graph - is it linear, quadratic, or exponential? Determine the circuit time constant from the graph. Determine the inductance of the simulated inductor from the time constant, the resistors in the circuit, and the internal resistance of the inductor measured in step 2.b (iii).

Procedure 3: Design with Time Constants (40 points) Many systems are designed to have actions occur after a time delay. Consider a car alarm, for example, that senses motion by closing a switch. If the alarm goes off the instant the switch is closed,

there would be a lot of false alarms. On the other hand, once the alarm is on, it should stay on for some time after the motion stops and the switch opens, to encourage the bad guys to leave. In this design, the manual switch will simulate the motion sensor. (A real motion sensor would probably make intermittent contact while moving, while the manual switch will stay open or closed when switched, so the manual switch is an approximation.) Most switch-type sensors are single throw, that is, they are either open or closed, rather than having two contacts like the manual switch in the lab kit. That's because SPST is cheaper than SPDT. You can use the lab kit SPDT switch as an SPST switch by not connecting one of the contacts. The part of car alarm, will be played by a comparator circuit (Figure P3-1). A comparator compares two voltages (hence the name). If the first voltage is higher than the second, the comparator output saturates high, near +Vcc. If the second voltage is higher than the first, the comparator output saturates low, near -Vcc. Thus the comparator converts an analog voltage (one that can take on an infinite number of values) into a digital one (high or low, 1 or 0, on or off). A comparator is a simple form of an analog-to-digital converter (ADC).

3.a (5 points) Set-up Construct the circuit of figure P3-1. Adjust the 100 K pot to vary V-. Adjust the 10 K pot to vary vin.

Measurements and calculations Complete Table below. V- vin Expected LED State Observed LED State

3.0 V 3.0 V 6.0 V 6.0 V

2.9 V 3.1 V 3.1 V 8.0 V

Measure the low limit of the comparator sensitivity. (Turn vin all the way down to 0 V, and lower V- until the LED turns on. Measure the value of V-. Compare to vin) Measure the high limit of the comparator sensitivity. (Turn vin all the way up to battery voltage and raise V- until the LED goes out. Measure the value of V-.)

3.b (30points) Set-up Design a car alarm time delay circuit to the following requirements: The output of your time delay circuit will be the input (vin) to the comparator circuit of step 3.a. Replace the 10 K potentiometer with your time delay circuit. You may choose a value for the comparator voltage setpoint and use the 100 K potentiometer to set it. (In a real design you would of course use a voltage divider for this function, but this design focuses on the time constants.) The "alarm" in this design is the LED. When it is brightly lit, the alarm is on. When the LED is dark, the alarm is off. The input to your circuit is a 9V battery in series with a SPST switch. When the switch has been open for a long time, and is closed, there should be a 10 second delay before the alarm picks up (turns on). When the switch has been closed for a long time, and then opened, there should be a 4 second delay before the alarm resets (turns off). Use parts from your lab for the design.

Measurements and calculations Submit the circuit diagram of your design with all values noted. Note-The comparator can be shown as a block diagram. However, note the comparator voltage set point. Submit design calculations showing how you arrived at your component values. Measure and record the on and off times you obtained.

*Modifications: Lab modified in week of Feb20, 2011 by Nava Aghdasi