E11 Lab #3
2004

Lab report due the next time you come to lab.

Before you start this lab, be sure to read the lab rules.

First Order Time Domain Response

This laboratory exercise will familiarize you with the time response of first order circuits.  You will be analyzing a wide variety of circuits, so if you can come up with a common framework for the analysis, your work will be much easier.   I suggest you read 195-197 of your text.  If you follow the procedure listed there, your analysis will be much easier.

This lab has a full write-up.  You should review the format required before writing your report.

## Before you begin:

Measuring time constants with the digital scopes

To measure the time constant of a signal, you can follow this procedure:

1.) Get an image similar to the one below, which shows the input at the top of the screen, and the output at the bottom.

2.) Put voltage cursor #1 (bottom cursor=43.75mV) so that it measures the steady-state voltage of the output, and put cursor #2 so that it measures the initial voltage (top cursor=1.000V).  Make sure you record these values, you will need them in your report.  Also make sure that the cursors are set to measure from the appropriate channel (channel 2 in the image above).

3.) Note the value of DV.  The time constant occurs when the voltage difference is equal to e-1 (or 37%) of this value.  In this image DV=956.2mV, so the time constant will occur when this difference decreases to 352mV.

4.) Move voltage cursor #2 until the voltage difference is the value calculated in the previous step.  This is shown by the yellow marking labelled DV in the image below.

5.) The time constant is equal to the difference in time between t=0 (when the input changes), and when the voltage difference has been reduced to 37% of its original value.  Use the time cursors (as shown above) to measure the time constant (1.080 seconds in this image).  Make sure you record this value as well.  Note that I expanded the time scale from the previous image to get a more accurate measurement.

The 555 timer/oscillator

In this lab you will be using an integrated circuit that is new to you, the 555 timer (datasheet) which can use first order circuits to make oscillators.   A block diagram (from the datasheet) is shown below,

but you needn't concern yourself with what is inside.  Here is a connection diagram to make the device work as an oscillator (from the datasheet).

For our purposes we can model the device as shown below.  The pins on the integrated circuit (1 through 8) are shown in dark green.  Voltages important for analysis are shown in red.  Note R1, R2, R3 and the switch are internal to the device.  We add RA, RB, C and the speaker (in addition to Vcc and ground).

As far as we are concerned there are only three facts that are necessary to understand how this circuit works.

1. If the voltage Vc is greater than V2, the switch closes.

2. If the voltage Vc is less than V1, the switch opens.

3. If the voltage Vc is between V1 and V2, the switch does not change states.

If you hook up the circuit as shown, the voltages on pin 3 (attached to the speaker) and pins 2 & 6 (labeled Vc) look like this (from datasheet):

When the voltage Vc (lower trace) is between V1 (1.67 volts) and V2 (3.33 volts) and the switch is open the capacitor charges with a time constant of (Ra+Rb)C.  When the voltage gets to V2 (3.33 volts) the switch closes and the voltage drops with a time constant of RbC.  When the voltage drops to V1 (1.67 volts) the switch opens and the capacitor charges ...

It can be shown the the time that the output is high (Vc rising) is given by:

The time the output is low (Vc falling) is given by:

The frequency of oscillation is given by:

In deriving these equations consider the following:

• to find T1, let t=0 be the time at which the output just goes high.

• What is Vc(0)?

• What would be the forced value of Vc (i.e., Vc(t) as t goes to infinity))?

• What is the time constant.

• T1 is defined by Vc(T1)=Vcc*2/3.

• to find T2, let t=0 be the time at which the output just goes low.

• What is Vc(0)?

• What would be the forced value of Vc (i.e., Vc(t) as t goes to infinity))?

• What is the time constant.

• T2 is defined by Vc(T2)=Vcc*1/3.

Setting up the function generator

Connect your signal generator directly to the oscilloscope.  Set the output of the signal generator to give a square wave that goes from 0 to 1 volt (the frequency isn't important for now).  If you don't get this correct your analysis will be much more difficult.  If you are not sure you have it set properly, ask me.  If you don't recall how to do this, refer to the first lab.  After setting the amplitude and DC offset, don't adjust these knobs for the remainder of the lab.

To analyze some of the circuits you will need to consider the internal impedance of the function generator.  The Thevenin equivalent of the function generator is an ideal voltage source, Vs, in series with a 600 W resistor.  In some of the circuits below, the resistor will affect your measurements. This is depicted in the diagram below.

## Procedure:

### Circuit 1: A 1st order RC circuit.

Remember: Don't change the amplitude or DC offset of the function generator!

Connect the circuit below with Vi coming from the function generator, R=1kW, C=1mF, and your function generator set to about 50 Hz (the exact frequency isn't important).  For this circuit it is easier to use the large resistor and capacitor boxes than it is to use the breadboards.

1. Set the triggering so that a falling edge of the input is at the center of the screen (trigger on the input, slope set to falling edge)  and set your scales as large as is convenient so that you can get an accurate measurement.  Measure and record the time constant and initial and final values of the output and of the input.  Print the screen of the oscilloscope showing both the input and the output.
2. Double the resistance and repeat the measurement of time constant and initial and final values of voltage (you don't need to print the oscilloscope screen).
3. Set the resistance to its original value.  Predict and then observe the output if the capacitance is doubled.   No measurements or recording necessary.
4. Put the resistance and capacitance back to the original values.  Set the triggering so that a rising edge of the input is at the center of the screen, and repeat part a.

### Circuit 2:  A 1st order LR circuit -- This circuit is optional; you may continue to Circuit 3.

Remember: Don't change the amplitude or DC offset of the function generator!

Connect the circuit below with Vi coming from the function generator, R=1kW, L=112mH, and your function generator set to a frequency that allows the output to come to steady-state before the input changes. Set the triggering so that a falling edge of the input is at the center of the screen, and set your scales as large as possible so that you can get an accurate measurement.

1. Print the screen of the oscilloscope showing both the input and the output.   Measure and record the time constant and initial and final values of the output and of the input when the input is at a rising edge.
2. Predict and then observe the output if the resistance is doubled.   No measurements or recording necessary.

### Circuit 3:  The 555 Oscillator - another application of RC circuits

In the last lab you used an RC circuit to demodulate an AM signal.  This week, we'll use an RC circuit to create an oscillator with the help of an LM555 timer. Hook up the oscillator circuit with RA=33 kOhm,  RB=20 kOhm and C=0.1 uF.  Use Vcc=5 V.  The circuit is repeated below for your convenience. Note that I have put the output of the LM555 through a 1k potentiometer (located on the bottom of your breadboard) so you can control the volume.

 RA=33 kOhm RB=20 kOhm C=0.1 uF Vcc=5 V

What do you hear from the speaker?  (If you don't hear anything try turning the potentiometer)  Observe pin 6 and pin 3 on the oscilloscope and get a printout.  Measure and record the frequency of oscillation.  Make sure you understand why the circuit oscillates.

Try this - put your fingers across the leads of the capacitor or the resistors.  What happens?

A siren's song -- this section is optional.

Let's spice up the circuit a little bit.  Measure the voltage on pin 5.  It should be about 3.33 volts.  We are going to use the signal generator to raise and lower this voltage.  Carefully set up your Wavetek signal generator with a 1 V peak-peak triangle wave at 500 Hz with a DC offset of about 3.33 volts.  If you can't quite get down to 1 V, that's find -- just make the peak-to-peak voltage as close to 1 V as you can.  It is important that you get this right -- if you are not sure, ask me to help you.  Change the frequency to 0.5 Hz (without changing any other controls).

After you have set the controls, attach the Wavetek generator to pin 5 of the LM555.  What do you hear?  Is the frequency increasing as the voltage on pin 5 increases or as it decreases?  Why?  Try looking at the voltage on pin 6 (Vc) and try to understand what is happening by refering to the diagram below.

Recall:

1. If the voltage Vc is greater than V2, the switch closes.

2. If the voltage Vc is less than V1, the switch opens.

3. If the voltage Vc is between V1 and V2, the switch does not change states.

You don't need to do any calculations here, but you should understand qualitatively what is going on.

## Before You Leave

Make sure the lab is cleaned up, and that you have all the information you will need for your report (see below).  Make sure the resistors are put back in the proper drawers -- either measure them with an ohmmeter, or read the color-code (how to read the color-code).

This lab has a full report so you should review the foraml lab format. Your report should include, at least, all the information listed below in the context of the formal lab write-up .   The report should be well-organized and coherent.

• In the theory section:
• Circuit 1:  In the theory section, derive expressions for the initial and final values of the voltages, and the associated time constants for each part of the circuit.
• Circuit 2:  In the theory section, derive expressions for the initial and final values of the voltages, and the associated time constants for each part of the circuit.  This circuit was optional.
• Circuit 3:  In the theory section, derive expressions for the T1, T2 and fosc.  As part of the derivation, explain how the circuit works.
• In the results section:
• Include all oscilloscope printouts for the circuits you built.  Make sure they are well labeled, with a title and a description of each trace on the printout.
• Results table: Include a table summarizing all of your results, both measured and theoretical for circuits 1 and 2.  Include the time constant and the initial and final value for each measurement.
• For the 555 oscillator include the measured and calculated frequency of oscillation.
• In the discussion section:
• Note the accuracy of your measured time constants compared with calculated.
• Describe what happened when you connected the Wavetek to pin 5 of the 555 oscillator.  This section was optional.

email me with any comments on how to improve the information on this page (either presentation or content), or to let me know if you had any particular difficulties with this lab.