2A Lab 6 - 2009

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1 © Bob York

ECE 2A Lab #6

Lab 6

First-Order RC/RL

Circuits

Overview This lab will explore the transient response of simple RC and RL circuits tounderstand therole of the time constant. In the process we will introduce the based concepts of differentiator, integrator, and frequency filtering circuits. We will then combine theRC timeconstant material with an earlier comparator circuit from Lab #4 to create asimple timer.

Table of ContentsBackground Information 2

Capacitors 2 Inductors 3

References 4 Pre-lab Preparation 5

Before Coming to the Lab 5 Required Equipment 5 Parts List 5

In-Lab Procedure 5

6.1 RC Circuits 5

RC Time Constant 5 The Circuit as an Integrator 6 The RC Circuit as a Low-Pass Filter 6

An RC Differentiator Circuit 7 6.2 RL Circuits 7

RL time constant 7 An RL differentiator/High-Pass Filter 7

6.3 A Simple RC Timing Circuit 8



2 First-Order RC/RL Circuits

© Bob York

Background Information

Capacitors

Capacitors are made from a layer of insulating material sandwiched between twoconductingsheets. The total capacitance generally scales with the materials and geometryaccording to

rAC

d

(6.1)

where r is an intrinsic property of the insulator called the “dielectric constant”,

d is thethickness of the insulator, and A is the net surface area of the conducting sheets. Large

capacitors therefore require a large sheet area and thin insulators with the maximumpossibledielectric constant.

Capacitors are usually classified according to the type of insulating material that isused.“Film” capacitors use a thin film of material such as polypropylene, polystyrene,

Teflon,Mylar,etc. These films are then stacked together with metal electrodes (either aseparate foilor a thin layer of metal coating on the film). “Ceramic” capacitors use a high

dielectric-constant material, generally barium titanate or some related ceramic material, whichis mixedin a thin paste between metal electrodes and then hardened together (“fired”) in ahigh-temperature furnace. “Electrolytic” capacitors use a thin oxide layer on one of theelectrodes(usually aluminum oxide on aluminum) as the insulator, with a liquid electrolyte usedtoinsure an intimate contact between the second electrode and the oxide. Figure 6-1illustratessome of the common capacitor types.

Film Capacitors•Low loss, low leakage•Larger than ceramics, but

tighter tolerance and better

performance for a given price

Ceramic•Small size, High voltage•Tolerance, temp. dependence,

leakage, etc. vary strongly withmaterial; cost tradeoff

Electrolytics•Very high capacitance density•±20% tolerance•Large size, poor loss and leakage

characteristics



Figure 6-1 – Comparison of commonly-available through-hole capacitortypes.

It is difficult to control the capacitance values precisely during the manufacturingprocess,so capacitors are specified for a certain “tolerance”. The statistics are essentially the

same aswe discussed for resistors, and the same system of values applies for capacitors: E6for±20%, E12 for ±10%,etc. Electrolytic capacitors usually have a poor tolerance,

typically±20%, but ceramic and film capacitors can be obtained with tightertolerances. There are two very important practical issues with capacitors that you need to be

aware of.One is thevoltage rating: This is the maximum voltage that the capacitor can withstandforsome period of time. If this voltage is exceeded the insulating material will fail and

a largecurrent could flow, destroying the device. The second issueis

polarity : some capacitors,notably electrolytics and tantalum capacitors, are not reversible; they must beinserted in sucha way that any DC voltage will appear across its terminals in a specified polarity. Socare

Background Information3

must be taken when inserting them in a circuit—

a polar capacitor mounted in the wrong way

will self destruct . In the case of electrolytics, this happens because one voltagepolaritypromotes a chemical oxidation-reduction

processbetween the electrolyte and the insulating oxide

that slowly destroys the insulator. Electrolyticshave been known to erupt rather dramaticallywhen biased improperly. For this reason, polar

capacitors usually have some marking on thepackage to indicate the correct insertion; Figure6-2 illustrates the markings for a typical

electrolytic capacitor. In a circuit schematicpolarcapacitors are usually indicated by a “+” sign onone terminal as shown.

There are several other non-idealities thataffect the behavior of capacitors in circuits. Unfortunately too many to discuss herein anygreat detail! They suffer from leakage currents, vary with temperature and humidity,

andmay have some problems at high frequencies. These issues will not be critical in ECE2, butthey are important factors for engineers to understand and deal with in commercialdesigns.In ECE 2 we will generally use inexpensive ceramic capacitors for small-values

(<1μF)and electrolytics for the larger values (>1μF). The actual capacitance value ismarked in avariety of different ways. For electrolytics the value is usually stamped clearly asshown inFigure 6-2. For ceramics and film

capacitors a three-digit code is morecommonly used, illustrated in Figure 6-3.

This code gives the value in picofarads

(121pF10F ). Beware that this is notthe only capacitor code in use! Sometimesthere is a 4-digit number which represents

the actual value in pF (i.e.no multiplier),and other times a decimal value is shown(like “.033”) which is the capacitance in

μF! Sometimes (but not always) there is aletter following the code that indicates thetolerance, and sometimes (but not always) the voltage rating is shown. To furthercomplicatethings, many modern devices are so tiny and the lettering so small and faint that it isoftenhard to see the markings unless you have especially good eyesight (a magnifyingglass is agood investment for this line of work!). If the markings are confusing or ambiguous,outadvice is to go MEASURE the capacitance. In the ECE 2 lab there is an “LCR” meterthatwill measure a wide range of capacitor and inductorvalues.Inductors

Inductors are usually made by coiling wire around some cylindrical or toroidal(doughnut-shaped) form. This winding form is often (but not always) a solid magnetic materialsuch asiron or iron-oxide (“ferrite”) called the “core”. The total inductance usually varieswith thematerial and geometry according to

2rNAL

(6.2)

Long-lead is “positive”

“-”sign on package

indicates “negative”lead

Value and voltage ratingprinted on package

Figure 6-2 – Symbol for a polar capacitorand associated markings for electrolytics.

451010pF10pF

100nF

0.1F

First two“value”digits

Third “multiplier”digit



451010pF10pF

100nF

0.1F

First two“value”digits

Third “multiplier”digit

Figure 6-3 – Three-digit code used for most of theceramic capacitors in ECE 2.


© Bob York

where r is an intrinsic property of the core material called the “magneticconstant”,

N is

the number of turns of the wire, A is the average area of each turn, and is the overall

length of the winding. Large inductors therefore require a lot of turns, a large turnarea, and acore with a larger .

In some respects inductors are very uncomplicated devices—after all, what couldbesimpler than a coil of wire? But some complexity is hiding in the physics of the corematerialwhich ultimately plays a significant role in the I-V characteristics of the device. Most

magnetic core materials lead to nonlinear behavior at certain current levels, and alsocan limitthe maximum operating frequency of the devices. But there are two even more basicproblems with inductors: 1) they are HUGE in comparison to other circuitcomponents, and2) they do not lend themselves easily to mass production and hence do not benefitfrom thesame economies of scale that other passive components enjoy. Because they are sobig andexpensive they are used sparingly in modern microelectronics, mostly found today in

applications such as power-electronics (e.g.switch-mode power supplies, AC-to-DC and DC-to-DC converters), high-frequency chokes, high-power filters, and certain radiocircuits.



Solenoidal Inductors•Inexpensive, low-profile

•Limited range of inductance values•Poor confinement of magnetic fields

Toroidal Inductors•Wide range of inductance and power handling

•Good confinement of fields•Larger and more expensive than solenoidal

inductors

Figure 6-4 – Comparison of common inductors.

We remarked earlier that capacitors have an inconsistent marking system.Inductors areeven worse—most have no markings at all! In addition there is no consistent set of

valueslike the decade-based systems used with resistors and capacitors (E6, E12,E24,

etc.); theavailability of certain values seems to be driven by demand and are very application-specific.So the only good recourse for an experimentalist is to measure the inductancedirectly with anLCR meter. But note: because the properties of the core material depend stronglyon theamount of current in the windings, most inductors are designed to have a certaininductanceat some specified DC current level, and it is not uncommon for inductances to vary

significantly around this nominal specification at other currentlevels.References

http://en.wikipedia.org/wiki/Types_of_capacitor http://en.wikipedia.org/wiki/Ceramic_capacitor http://en.wikipedia.org/wiki/Electrolytic_capacitor

http://en.wikipedia.org/wiki/Inductor

Pre-lab Preparation5

Pre-lab Preparation

Before Coming to the Lab

Read through the details of the lab experiment to familiarize yourself with thecomponents and testing sequence.

One person from each lab group should obtain a parts kit from the ECEShop.Required Equipment

Provided in lab: Bench power supply, Function Generator, Oscilloscope, DecadeBox Student equipment: Solderless breadboard, and jumper wirekitParts List

QtyDescription

110mH 19DCR power inductor2PC mount tactile switch10.01uF 50V ceramic capacitor, radial lead

2100uF 25V electrolytic capacitor, radial lead

We will also use the 741 op-amp, LEDs, and selected resistors fromearlier labs

In-Lab Procedure

6.1 RC Circuits

RC Time Constant Build the RC circuit shown in Figure 6-5, using the decade box for theresistor,

R, and the0.01 μF capacitor in your kit. Note that the 50 Ω resistor is just shown forreference—itrepresents the internal resistance of the

function generator. You can verify thecapacitor value using the LCR impedancemeter in the lab. Adjust the output of the

function generator to a 1 kHz square wave,with an amplitude of 1V (2 volts peak-to-peak). Be sure that the DC offset switch

on the function generator is off (pushed in)and that the vertical scope inputs are DCcoupled (not AC coupled). It will be

convenient to view the input and outputsignals simultaneously on the oscilloscope screen, which is accomplished by theconnections shown below. Set the vertical positions so that the 0 volt (ground)level isthe center of the screen for bothchannels: Starting withR=100 Ω, observe and record the input and output waveforms. They

shouldbe similar. Now increase the resistance to 5 kΩ and record the resultingwaveforms inyour notebook. Physically the series resistance limits the flow of current so thevoltage

Vg

Input(Ch1)

Output(Ch2)50Ω

C

R

Function

Generator

0.01μFVinVout

Vg

Input(Ch1)

Output(Ch2)50Ω

C

R

Function

Generator

0.01μFVinVout

Figure 6-5 – A simple first-order “RC” circuit.




© Bob York

across the capacitor rises more slowly as the resistance is increased. Expand thetime tozoom in on one transition, and use the cursors on the oscilloscope to estimate thetimeconstant, , from the waveform; remember, is time it takes for the voltage change by1163%e of the total step voltage (final value minus initial value). Compare with the

theoretical prediction based on theRC product.Another figure of merit commonly used in such cases is the rise-time,

rt , and fall-time,ft ,defined as the time it takes for the signal to progress from 10% to 90% of the totalstep size(final value minus initial value). The rise time can beexpressed as

0.9ln2.20.1rtRC (6.3)

Use the cursors again to estimate the risetime/falltime and compare with theprediction of (6.3). For this measurement it may help to adjust the vertical sensitivity so that

thewaveform fills the screen.

The Circuit as an Integrator

Now increase the resistor to 20 kΩ. The time constant is now longer than theduration of the square pulse so the output waveform does not quite reach the peak value of

the inputwaveform. Increase the resistance again to 100 kΩ and record the resultingwaveform inyour notebook. You will probably have to adjust the vertical scale since the peakamplitude will continue to shrink. Can you understand what is happening? Theoutput isnow approximately a triangular wave, which is essentially integral of the inputsignal.Verify that the circuit is acting as an integrator by changing the input waveform totriangular and sine waves, making appropriate plots of both in yournotebook. The important point here is that there are two time-periods involved: the RC time

constant ,and the time-periodT of the square wave excitation. ForT we see the full RC chargingtransient after every transition, but forT we only see the initial linear part of thecharging transient, and hence the circuit functions as anintegrator. In the above steps we adjusted the value of the resistance to observe theintegratorbehavior. Alternatively we could keep the resistor fixed and change the

frequencyinstead. At approximately what frequency will the circuit behave as an integratorfor aresistor value of 10kΩ? Verify your answer experimentally using a square-waveexcitation.

The RC Circuit as a Low-Pass Filter

Our focus so-far has been on the transient response of the RC circuit due to a stepfunctionexcitation (the leading and falling edges of the square-wave). But for sinusoidal (AC)excitation the output will also be sinusoidal, so it makes more sense to focus on howtheamplitude or phase changes as a function of

frequency. Switch the function generator to a sinusoid with a 1V amplitude (2V peak-to-peak)andzero DC offset. Starting with a frequency of 100 Hz, record the output amplitude

versusfrequency up to 100 kHz, usingR=5 kΩ. Since we are covering several decades of frequency it is best to choose the frequencies appropriate to a log scale like this:100 Hz,200 Hz, 500 Hz, 1 kHz, 2 kHz, 5 kHz,etc. Take data quickly; this step should not last

long. In your lab report you will plot your results on a log scale infrequency.In the context of sinusoidal signals the simple RC circuit of Figure 6-5 is called a “low-

passfilter”, because low frequency signals will pass through but high frequency signals get



RL Circuits7

strongly attenuated. There are many uses for filters in electrical engineering; asimple andfamiliar example is the cross-over network in an audio speaker system or surround-soundsystem, which directs low frequency audio to the big “sub-woofers”.

An RC Differentiator Circuit

By simply switching the placement of thecapacitor and resistor as shown in Figure 6-6

the operation of the circuit can be changedsignificantly.

Build this circuit, and drive it with a 1 kHzsquare wave using a 5 kΩ resistor. Sketch

the resulting waveforms in your notebook.Can you see that the circuit is now acting asa differentiator? Prove this to yourself by

changing the excitation to triangular andsine waves. Then using the square wave signal again, zoom in on one of thetransitionsby adjusting the time base. Can you identify any characteristic property of thenetworkfrom the shape of this signal?

6.2 RL Circuits

The RL circuit is very similar to the RC circuit in terms of the mathematical form of theresponse, despite very different physical mechanisms involved. Therefore we will notexamine this case quite as thoroughly:

RL time constant

Build the circuit of Figure 6-7 using a 10mH

inductor and a 100 Ω resistor. As before,drive the circuit with a 1 kHz square waveand estimate the time constant. Compare

with the theoretical prediction. Can youreconcile the data with the theory? Try toidentify extra sources of resistance in the

circuit. Sketch the waveforms in yournotebook and compare with the earlier RC

circuits for similarities.

An RL differentiator/High-Pass Filter

Now switch the order of the inductor and

resistor to construct the circuit of Figure 6-8,this time using a 1 kΩ resistor, and verifythe action of this circuit as you did earlierfor the RC differentiator circuit.

This circuit also functions as a high-passfilter, because only high frequency signals

go through without attenuation. Show thatthis is true by taking data over frequency for

Vg

50ΩC

RFunction

Generator

0.01μFVinVout

Vg

50ΩC

RFunction

Generator

0.01μFVinVout

Figure 6-6 – RC (high-pass) circuit.

Vg

50ΩL

RFunction

Generator

10mH

VinVout

Vg

50ΩL

RFunction

Generator

10mH

VinVout

Figure 6-7 – RL (low-pass) circuit.

Vg

50Ω R

Function

Generator

L

10mHVinVout

Vg

50Ω R

Function

Generator

L

10mHVinVout

Figure 6-8 – RL (high-pass) circuit.




© Bob York

a sine-wave excitation as you did earlier in connection with the RC low-pass filter.Inyour lab report you will make a careful plot of thisdata..

6.3 A Simple RC Timing Circuit

Time constant circuits arise in a number of different contexts in electricalengineering. Oneparticular application is a simple timer function where the RC charging time isexploited tocreate a known time-delay.

The circuit in Figure 6-9

combines a very simple RCcircuit (inside the dashed box)with the op-amp comparator

circuit that we examined in Lab#4. A simple adjustable voltagedivider circuit is used to set the

reference voltage for the

comparator, refV . The circuitfunctions as follows: with the

switch open the capacitor ischarged to +5V, and since this isalways refV the output will stayin its high state (near +5V),lighting the red LED. When theswitch is pressed the capacitor is quickly discharged to 0V and the output goes low,switchingon the yellow LED. The capacitor then begins to charge up again throughresistor

R. Theoutput stays low until the voltage across the capacitorreaches

refV , at which point the redLED is switched back on. So the yellow light is on for a short period of time after thebuttonis pressed, and this time period is set by the RC time-constant

and

refV .

Start building this circuit by first mounting the 741 op-amp and establishing theproperbias. Refer to the data sheet for the pinout, and use ±5V for the power

supplies. Next, add the 10k trimpot and

1k resistor, then add the LEDs

and 510 Ω bias resistors. Theresistors and LEDs are leftoverparts from earlier labs.

Lastly add the RC timingnetwork and the pushbutton

“tactile” switch. Note: this isour first circuit using a large

electrolytic capacitor, so besure you are familiar with therelevant material from thebackground section;electrolytics must be inserted in the correct

polarity !!

The tactile switch we are using is called a “momentary on” switch, meaning that it is

normally off until someone presses the button. A typical pinout is shown in Figure 6-10, butyou should use your ohmmeter to make a simple continuity test to verify the correctpinconnections.

+5V

-5V

+

-LM741

Vref

+5V

+5V

Switch

10kΩ

100μF

510Ω

510Ω

Red

Yellow

1kΩ10kΩpotentiometer

C

R

wipe

r

+5V

-5V

+

-

+

-

+

-LM741

Vref

+5V

+5V

Switch

10kΩ

100μF

510Ω

510Ω

Red

Yellow

1kΩ10kΩpotentiometer

C

R

wipe

r

Figure 6-9 – A simple LED timer circuit.



Figure 6-10 – Typical pinout for a tactile pushbuttonswitch.

A Simple RC Timing Circuit 9

Now turn on the power-supplies and adjust the potentiometer to 15(1)3.16Ve . This

sets the threshold voltage such that the time period is exactly one time constant.After thepower-supply has been on for a few seconds the red LED should be on, and theyellowLED should be off.

Now press the button and release it. Use your watch to monitor how long theyellowLED stays lit, and compare this with the theoretical prediction

based onRC.

Can you calculate therefV that would be needed to keep the yellow LED alight fortwotime constants? Adjust the potentiometer accordingly and verify your design.

Includethe details of the calculation in your labreport. Now design the timer so that the yellow LED stays lit for 10 seconds. You will need

to use a different charging resistorR. Calculate the necessaryR and refV and verify yourdesign experimentally. Include the details of the calculation in your labreport.

Congratulations!

You have now completed Lab 6

As noted in the previous lab: keep all your leftover electricalcomponents!

Notes on the Report

In your report, you should (wherever possible) compare the theory and experiment,anddiscuss why the circuits behave as they do for different combinations of resistance(timeconstant) and frequency. For example, in the case of the RC circuit with a square-waveexcitation the output waveform

closely resembles the inputwaveform when T ; thisoccurs because the charging or

discharging transients arecompleted well before the nextpulse transition occurs. Be sure

to include any necessarymathematics to support you’reanswers. If you use a result

from your textbook, referencethe relevant equation numberand/or page.

Programs like Matlab,Mathematica, etc.can and

should be used wherever possible. For the output voltage-versus frequency plots youshoulduse a log-log scale. Figure 6-11 shows a log-log plot done in Excel (the file for thisplot is onthe course web site, as well as a brief exceltutorial). The time constant you found in connection with theRL Time Constant section should

have differed noticeably from what you would predict based on the resistance shownin theschematic. Be sure to explain a possible source of thisdifference.

0.0001

0.001

0.01

0.1

1

10

110100100010000100000

Frequency, Hz

Am

plitude

, Volt

s

Figure 6-11 – Example of a log-log (Bode) plot inExcel.

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2A Lab 6 - 2009