EE122_Labs_02_fall2002

EE122

Prof. Greg KovacsReviewed by Ross Venook

PRELAB 1:PHYSICAL & VIRTUAL

INSTRUMENTSFOR ELECTRONICS

The Future Begins Tomorrow!Motto of YoyoDyne Engineering in the movie Buckaroo Banzai

OBJECTIVES

Review of basic instruments (physical and virtual).

Review of electronic components.

Introduction to the design process.

THE BASICS OF ELECTRONIC INSTRUMENTS

The whole purpose of this prelab is to prepare you for going intothe lab and using various electronic instruments. There are twotypes of instruments that you should be familiar with: physicalinstruments and virtual instruments

Physical instruments are the type you can pick up (admittedly, youneed help lifting the big ones!). You are probably familiar withseveral physical instruments such as multimeters, battery testers,etc.

Virtual instruments are those that are mainly (or entirely) softwareand are used with computers. The main virtual instrument that wewill use in this course is a variation of the program “SPICE” whichallows circuit designs to be simulated on a computer. This meansthat you can design and “prototype” an electronic circuit entirely insoftware. You don’t even need a soldering iron!

INTRODUCTION TO PHYSICAL INSTRUMENTS

Please refer to the lecture materials regarding the instruments tobe used in the laboratory.

The Hewlett-Packard Model 34401A Digital Multimeter

This is an auto-ranging digital meter capable of measuring severalbasic electrical parameters (hence the names “multimeter,” “digitalmultimeter,” or “DMM”, “digital voltmeter,” or “DVM”.... we'll refer toit as a DVM from here on). The basic principle of early meters wasto magnetically deflect a mechanical needle in proportion to anelectrical current. The electrical parameter to be measured wasobtained by noting the position of the needle against a numericalscale behind it. By converting the desired electrical parameter intoa current to deflect the needle, voltage, resistance, and of course,current could be measured. While so-called analog meters stillturn up occasionally, digital meters have largely taken their place.Here, the electrical parameter being measured is digitized anddisplayed as numbers (no squinting at a needle required). Somenewer digital multimeters even include a “simulated needle” toprovide a graphical display of varying levels of voltage, for example.

Briefly consider the measurement capabilities (“specs”) of theHewlett-Packard 34401A. In the "old days" (a few years ago), wereally worried about the basic accuracy of DVM's, since they typicallyonly had a few digits (e.g.,, 3 1/2, where the "1/2" digit can read 1or 0). Typical accuracies were 0.1%. Now, DVM's like the 34401Ahave many digits (6 1/2 in this case) and basic accuracies on theorder of 0.002% or better for all functions! What input range youset the DVM to used to be a big issue, but now they are "intelligent"(microprocessor controlled) and automatically select the best rangeto give you the most accuracy.

The HP 34401A can measure AC (RMS) or DC current and voltage,resistance, as can virtually any DVM. It can also measure frequency,test diodes and provides a "continuity" function that beeps whenthere is a good connection (or unwanted short-circuit) between thetwo input leads. Six and 1/2 digits of display are more than adequatefor nearly any application in EE122 (and elsewhere, for that matter),so we won't spend much time on accuracy here (if you want to,refer to the manual in the lab).

DC or AC voltages can be measured up to 1000 V with a maximumresolution (on the 100 mV full-scale range) of 100 nV!!! Resistancescan be measured up to 100 MΩ, with a maximum resolution of 100µΩ (on the 100Ω full-scale range). DC or AC current can bemeasured up to 3A (a fuse will blow above that, so be

The continuity or"beep" function isextremely usefulwhen debuggingcircuits you areworking on... justturn off the powerand verify that theconnections you want are there andthat there aren't anyyou don't want!!!

PRACTICALPOINT !!!!!!!

careful!) with a maximum resolution of 10 nA (!) (on the 10 mAfull-scale range).

AC voltages are read as true RMS (root mean square). The RMSfunction is frequency-dependent (an actual analog computationalcircuit is used). A plot of the accuracy (using specs from the manual)shows that you really have to be careful for low or high frequencies.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

1

10 100

1000

1000

0

1000

00

1000

000

Acc

urac

y (%

)

Frequency (Hz)

0.04%

An important concept for any instrument is the input impedance.This specification is an indication of how much of a load theinstrument places on the circuit you are measuring. For the HP34401A, the input impedance is 1 MΩ (10 MΩ for DC measurements)in parallel with less than 100 pF of “shunt capacitance” betweenthe leads.

IF YOU ARE NOT USING AUTORANGING, ALWAYS USETHE DIGITAL VOLTMETER (DVM) SETTING THAT YIELDSTHE LARGEST NUMBER OF SIGNIFICANT FIGURES.Otherwise, you are getting much less information than it can deliver.(Also remember to take off your shades when using oscilloscopes...)

The Hewlett-Packard Model 1740A Oscilloscope

The 1740A is a two-channel oscilloscope operating from DC to100 MHz. You generally use an oscilloscope when you want tolook at the actual shape of a signal versus time (or if you just wantto play with something with lots of knobs...) Figure 2 below is aquick reminder of how an oscilloscope works....

PRACTICALPOINT

HORIZAMP

VERTAMP

INPUT SIGNAL TODISPLAY

HORIZONTAL SWEEPSIGNAL

ElectronBeam

Source

CRT Screen

Figure 2: A block diagram illustrating how an analog oscilloscope works. Theinput signal is amplified and applied to the vertical deflection plates to move theelectron beam up and down. A ramp signal is applied to the horizontal deflectionplates to move the beam left to right at a desired rate. The electron beam hittingthe phosphor on the inside of the cathode-ray-tube (CRT) glows (for some timeafter the beam moves on) leaving the image of the input signal on the screen.

Besides the setting of the vertical gain (to see the part of the inputsignal you are interested in) and the horizontal sweep rate (tosweep the beam from left to right at the appropriate speed to seewhat you are interested in), the triggering of the oscilloscope mustbe set up correctly (or else you will see stuff on the CRT screenthat is about as relevant to your edification as “Leave it to Beaver”reruns, not to mention the fact that you’ll really look clueless!). Thetrigger circuitry in an oscilloscope determines at which point on awaveform to begin the horizontal sweep. Trigger circuits work bydetermining the slope of the input signal (positive- or negative-going)and comparing the input signal to a reference voltage (the triggerlevel). When the input signal crosses the trigger level in theappropriate direction (i.e., with the correct slope) the trigger circuitinitiates a horizontal sweep. If this is happening fairly often, astable display is seen on the oscilloscope screen. Figure 3 belowillustrates the effects of the trigger settings.

4

volts

time

time

volts

Figure 3: Illustration of the effect of trigger settings on the display of theoscilloscope. Case A shows a positive slope and a trigger level that is crossedmore than once per cycle of the waveform. Notice the garbled display. Case Bshows a better choice of trigger level, still with a positive slope. Case C shows theeffect of changing the slope to negative while keeping the same trigger level.

You should note that most oscilloscopes have several triggeringmodes. The most important ones are normal (“NORM”), automatic(“AUTO”), and line frequency (“LINE”). Normal mode operates asillustrated in Figure 3 above. Auto mode operates more-or-lesslike normal mode, but it helps you find a good trigger pointautomatically. Line mode uses the beginning of each 60 Hz cycleof the AC power to start a sweep (this is good for determining ifyou are looking at 60 Hz power-line noise on a signal).

Always start out using AUTO triggering if you are notsure about all of the other settings!

The oscilloscope has a frequency response that greatly exceedsthat of the DVM described above. Try writing down the numbersfrom the DVM while measuring a 0.1 Hz sine wave, graphing thedata points on a piece of paper as you go (just kidding, but if youpull it off, try it for 1 Hz!). No way that’s going to work is there?!?Now you get it don’t you... Oscilloscopes can be pretty handy!

Its input impedance is 1 MΩ shunted by approximately 20 pF (don’tworry, there won’t be another problem to work out here, but atleast think about it will you!).

The input voltage ranges are 5 mV/div to 20 V/div, with an accuracyof 3% (there is a built-in calibrator). The input voltage must bekept below 500 V peak-to-peak or you will see (in order): 1) smokecoming out of the oscilloscope, 2) the T.A. coming over to your

PRACTICALPOINT

bench with a fire extinguisher, 3) your checking account balancedropping by the cost of repairing a fried oscilloscope....

The timebase sweep rate range is 50 ns/div to 2 s/div with anaccuracy of +/- 3%.

The HP Model 33120A 15 MHz Function Generator

The 33120A is the main function generator you will use. It cansynthesize all of the basic waveforms (square, sine, triangle, ramp,etc., as well as noise and programmable “arbitrary” waveforms). Itcan also synthesize AM and FM waveforms with somewhat limitedparameters. It is menu-driven and quite intuitive. During the lab,you are encouraged to study its user’s manual.

The HP Model 8904A Multifunction Synthesizer

The 8904A is a four-channel signal generator, and likely only toserve as a backup instrument to the 33120A. Each channel can beset independently to a chosen frequency, phase, amplitude andwaveform. These channels can then be fed simultaneously to thesame output, the resulting voltage being the sum of the voltage ineach channel. Alternately, the output of one channel can bemultiplied by that of another, thus providing amplitude modulation(AM). Frequency modulation (FM) can also be achieved usingthis unit. Such a synthesizer is an important tool for generatingtest signals to use as inputs to circuits (or to demonstrate testinstruments!).

An interesting feature of this unit is the multiple outputs that can besummed. This allows you to prove to yourself some of the conceptsabout Fourier series that you have probably been dying to test...As you may recall, the Fourier series for a signal tells you whatcombination of amplitudes and frequencies of sine and cosinewaves to sum together to make the original signal.

Overview of Spectrum Analyzers

The Spectrum Analyzer is the frequency domain counterpart of anoscilloscope in the time domain. In other words, it can give you aplot of amplitude vs. frequency as opposed to amplitude vs. time.In practice, you look at the amount of energy present at eachfrequency plotted as the y-axis against the frequency (the x-axis).

Spectrum analyzers are extremely useful instruments, providingnearly instant information about the frequency content of signals.They can also be used to assess such things as the frequencyresponses of filters, distortion in amplifiers, and noise levels insignals.

There are two types of spectrum analyzers: analog and digital. InEE122, you will probably only deal with the digital type, but theanalog ones are important enough that they need to be considered.

Analog Spectrum Analyzers

Basically, an analog spectrum analyzer is like a fancy radio, wherethe tuning is swept between two frequencies.

Analog spectrum analyzers are represented by the block diagramshown below... A local oscillator (voltage-controlled-oscillator, or"VCO") is mixed with (multiplied by) the input signal. This is thebasic principle behind heterodyne radios -> the frequency of interestis "heterodyned" down to a lower frequency at which a fixed ("band-pass") filter is centered so that only a "chunk" of spectrum of width∆ (the bandwidth of the band-pass filter) is passed to the “envelopedetector.” The envelope detector is a circuit, such as an AC-to-RMSconverter, that computes the energy coming out of the bandpassfilter at a given time.

This has the same effect as sweeping a band-pass filter ofwidth ∆ through the frequency spectrum and looking at its output.

The energy (i.e., RMS voltage) value measured for a given frequencyis fed to the y-axis of an oscilloscope. Simultaneously, the x-axisis swept in synchrony with the control voltage fed to the localoscillator. Thus, the frequency that is heterodyned down by thedetector is varied as the beam is swept across the x-axis.

What about the negative frequency component?It is reflected about f=0 and simply adds to the term at fo...

You can't physicallyhave negative frequencies...

Figure 4: Block diagram of an analog spectrum analyzer.

If the frequency of the VCO is swept from fo to some maximumfrequency, fm, over the period T, then the frequency spectrum isdivided into N frequency resolution "cells" (or regions of thefrequency spectrum that are passed by the bandpass filter into theenvelope detector at a given time) given by,

N = fm - fo∆

with a time spent per "cell" given by,

Tcell = TN

Therefore, it is clear that the response time of the filter, tc, must bemuch less than Tcell if the output is to be meaningful. Since it isknown (not necessarily by you, yet!) that tc is approximately 1/∆, wecan obtain a simple equation telling us how fast to sweep the VCOfor a given frequency range and filter bandwidth...

τc ≈ 1∆

<< Tcell = TN

= T∆fm - fo

Or, rearranging,

T >> fm - fo∆2

= N2

fm - fo

This result tells us that for a high resolution (small ∆), we needlong sweep times. For example, with ∆ = 100 Hz, fm = 20 KHz andfo = 0 Hz, the sweep time should be greater than 2 seconds! If thesweep time is too fast, "blurring" of the spectrum occurs.

O.K... these are theONLY equations in thiswhole prelab... thinkyou can handle 'em?

OOOH! subtraction!

AAHH! division!

GOSH! an exponent...

Typically, a storage tube CRT is used to "hold" the results of thesweep if you need to use long sweep times.

This type of spectrum analyzer can be easier to construct if highfrequencies are to be examined, but cannot directly provide phaseinformation about the different components of the input signal. Also,this type of spectrum analyzer can be "tuned in" to a single frequencyand used to study instantaneous changes over time (used morelike a radio).

Digital Spectrum Analyzers

Digital spectrum analyzers first digitize (record a continuous analogfunction as rounded numbers with n bits of precision using ananalog-to-digital converter) and discretize (sample at a highfrequency) the input waveform so that it is simply numbers. Thenthey take a discrete Fourier transform (DFT) of the data to computethe frequency components. This type of spectrum analyzer canprovide phase information but needs to have a fast enough digitizerto handle the frequency range of interest.

Figure 5: Block diagram of a digital spectrum analyzer.

Hewlett-Packard Model 3561A Dynamic Signal Analyzer

This instrument obtains frequency domain information from time-domain input signals by digitizing them and digitally computing thedesired results using the “Fast Fourier Transform,” which is acomputationally efficient version of the DFT.

Think (if you can) about some situations in which you would wantto use each type of instrument. If you don’t do this, its o.k., becausewe’ll force you to try them all out anyway when you do the lab!

NOTE that you can always capture a signal using the digitizingoscilloscope (see below) and compute the Fourier spectrum of thedata using your computer (e.g., with the FFT or DFT in Matlab).Depending on the resolution, this method could be either more orless accurate than using the 3561A. Of course, it’s not real-time...

Hewlett-Packard INFINIUM Digitizing Oscilloscope

This instrument is a digitizing oscilloscope or digital storageoscilloscope (“DSO”). The DSO is a versatile instrument thatoperates by digitizing the input signals with an analog-to-digitalconverter, storing the corresponding numerical values, and thendisplaying them on a display. This allows a waveform (even froma “one-shot” event) to be stored indefinitely as numbers. Theresulting display can be modified (zoomed in on, scaled, etc.) andprinted. Also, since the information is already stored as numbers,measurements on the waveform are easy and accurate, and mostcan be displayed in “real-time” on the device (frequency, peak-to-peak voltage, amplitude, etc...). This makes many measurements(such as those done for EE122 labs!) much easier.

Please refer to the User’s Manual for detailed instructions (whichare pretty simple). Also, please be careful to observe that you cansave acquired waveforms to disk and then import them into acomputer for further analysis or incorporation into write-ups.

Wait... there's more...

INTRODUCTION TO SPICE: A VIRTUAL INSTRUMENT

Spice (and several variations that are now available) is a circuitsimulation tool that can be run on many types of computers, frommainframes to personal computers. This prelab provides anoverview of Spice. Additional information will be available asseparate handouts and by referring to the various books andmanuals for Spice in the lab room, or on the web. Be sure to readthe manuals that apply to the version of Spice you are using!

IF YOU ARE USING A GRAPHICAL INPUT SPICE (Suchas PSPICE), you can basically ignore this section sincethe schematic entry for those tool is GRAPHICAL - youjust draw the schematic, hook up your virtual instruments,and run.

To get an overview of the Spice-type circuit simulators, begin byconsidering how you can specify a circuit to a computer. This canbe done by making a list of each component in the circuit (includingits characteristics/value) that includes any points where componentsconnect together. These interconnection points are referred to asnodes. The complete list of parts and connections is sometimesreferred to as a ‘netlist,’ or a ‘deck’ which you’ll hear about shortly.The example circuit shown below has the components named andthe nodes numbered.

Rs 240 Ω Lx 4.2 H Cx 0.006 pF

RL 10 KΩ+-Signal Source

Node 0 (ground)

Node 2 Node 3

Node 1 Node 4

Vin

Quartz Crystal Equivalent Circuit

Figure 6: Example circuit showing components’ names and “Spice-style” nodenumbering. Note that ground must always be node 0 in most versions of Spice.The numbering of the other nodes is arbitrary.

The list representation of this circuit is shown below:

Cx 4 3 0.006PFLx 2 3 4.2HRL 4 0 10KRs 1 2 240Vin 1 0 AC 1.end

Tells SPICEthat this isthe end ofthe list.

ValueComponent ConnectionNodes

Notice that the nodes are listed for each “pin” of each componentin the list. This tells the software how they are connected together.Incorrect “wiring” of Spice components is one of the most commonsources of problems with Spice simulations, not unlike in the lab!While most devices you will be using in simulation (resistors,capacitors, etc...) are “two-terminal,” for devices with more terminals,such as transistors, there are naturally more connections listedafter the first entry for the device.

Using terminology from the days when you used to have to entersuch lists on a deck of punched paper cards, such a list is oftenreferred to as a “Spice deck.” Such a deck can be input directly tothe Spice program as a text file. Using commands that will bediscussed below, Spice can calculate the DC levels in the circuit,its time-domain response to various AC input signals, and itsfrequency response. As you will see, Spice is a very powerful toolfor circuit design. As you use Spice in this course, try to thinkabout how hard the prelabs would be if you had to do all of thework by hand!

Additional commands are necessary to tell Spice what it is thatyou want to simulate. To study the frequency response of thecircuit in Figure 6, add the following line before the “.end” command:

.AC DEC 20 100K 10MEG

This tells Spice that you want to calculate the response of thecircuit sweeping by DECades at 20 frequency points from 100KHz to 10 MHz (Mega, or 1 million, is expressed as either ‘X’ or‘MEG’ because Spice is case-insensitive and ‘m’ is used for ‘milli’).Figure 7 below is the output of Spice when given the deck shownabove (a log/log plot is shown in Figure 7).

100KHz 1MHz 10MHz1nV

10nV

100nV

1uV

10uV

100uV

1mV

10mV

FREQac3

ac3.V(4)

Figure 7: Frequency response of the circuit in Figure 6.

For PSpice, youneed to add a".probe" linebefore ".end" line to generate a plotoutput file...

NOTE!

Warning: plots can be deceiving/useless if the axes are scaleddifferently than you expect. Be sure to plot using appropriate scaling.

Later on, we will consider transient analysis in the time domain inmore detail, but for the time being, here is how you would changethe above Spice deck to look at the circuit’s response to a 1millisecond wide square pulse:

Ideal crystal response to a short input pulse.Cx 4 3 0.006PFLx 2 3 4.2HRL 4 0 10KRs 1 2 240Vin 1 0 PWL (0,0 0.1u,1 1u,1 1.1u,0).TRAN 1u 50u.probe.end

The “Vin” statement before the “.end” command tells Spice to inputa P iece-Wise-Linear waveform that starts out at 0 V at time=0,climbs to 1 V at 0.1 µS, stays at 1 V until 1 µS, and falls to 0 V by1.1 mS. The “.TRAN” statement tells Spice to carry out transientanalysis over the time 0 to 50µS, taking steps of 1µS. Figure 8below shows the input pulse. Figure 9 below shows the results ofthe transient analysis (note the oscillation.... eventually it is dampedout). You should note that transient analysis takes a lot morecomputation than frequency analysis (and therefore much moretime). The way to keep them fast is to set up the “.TRAN” statementso that the total time divided by the time step (number of time stepsto compute) is reasonable (i.e., not 10,000... probably a few hundredis best). This is because Spice computes the voltage at eachnode for each time step by solving all of those equations we wantto avoid. It is fast, but not that fast. Even rather simple circuits willtake a long time to simulate if you use a zillion timesteps!

0.0S 1uS 2uS 3uS

uS

-1V

0.0V

1V

2V

V

TIMEtran3

Figure 8: Input pulse applied to circuit in Figure 6 for transient analysis.

Here, ".probe"is added forPSpice. . .

0.0S 10uS 20uS 30uS 40uS 50uS

uS

-400uV

-300uV

-200uV

-100uV

0.0V

100uV

200uV

300uV

400uV

uV

TIMEtran3

Figure 9: Output of circuit in Figure 6 in response to the input pulse.

Exercises - Prelab 1

Work With Your TeamEXERCISE 1: Consider the situation illustrated in Figure 1 below. What is theactual voltage at the outputs of the simple circuit at the left? What is the voltagemeasured at the meter when connected to the circuit on the left (note the old-fashionedanalog meter is the symbol still used for most schematics!)?

"IDEAL" METER

1 MΩ 100pF1.00 V

1 MΩ

Figure 1: Equivalent circuit of HP 34401 measuring an external test circuit.

Now describe what you would measure if the battery on the left was replaced with a 1VRMS AC voltage source at 10 Hz. How about 10 KHz? Do you see why it is asimportant as considering what you are measuring to consider what you are measuringit with?

EXERCISE 2: Consider the accuracy of your measurement when reading the traceon the CRT screen with your eyes... If the beam is 2 mm wide and the entire screen is 8X 10 cm, what is the basic accuracy of your measurements (as a percentage)? Are theaccuracies the same for both axes?

EXERCISE 3: Consider a circuit consisting of a signal generator (AC voltage source),vs, having a source resistance, Rs, connected to a load (R in parallel with C). The loadvoltage is vL.

+-Vs

Rs

R CVL

+

-

+

-

Figure 2: Simple, one-pole low-pass filter.

Derive an expression for the transfer function, T(f) ≡ vLvs

, as a function of frequency.

Derive a formula for the (upper) cut-off frequency, fu (the frequency at which the outputsignal is at 1/2 power or 3 dB down). Note that 3 dB down corresponds to an amplitudeof 0.707 (one over the square root of two) times the starting amplitude (at DC). Thismakes sense because the power in a signal into a given resistance goes as thesquare of the voltage (P = V2/R). One-half the power means the voltage would have tobe the square root of 1/2, or 0.707...

Above fu, what is the roll-off rate of the amplitude versus frequency (dB/decade)? Hint:your equation should show that the output voltage is 20 dB lower per decade ofincrease in frequency - in other words, the signal should be 10X smaller if the frequencyis raised 10X.

If the load consisted of two identical parallel RC circuits, what would the roll-off ratebe? (i.e., put a second parallel RC stage in parallel with the parallel RC shown inFigure 2, and recalculate the transfer function)

As your transfer function should show, this circuit is a low-pass filter. As the frequencyincreases, the output voltage, vL decreases because the capacitor tends to act morelike a short circuit to ground.

Design a simple RC low-pass filter (as shown above) that has an upper cut-off frequencyof 3 kHz (top of the voice band), assuming that Rs = 1 kΩ. Use standard components(see table on the course webpage).

Use the expression you derived above to select the components. Make a SPICE deckand verify that your design is correct (generate frequency and phase response plots).

That's All Folks!

EE122

Prof. Greg Kovacs

LAB 1: HANDS-ONLEARNING WITH ELECTRONIC

TEST INSTRUMENTSWe’re having fun now, aren’t we?

Prof. Bernard Widrow

Note: There are no “right” or “wrong” answers here. The idea is to learnand explore as a team. Record your observations in your lab books andthen (more neatly) in your write-up, which is due at the beginning of thenext lab. That said, please be sure to check with your TA to see whatformat, and what level of detail/rigor s/he expects.

1) Familiarize yourself with the basic operation of all of the instruments onyour bench. Please refer to the user’s manuals (particularly for the digitaloscilloscope) to get a sense for the instruments’ features.

Do not worry about all of the details, as you will learn these as you go.

2) Use the digital multimeter to measure the resistance of various objects(some resistors, your fingertips, some wire). Note the values of the resistorsas they are marked, and the values you measure. Note the resistance ofyour fingertips and how you made the measurements (e.g., two leads onone finger, one lead in each hand, etc.). Yes, these instructions areintentionally vague. Play around. Have fun.

3) Connect the 33120A function generator to the input of the digitizingoscilloscope (Infinium). Note that the voltage that you set the functiongenerator to assumes that you have connected a 50 Ω load (i.e., a 50 Ωresistor to ground). If you do not do this (e.g., use the scope probe, whichis high impedance) the output voltage will be larger (theoretically doublewhat you set it to if it is into a very high impedance). Why is this? Whathappens when you change the input impedance of the Infinium between 1MΩ and 50Ω?

Set the generator to produce a 1 V (peak-to-peak) sinewave at 10 kHz.Set up the oscilloscope so that you have a steady display of a few cycleson the screen (you may have to adjust the triggering). Measure theamplitude.

Capture the waveform to disk and import it into your computer to include

in your Lab 1 report. Import it into an Excel spreadsheet (or spreadsheetprogram of your choice) and plot its square (i.e., compute the square ofeach point’s value and plot the squares versus time).

Set the generator to produce a squarewave at the same amplitude andfrequency. Zoom in (show just a microsecond or so) to the time aroundthe rising edge. Capture the waveform to disk. Do the same for the fallingedge (remember to set the triggering for the falling edge!). Capture thewaveform to disk.

4) Connect one of the small electromagnets to the oscilloscope’s input.Hold it up to various things (operating power supply, oscilloscope, AC linecords, etc.). Look at the signal you pick up and comment on what yousee. If you can, try using the dynamic signal analyzer to look at thefrequency components of the signal (do not worry about capturing thewaveform, but comment - e.g., is there a lot of 60 Hz line pickup?).

For example, tomake a "simple"amplifier with a

A fun op-amp project!

EE122

Prof. Greg Kovacs

PRELAB 2:BASIC OP-AMP CONCEPTS

My favorite programming language is solder.Todd K. Whitehurst

OBJECTIVES (Why am I doing this prelab?)

• To obtain a practical understanding of what operationalamplifiers (“op-amps”) are and some applications forwhich they can be used.

• To understand the basic op-amp circuit configurations.

• To understand the basic characteristics (good and bad)of op-amps before measuring some of them in the lab.

INTRODUCTIONA circuit model of an ideal operational amplifier is shown in Figure1 below. The basic idea is that it is a three-terminal device withtwo inputs, one inverting (- symbol) and the other non-inverting (+symbol). The output signal of the op-amp is given by the differencebetween the voltages applied to the two inputs, multiplied by thegain, A, of the op-amp. The inputs of the ideal op-amp are suchhigh impedance that no current flows into them (on the ideal circuitdiagram, note that they are shown as not connected to anythinginside the op-amp!).

+-

V2

V1

A(V2-V1)

Figure 1: Circuit diagram of an “ideal” op-amp.

As explained above, the device shown in Figure 1 would give anoutput in response to the difference between the two inputs. What

op-amp and tworesistors!

would this be good for? It turns out that it is good for such a largenumber of things that we can barely cover the basics in the timeavailable in this course! It can be used to make amplifiers,integrators, differentiators, comparators, precision rectifiers,oscillators, filters, and a whole mess of other things!

The basic characteristics of the “ideal” op-amp can be roughlysummed up with the following five points:

1) The input impedance is infinite - i.e., no current ever flowsinto either input of the op-amp.2) The output impedance is zero - i.e., the op-amp can drive(supply enough current for) any load impedance at any voltage.3) The open-loop gain (A) is infinite.4) The bandwidth is infinite.5) The output voltage is zero when the input voltagedifference is zero.

Quite often, typical integrated circuit op-amps can be consideredto be “ideal,” but as you all know, there aren’t many truly idealthings around. We’ll get into all of the imperfections of real op-ampslater on (bet you just can’t wait!).

To simulate the ideal op-amp shown in Figure 1 in Spice, thefollowing text would be required:

EXXXXXXX N+ N- NC+ NC- GAIN

where a voltage-controlled-voltage source (whose name must beginwith “E”1) has positive and negative outputs (N+ and N-, respectively)and is controlled by a positive and a negative control voltage (NC+and NC-, respectively). The “open-loop gain” of the voltage sourceis determined by the value used for “GAIN.”

A Spice line corresponding to the circuit in Figure 1 might be:

Eout 3 0 2 1 100K

if you wanted to simulate an open-loop gain of 100,000. Note that

1Of course, you can replace the “X”s with any meaningful characters....

the negative output node is connected to Spice ground (node 0).

Also note that you must always be careful about the ordering of thenodes... It is easy to switch the NC+ and NC- nodes and “invert”your design! One big difference between this “ideal” op-amp anda “real” op-amp is that the model can swing its output between +/-infinity and “real” op-amps cannot swing beyond their power supplyvoltages.

Note that “real” op-amps can also be modeled quite well, althoughit can get somewhat complex to simulate all of their imperfections!This will be discussed below.

The basic circuit configurations for op-amps will be covered belowafter a brief message about feedback (since it is used in nearly allop-amp circuits). It is not the purpose of this course to give you anin-depth overview of feedback.... Instead, the point is to show yousome ways to use it!

FEEDBACK: WHAT IS IT ANDWHERE CAN I GET SOME?

As you may already know, there are two types of feedback:regenerative (positive feedback) and degenerative (negativefeedback).

In general, positive feedback is not great for amplifiers.... it tends tomake transistors blow up and smoke emerge from circuits (not tomention oscillations)... Of course, if you want to make an oscillator,positive feedback may be just the thing you need....

On the other hand, negative feedback is great (not always thecase when used with people)! It is used in most amplifiers andoffers to improve your circuits in several ways:

• The gain of the circuit is made less sensitive to thevalues of individual components.

• Nonlinear distortion can be reduced.

• The effects of noise can be reduced.

• The input and output impedances of the amplifier canbe modified.

• The bandwidth of the amplifier can be extended.

Sounds good, doesn’t it? All you have to do to “get some feedback”(of the negative kind) is to supply a scaled replica of the amplifier’soutput to the inverting (negative) input and presto! Of course, ifyou use negative feedback, the overall gain of theamplifier is always less than the maximum achievableby the amplifier without feedback.

For a more detailed preview of feedback, see Sedra & Smith,

Chapter 8.

For the ideal op-amp shown in Figure 1, without feedback the gainof the amplifier would be A (otherwise referred to as the “open-loop” gain, meaning that there is no closed feedback loop).

The best way to understand the effects of feedback on the actualcircuits of interest is to dive right in and have a look at them (ofcourse, there will be a few exercises to do as well....).

WHAT CAN YOU DO WITH OP-AMPS?

This section contains an overview of some basic op-amp circuits.These are the fundamental building-block circuits from which themajority of op-amp application circuits are built. This overviewcovers the “bottom lines” on these circuits. For more detail, seethe textbook or some of the references listed at the end of thisprelab. Also note that later we will cover some of the more“advanced” op-amp circuits....

THE VOLTAGE FOLLOWER

The voltage follower (or unity-gain buffer) is the simplest op-ampcircuit. It produces an identical “copy” of its input at its output. Thefirst question that might come to mind is ‘why not use a devicecalled “wire” to accomplish this?!’ By connecting the output of onestage directly to the next stage the signal itself could be adverselyaffected (e.g.,, if the input impedance of the next stage is too lowand the input-driving device cannot drive enough current). With avoltage follower in place, however, the input signal is connected toa very high-impedance input and a copy of it is made available ata very low-impedance output (i.e., the output “follows” the input,and the op-amp makes sure that both sides are happy).

As shown in Figure 2 below, the output of the op-amp is connecteddirectly to the inverting input. The input signal is applied to thenon-inverting input. As for all op-amp circuits using negativefeedback, the circuit automatically keeps the voltagedifference between the two inputs at zero (or very nearlyso!). This is a key point! If you remember that, op-amp circuitsgenerally make a lot more sense! (The truth of the matter is that ifthe voltage difference were exactly zero, the output of the op-ampwould be zero too... in practice the difference is on the order of amillivolt, and the error introduced by assuming it is zero is negligible.)

V- VOUTV+

VIN

Figure 2: The voltage follower, or buffer.If one works out the math, it is clear that the output voltage can beobtained by substituting,

V- = VOUT

into the basic op-amp equation,

VOUT = A V+ - V-

which yields,

VOUT = A1 + A

V+

Since the op-amp’s open-loop gain is very large (infinity for theideal op-amp), the output voltage thus equals the input voltage.

THE INVERTING AMPLIFIER

The next op-amp configuration is the inverting amplifier, whichproduces an inverted (180° out of phase if purely sinusoidal orotherwise symmetric) output with respect to the input signal. Theoutput signal is also amplified by a factor that is determined by theratio of the two resistors shown in Figure 3. (You get to derive thisrelationship as a Prelab Exercise!)

R2

R1

iin

i fb

VOUTVIN V-

V+

Figure 3: The inverting amplifier.

The intuitive way to analyze this circuit is to consider that , sincethe non-inverting input is grounded and negative feedback is used,the inverting input will be kept at “virtual” ground by the feedback.Thus, the currents iin and ifb must be equal. (We could also seethat these currents must be equal by noting that very little currentcan enter the high-impedance terminals of the op-amp) This meansthat the output of the op-amp must swing far enough that a current

through R2 is drawn that equals iin. If R2 is larger than R1, therequired output voltage from the op-amp is larger than the inputvoltage.... AHA! GAIN AT LAST!

To see why the V- input must be at or near ground in this case,consider that ,

VOUT = A 0 - V-

or

V- = - VOUTA

Since A is very large, V- ends up being very near zero.... Thiscomes back to the statement made above that the voltage differencebetween the inverting and non-inverting inputs is very small, butmay not actually equal zero. This is because A is not infinity inreal op-amps, among other reasons.

Derive the voltage gain of the circuit in Figure 3 assuming that R2was replaced by a capacitor (more on this circuit below). Computethe input impedance of the circuit for both cases (again considerthe assumptions about V-....)

2.

THE NON-INVERTING AMPLIFIER

The non-inverting amplifier looks a lot like the inverting amplifierexcept that the input signal is applied directly to the non-invertinginput and R1 is grounded at one end.

A key point to note here is that the V- node is not avirtual ground in this configuration! The important thing toconsider is that the voltage difference between V+ and V- is keptnear zero. In other words, V- ≈ VIN. You will also derive the transferfunction (Vout/Vin) for this circuit in the Prelab. I bet you can’t wait!

R1

R2

i1

i2

VOUT

VIN

V-

V+

Figure 4: The non-inverting amplifier.

THE SUMMING AMPLIFIER

2Here you can again consider the way the feedback loop holds the V- input at “virtual ground” bynegative feedback. You could also look at it using the Miller Approximation...

The (inverting) summing amplifier shown in Figure 5 below, canbe used for adding together several input signals (this circuit formsthe heart of audio mixers used in recording studios).

Rf

R3

R2

R1

R4

Rn

i f

VOUT

V1

V

V-

+

V2

V3

V4

Vn

i1

Figure 5: The (inverting) summing amplifier.

THE INTEGRATORR2

R1

C1

VOUT

V

V-

+

VIN

iin

Figure 6: The op-amp integrator.

The op-amp integrator shown in Figure 6 has one component, R2,that is not needed in “ideal” integrator circuits. Its purpose is tolimit the DC gain of the op-amp so that its small DC offset voltagewill not charge up the capacitor.

For DC inputs, the gain can be found as for the inverting amplifierto be (yeah, this is part of the answer to Exercise 1, but you haveto show your work!),

VOUTVIN

= - R2R1

For AC inputs of sufficiently high frequency that R2 can be neglected(assuming no R2), one can write the equations for the currents thatmust be equal in the input and feedback circuits (again noting thatthe V- input is a virtual ground),

iin = ifb

thus,

vinR1

= - C1d voutdt

From which the output signal from the “ideal” integrator circuit(without R2) should be,

vout = - 1R1 C1

vindt

But this only works for frequencies above the point where the effectof R2 dominates the DC gain of the circuit. The frequency belowwhich the circuit’s behavior becomes more like a DC amplifierthan an integrator is given by:

fmin = 12π R2 C1

THE DIFFERENTIATOR

R2

R1 C1

VOUT

V

V-

+

VIN

iin

i f

Figure 7: The op-amp differentiator.

In the differentiator circuit shown in Figure 7, there is also acomponent, R1, that is sometimes not shown in “textbook” op-ampdifferentiator circuits. Its purpose is to limit the high-frequency gainof the differentiator so that the circuit does not get swamped byhigh frequency noise (which may have a large derivative despite asmall amplitude).

For “low-enough” frequencies that the input impedance is dominatedby C1, iin and i f can be equated to show that,

vout = - R2 C1 dvindt

As for the integrator above, there is a frequency range over whichthe differentiator will not work very well. In this case, there is an

upper frequency above which the circuit simply acts as an invertingamplifier. The maximum frequency is given by:

fmax = 12π R1 C1

For higher frequency AC inputs, the gain approaches (you guessedit!),

VOUTVIN

= - R2R1

AN “UNAUTHORIZED” HISTORY OF OP-AMPS

The term operational amplifier dates back to the days of the analogcomputer.... Before every 12-year-old kid had a personal computerwith tons of RAM, people used analog computers a lot. The sliderule is an example of an analog computer that can double as aneating utensil if necessary. Other analog computers had lots oftubes, got very hot, and seldom worked well (it is interesting tonote that the term “de-bugging” as applied to computer programsdates back to the physical removal of bugs such as moths fromtube-filled computers into which they were attracted). These glass-and-metal contraptions often used analog techniques to computeintegrals, differentials, and so on (as we have just seen, these arerelatively straight-forward things to do with analog components).The basic sub-circuit of the computational units was the so-called“operational amplifier” which usually consisted of two or more tubesand took up the volume of a small engineering textbook. Ascomputers were miniaturized, and with the advent of transistors,op-amps became increasingly smaller until they were only the sizeof a pack of matches (you know, those things people used to useto light cigarettes). Inside the outer casings were lots of discreteresistors, transistors, capacitors, etc., soldered together and “potted”with plastic resin in to one solid chunk. These “blob-amps” eventuallygave way to the integrated circuit op-amp that we use today. Figure8 below indicates that there have been considerable improvementsin integrated op-amps over the years, but no matter what, marketingguys are always the same....

LM741 MonolithicOperational Amplifier

LT 1028 Ultra-HighPerformance Op-Amp

Features:• Ultra high performance• It works (often)• 1MHz Gain-Bandwidth Product• Monolithic• Low cost

Features:• Ultra high performance• 75 MHz Gain-Bandwidth Product• 35 nV/√Hz noise• 12 nA Input Offset Current• Low cost

Marketing hasn't changed!

1972 2000

Figure 8: Comparison of parts of two “typical” op-amp data sheets from 1972 and2000. Note that performance has changed, but marketing has not.

BASIC PARAMETERS OF OP-AMPS

This section is concerned with discussing the various electricalparameters of real op-amps. Some of the parameters are “features”that improve performance. Others are “imperfections” that hinderit. (You can get a good sense for what category any specificationfalls into by looking at the data sheet!)

We will now consider the major specifications of operationalamplifiers.

OFFSET VOLTAGE

If an op-amp were perfectly balanced, the DC output voltage, VOUT,would be zero when no differential voltage is applied to the inputs.Owing to minor imbalances, this is not the case. A real op-amp canbe thought of as a perfect op-amp with a small offset voltage, VOFF,applied differentially to the inputs.

Due to the large voltage gain, even a small VOFF can result in alarge VOUT. With a circuit gain of 100,000, a typical offset voltage of1 mV would result in an output voltage of 100 V. Since thepower-supply voltages are much smaller than 100 V, the amplifierwould “rail” (the output will be near V+ or V -, depending on inputpolarity).

Many op-amps have two pins to which an external potentiometer(variable resistor) connected to a DC voltage can be connected to“null” out VOFF, if needed.

GAIN, BANDWIDTH, AND STUFF LIKE THAT...

The open-loop gain (‘A’) is the specification that indicates themaximum gain of the op-amp (this is the gain that you would obtainwithout any feedback, hence the name). Open-loop gains of op-amps are generally very high (on the order of 100K to 1MEG!). Asyou will see in the lab, that means that the open-loop gain is ratherhard to measure since the op-amp’s output can only swing to nearthe power supply voltages (thus it is hard to apply a small enoughsignal to the input so that you get an undistorted output, evenwithout worrying about offset!).

So, open loop gain is essentially infinite, but, since op-amps arenot infinitely fast, their gain decreases as the input frequencyincreases. This makes sense, since for a higher frequency, thetransistors inside must swing the output faster and faster to reachthe same output amplitude. In practice, the output eventually cannotswing fast enough and the amplitude of the output signal falls withincreasing frequency... which brings us to the term slew rate.

The slew rate specifies the maximum rate at which the op-amp canswing its output. Slew rate is traditionally given in units of V/µS(but newer op-amps, that can swing at over 5,000 V/µS make youwonder if we will change to V/nS...).

The unity-gain bandwidth is the frequency at which the open-loopgain of the op-amp falls to one. As you can see in Figure 9, below,the open-loop gain falls rapidly above the low frequency cutoff (or“break” frequency) fu which is defined as the frequency at whichthe gain has fallen 3dB from the DC value, as shown in the “close-up”in Figure 10 below.

The slope of the open-loop (voltage, not power!) gain curve is -20dB/decade (-6 dB/octave). In other words, for a ten-fold increasein frequency, the gain falls ten times. This first-order low-passeffect is due to the "dominant pole” of the op-amp (typically due toan on-chip capacitance put there to ensure stability of the circuit).Such capacitors (“compensation capacitors”) are often used in evensingle-transistor amplifiers to obtain a controlled gain roll-off.

Measuring the slew rate of a lobster with a piece of bungie-cord....

-3 dB

fu1.0h 100h 10Kh 1.0Mh 10Mh

FrequencyV(5)/V(1)

1.0M

100

10m

Figure 9: Simulation of the open-loop gain of the 741 op-amp. The plot is theoutput voltage divided by the input voltage, shown with log/log axes. Note thatthe gain falls very rapidly, beginning at very low frequencies.

1.0h 3.0h 10h 30h 100h

FrequencyV(5)/ V(1)

1.0M

100K

10K

fu

Figure 10: Close-up view of the open-loop gain near the cutoff frequency, fu

(approximately 9 Hz in this case).

30

Traditional costumes of analog circuit designers.

NICE HAT!

The unity-gain bandwidth is the frequency at which the open-loopgain falls to 1, as shown in Figure 11 below.

100Kh 300Kh 1.0Mh 3.0Mh 10Mh

FrequencyV(5)/ V(1)

100

1.0

10m

fT

Figure 11: Close-up view of the open-loop gain near the unity-gain frequency, fT

(approximately 1 MHz in this case).

A very important fact is that the product of the gain andthe cutoff (3dB) frequency is constant at any point onthe response curve of the amplifier.

This means that you are always trading off gain for frequencyresponse! The more gain, the sooner the response begins to rolloff. Another way of looking at this is that at higher gains, you getcloser to the open-loop gain situation, where the roll-off begins atfu, and at lower gains, you are closer to the unity-gain situationwhere the gain extends out to fT. This gain/frequency responsetrade-off is expressed as the gain-bandwidth product of the op-amp.

The gain-bandwidth product is a key parameter in the selection ofop-amps since it expresses the limits for amplification/frequencyresponse performance!

Note that to ensure that op-amp circuits operate without distortion,you should design the circuit so that the gain at your maximumfrequency is no more than approximately 1/10 th to 1/20 th of theopen-loop gain at that frequency. In other words, leave yourself a10-20X safety factor! (For precision circuits, such safety factorsmay be quite a bit larger, but their determination is beyond thescope of these notes!)

STABILITY AND COMPENSATION

Real op-amps have an open-loop gain roll-off with frequency thatis approximately first-order (-20 dB/decade) over much of their usefulbandwidth. The major internal capacitance that causes this roll-offis often referred to as the “dominant pole” of the amplifier (mentioned

RULEOF

THUMB!

previously). At higher and higher frequencies, other capacitanceeffects come into play as additional poles (sometimes there arethree or more). This means that the open-loop phase response ofthe amplifier will eventually reach -90° times the number of poles....If the phase is between +180° and -180° when the gain of theamplifier reaches a gain of unity (0 dB), everything remains stable.

However, if the phase crosses -180° before the (closedloop) gain falls to unity, oscillations will probably occur(since an inverted replica of the amplifier’s output is fedback into the inverting input, resulting in positivefeedback)! If an op-amp circuit is unstable, almost anynoise present in the circuit will have enough of a high-frequency component to cause the circuit to oscillate.

In other words, if the phase crosses -180° at a frequency wherethe gain of the amplifier is less than unity, the amplifier is“unconditionally stable!” The most common way to guaranteestability is to compensate the amplifier with some additionalcomponents that shape its frequency response so that its gain isless than unity by the time the phase hits -180°. This does, however,compromise the high-frequency response of the amplifier!

In practice, higher gain circuits have less of the output signal fedback to the input, and are thus less susceptible to instability. Thus,the lower the closed-loop gain, the more likely it is that compensationwill be required. You will see this first hand in the lab.

Most op-amps are “internally compensated,” which means that thecomponent(s) required to guarantee stability are included on thechip itself. Some of the older op-amps, and those designed forhigh-speed operation, are “externally compensated,” which meansthat you, the designer, must choose external components to assurethat the amplifier will not become unstable.

COMMON-MODE SIGNAL REJECTION

If op-amps were perfect difference amplifiers, then the output shouldalways be zero if you apply the same signal to the non-invertingand inverting inputs at the same time, right? Well, as you mightguess, they are not perfect at this either.... Such a signal, appliedto both inputs at the same time, is called a common-mode signal.Common-mode rejection is important to consider becausesometimes external noise is applied to op-amps unintentionally...

POWER SUPPLY REJECTION

If you think about it, a good amplifier should be relatively insensitiveto undesired variations in the voltages that are powering it. MostDC power supplies have some “ripple” and it would be bad if thatripple was picked up (and/or amplified!) by the op-amp. Op-ampsare generally very good at rejecting variations in their power supplyvoltages (i.e., not reflecting them at their outputs).

OUTPUT VOLTAGE SWING

A note about power supplies is that, while the op-amp can swingits output nearly to the supply voltages (usually +/- 12 or 15 volts),it can’t swing them farther. What happens when the input signal isso large that the op-amp circuit’s gain calls for a swing beyond thesupply voltages is that the amplifier’s output will “clip” (i.e., thevoltage hits either “rail” and stays at that supply level until the inputreturns to the linear range of the op-amp). This is the effect thatcauses the nasty audio distortion when you turn an amplifier uptoo loud. (A note for you rock & rollers: at high enough volumes,your ear drum will clip too!)

"We don't need no education...."

OTHER OP-AMP PARAMETERS

Other op-amp parameters that are often considered (but will not bediscussed in depth here) are the noise performance of the op-amp(referring to its internally-generated noise), its power consumption,its input impedance (sorry folks, it’s not infinity, but often darn close!),

GOLDEN RULE OF

OP-AMP SIMULATION:

The lousier the op-amp,

The harder it is to simulate!

and many others. If you are interested, you should refer to some ofthe references given at the end. Also be sure to check out thedatasheets for some common op-amps (741, 411, 1056, etc...) thatare on the manufacturers’ or the course’s websites.

HOW TO MAKE SPICE SIMULATE “REAL” OP-AMPS

As discussed above, it only takes one line to specify an “ideal”op-amp in Spice. However, it is considerably more complex tomodel the imperfections of op-amps! (Interesting that we have towork so hard to simulate things we don’t really want at all!) Whilethe details of these models are beyond the scope of thiscourse, the interested reader (is there any such thing?) can inquireto obtain some more information. An example model of the UA741(a somewhat obsolete, but still useful, op-amp) is listed below andis available on the lab computers or the web.

Most op-amp manufacturers provide downloadable “macromodels”for the majority of their op-amp products.

* UA741 operational amplifier "macromodel" subcircuit* connections: non-inverting input* | inverting input* | | positive power supply* | | | negative power supply* | | | | output* | | | | |.subckt UA741 1 2 3 4 5*c1 11 12 4.664E-12c2 6 7 20.00E-12dc 5 53 dxde 54 5 dxdlp 90 91 dxdln 92 90 dxdp 4 3 dxegnd1 98 0 3 0 0.500000egnd2 99 98 4 0 0.500000fb1 7 99 vb 10610000.000000fb2 7 99 vc -10000000.000000fb3 7 99 ve 10000000.000000fb4 7 99 vlp 10000000.000000fb5 7 99 vln -10000000.000000ga 6 0 11 12 137.7E-6gcm 0 6 10 99 2.574E-9iee 10 4 dc 10.16E-6hlim 90 0 vlim 1Kq1 11 2 13 qxq2 12 1 14 qxr2 6 9 100.0E3rc1 3 11 7.957E3rc2 3 12 7.957E3re1 13 10 2.740E3re2 14 10 2.740E3ree 10 99 19.69E6

ro1 8 5 150ro2 7 99 150rp 3 4 18.11E3vb 9 0 dc 0vc 3 53 dc 2.600ve 54 4 dc 2.600vlim 7 8 dc 0vlp 91 0 dc 25vln 0 92 dc 25.model dx D(Is=800.0E-18).model qx NPN(Is=800.0E-18 Bf=62.50).ends

To use this and other subcircuits in Spice, you need to insert a linein your deck that begins with an “X” to make each “copy” of thesubcircuit. An example of a unity-gain circuit made with the UA741subcircuit is shown below.

X1 1 2 3 4 2 UA741Vplus 3 0 15VVminus 0 4 15VVin 1 0 AC 1 0.AC DEC 100 1hz 10MEG.probe.end

Note that you have to explicitly specify the power supplies for theseop-amp subcircuits.

WHY ARE THERE SO MANYDARNED OP-AMPS AROUND?

At last count, there were hundreds of types of operational amplifierscurrently available from U.S. manufacturers. An astute reader (i.e.,one who noticed the above heading) might ask, “Why are there somany darned op-amps around?” The answer has to do with eitherthe basic functions of the op-amps or with the details of theirspecifications.

Examples of the different basic op-amp functions include powerop-amps (that can output several amperes of current), high-speedop-amps (that can operate at frequencies of hundreds of MHz),dual or quad op-amps (that include two or four amplifiers in asingle i.c. package), and so on.

Examples of different specifications include low-noise, low-power,high-gain, low-offset voltage, and other specific improvements inop-amp characteristics, such as those discussed above.

Other factors in choosing op-amps include such basic things asthe semiconductor technology with which they are built.... Some,like the 741, use strictly bipolar transistors. Others, such as the

Often, you can get these free or cheap if you call and tell them you are a student!

LF411 use JFET inputs to increase their input impedance anddecrease their noise. Still others are built with CMOS circuits forlower power.... If you are serious about designing with op-amps, itwould be very useful to look through a few modern databooks tosee what’s out there!

GOOD FURTHER READING ON OP-AMPS

(This is only a sampling, not a comprehensive list....)

T. C. Hayes and P. Horowitz, “Student Manual for The Art of Electronics,” CambridgeUniversity Press, 1989, pp. 163-243

H. M. Berlin, “Design of Op-Amp Circuits,” Howard W. Sams & Co., 1990

W. C. Jung, “IC Op-Amp Cookbook,” Howard W. Sams & Co., 1989 (?)

"Analog Devices 1992 Amplifier Applications Guide," Analog Devices, Inc.,Norwood, MA, 1992, (617) 329-4700

“The Handbook of Linear IC Applications,” Burr-Brown, Co., International AirportIndustrial Park, P.O. Box 11400, Tucson, AZ

“Linear Technology Applications Guide,” Linear Technology, Co., Milpitas, CA

“National Semiconductor Linear Applications Guide,” (more than one volume thesedays!), National Semiconductor, Co., Santa Clara, CA

ENGINEERING UNITS REVIEW

1012 helluva-109 heckuva-106 lotsa-103 buncha-10 decca-10-3 silli-10-6 pismo-10-9 banana-10-12 doodoo-10-15 nono-10-18 nada-

(from “Science Made Stupid,” by Tom Weller)

Exercises - Prelab 2

Work With Your TeamEXERCISE 1:

Derive the voltage gain of the inverting amplifier (Figure 3) in terms of R1 and R2. Hint:remember that V- will be approximately zero volts. Remember to show your work.

EXERCISE 2:

Derive the voltage gain of the circuit shown in Figure 4 (non-inverting amp) in terms ofR1 and R2. Hint: remember the fact that the input current to the op-amp is (almost)zero. What is the input impedance of this circuit (assuming an ideal operationalamplifier)?

EXERCISE 3:

Derive an expression for the output signal of the circuit in Figure 5 (inverting summingamplifier) in terms of the resistors shown and the input signals V1 through Vn. Hint: allof the input resistors are connected to a virtual ground...

What is the input impedance at each of the input resistors?

Comment on how you could use this circuit for an audio mixer (e.g., in a recordingstudio). Comment on how you could use it for an audio equalizer (hint: think about abank of filters in front of it).

EXERCISE 4:

Design an integrator (assume an ideal op-amp with an open-loop gain of 100K) thatwill provide a triangle wave output of 1 V peak-to-peak for a 1 V peak-to-peak squarewave input at 1 Khz. Start with a sketch of the waveforms and consider the scaling ofR1 and C1 to get the correct output signal. Hint: sketch the waveforms and considerthe time over which you are integrating things!!! Start out with a value of R2 chosen toobtain a DC gain of 10. If you are not using a graphical-input SPICE, your Spice deck(why?) should look like this (you replace the “?” marks with your chosen componentvalues):

Op-Amp Integrator Simulation*YOU fill in the component values!R1 1 2 ?

Actually, this plot was made using a 2V Peak-to-Peak inputsignal.... Yours should use 1V Peak-to-Peak...

CI2 2 3 ?R2 2 3 ?E1 3 0 0 2 100KVin 1 0 pulse(-0.5 0.5 0 5nS 5nS 500uS 1mS).TRAN 100uS 10mS.probe.end

Simulate the circuit in the time domain using an ideal op-amp in the above Spicedeck. When you get it “right,” you should get some output from Spice that lookssomething like Figure 12 below.

0.0S 2mS 4mS 6mS 8mS 10mS

mS

-10V

0.0V

10V

V

TIMEtran3

V(1) V(3)

Figure 12: Example output of an integrator with square wave input.

What is wrong with this picture? The integrator is starting out with initial conditions of-1V DC applied to its input. The way Spice works, it first computes the initial conditionstherefore, the circuit’s output starts at +10V!

Modify your Spice input (or your plot) to obtain a “nice” looking plot of the integrator inoperation after it has “settled down.” (Don’t try for perfection here! Just show that theoutput amplitude is close to what you designed for!)

Now try changing R2 to get DC gains of 5 and 1. What effect does this have on theoutput waveform and the time to “settle down” to a steady-state output waveform? Is itwhat you expected?

Obtain the gain and phase responses versus frequency for your integrator designusing Spice.

Actually, this plotwas made from acircuit with a 2VPeak-to-Peakoutput... yours should be 1 VPeak-to-Peak...

EXERCISE 5:

Design a differentiator that, when placed in series with the integrator you designedabove, gives you back the 1 V peak-to-peak square wave that you input to the integrator.Verify that it works using Spice. You should get some output that looks at least asgood as Figure 13 below. Obtain the frequency and phase responses of theintegrator/differentiator combination. Comment.

10mS 11mS 12mS

mS

-2V

0.0V

2V

V

TIMEtran2

V(1) V(3) V(6)

Figure 13: What your simulation results should look like (or close).

EXERCISE 6:

Using the UA741 subcircuit model (available on the lab computers, on the web, or inthe PSpice parts browser), simulate the frequency and phase response of a gain-of-100inverting amplifier built with the 741.

Then determine the slew rate of a unity-gain amplifier using the 741 model by runninga transient analysis with a pulse input signal at a frequency that makes the 741 havedifficulty keeping up with the input voltage swings (try around 100 KHz).

That's All Folks!

EE122

Prof. Greg Kovacs

LAB 2: WHAT IS AN OP-AMPANYWAY?

What in the world is electricity?And where does it go after it leaves the toaster?

Dave Barry

NOTE: This is not a “spoon-fed” lab. You will not be told which buttons topush. You will have to plan and execute the necessary measurements.The TAs will, of course, be there to guide you.

You will not be told exactly what to put in your write up. The idea is thatyou present your data and what you learned from it. Typically, you willmake plots and analyses a part of the write-up. Write-ups must not belonger than ten pages. But, they must be a sufficiently clear and completeaccount of your experiments with commentary on the results.

INTRODUCTION

In this lab session, you will use a solderless breadboard, illustrated below. This is areally useful tool for prototyping circuits without soldering (you DO know what solderingis, don't you grasshopper?).

You can put ordinary "dual-in-line" integrated circuits into the central area of thebreadboard and be able to connect multiple wires to each pin. You can also puttransistors, diodes, resistors, capacitors, etc., into the holes.

You should carefully look at the figure below so you get a sense for theinternal connections of the pins.

If you don't do that, you can waste a LOT OF TIME!!!.

Each set of five pins are shortedtogether internally so you canmake multiple connections to onei.c. pin or component lead...

Each of the long rows of pins is shortedtogether so you can use them as powersupply and ground lines...

Figure 1: Layout of a standard solderless breadboard, showing the internalelectrical connections. Please take note of this carefully! (On some olderbreadboards, the four long “bus” connections on opposite sides of theboard are split in the middle - you must jumper them in the middle if youwant them to be connected the whole way across the breadboard.)

LM741

N.C.

OffsetNull

OffsetNull

V+

V-

Out

-IN

+IN

1

2

3

4 5

6

7

8

-

+

Figure 2: Typical op-amp pin-out. Please refer to the datasheets for the exactdevices you are using, just to make sure!

-

+

You should note that virtually all single op-amps in 8-pin DIP’s("dual in-line package") are pin-for-pin compatible. In other words,you can just plug any of them into a pre-existing circuit configurationand go. There are some exceptions however (particularly in theoffset-null circuits), so always check the data sheets!

Before you begin constructing your op-amp circuits, you should set the current limits to50 mA (to limit the maximum current in case something is wired up wrong). Your TAshould demostrate this procedure, as it is an important safety consideration...if not foryou, certainly for your circuit.

Be sure to turn off the power before you change op-amps.

1) This set of experiments calls for exploring the basic properties of somecommon op-amps. In each case, build the circuit and test at least two ofthe op-amps available (you must use the 741 and the LT1056 or equivalentthe TAs will give you).

Be constantly on the alert for output oscillations. Not all op-amps areunity-gain stable. For example, the LT1221 is only stable for gains ≥ 4.Thus, you would not use the LT1221 for a unity-gain experiment.

ALWAYS use 0.1 µF decoupling capacitors on each power supplyrail, right next to each op-amp. Use one capacitor from the positiverail to ground and one from the negative rail to ground.

Set up an inverting op-amp circuit with an inverting gain of ten and anoutput load resistor (to ground) of 2 kΩ (you may need to use two 1 kΩresistors in series). Use ± 15 V supplies. You may wish to put an input50 or 51 Ω resistor from the signal generator’s output to ground so thatthe amplitudes on the signal generator are correct (they assume a 50 Ωload). Choose an input signal amplitude such that, for each gain you use,the output swing is ± 10 V (20 volts peak-to-peak) at a low frequency like100 Hz.

For each op-amp tested record the gain and phase in response to asinewave at a series of frequencies you choose to illustrate its performance.A good approach is to use log steps (1 - 2 - 5 - 10 - 20 -... and so on). Donot take too many measurements, but try to go high enough to see the 3dB frequency (you will not necessarily be able to get there for the fasterop-amps). Record your observations and all input voltage and otherdetails.

Repeat for a gain of 100. If you are clever, you can wire up more thanone “copy” of the circuit and make measurements faster.

Comment. Is this in keeping with a “gain-bandwidth product?” If you want,you might want to hunt for the 3 dB frequency at a gain of 1000.

PRACTICALPOINT

2) Wire up at least two unity-gain stable op-amps (741 and LT1056) in unitygain configuration. Drive them with a 1 VPP squarewave with the signalgenerator terminated into 50 Ω and an op-amp load resistance of 2 kΩ toground. Using the digital oscilloscope, calculate the slew rates for eachop-amp on the rising and falling edges of the squarewave.

Try the same op-amps at a gain of ten, and also try a fast op-amp (LT1221).

How do your measurements compare to slew rates reported in the datasheets?

When you are done measuring them, try without the power supply decouplingcapacitors. Do you see why they are needed?

3) Build the integrator and differentiator you designed in the prelab. If youcannot get the exact component values, approximate, but be consistent inboth circuits. Test with the LT1056 or equivalent the TA suggests. Observeand compare to your simulations. Try hooking them in series (integratorfirst) and putting in a squarewave - what do you get out?

Note: There are no “right” or “wrong” answers. The idea is to learn andexplore as a team. Record your observations in your lab books and then(more neatly) in your write-up, due at the beginning of the next lab. Also,be sure to address any comments your TA had for your previous write-up.

EE122

Prof. Greg Kovacs

PRELAB 3:MORE OP-AMP CIRCUITS!

If you can’t fix it, make it a feature...Anonymous

OBJECTIVES (Why am I doing this prelab?)

• To gain insight into op-amp application circuitsbeyond those considered in Lab 2.

• To understand the basics of analog filters.

• To understand comparator and Schmitt-Triggercircuits.

• To understand some linear and nonlinear oscillators.

INTRODUCTION TO ACTIVE FILTERSOne of the basic building blocks for analog circuits is the filter. Thepurpose of filters is generally to achieve some frequency selectivityby processing input signals so that desired signal frequencies arepassed through the filter (sometimes amplified as well) andundesired frequencies are attenuated. As electrical engineers (ortheir ancient equivalents) have known for many years, filters canreadily be constructed from passive components (resistors,capacitors and inductors).

The advent of active components has led to tremendousimprovements in filter performance, as indicated in the “Pro’s andCon’s” list below:

Pros of Active Filters1) elimination of inductors2) low cost (largely due to item 1)3) smaller size and weight (due to item 1)4) high isolation (high input impedance, low output impedance)5) characteristics relatively independent of loading (due to item 4)6) user-defined gain

Cons of Active Filters1) requirement for power2) limited dynamic range (lower limit due to noise, upper limit due

For more details on filters, see Horowitz & Hill or the references listed at the end of the filters section.

to clipping)3) limited frequency range (lower limit due to large capacitors,upper limit due to active device performance)

While many filtering applications now use digital filters to obtainvirtually arbitrary transfer functions, analog filters are still requiredin such cases at the analog inputs and outputs of the digital systems.In addition, analog filters form vital parts of several commonelectronic devices such as radios, televisions, and home audioequipment3.

THE BASIC TYPES OF FILTERThere are five basic filter types that bear consideration at this point(shown below in Figure 1): low-pass, high-pass, band-pass, notch,and “all-pass” (more on that last, weird-sounding one later). Low-pass filters (by far the most common type) ideally pass all frequenciesbelow a specific cut-off frequency. High-pass filters ideally passall frequencies above a specific cut-off frequency. Band-passfilters ideally have a passband between a low and a high cut-offfrequency and reject frequencies outside of this band (thestopband). Notch filters ideally reject only a specific, and oftenvery narrow, band of frequencies, passing all others. All-passfilters ideally pass all frequencies equally in amplitude (as thename implies!), but change the phase of the input signals dependingupon their frequency (more on this later).

Figure 1: The “gain” (or “frequency”) response of the basic types of filters.Unfortunately, none of these “brick-wall” filters can be realized. Actual filters havemore “rounded” transfer functions...

3For frequencies between approximately 0.1 Hz and 100 KHz, op-amp filters are generallyreasonable. Above these frequencies, LC filters are small and inexpensive, and are typically used.

REALLY SIMPLE FILTERS!

To start the discussion, it is worthwhile to review some basic, passiveRC filters and get a sense for where their poles and zeros are onthe S-plane4 (or, for the less-informed reader, what poles, zerosand the S-plane are!).

For the first-order, RC low-pass (the schematic of which is shownin Figure 2 below), the transfer function can be shown (easily!) tobe:

voutvin

= a0Sω0

+ 1

with the single pole at S = -ωo as shown in Figure 2 below (ao isthe gain for low frequencies). The cutoff frequency of this filter isgiven by,

ω0 = 2πfc = 1RC

V Vin out

R

C

Figure 2: Schematic and pole position of the first-order, RC low-pass filter.

The frequency and phase response of this filter is shown in Figure3 below.

In this example, the cutoff frequency (shown as fc in Figure 2) is1KHz. At this frequency, the amplitude of the filter’s output hasfallen to 0.707 times its amplitude in the “passband” (frequencyrange without significant attenuation) and the phase is at - 45°.

In addition, the cutoff frequency in radians, ωo, is the distance ofthe pole from the jω axis (measured perpendicular to the jω axis,

4If you hadn’t remembered by now, S is the Laplacian operator, and the complex frequencyvariable (S = σ + jω )

as shown in Figures 2 and 4).

0.707 V

- 45°

1 KHz

Figure 3: Gain and phase responses of the first-order, RC low-pass filter.

For the first-order RC high-pass (the schematic of which is shownin Figure 4 below), the transfer function is:

voutvin

= a1SS + ω0

with a single pole at S = -ωo and a single zero at S = 0 (a1 is thegain for high frequencies). The cutoff frequency is, of course, thesame.

R

CV Vin out

Figure 4: Schematic and pole position of the first-order RC high-pass filter.

0.707 V

+ 45°

1 KHz

Figure 5: Gain and phase responses of the first-order, RC high-pass filter.

As you can see, the poles and zeros correspond to the values of Sthat set, respectively, the denominator or numerator of the transferfunction equal to zero. If you plug a specific sinusoid (s = 0 + jω)into the transfer function, you get the relative response to an inputat that frequency (ω).

A pole will make the frequency response of the circuit fall off at arate of -20dB/decade (-6db/octave) when the frequency exceedsthe cutoff frequency (the point at which the response is 3 dB lowerthan in the passband, or ≈ 0.707 times the passband amplitude).

A zero, on the other hand, gives the circuit infinite attenuation ofthe input signal at zero frequency (D.C.), and decreasing attenuationup until the cutoff frequency, above which the frequency responseflattens out. For a zero, the rate of increase in output amplitude is+20db/decade.

From inspection of the circuits in Figures 2 and 4, it should beclear (for these simple cases) how the capacitor’s infinite DCimpedance and AC impedance that decreases with increasingfrequency can give rise to the observed frequency responses.

For the high-pass filter shown in Figure4, two additional observationsshould be made. First, the zero alone would make the frequencyresponse of the circuit continue to increase to infinity, but thecoexistent pole at the cutoff frequency “cancels out” the zero toflatten the response. Second, you cannot have a zero without apole in real circuits.

HOW TO “VISUALIZE” POLES AND ZEROS

In general, the transfer function of a filter is of the form,

T S = A SB S

= S - Z1 S - Z2 S - Zm

S - P1 S - P2 S - Pn

where the numerator is a polynomial, A(S), which defines the zeros(Z1 ... Zm), and the denominator is also a polynomial, B(S), whichdefines the poles (P1 ... Pn, where n is the order of the transferfunction). Physically, the order of a filter is equal to the number ofpassive energy-storage elements (capacitors and inductors) in thecircuit. Mathematically, the order of the filter is the order ofdenominator polynomial of its transfer function, n. For example,the transfer function of an nth order low-pass filter falls off as fn forfrequencies well above the cutoff frequency (where f is the frequency,of course!).

The best way to remember the “big picture” about the influence ofpoles and zeros on a circuit’s transfer function to make use of asimple (dumb?) analogy: the circus tent! Think of the poles as justthat... poles to hold the tent’s canvas off the ground. Think of zerosas tent pegs, hammered through the canvas and into the ground.With this in mind, look at Figure 6 below...

Figure 6: S-plane plot of the transfer function of a second-order low-pass filter.The plot is ‘cut’ along the jω axis to reveal the frequency/gain response.

Figure 6 (above) shows the S-plane plot of the transfer function,

LPF S = 1S + 1+4j S + 1-4j

= 1S2 + 2S +17

which represents a simple, second-order low-pass filter. Addingtwo zeros at the origin gives the transfer function,

HPF S = S2

S + 1+4j S + 1-4j

which represents a simple second-order (as mentioned above, thezeros don’t count in the order) high-pass filter, whose magnituderesponse is shown in Figure 7 below. The zeros serve to cancelthe roll-offs of the poles to allow the filter’s response to flatten-outat frequencies relatively far above the cutoff frequency (here thecutoff frequency is 4 radians per second... ω = 4).

Figure 7: S-plane plot of the transfer function of a second-order low-pass filter.

Again, the plot is cut along the jω axis to reveal the frequency response (σ=0).

More complex frequency responses can be realized by using morepoles and zeros! You can arrange the poles and zeros of a filter toachieve very sharp cutoff slopes, but the ultimate slope of the filter’s

5 just a reminder that “stopband” is the frequency range in which the filter “stops” or attenuatessignals...

frequency response (well into the stopband5) is always -20

Tourists in S-Plane-Land...

dB/decade times “the number of poles minus the number of zeroes”!One of the ways to obtain steeper cutoff slopes is to use inductorsas well (however, as discussed above, RLC filters are generallycostly, bulky, and heavy).

WHAT IF YOU PUT LOTS OF FILTERS IN SERIES?

You might think that simple, higher order filters could be obtainedby cascading identical, passive RC filter stages such as those shownin Figures 2 and 4. In practice, however, this does not work, sinceeach succeeding filter stage loads the preceding ones and alterstheir frequency responses (the poles and zeros can interact witheach other!). The loading and interaction effects result in a very“mushy” frequency response for higher-order filters built in thisway, as shown in Figure 8 below.

1.0h 100h 10Kh 1.0Mh

FrequencyV(2) V(3) V(4) V(5) V(6) V(7) V(8) V(9) V(10) V(11)

1.0V

1.0mV

1.0uV

Figure 8: Frequency responses of ten series RC low-pass filters, each with acutoff frequency of 10 Hz.

Taking cascaded low-pass filters as an example, if buffer amplifiers(such as unity-gain stages) were used to provide isolation betweenidentical passive low-pass sections, the cutoff frequency wouldshift lower and the ultimate slope of the frequency response wouldbe made steeper, but the loading effects would be eliminated,giving a flatter passband and a sharper initial roll-off (as shown inFigure 9 below). (This idea is explored more thoroughly in Horowitz& Hill’s, “The Art of Electronics.”)

1.0h 100h 10Kh 1.0Mh

FrequencyV(2) V(4) V(6) V(8) V(10) V(12) V(14) V(16) V(18) V(20)

1.0V

1.0mV

1.0uV

Figure 9: Frequency responses of ten BUFFERED series RC low-pass filters,each with a cutoff frequency of 10 Hz.

It turns out that the practical application of more complex filterstypically involves placing various first- and second-order filtersections in series (thereby forming an overall transfer function thatis the product of the individual transfer functions).

The good isolation of active filters (i.e., filters that useop-amps) allows this to be done! Therefore, second-orderactive filter stages will be studied in some detail, followed by anoverview of how to make more complex filters with them.

THE BASIC SECOND-ORDER TRANSFER FUNCTIONS

It turns out that, for most op-amp active filters, the basic buildingblock is the second-order stage. Therefore, it makes sense toconsider them in some (but not too much) detail...

The three basic second order transfer functions (LPF = low-pass,HPF = high-pass, and BPF = band-pass) are shown below:

LPF S = A

S2 + SωoQ

+ ωo2

Figure 10: Transfer function and plot for low-pass filter.

KEYPOINT

HPF S = AS2

S2 + SωoQ

+ ωo2

BPF S = AS

S2 + SωoQ

+ ωo2

Figure 10 (cont...): Transfer functions and plots for high-pass (above) andband-pass (below) filters.

For the formulas shown above, ωo is the cutoff frequency for thehigh- and low-pass filters (and the center frequency for thebandpass) and Q is the “quality factor” that determines how far thepoles are from the jω axis for the low-pass, high-pass, and bandpassfilters (the closer they are, the more the “peaking” of the frequencyresponse).6

6Sometimes, the “damping factor,” d, is used instead of Q, since it is directly proportional to thedistance between the poles and the jω axis.

Pole Distance from jω Axis = ωo2Q

A large Q (small d) means that the poles are near the jω axis, thatthe filter’s frequency response is very “peaked” near ωo, and thatits tendency toward oscillations is high (Q = ∞ is an oscillator).

For the low- and high-pass cases, it can be shown that themaximally-flat (best roll-off without peaking) occurs for,

Q = 12

This is the “Butterworth” filter response, which is what you need formany applications! Other Q values are often required when multiplesecond order stages are cascaded in more complex designs.

The “ultimate” roll-off slope of the second order high- or low-passfilter is -40 dB/decade, as expected... For the band-pass case, ωo

is the center frequency and the bandwidth (frequency rangebetween the lower cutoff frequency ω1 and the upper cutoff frequencyω2) is determined by Q,

BW ≡ ω2 - ω1 = ωoQ

For the bandpass filter, the “ultimate” roll-off slope is -20 dB/decadeon either side of the center frequency (it’s still second-order, butthe roll-off rate is “split” because there are two roll-offs!).

There are many active filter topologies (basic circuit layouts) thatare possible, but in practice, only a few are actually used. Sincewe can only consider the most common type within the scope ofthis course anyway, let’s get on with it!

The most commonly used filter is probably the low-pass, and themost common implementation is the voltage-controlled-voltage-source (VCVS), or Sallen and Key, filter. The simplest type ofthe Sallen and Key filter is the unity-gain version shown in Figure11 below, along with a corresponding RLC filter (non-unity gainversions will not be considered within the scope of EE122).

KEYPOINT

Figure 11: comparison of the second-order Sallen and Key low-pass filter sectionand a corresponding RLC low-pass filter. It should be noted that the op-ampdoes not replace the inductor, but merely produces a transfer function that isequivalent to the RLC filter’s transfer function.

The Sallen and Key circuit uses a single op-amp, two capacitorsand two resistors to obtain a second-order transfer function. Sincethis is a unity-gain circuit, it does not amplify signals within thepassband (desirable in many applications).

THE “SCALABLE” FILTER

A very practical design method for such filters is to use a “normalized”or “scalable” filter stage and scale the component values toobtain the desired damping (d is typically used in the design books...just remember that it is 1/Q) and cutoff frequency. A Sallen andKey low-pass filter normalized to a cutoff frequency of 1 KHz andan input resistance of 10 KΩ is shown in Figure 12 below.

SAME RESPONSEBUT

DIFFERENT PARTS!

0.0162Q

µF

0.016 2Q µF

10 KΩ 10 KΩV

in

Vout

Figure 12: A unity-gain, Sallen and Key low-pass filter stage normalized to a cutofffrequency of 1 KHz, and a resistance of 10 KΩ .

The capacitor values are usually shown in terms of “2Q” since thelocations of the poles are given (in terms of R and C) by,

P1,2 = - ωo2Q

± jωo 1 - 12Q 2

Scaling the filter (EASY!) is accomplished as follows:

To scale to a new cutoff frequency, first compute theratio of the old to the new cutoff frequency. Then eithermultiply the resistances by this ratio or multiply thecapacitances by it (just think in terms of scaling the RCtime constant up or down!).

To scale to a new impedance (without altering the RCtime constants), first compute the ratio of the new to theold impedance. Then multiply all resistances by theratio and divide all capacitances by it.

Then all you have to worry about is the degree of peakingyou want... Just scale the components with values givenin terms of Q on the schematic (capacitors for low-pass,resistors for high-pass, and resistors for the bandpassexample used here) to get the Q you want! Simple!

As an example, we will examine the design of a second-orderlow-pass “maximally-flat” filter with a cut-off frequency of 300 Hz,and resistance normalized to 1KΩ (we could normalize to whateverresistor values are around in lab, 1KΩ is used here for simplicity).Such a filter could be used to select the bass frequencies fromaudio in order to drive a “sub-woofer” in a killer stereo system.

How about aworked example?

THIS IS SOMEVERY PRACTICAL INFORMATION....

PLEASE CHECK IT OUT!

The resistances should first be normalized to 1KΩ. This meansreplacing the resistances shown in Figure 12 with 1KΩ resistorsand scaling the capacitances to keep the RC time constant thesame.... Since the resistances went down ten-fold, multiply thecapacitances both by ten...

To scale the frequency to 300 Hz from 1KHz, the RC time-constantmust be multiplied by the ratio of the frequencies, i.e.,:

RCnew = RCold1000 Hz300 Hz

Since we need to keep the 1KΩ resistor values, you must multiplythe capacitor values by this ratio.

To get a “maximally-flat” response, you need to substitute Q =0.707 into the equations defining the capacitor values in Figure 12(you multiply the one in the feedback loop by 2Q, and so on...).

The final design ends up being that shown in Figure 13 below.

0.376 µF

0.753 µF

1 KΩ 1 KΩV

in

Vout

Figure 13: A unity-gain, Sallen and Key low-pass filter stage scaled to a cutofffrequency of 300 Hz, and a resistance of 1 KΩ .

To test the design, you can use the following SPICE deck (orgraphical SPICE entry):

300Hz Sallen and Key LOW-PASS FILTERVin 1 0 AC 1VR1 1 2 1KCfb 2 Vout 0.753UFR2 2 Vninv 1KCg Vninv 0 0.376UFE1 Vout 0 Vninv Vout 100K.AC DEC 20 1Hz 100KHz.PROBE.END

You obtain a frequency response as shown in Figure 14 below.

300 Hz

0.707 V

Figure 14: Frequency response of example 300 Hz low-pass filter (plotted on alinear y-axis scale).

If you use the nearest available “real” capacitor values of 0.68 µFand 0.33 µF, the cutoff frequency shifts to about 340 Hz but thefilter’s shape is roughly the same. This would be o.k. for someapplications, but if accurate cutoff frequency were required, youmight have to scale to a different resistance to use the “standard”capacitors better (you have way more choices of values for resistorsthan capacitors!).

To test the filter design’s time-domain performance with a 10 mS,1V square pulse, change the Spice deck so that the “Vin” linereads:

Vin 1 0 pwl(0 1V 10mS 1V 10.001mS 0V)

and replace the “.AC” line with:

.TRAN 100US 30mS

The results are shown in Figure 15 below.

Figure 15: Time-domain testing of the example filter.

WHAT ABOUT HIGH-PASS?

To obtain the high-pass “equivalent” to the filter shown in Figure12, simply swap the positions of the resistors and capacitors, takingnote that their values change, as shown in Figure 16 below. Thescaling is done exactly as described above.

µF0.016

Vin

Vout

µF0.016 10 K 2Q Ω

10 KΩ2Q

Figure 16: Unity-gain, Sallen and Key high-pass filter stage normalized to a cutofffrequency of 1 KHz, and a resistance of 10 KΩ .

Yuppies sometimes get the idea that a filter is a status symbol...

Gee Bill, I hear you traded in your BMW for a low-pass filter! Biff and I think it might be better to go for a notch filter.... we heard they were more exclusive...

These people are so dumb, it makes me want to chuck my cookies! Even doing my EE122 Prelab would be better than this!

BANDPASS ANYONE?

The type of bandpass filter described below is not a Sallen andKey type. It is called the multiple-feedback bandpass7. This circuitis shown in Figure 17 below, and implements the second-orderBPF equation shown above (in Figure 10), normalized to 1 KHz.

µF0.016

Vin Vout

µF0.016

10 K 2Q

10 KΩ2Q

Ω

Figure 17: Multiple-feedback bandpass filter with a 1KHz center frequency.

This circuit can be scaled up or down in impedance and frequencyas described above for the low-pass filter. It should be pointed outthat this circuit has a gain of -2Q2 at the center frequency (whichmeans that you might have to use an input attenuator for largesignals and high Q’s). Also note that the op-amp must have anavailable gain of at least 20Q2 at the center frequency to avoiddistortion (i.e., take GB product for op-amp, divide by the centerfrequency, and you should have at least 20Q2 gain available).

7Sallen and Key bandpass filters can be built, but they have some limitations in terms of tuningand the requirement of a high op-amp gain bandwidth product.

ALL-PASS? MAYBE IN LIBERAL ARTS. THIS IS EE!

The last filter to be covered here is the “all-pass” filter. It passes allfrequencies equally, but shifts the phase of the input signal withfrequency, from 0° at low frequencies to -90° at the center frequency(ω o = 1

RC) to -180° at higher frequencies. Such filters are sometimes

used to equalize the delay in communications systems (since delayis really the same thing as phase shift, after all). A simple all-passfilter circuit is shown in Figure 18 below.

R

R

R

C

Vin

Vout

Figure 18: A simple op-amp all-pass filter circuit.

The transfer function of the circuit shown above is,

T S = 1 - SRC1 + SRC

(This is not really a “scalable” filter... it is simpler: just choose theRC time constant for the center frequency and make all of theresistors the same value.) If you are not convinced that the gain isreally one for all frequencies, substitute jω for S in the above equationand determine the magnitude.

MORE COMPLEX FILTERS

As mentioned above, more complex filters are generally obtainedby cascading several second-order sections (perhaps with a first-order section as well, if an odd order is required). This discussionis intended to provide only a simple overview of these more complexfilter types, the design of which is somewhat beyond the scope ofEE122. The basic idea is that the poles of these filters are distributedso that the response on the jω axis (frequency response) has thedesired shape.

The classical, “maximally-flat” filter response is that of the Butterworthfilter. This response (an example of which is shown in Figure 19below) is obtained by arranging the filter’s poles around the unitcircle in the S-plane, at the solutions to the equation,

S = - -1 n1

2n

where n is the order of the filter. The poles end up being locatedat equal distances from each other around the unit circle.

Figure 19: S-plane plot of the response of a 6th-order Butterworth low-pass filter.The insets at upper left show the frequency response and pole positions (linearscaling).

-3.0 -2.5 -2.0 -1.5

-1.0

-0.5

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

The other commonly used complex filter is the Chebyshev type.Here, the poles are arranged around an ellipse in the S-plane toachieve much steeper roll-off than the Butterworth, traded off againstripple in the pass-band. These filters are generally specified interms of order and ripple, which determine the relative steepnessof the slope beyond the cut-off frequency. An example of aChebyshev filter response is shown in Figure 20 below.

Figure 20: S-plane plot of the response of a 6th-order (0.5 dB ripple) Chebyshevlow-pass filter. The insets at upper left show the frequency response and polepositions (linear scaling).

EVEN MORE NERDINESS...

For readers interested in obtaining further information on filter designand implementation, these are several worthwhile references:

Lancaster, D., “Active Filter Cookbook,” Howard W. Sams & Co., Carmel, Indiana,1975

Huelsman, L. P., and Allen, P. E., “Introduction to the Theory and Design ofActive Filters,” McGraw-Hill Book Co., New York, New York, 1980

-2

0

2

jw

-1

1

-1.0 -0.5 0.0

THE COMPARATOR AND THE SCHMITT TRIGGER

A comparator is a basic circuit that is very useful for determiningwhen an input voltage crosses (equals or exceeds) a pre-setreference voltage. The comparator circuit shown in Figure 21 belowdoes this function by swinging its output voltage fully to the positivesupply rail when the input voltage vi exceeds the reference voltageVref. It is easy to see that this circuit is simply the one used in Lab 2to examine the open-loop behavior of the op-amp, but withsufficiently large input signals to saturate the op-amp’s output. Inother words, the comparator has only two output states!8

This makes it a one-bit analog-to-digital converter!9

Note that comparators can be used in inverting and non-invertingmodes depending upon which input, V+ or V- receives the inputsignal (clearly, the remaining input is connected to the referencevoltage). While a precision reference voltage is often generatedusing a zener diode (or a voltage-reference chip), a voltage divideris often perfectly adequate.

V

V

ref

in

Vout

Figure 21: A simple op-amp comparator.

The comparator shown in Figure 21 above can be simulated (usinga simulated “741” op-amp in this case) using the following Spicedeck, not including the 741 macromodel from Prelab 2, a 1 KHz,10 V peak sinewave is used as a test input, with results shown inFigure 22 below:

741 Comparator SimulationX1 Vninv Vref 4 5 Vout UA741Vplus 4 0 12VVminus 0 5 12V

8 In practice, that is. For very small input signals, the op-amp will simply provide an amplifiedreplica of the input signal at its output. For practical op-amps, with gains of over 1 million, this really doesn’thappen!

9 It is worth pointing out that an important class of analog-to-digital converter, the so-called “flash”A/D’s, is made of a series of op-amp comparators, each with a progressively higher reference voltage andall connected to the input signal with their remaining inputs. This results in a “thermometer-type” output,where, for a given input voltage, all of the comparators below a certain point are “ON” and those abovethem are “OFF.” Digital logic circuits are used to convert this to the binary output of the A/D.

R1 4 Vref 1.4K

R2 Vref 0 1.0KVin Vninv 0 sin(0 10 1000).TRAN 10uS 2mS.probe.end

0.0ms 0.5ms 1.0ms 1.5ms 2.0ms

TimeV(Vref) V(Vout) V(Vninv)

0V

-15V

15V

Figure 22: Results of simulating a comparator with the 741 op-amp macromodel.The reference voltage was +5V and the input signal was a 20V P-P sinewave.

Note that the reference voltage was set by the voltage dividermade of R1 and R2 to be 5V. A zero-crossing detector is the samecircuit, with the reference voltage set to zero volts. It is useful fordetermining when the input voltage crosses zero in either direction.

The Schmitt trigger (shown in Figure 23 below) is a type ofcomparator that adds a useful feature by the use of positive feedback:hysteresis. This means that there are two distinct threshold voltagesthat each control either the positive- or negative-going swings ofthe op-amp’s output voltage. For example, if the positive-goingthreshold were 1 V, the output voltage would swing to near thepositive supply rail when the input signal exceeded 1 V. If thenegative-going threshold were 0.5 V, the output voltage would notswing back toward the negative supply rail until the input signalwent below 0.5 V.

R1 R2Vin

Vout

R3

R4

Vref

Figure 23: The basic op-amp Schmitt-Trigger circuit.

This hysteresis effect can be very useful if you want to use thecircuit’s output signal to initiate some event (such as the horizontalsweep of an oscilloscope) when a threshold is crossed, but do notwant noise on the input signal to prematurely swing the outputsignal the wrong way. This problem was illustrated in the aboveSpice simulation exercise.10

Design of a Schmitt Trigger (not always easy) of the type shown inFigure 23 involves the selection of the four resistors, R1, R2, R3,and R4. The hysteresis (the upper and lower thresholds) are definedby R1 and R2, and the mean threshold voltage (in the center of thehysteresis curve) is set by R3 and R4.

To understand the operation of this circuit, consider that with positivefeedback (and no negative feedback to counterbalance it), the outputof the op-amp will be at either the positive or negative maximumsof its voltage swing (Vsat+ and V sat- , respectively). (As before, sincethere is no negative feedback, the two op-amp inputs will not bekept at the same voltage by the op-amp!)

Once you realize that, you can work out that the voltage at thenon-inverting input is given (by superposition), to be:

V+ = VoutR1

R1 + R2+ V in

R2R1 + R2

where, as mentioned above, Vout can be either Vsat+ or Vsat- . The“trip-point” or threshold of the overall circuit in each direction of thehysteresis curve is defined by setting V+ equal to the referencevoltage set by R3 and R4 and Vout to either Vsat+ or Vsat- . You canthen easily solve for the upper and lower thresholds, respectively:

VU = VrefR1 + R2

R2- Vsat-

R1R2

and VL = VrefR1 + R2

R2- Vsat+

R1R2

(Note that Vsat- is negative!)

10 In a way, the 741 op-amp helps minimize the problem illustrated by applying a signal plus noiseto the input of the comparator. It is such a slow op-amp that it cannot respond to all of the noise purturbationsthat would cause multiple output transitions. Faster op-amps can really messup in this situation!

A simplified example, with the inverting input (the reference voltage)connected to ground, is given by the following Spice deck fragmentand the plot shown in Figure 24 below:

X1 Vninv 0 4 5 Vout UA741Vplus 4 0 12VVminus 0 5 12VR1 Vinput Vninv 1KR2 Vout Vninv 10KVin Vinput 0 pwl(0 -10 0.5mS 10V 1mS -10V).TRAN 10uS 1mS.probe.end

You can readily observe from the above plot that the Schmitt Triggerhas well defined positive and negative trip-points, as desired. Inthe example, setting vref = 0V simplifies the above equations (goodto remember when designing zero-crossing detectors).

Figure 24: Simulation of a Schmitt Trigger with a 0V reference voltage and upperand lower trip-points of approximately +1.1 and -1.1 V, respectively.

OP-AMP OSCILLATORS

In this section we will consider two of the several types of oscillatorsthat can be built using operational amplifiers. Squarewave, triangle-wave, and sinewave oscillators will be considered in some detail,followed by a brief discussion of the other types of waveforms thatcan be generated using op-amps.

LINEAR OR NONLINEAR... THAT IS THE QUESTION

There are two basic types of oscillators that can be built with analogcomponents: linear and nonlinear.

Nonlinear oscillators turn out to be the easiest to build! This categoryincludes oscillators that rely on saturation or other nonlinear circuitproperties to work. Since you should know by now that it is relativelyeasy to get semiconductor devices to be nonlinear, this should bea piece of cake, right? The most common nonlinear oscillator isthe square-wave oscillator, where you simply let the amplifieralternate between its positive and negative maximum output voltageswings (i.e., saturation!).

A linear oscillator ideally produces a pure sinusoidal output at asingle frequency (hopefully). To achieve linear oscillation, a linearamplifier must oscillate without external stimuli (other than a start-uptransient to get it going, perhaps). In order to understand this typeof oscillator, a minor excursion into theory (GAK!) will be required(it’s worth it, since a little bit of intuitive understanding goes a longway!).

What is required to make a linear oscillator (that works, that is!) isthe arrangement shown in Figure 25 below.

Figure 25: Block diagram of a linear (sinusoidal) oscillator showing a linear amplifierof gain A, and a feedback loop of gain β.

A linear amplifier of gain A provides an output voltage vout that isfed through a feedback loop with gain β, and summed back intothe input of the amplifier. The overall gain of the circuit with feedback,Af(S), is given by,

Af S = A S

1 - A S β S

where S is the Laplacian operator (“Hello operator... get me Barney’sBurrito Barn please!”).

Without going into all of the details, but by examining thedenominator of the above equation, it is easy to see that the overallgain can be made infinity by setting the “round-trip” gain aroundthe entire feedback loop so that,

A S β S = 1

This condition, known to those who care as the Barkhausen Criterion,appears to make the circuit blow up! Actually, it is a necessarycondition for this type of oscillator to work. Intuitively, however thefact that the overall gain is infinity means that the output of thecircuit is some signal (to be determined!), even with NO input at all!Thus, to make an oscillator, we set the input to the block diagramin Figure 25 to 0V, and let the thing oscillate! If you are cleverenough to arrange it so that the Barkhausen Criterion is met atonly a single frequency, you will get a very pure sinewave out (if itis met at multiple frequencies, you might get an interesting mix offrequencies). More on this below, after a thrilling look at nonlinearoscillators.

SQUAREWAVE OSCILLATORS: REAL FUN AT LAST ORJUST ANOTHER NONLINEAR CIRCUIT?

The square-wave oscillator can be obtained by a simple modificationof the “alternative” Schmitt trigger circuit discussed in the footnoteabove. All you have to do is add a negative feedback resistor anda capacitor from the inverting input to ground, as shown in Figure26 below. Noting that the output of the amplifier (given the positivefeedback from R1 and R2, will either be at Vsat+ or Vsat-, capacitorC1 will either be discharged or charged through R3. The voltageacross C1 will thus either rise or fall exponentially with a timeconstant R3C1 and be compared against the voltage at thenoninverting input of the op-amp, V+. When the voltage on the

capacitor reaches either the positive or negative trip point of theSchmitt Trigger (depending upon whether it is charging ordischarging), the output of the op-amp will swing to the oppositemaximum voltage, reversing the charge/discharge cycle. As youmight have guessed by now, this cycle repeats (you had betterhave guessed, since we are talking about OSCILLATORS here!).

It can be shown that the output frequency is given (approximately)by,

fo ≈ 1

2 R3 C1 ln 2R1R2

+ 1

R3

R1

R2

C1

Vout

Figure 26: An op-amp square-wave oscillator.

If you want a square-wave output of less amplitude than +/- Vsat ofthe op-amp, you can easily add a potentiometer to the output anduse it as an adjustable voltage divider. Another variation on thiscircuit uses two Zener diodes on the output to limit the voltageswing to the well-defined breakdown voltages of these diodes ratherthan to the saturation voltages of the op-amp (using diodes toestablish well-known voltages instead of the rails is another way todo this).

THE NEAT AND NIFTY TRIANGLE-WAVE OSCILLATOR(BUILD IT YOURSELF FOR PENNIES!)

A triangle-wave oscillator can readily be made from a square-waveoscillator by (remember Prelab 2?) integrating its output with anop-amp integrator. Of course, as you know by now, you have toappropriately scale the integrator’s time-constant to get the desiredoutput amplitude.

SINEWAVE OSCILLATORS

There are, as you might have guessed, many ways to makesinewaves! These days, probably the most versatile way to do thisis to digitally synthesize them. However, if you need sinewaves ofextremely high spectral purity, and may be willing to sacrificetunability over a wide frequency range, an analog oscillator maybe what you need. As discussed above, if the Barkhausen Criterioncan be met, one can design a nifty oscillator with only a fewcomponents! Continuing with the previous discussion, the overallloop gain must be one (1) and the overall phase shift must be zero(0) (recall the role of compensation capacitors in preventingunwanted oscillations by guaranteeing that the overall gain waskept to less that one when the phase reached zero.)

This all sounds good in theory, but in practice, you can’t build acircuit with an overall loop gain of exactly one! Componenttolerances, temperature effects, etc., limit our ability to do this. Whathappens in practice is that the gain is somewhat larger than oneand the amplitude of oscillations is limited either by the onset ofnonlinearity of the circuit (such as decreased gain or clipping) orby some clever gain-control circuit!

One of the best known analog sinewave oscillators that takesadvantage of this is the Wien Bridge Oscillator, one type of whichis shown in Figure 27 below. The basic operating principle behindthis type of oscillator is to provide both negative and positivefeedback in the same circuit, with the positive feedback slightlylarger, and through a tuned circuit make it satisfy the requirementsfor sinusoidal oscillation.

Examination of the circuit in Figure 27 will show that it has a negativefeedback circuit consisting of R1 and R2, setting the amplifier gainA to be (for the basic non-inverting amplifier),

A = 1+ R1R2

It can be shown (no, don’t worry, you won’t have to do the math!)that the positive feedback loop yields,

β = ωRC3ωRC - j 1 - ωRC 2

C

C

R

R

R1

R2

Vout

Vout

Figure 27: On the left, the classical Wien-Bridge Oscillator. On the right, thebasic Wiener-Bridge Oscillator, formed using four hot-dogs.

Setting Aβ = 1, it becomes apparent that when ω = 1/RC, β is equalto 1/3 (purely ohmic). This occurs at,

fosc = 12πRC

where the phases of the high-pass (upper) and low-pass (lower)RC stages in the positive feedback loop cancel out.

Therefore, if the amplifier gain A is set equal to 3, theBarkhausen Criterion (there, got to mention it again!) is met andthe oscillator should oscillate.... Unfortunately, this is rather difficultto do, since it is hard to set the Aβ product to exactly equal one!You can, however, adjust the value of R1, for example, to obtainstable oscillations (at least for a while...).

In the real world, ever-present noise sources tend to help startoscillators such as the one you just designed. In Spice models,sometimes you have to “kick-start” them with a transient pulse froma voltage (or current) source. This technique is used in this exercise.

The basic Spice deck is shown below (without the 741 macromodel):

X1 Vninv Vinv 4 5 Vout UA741Vplus 4 0 15VVminus 0 5 15VR1 Vinv 0 ?R2 Vinv 8 ?C1 Vout 7 ?R3 7 Vninv ?C2 Vninv 0 ?R4 Vninv 0 ?Istart Vninv 0 pwl(0 1mA 10us 0V).model dmod D.TRAN 100uS 8mS 0uS 100uS.probe.end

With any luck, you should be able to get some output like thatshown in Figure 28 below.

Figure 28: Spice output from the 741 op-amp-based wien bridge oscillator asdescribed above.

If the negative-feedback loop gain is too large, the oscillator willsaturate. If it is too low, oscillations will die out. One solution tothis amplitude-control problem is the circuit shown in Figure 29below. The feedback resistor R1 is split into two series resistors,R1a and R1b. Two diodes are connected “back-to-back” acrossR1b. Assuming that R1a > R1b, the diodes will begin to conductonly when the output amplitude begins to get too large, shuntingcurrent past R1b, and thus automatically reducing the gain of theamplifier. This provides closed-loop control over the gain of theoscillator and greatly enhances its stability.

Current pulse to "kick-start" the oscillator.

R1a

R1b

Figure 29: Diode-stabilized Wien-Bridge Oscillator.

Think about the design of a diode-stabilized Wien-Bridge Oscillator.All you have to do is realize that you want to split R1 in Figure 27into the two negative feedback resistors in Figure 29... The idea isto set up the two resistors so that the diodes begin to conduct atroughly the output voltage you want... (You will experiment withthis circuit in the lab.)

Exercises - Prelab 3

Work With Your Team

EXERCISE 1:

Design a high-pass “maximally-flat” filter with a cutoff frequency of 30 Hz and resistancenormalized to 1KΩ. Obtain its frequency and phase responses using Spice (use an“ideal” op-amp). In addition, obtain its time-domain response to the 10 mS, 1V squarepulse used to test the low-pass filter. Comment.

Make up a Spice deck that places your high-pass filter design in series with thelow-pass filter design given above in the Prelab text (see Figure 13). NOTE: youhave to be careful to rename some of the nodes when you “paste” the twoSpice decks together. This would be an improved “sub-woofer” driver, preventingspeaker damage from “near-DC” signals. Obtain the frequency, phase and time-domainresponses (using the same 10 mS, 1V square pulse for the time-domain stuff) usingSpice. Comment.

EXERCISE 2:

Design a 1KHz bandpass filter with Q = 10 using the circuit shown in Figure 16 above.Test your design using Spice and the 741 macromodel used in previous Prelabs(obtain the gain and phase responses). (Does the 741 meet the requirement for again-bandwidth product of at least 20Q2 at the center frequency?) Given the gain-bandwidth product cited by its manufacturer, does the 741 meet the requirement for anavailable gain of 20Q2 at the center frequency? (You will build this circuit in lab.)

EXERCISE 3:

Design an op-amp Schmitt Trigger with a threshold voltage of approximately +5Vand upper and lower trip points approximately 2 V on either side of the thresholdvoltage (i.e., +7V and +3V). Assume that the saturation voltages are +/- 12V and thatthe voltage divider of R3 and R4 is connected to +12V.

Simulate it using the 741 op-amp macromodel in Spice, with the “noisy” input signalagain a 10V, 1KHz sinewave plus a 3 V, 10KHz sinewave (the “noise”). Replace theinput voltage with two sinewave current sources and a 1 Ω resistor! (This is a goodSpice trick to know for generating complex waveforms.). If these trip points do notallow you to reject the “noise,” design another Schmitt Trigger that has appropriate trippoints. Obtain a “close-up” plot to verify the thresholds. Comment.

Try changing the voltage driving R3 and R4 to -12 V. What should the trip points benow?

Hint: The trick is to solve for the difference between the upper and lower thresholds,i.e., vU - vL , noting that (for practical purposes) Vsat- = -(Vsat+):

VU - VL = VrefR1 + R2

R2- Vsat-

R1R2

- VrefR1 + R2

R2+ Vsat+

R1R2

which yields,

R1R2

=VU - VL

2Vsat+

from which vref (and hence R3 and R4) can be computed using:

Vref =VU + Vsat-

R1R2

R1 + R2R2

It is often useful to include some “reference voltages” in your Spice deck when youwant to verify exact voltages. For example, to obtain a 4V and a 6V reference, youcould add the following lines:

VP6 Vsix 0 pwl(0 6 1mS 6)Rsix Vsix 0 1KVP4 Vfour 0 pwl(0 4 1mS 4)Rfour Vfour 0 1K

If you plot these voltages, they will act as reference markers. Note that the "pwl"statements are necessary for .TRAN analysis since DC voltages would all be zero!Likewise, for DC sweeps, the pwl’s wouldn’t work.

EXERCISE 4:

Design a 1KHz square-wave oscillator using the above circuit, assuming a 0.047 µFcapacitor, the use of the 741 op-amp macromodel, and standard11 5% resistor values(see the Standard Component Values sheet on the course website). Simulate yourdesign using Spice.

EXERCISE 5:

Design an integrator that will generate a 2V peak-to-peak triangle wave from theoutput of the 1KHz square-wave oscillator designed above. Hint: the output of theabove oscillator will be +/- Vsat! Simulate your design with Spice using an “ideal”integrator.

EXERCISE 6:

Design a 1KHz Wien-Bridge oscillator (try to use real component values, such as 0.01µF capacitors, since you will have to build it in the lab). Simulate your design in Spiceusing either an ideal op-amp or an op-amp macromodel of your choosing (e.g., the741). Can you get it to oscillate?

11 Welcome to the Real World™, folks! Real resistors do not come in 27π Ω values! They arearranged in odd-seeming values that repeat for each decade of values. For 5% tolerance resistors, theyare approximately 20% apart in value. Real capacitors come only in rather annoying values, often spacedfarther apart than 20%. Don’t worry, you’ll get used to it!

EE122

Prof. Greg Kovacs

LAB 3:MORE OP-AMP CIRCUITS!

When all else fails, lower your standards.Anonymous

You will not be told exactly what to put in your write up. The idea is thatyou present your data and what you learned from it. Typically, you willmake plots and analyses a part of the write-up. Write-ups must not belonger than ten pages. If you have questions, please ask. We are here tohelp!!

INTRODUCTION

In this lab session, you will have to build and test many of the circuits youdesigned in the Prelab using a solderless breadboard.

BE CAREFUL TO OBSERVE THE CONNECTIONS OF EACHCOMPONENT!!! YOU CAN WASTE A LOT OF TIME IF YOU RUSHAND DON’T CHECK!

ALWAYS use 0.1 µF decoupling capacitors on each power supplyrail, right next to each op-amp. Use one capacitor from the positiverail to ground and one from the negative rail to ground.

Use ± 12 V supplies. You may wish to put an input 50 or 51 Ω resistorfrom the signal generator’s output to ground so that the amplitudes on thesignal generator are correct (they assume a 50 Ω load).

1) This experiment is designed to demonstrate the bandpass filter youdesigned in the prelab. Determine your circuit’s frequency response usinga 741 op-amp and with an LT1056. Do not measure a large number ofdata points by hand. You can use the dynamic signal analyzer and anoise source for a quick look and take only key measurements by hand,such as a few measurements in the pass-band, and both 3 dB frequencies.Determine the slope of roll-off for both low and high frequencies.

V+

V-

-

+

LM741

+12V

-12V

1

5

2

6

3

7

4

V

V

C

CR

R

11

2

2

in

out

Component locations for the band-pass filter.

Measure the center frequency, the maximum gain and the Q of the filteryou designed in the Prelab. To determine Q, plot an amplitude versusfrequency curve and determine the frequencies that correspond to the twohalf power points. Note that the HP35665A dynamic signal analyzer (onthe cart in the lab) can automatically generate Bode plots for you. Insteadof using it’s printer, however, you will save the data to disk and thenupload it into MATLAB for plotting. Your TA will describe the processduring lab.

2) In this experiment, you will test your Schmitt Trigger design.

V+

V--

+

LM741

-12V

-12V+12V

1

52

6

3 7

4

V

V R R

R

R

1 2

3

4

in

out

Component locations for the Schmitt trigger.

Determine the trip points of the Schmitt trigger you designed. Use as inputtriangular waves from the signal generator. Superimpose the input andoutput signals on the scope. Try using -12 V as the reference voltage, asshown below. Then try using +12 V. Is there any difference?

Try adding some noise to the input signal. How much noise can bepresent without “false” transitions at the output of the Schmitt Trigger?

You should use the multiple output signal generator (HP 8904A), whichcan sum multiple signals together.

NOTE Re: HP8904A

The 8904A is a four-channel signal generator. Each channel can be set independentlyto a chosen frequency, phase, amplitude and waveform. These channels can then befed simultaneously to the same output, the resulting voltage being the sum of thevoltage in each channel. Alternately, the output of one channel can be multiplied bythat of another, thus providing amplitude modulation (AM). Frequency modulation(FM) can also be achieved using this unit. Such a synthesizer is an important tool forgenerating test signals to use as inputs to circuits (or to demonstrate test instruments!).

An interesting feature of this unit is that the multiple outputs can be summed internally.

Remember that the total amplitude of the signal generator (all summedsignals) cannot exceed 10V ! Thus, when you add “noise,” you will haveto decrease the amplitude of the triangle wave.

Also, be sure to set the output of the signal generator to “float.”

3) In this experiment, you will test the square- and triangle-wave generatorsyou designed in the prelab. These circuits are key building blocks ofanalog function generators and music synthesizers.

Measure the amplitude, frequency, and duty cycle of the squarewavegenerator. Use your integrator design to generate a 2 V peak-to-peaktriangle wave. Comment on the performance of your design - how “perfect”do the triangle waves look compared to an equivalent amplitude andfrequency waveform from the signal generator?

Is there a DC component (offset) in the triangular wave? Is it positive ornegative? Turn the system off and on a number of times and see if oneach occasion the polarity of the DC component remains the same.

V+

V-

-

+

LM741

-12V

+12V

V+

V-

-

+

LM741

-12V

+12V

1

5

1

5

6

7

7

4

4

2

3

3

6 2R

R

R

R

R

CC

V

V

out1

out2

1

2

3

4

5

1 2

Component locations for the square- and triangle-wave oscillator.

4) This experiment is designed to allow you to explore your Wien Bridgeoscillator design.

Using a decade box, change R1A and determine over what range of resistancethe amplitude-control scheme insures an (apparently) undistorted sine-waveoutput.

Try varying R1A without the amplitude-stabilization diodes and note therange of resistance that allows the oscillator to work.

Compare the two and comment.

Observe the distortion visually (from the wave shape on the oscilloscopescreen) and also with the signal analyzer (connected to vout). If an audioanalyzer is available (ask your TA), you can directly measure the distortionin the sinewave. If not, you can estimate by summing the amplitudes of theharmonics and expressing that sum as a percentage of the amplitude ofthe fundamental frequency. Note that the HP3561A dynamic signal analyzercan automatically calculate the Total Harmonic Distortion (THD).

V+

V-

-

+

LM741

-12V

+12V

1

5

2

6

3

7

4

R R R

R

R

CC

D

D

1A 1B2

1

2

outV

D1, D2 are1N4148 or 1N914

Component locations for diode-stabilized Wien-Bridge oscillator.

EE122

Prof. Greg Kovacs

PRELAB 4:INTERFACE CIRCUITS

AAAAAAAHHHHH.... ZZZZZZ..... FTHFPHTHTF.....AAAAAHHHH!!!!

EE122 Student Who Tests Circuits with Wet Fingertips

OBJECTIVES (Why am I doing this prelab?)

• To investigate some of the ways we interfaceelectronics to the “real world.”

WHERE’S MY PRELAB TEXT ???

At this point, you should be working on your projects.Surprise! No prelab text to read!!!

While the materials in the lecture notes are sufficient, itwould make sense to flip through Horowitz and Hill toinvestigate some of the many variants of interface circuits.

You will notice that the Prelab 4 Exercises are muchmore design oriented than the previous ones. This trendwill continue until your prelabs are, in fact, just yourproject!

Exercises - Prelab 4

Work With Your Team

EXERCISE 1:

Design a low-cost seismic sensor. Start with a block diagram and then move on to aschematic. Simulate the circuit as well as you can (substituting a signal generator forthe geophone). The following is a suggested description, but the details are left to you:

The first stage should be an amplifier with a variable gain. You may have arough idea about the signal levels if you played with the geophone during thelast lab. If not, don’t worry, but be prepared to adjust the gain.

The second stage should be a 2nd order low-pass filter (suggested cut-off 30-40Hz) designed using the “Filter Perfect” program from Burr-Brown. This programis available on the lab computers, but may also be downloaded from the coursewebsite. You may wish to use a Chebychev or a Butterworth type. You mayalso wish to explain what type you chose, and why.

The final stage should be a comparator or Schmitt trigger (your choice) thatdrives an LED to indicate that the seismic signal has exceeded a threshold thatyou choose.

Simulate as much of the circuit as you can, providing the filter’s transfer function (gainand phase) and step response, and verifying end-to-end operation all the way throughto the comparator output (if you have no idea about the geophone signals, simplychoose, and be ready to change your design in the lab if necessary).

Turn in a complete schematic showing all component values and types (be sure youcan actually build this circuit using parts available in lab).

Be sure to consult data sheets to make sure the LED current is within specifications forthe op-amp you choose.

EXERCISE 2:

Come up with at least two possible project ideas that you and your partner mightconsider for this course’s Final Project.

Please include a few sentences of description (functional) of each, and perhaps asimple block diagram of each.

These will be evaluated and used to provide helpful feedback.

EE122

Prof. Greg Kovacs

LAB 4:INTERFACE CIRCUITS.

The path to measuring open-loop gain is as narrow aswalking the razor’s edge

A Stanford Dali

You will not be told exactly what to put in your write up. The idea is thatyou present your data and what you learned from it. Typically, you willmake plots and analyses a part of the write-up. Write-ups must not belonger than ten pages. If you have questions, please ask. We are here tohelp!!

INTRODUCTION

In this lab session, you will have to build and test many of the circuits youdesigned in the Prelab using a solderless breadboard.

BE CAREFUL TO OBSERVE THE CONNECTIONS OF EACHCOMPONENT!!! YOU CAN WASTE A LOT OF TIME IF YOU RUSHAND DON’T CHECK!

ALWAYS use 0.1 µF decoupling capacitors on each power supplyrail, right next to each op-amp. Use one capacitor from the positiverail to ground and one from the negative rail to ground.

Use ± 12 V supplies. You may wish to put an input 50 or 51 Ω resistorfrom the signal generator’s output to ground if you are using it to test yourcircuits. This is done so that the amplitudes on the signal generator arecorrect (they assume a 50 Ω load).

Build the low-cost seismograph circuit you designed in the prelab.

This is your first effort to implement a complete system that you havedesigned. As such, it is up to you to decide how to test the circuit’sfunctionality. Below are a set of steps that you should take as suggestionsfor how to proceed. They are certainly not comprehensive, but should getyou started. Remember...have fun!

Measure its total noise (give as an RMS value) while the input to the circuitis grounded (no geophone).

Verify the filter’s transfer function, step response, and the entire circuit’send-to-end performance as you did with virtual instruments in the prelab.

Adjust the front-end gain as necessary.

Attach the geophone and test the circuit.

Look at the time-domain signal (oscilloscope) and the frequency-domaincontent (dynamic signal analyzer).

Describe your experiments - what can you detect?

EE122

Prof. Greg Kovacs

PRELAB 5:OPTOELECTRONIC CIRCUITS

It’s o.k. if we lose money on the product, we’ll just makeit up in volume!

Harvard MBA Graduate

OBJECTIVES (Why am I doing this prelab?)

• To learn about interfaces between the optical worldand the electronic world.

WHERE’S MY PRELAB TEXT ???

At this point, you really should be working on your projects.Surprise! Again, no prelab text to read!!!

While the materials in the lecture notes are sufficient, itwould make sense to flip through Horowitz and Hill toinvestigate some of the many variants of optoelectroniccircuits.

You will notice that the Prelab 5 Exercises are muchmore design oriented than the previous ones, except forPrelab 4, which is similar.

Exercise - Prelab 5

Work With Your Team

Design an optical data transmitter and receiver. You can use LEDs or lasers as theoutput devices, and a photodiode or phototransistor as the input device. You must notuse more than 20 mA drive current for LEDs. If you use a laser, the drive voltage forthe laser module must not exceed 5 V.

Your transmitter should frequency-modulate an incoming voltage signal (from a stereo,a microphone, a function generator, etc...) and send out the modulated waveformthrough the light source of choice. Though you are free to design your own FM block,we suggest using an AD654 (see datasheet/application note on the web).

Visible light is probably the best, but you can use IR if you dare...

Modulate the light at a sufficiently high frequency that 60 and 120 Hz flicker from roomlights will not affect your receiver.

Your receiver will not be required to demodulate on its own. The signal analyzer (highfrequency) can perform FM demodulation if it is given a clean FM signal. You will haveto receive the signal, clean it up (remove unwanted frequencies) and pass it withsufficient energy to the demodulator.

Use a transresistance amplifier to capture the light signal - you will only need to passthe AC signal, so you may want to design it so that the DC gain is minimal. The bestway to do this is to use a low feedback resistance value (e.g., 10 kΩ), AC-couple usinga series capacitor into a second amplifier stage where more gain is provided.

Consider using analog filters to fight noise.

Flesh out the design, select components, and simulate what you can.

Comment on the design tradeoffs you considered - gain, bandwidth, power, etc.

Carry out a design review with your partner and, if you can, with another team.

EE122

Prof. Greg Kovacs

LAB 5:OPTOELECTRONIC CIRCUITS.

Is this guy ever bright!

One LED talking about another.

You will not be told exactly what to put in your write up. The idea is thatyou present your data and what you learned from it. Typically, you willmake plots and analyses a part of the write-up. Write-ups must not belonger than ten pages. If you have questions, please ask. We are here tohelp!!

INTRODUCTION

BE CAREFUL TO OBSERVE THE CONNECTIONS OF EACHCOMPONENT!!! YOU CAN WASTE A LOT OF TIME IF YOU RUSHAND DON’T CHECK!

ALWAYS use 0.1 µF decoupling capacitors on each power supplyrail, right next to each op-amp. Use one capacitor from the positiverail to ground and one from the negative rail to ground.

If you use a signal generator, you may wish to put an input 50 Ω resistorfrom the signal generator’s output to ground if you are using it to test yourcircuits. This is done so that the amplitudes on the signal generator arecorrect (they assume a 50 Ω load).

This is your second effort to implement a complete system that you design.Build the opto-electronic FM transmitter and receiver circuit you designedin the prelab. You will probably have to make some modifications to thecircuit in the lab. As with last week, we provide you with a few necessary,but not sufficient, suggestions for characterizing your circuit. Have fun!

If you are using a laser diode module from a laser pointer, thedrive voltage must not exceed 5 V.

How far can you transmit before you can no longer detect the signal?

Can you estimate the channel capacity? (You will need Shannon’s ChannelCapacity equation from the Lecture Notes)

Describe any design changes you made in the lab. Why weren’t theyobvious from the simulations you did?

In addition to your normal lab write-up (which adequately describes thecircuit you have built, tests you have run on it, and an evaluation of itsperformance), please summarize in a few sentences the key points youlearned from this exercise, focusing primarily on the design and planningaspects.

EE122

Prof. Greg Kovacs

PRELAB 6:ADDITIONAL CIRCUIT

CONCEPTS

If you don’t know where you’re going,any path will take you there.

Unknown

OBJECTIVES (Why am I doing this prelab?)

• To learn about oscillators and how to simulate themin Spice.

Exercise - Prelab 6

Work With Your Team

EXERCISE 1:

Design and simulate a simple quartz-crystal controlled oscillator.

Use the quartz crystal model given in the “grab-bag” lecture - you may want to adjustthe component values to change the frequency. Note, also, that the numbers listed inthe lecture do not necessarily reflect a complete set of values for the circuit shown.They are typical values one might find associated with quartz crystals.It may not work at first, and require some effort... You do not need to see sustainedoscillations. But, do what is necessary to see transient oscillations at the crystal’sresonant frequency after a ‘kick-start,’ and plot this response.

Choose any circuit you like, but the simpler the better. Suggestion: see LinearTechnology Application Note AN-12, figure 1E (shown below). Other topologies canbe found in Horowitz and Hill.

EXERCISE 2:

Simulate as much of your proposed EE122 final project circuitry as you can. Acquirethe plots that most clearly elucidate the successful simulation of pertinent circuit blocks.

Prepare a brief write-up that explains what simulations you carried out..

Prepare TWO transparencies to briefly present your design to the class. (Think: “blockdiagram”)

EXERCISE 3:

Prepare a plan of action for testing your designed (and now simulated) circuit blocks inthe lab this week. Of course you may want to refer to previous labs to be sure you aretesting all that you should.

EE122

Prof. Greg Kovacs

LAB 6:ADDITIONAL CIRCUIT

CONCEPTS

100 % of the shots you do not take do not go in.

Wayne Gretzky

ALWAYS use 0.1 µF decoupling capacitors on each power supplyrail, right next to each op-amp. Use one capacitor from the positiverail to ground and one from the negative rail to ground.

Use ± 12 V supplies. If you use a signal generator, you may wish to putan input 50 Ω resistor from the signal generator’s output to ground if youare using it to test your circuits. This is done so that the amplitudes on thesignal generator are correct (they assume a 50 Ω load).

This week’s lab is simple to describe:Work on circuits relevant to your proposed final project.

As has been the trend with Labs 4 and 5, you are left to determine foryourself what this means. But, we will still keep you honest:

Prepare a brief (4 - 5 pages) write-up of the experimental work you do inthis lab session. Your experiments need not be in the form of a coherentlesson, but the report should be well-organized and complete.

Remember: the TAs are there to help you in lab. They will not design andbuild your circuits for you, but they will give you ideas, places to look forwritten resources, and insight into what steps you might take to fully testyour circuit before integration. And, as always, have fun.

EE122

Prof. Greg Kovacs

PRELAB 7:ENTERING THE HOME STRETCH

Where, oh, where did the prelabs go... now I actuallyhave to worry about my project!

Unknown

OBJECTIVES (Why am I doing this prelab?)

• To work on my EE122 project.

Exercise - Prelab 7

Work With Your Team(and Another Team)

EXERCISE 1:

Carry out a design review on your project with another team. Schedule a time, meet,and review each other’s designs.

Submit a one paragraph note documenting the design review and any suggestionsmade for both your project as well as the other team’s project.

Please try to take this seriously and help each other. A little outside opinion can go along way.

EE122

Prof. Greg Kovacs

LAB 7:THE HOME STRETCH

We’re having fun yet.

Unknown

Continue to work on circuits relevant to your proposed final project.

Prepare a brief (1 - 2 pages) write-up of the new work you do in this labsession (this should be fully distinct from the write-up prepared for Lab 6).We know that you are very busy trying to get your project to work.Experience shows, however, that the time spent carrying out a write-up issaved two-fold during the composition of the Final Report.