Chapter 1L
Lab 1: DC Circuits
Contents
1L Lab 1: DC Circuits
1L.1 Voltage Divider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1L.2 Ohm’s Law Applied to Convert a Meter Movement into a Voltmeter & Ammeter . . . . .
1L.2.1 Internal Resistance of the Movement . . . . . . . . . . . . . . . . . . . . . . . .
1L.2.2 10V Voltmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1L.2.3 10mA Current Meter (“ammeter”) . . . . . . . . . . . . . . . . . . . . . . . . .
1L.3 The Diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1L.4 Ivs.V for Some ‘Mystery Boxes’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1L.4.1 Estimate % Error Caused by the Instruments . . . . . . . . . . . . . . . . . . . .
1L.4.2 Where should DVM and Ammeter go, for Large RLOAD ? (nothing to build, here!)
1L.5 Oscilloscope & Function Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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REV 11 ;August 29, 2015
A preliminary note on procedure
The principal challenge here is simply to get used to the breadboard and the way to connect instruments to
it. We do not expect you to find Ohm’s Law surprising. Try to build your circuit on the breadboard, not in
the air. Novices often begin by suspending a resistor between the jaws of alligator clips that run to power
supply and meters. Try to do better: plug the two leads of the DUT (“Device Under Test”) into the plastic
breadboard strip. Bring power supply and meters to the breadboard using banana-to-wire leads, if you have
these, to go direct from banana jack on the source right into the breadboard. Below is a sketch of the poor
way and better way to build a circuit.
1 Revisions: insert Ray redraws (2) (9/14); respond to Paul notes (8/14); use main header file (6/14); add index (7/12); add breadboard
photo (9/08); place diode earlier than mystery boxes; correct Thev model load resistor: from 10k to 7.5k (9/06); add list of lab exercises;
place time boxes after headings (8/05); Large-R exercise, 3.2, changed to paper exercise rather than experiment (1/05); Changed from
10k R’s because ours are out of spec (1/04); Re-ordered, to place straightforward exercises first, subtle ’where to probe’ issues near the
end; two DVM placements illustrated; breadboarding detailed. 1/03.
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1
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10
Lab 1: DC Circuits
2
Figure 1: Bad and Good breadboarding technique: Left: labor intensive, mid-air method; Right: tidy method: circuit wired in place
Color Coding, and Making the Circuit Look Like Its Diagram
This is also the right time to begin to establish some conventions that will help you keep your circuits intelligible:
Here is a photo of one of our powered breadboard boxes, showing the usual power supply connections.
Figure 2: Breadboard power bus connections, again
The individual breadboard strips make connections by joining inserted wires in small spring-metal troughs:
Lab 1: DC Circuits
3
Figure 3: Single breadboard strip: a look at underside reveals the pattern of connecting metal troughs
Use a variable regulated DC supply, and the hookup shown in the first figure, below, Fig. L1.3.
• Caution!: you must not connect the external supply to the colored banana jacks on the powered breadboard (Red, Yellow, Blue): these are the outputs of the internal supplies of the breadboard, and even
when the breadboard power is OFF, these connectors tie to internal electronics that can be damaged by
an attempt to drive it. The same warning applies to the three white horizontal power supply “buses” at
the top of the board, strips that are internally tied to those three internal power supplies. (In case you
are curious, Red is +5, while Yellow and Blue are adjustable, and normally are set to about ±15V.)
Note, by the way, that voltages are measured between points in the circuit, while currents are measured
through a part of a circuit. Therefore you usually have to “break” or interrupt the circuit in order to measure
a current.
1L.1 Voltage Divider
Time: 15 min.
Figure 4: Voltage divider
Construct the voltage divider shown in fig. 4 (this is the circuit described in AoE Exercise 1.9, §1.2.5, except
that we have substituted 15k R’s). Apply Vin = 15 volts (use the DC voltages on the breadboard). Measure
the (open circuit) output voltage. Then attach a 7.5k load and see what happens.
Now measure the short circuit current. (That means “short the output to ground, but make the current flow
through your current meter.” Don’t let the scary word “short” throw you: the current in this case will be very
modest. You may have grown up thinking “a short blows a fuse.” That’s a good generalization around the
house, but it often does not hold in electronics.)
From IShortCircuit and VOpenCircuit you can calculate the Thevenin equivalent circuit.
Now build the Thevenin equivalent circuit, using the variable regulated DC supply as the voltage source, and
check that its open circuit voltage and short circuit current match those of the circuit that it models. Then
attach a 7.5k load, just as you did with the original voltage divider, to see if it behaves identically.
Lab 1: DC Circuits
4
A Note on Practical use of Thevenin Models
You will rarely do again what you just did: short the output of a circuit to ground in order to discover its RThevenin (or “output impedance,”
as we soon will begin to call this characteristic). This method is too brutal in the lab, and too slow when you want to calculate RTh on paper.
In the lab, ISC could be too large for the health of your circuit (as in your fuse-blowing experience). You will soon learn a gentler way to get
the same information.
On paper, if you are given the circuit diagram the fastest way to get RTh for a divider is always to take the parallel resistance of the several
resistances that make up the divider (again assuming Rsource is ideal: zero ohms)a . So, in the case you just examined:
= R1 II R2 = 7.5k
R1
15k
RThev
R2
15k
Figure 5: RTh = parallel resistances as seen from the circuit’s output
a A hard point to get used to, here: look at all paths in parallel, going to any fixed voltage, not just to ground. See the Manual’s attempt to
rationalize this result, pp. 8-9.
1L.2 Ohm’s Law Applied to Convert a Meter Movement into a Voltmeter & Ammeter
Time: 25 min., total
A Thevenin model is extremely useful as a concept; but you’ll not again build such a model. The circuit
you just put together is useful only as a device to help you get a grip on the concept. Now comes, instead, a
chance to apply Ohm’s Law so as to make something almost useful!– a voltmeter, and then a current meter
(“ammeter”).
You will start with a bare-bones “meter movement”–a device that lets a current deflect a needle. This mechanism is basically a current-measuring device: the needle’s deflection is proportional to the torque developed
by a coil that sits in the field of a permanent magnet, and this torque is proportional to the current through the
coil. Here’s a sketch2
Figure 6: Mechanism of analog current/volt-meter
An analog “multimeter” or VOM (volt-ohm-milliammeter) is just such a movement, with switchable resistor
networks attached. We would now like you to re-invent the multimeter.
2 Source:
after Google images file: “analog meter movement.” Source unknown.
Lab 1: DC Circuits
Time: 10 min.
1L.2.1
5
Internal Resistance of the Movement
You could design a voltmeter–as you will in the next subsection–simply assuming that the movement’s
RINTERNAL is negligibly small. The resistance of this movement is low–well under 1kΩ. But let’s be more
careful. Let’s first measure the internal resistance. Here, please note, we want you to work with a simple bare
meter movement, not with a multimeter. (It’s more fun to start from scratch.)
Do this measuring any way you like, using the variable power supply, DVM (digital voltmeter–really a
multimeter, despite its name), and VOM if you need it. There are several good ways to do this task. The
meter movements are protected. Don’t worry about burning out the movement, even if you make some
mistakes. Even ”pinning” the needle against the stop will not damage the device, we found by experiment–
though in general you’ll want to avoid doing this to analog meters. We have provided diodes that protect the
movement against overdrive in both forward and reverse directions. You should note, as a result, that these
diodes that protect the movement also make it behave very strangely if you overdrive it. (No doubt you can
guess what device it behaves like!) So, don’t use data gathered while driving the movement beyond full scale.
Sketch the arrangement you use to measure RINT , and note the values of RINTERNAL and of IFULL−SCALE.
Time: 10 min.
1L.2.2
10V Voltmeter
Show how to use the movement, plus whatever else is needed, to form a 10-volt-full-scale voltmeter (that just
means that 10V applied to the input of your circuit should deflect the needle fully). Draw your circuit. Note:
this is a good time to start getting used to our canny use of approximations, as we design. As you specify the
resistor that you want to add to the bare meter movement, recall that you are limited to “5% values”—resistors
whose true value is known only to lie within ±5% of the nominal value.
10V-full-scale voltmeter, made from meter movement plus ? (Your drawing)
Does the movement’s internal resistance cause a significant error? (What does “significant” mean? Well,
you might compare the contribution of RINT against the contribution of error from your uncertainty about the
value of the resistor that (we hope!–) you have included)
1L.2.3
10mA Current Meter (“ammeter”)
Time: 5 min.
Show how to use the movement, plus whatever else is needed, to form a 10-mA-full-scale ammeter, and test
your circuit.
10mA-full-scale ammeter, made from meter movement plus ? (Your drawing)
Lab 1: DC Circuits
6
1L.3 The Diode
Time: 10 min.
Here is another device that does not obey Ohm’s law: the diode. (We don’t expect you to understand how the
diode works yet; we just want you to meet it, to get some perspective on Ohm’s Law devices: to see that they
constitute an important but special case.
We need to modify the test setup here, because you can’t just stick a voltage across a diode, as you did for
the resistor and lamp above@foot(Well, you can; but you can’t do it twice with one diode!) You’ll see why
after you’ve measured the diode’s V vs I. Do that by wiring up the circuit shown in fig. 7.
Figure 7: Diode VI measuring circuit
¿ In this circuit you are applying a current, and noting the diode voltage that results; earlier, you applied
a voltage and read resulting current. The 1k resistor limits the current to safe values. Vary R (use a 100k
variable resistor (usually called a potentiometer or “pot” even when wired, as here, as a variable resistor), a
resistor substitution box, or a selection of various fixed resistors), and look at I vs V. First, get a feel for the
behavior by sweeping the R value by hand, and noticing what happens to the diode current. Then sketch the
plot in two forms: linear and “semi-log,” in figure L1.14.
diode current
First, get an impression of the shape of the linear plot; just four or five points should define the shape of the
curve. Then draw the same points on a semi-log plot, which compresses one of the axes. (Evidently, it is the
fast-growing current axis that needs compressing, in this case.) If you have some semi-log paper use it. If
you don’t have such paper, you can use the small version laid out below. The point is to see the pattern.
Figure 8: Diode I vs V: linear plot; semi-log plot
See what happens if you reverse the direction of the diode.
How would you summarize the V vs I behavior of a diode?
Lab 1: DC Circuits
7
Now explain what would happen if you were to put 5 volts across the diode (Don’t try it!). Look at a diode
data sheet, if you’re curious: see what the manufacturer thinks would happen. The data sheet won’t say
“Boom” or “Pfft,” but that is what it will mean.
We’ll do lots more with this important device; see, e.g., § 1.6 on page 43 in AoE.
1L.4 Ivs.V for Some ‘Mystery Boxes’
Time: 40 min.
Figure 9: Circuit for measurement of I vs V
Find two mystery boxes which we have set up for you (we will call these “DUT”’s: Device Under Test).
These are two-terminal devices, one of which is an ordinary resistor, the other an odder thing. The devices
are hidden inside black plastic 35mm film cans. Apply voltages in the range 0 to a couple of volts, using
a variable power supply, and note voltage and current pairs. For the range between 0 and 1V, measure at
increments of 0.1V (because this is the range where you need a detailed picture).
Sketch a graph of a few points to get the trend. Turning the power-supply voltage knob by hand, you may be
able to get a sense of the shape of the curve, or see where more points are needed.
Decide which device is which: which ordinary, which odd. Warning: keep the applied voltage below 7V, or
you may destroy one of the DUT’s.
To make your task challenging, we ask that you measure voltage and current simultaneously, as you do
this exercise. We ask this so that you will be obliged to consider the effects of the instruments on your
measurements (more on this point, below).
Effects of the instruments on your readings
Consider a couple of practical questions that arise in even this simplest of “experiments.”
A Qualitative View
Is the voltmeter measuring the voltage at the place you want, namely across the object under test? Or does
the voltage reading include the effect of the ammeter, in your arrangement? Does that matter? If you are
measuring the object’s voltage precisely, then are you reading its current or are you measuring the current in
object plus the current passing through the DVM as well? If you can’t have it both ways (as you can’t), and
must live with one of the two errors, which experimental setup gives you the smaller error?
Below are two figures sketching the two possible placements of the voltmeter.
Lab 1: DC Circuits
8
reading current
meter’s internal
resistance
Figure 10: Measuring I and V simultaneously: only one instrument gets a true reading at DUT
Figure 11: Measuring I and V simultaneously: only one instrument gets a true reading at DUT
If you know (and we’ll reveal this fact to you, now!) that the LOAD resistance is under 1k ohms (“resistance”
or some near-equivalent; we’re not promising you Ohmic behavior), then you can judge which of the two
setups illustrated above gives the truer pair of I and V readings. Use that preferred setup to get a set of I and
V readings, and try to infer an R value, if you can.
1L.4.1
Estimate % Error Caused by the Instruments
Once you have your best estimate of R in hand, estimate the errors that the instruments cause. Specifically,
when the ammeter is on the 10mA full-scale range, what percentage error in inferred R results from the
presence of...
• ammeter, when you measure V where the ammeter causes an error? _______.
• voltmeter, when you measure V where the ammeter causes no error? _______.
After getting answers to these questions, probably you can say what an ideal voltmeter (or ammeter) should
do to the circuit under test? What does that say about its “internal resistance”? (Perhaps you caught on to this
theme, pages earlier!)
Now sketch the curves described by your data points. Don’t work too hard: it’s the shapes that we’re after.
The resistor isn’t very interesting (what’s its value?); the mystery device is a little more intriguing.
Lab 1: DC Circuits
9
Here’s a place to draw these curves:
Figure 12: Two contrasted I vs V curves (your drawings)
What do you suppose the mystery gadget is? We hope you saw its “curve.” In fact, it’s made of material much
like what forms the resistor. Why does its I-V curve look different? The bend can be useful: weeks from
now, in Lab 10a, we will exploit this curvature to make a circuit regulate its own gain. Now you have earned
the right to open up the film canister and discover what’s inside!
1L.4.2
Where should DVM and Ammeter go, for Large RLOAD ? (nothing to build,
here!)
Now you may have “learned,” in the previous exercise, where to place the voltmeter, so as to get the best
simultaneous I and V readings. Just to make sure you don’t go away thinking you’ve learned something3 ,
we’d like you to try a pencil-and-paper exercise, this time assuming that the DUT—RLOAD —is a very large
resistance: 10MΩ. Assume that the DVM’s RIN = 10MΩ. (Note that we’re not asking you to carry out this
experiment; only to predict what you would see if you did do the experiment.)
If you placed your DVM at the load, the DVM would appear in parallel with the load. What percentage error
would this evoke in the simultaneous current measurement? In contrast, the voltage error caused by reading
upstream of the ammeter in this case would be no larger than in the case you tried in the lab experiment.
Perhaps now you can begin to generalize about which cases oblige one to worry about the DVM’s RIN .
3 Just
kidding.
Lab 1: DC Circuits
10
1L.5 Oscilloscope & Function Generator
(if time: you’ll get a big scope workout next time, in Lab 2; these exercises simply give you a head start)
We’ll be using the oscilloscope (“scope”) and function generator in virtually every lab from now on. Today,
voltmeters were sufficient–and, in fact, more convenient than an oscilloscope, because our circuits’ voltages
and currents have been politely sitting still, giving us time to measure them! If you are familiar with the
scope, go right on to the first real exercise in Lab 2, 2-1–or go home, having earned a rest.
The scope soon will become our favorite instrument as soon as we begin to look at signals that are not static
(called “DC,” in electronics jargon): signals that, instead, vary with time. (Lab 2 is concerned exclusively
with such circuits, and with rare exceptions this will be true of all our work after today.) The scope draws a
plot of voltage (on the vertical axis) versus time (on the horizontal axis).
Get familiar with scope and function generator (a box that puts out time-varying voltages: waveforms; things
like sine waves, triangle waves and square waves) by generating a 1000 hertz (1kHz, 1000 cycles/sec) sine
wave with the function generator and displaying it on the scope. Connect the function generator directly to
the scope, using a “BNC cable,” not a probe.
If it seems to you that both instruments present you with a bewildering array of switches and knobs, don’t
blame yourself. These front-panels just are complicated. You will need several lab sessions to get fully used
to them–and at term’s end you may still not know all: it may be a long time before you find any occasion for
use of the holdoff control, for example, or of single-shot triggering, if your scope offers this.
Play with the scope’s sweep and trigger controls. Most of the discussion, here, applies fully only to an analog
scope. The digital scope automates some functions, such as triggering and gain setting, if you want it to. We
suggest that you ought not to begin your scope career using such fancy features: beware the mind-stunting
button labelled AUTOSET!.
Specifically, try the following:
• The vertical gain switch. This controls “volts/div”; note that “div” or “division” refers to the centimeter
marks, not to the tiny 0.2 cm marks);
• The horizontal sweep speed selector: time per division.
– On this knob as on the vertical gain knob, make sure the switch is in its CAL position, not VAR
or “variable.” Usually that means that you should turn a small center knob clockwise till you feel
the switch detent click into place. If you don’t do this, you can’t trust any reading you take.)
• The trigger controls. Don’t feel dumb if you have a hard time getting the scope to trigger properly.
Triggering is by far the subtlest part of scope operation. “Trigger” circuits tell the scope when to begin
moving the beam across the screen: when to begin drawing a waveform. When you think you have
triggering under control, invite your partner to prove to you that you don’t: have your partner randomize
some of the scope controls, then see if you can regain a sensible display (don’t let your partner overdo
it, here).
– Beware the tempting so-called “normal” settings (usually labeled “NORM”). They rarely help,
and instead cause much misery when misapplied. Think of “normal” here as short for abnormal!
Save it for the rare occasion when you know you need it. “AUTO” is almost always the better
choice.
∗ the scope waits around till triggered. In AUTO mode, it sweeps either when triggered, or
when it has waited so long that it loses patience. Thus you always get at least a trace, in
AUTO mode.
Time: 30 min.
Lab 1: DC Circuits
11
∗ NORMAL, in contrast, makes the scope infinitely patient: it will wait forever, drawing nothing on the screen, until it sees a valid trigger signal. Meanwhile, you look at a dark screen;
usually, that is not helpful!
∗ Trigger “source”: here’s another way to go wrong: trigger can be set to look at either of the
scope’s two input “channels” (CH1 or CH2), or at the external BNC connector, called EXT.
Switch the function generator to square waves and use the scope to measure the “risetime” of the square wave
(defined as time to pass from 10% to 90% of its full amplitude).
At first you may be inclined to despair, saying “Risetime? The square wave rises instantaneously.” The scope,
properly applied, will show you this is not so.
A suggestion on triggering:
It’s a good idea to watch the waveform edge that triggers the scope, rather than trigger on one event and watch another. If
you watch the trigger event, you will find that you can sweep the scope fast without losing the display off the right side of the
screen.
So, to measure risetime of a signal connected to Channel One, trigger on Ch 1, rising-edge.
What comes out of the function generator’s SYNC OUT or TTL4 connector?
Look at this on one channel while you watch a triangle or square wave on the other scope channel. To see
how SYNC or TTL can be useful, try to trigger the scope on the peak of a sine wave without using these aids;
then notice how entirely easy it is to trigger so when you do use SYNC or TTL to trigger the scope.
Triggering on a well-defined point in a waveform is especially useful when you become interested in measuring a difference in phase between two waveforms; this you will do several times in the next lab. You can
use a zero-crossing (where the waveform crosses the midpoint of its excursion), or, when using SYNC OUT,
you can use the peak or trough of the waveform.
How about the terminal marked CALIBRATOR (or “CAL”) on the scope’s front panel? (We won’t ask you
to use this signal yet; not until Lab 3 do we explain how a scope probe works, and how you “calibrate” it
with this signal. For now, just note that this signal is available to you). Postpone using scope probes until you
understand what is within one of these gadgets. A “10X” scope probe is not just a piece of coaxial cable.
Put an “offset” onto the signal, if your function generator permits, then see what the AC/DC switch (located
near the scope inputs) does.
Note on AC/DC switch:
Common sense may seem to invite you to use the AC position most of the time: after all, aren’t these time-varying signals that you’re looking
at “AC”–alternating current (in some sense)? Eschew this plausible error. The AC setting on the scope puts a capacitor in series with the scope
input, and this can produce startling distortions of waveforms if you forget it is there. (See what a 50 Hz square wave looks like on AC, if you
need convincing.) Furthermore, the AC setting washes away DC information, as you have seen: it hides from you the fact that a sine wave is
sitting on a DC offset, for example. You don’t want to wash away information except when you choose to do so knowingly and purposefully.
Once in a while you will want to look at a little sine with its DC level stripped away; but always you will want to know that this DC information
has been made invisible.
Figure 13: AC/DC scope input select
4 “TTL” stands for the equally-cryptic phrase, “Transistor-Transistor Logic.” That phrase names a kind of digital logic gate that you
will find described in classnotes D1. In the present context, “TTL” should be understood to mean simply “Logic-Level square wave,” a
square wave that swings between ground and approximately four volts.
Lab 1: DC Circuits
12
Set the function generator to some frequency in the middle of its range, then try to make an accurate frequency
measurement with the scope. (Directly, you are obliged to measure period, of course, not frequency.) You
will do this operation hundreds of times during this course. Soon you will be good at it.
Trust the scope period readings; distrust the function generator frequency markings; these are useful only for
very approximate guidance, on ordinary function generators.
(lab1 headerfile june14.tex; August 29, 2015)
Index
AC/DC (scope input select), 13
ammeter (lab), 6
breadboard (use of), 1–3
diode (lab) , 6–7
meter movement (analog), 5
multimeter (lab), 5, 6
oscilloscope (lab: first view), 11
triggering, 11–12
SYNC OUT (function generator output), 12
Thevenin model (lab), 4
TTL
syncing output from function generator, 12
TTL (function generator output), 12
voltage divider (lab), 4
13