# Laboratory Exercise 6 Op. Amps 2 Useful Op Amp Circuits

AI and Robotics

Nov 24, 2013 (4 years and 7 months ago)

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Laboratory Exercise 6

Op. Amps 2

Useful Op Amp Circuits

You’ve learned enough about analog electronics at this point to make some fairly realistic
chemical measurement circuits. We will start with one of the most common chemical
measurements, the pH
of an aqueous solution.

pH Meter Amplifier

The potential (voltage)

of a glass electrode
(
measured versus a reference electrode
)

follows the
equation

E =
C

-

2.303

(RT/F)

log a
H+

=
C

+

0.0592

V *

pH (at 298 K)

where
C

is a constant
, a
H+

is the activity

of the hydronium ion (often taken to be equal to the
molar concentration [H
+
]
)
, and the
calibration sensitivity

(slope of voltage
vs.

pH
)

is often
quoted

as 59
.2

(or 60)

mV/pH

unit
.
Both the
constant

and the slope of the response are expected to
depend on temperature
.
Clearly, pH measurement requires calibration, as do most instrumental
measurements
.
There are good descriptions of the glass electrode and the associated reference
electrodes in most ana
lytical texts.

Note that the
sensitivity

of the glass electrode (and

all other

potentiometric measurements
) is

low
:
59 mV per unit pH change

(
a
factor of 10 change in concentration
).
This is an example of a
signal
that

would benefit from
amplification
, if
we can
maintain reaso
nable signal to noise and
not distort the response
.
An amplifier for this purpose must have a very high input impedance,
optimally greater than or equal to

10
10

(10 G

)

because the glass electrode has an
output
impedance of abou
t 10
8

.
It would be nice if

the
amplifier
gain
was

ch unit
of
pH
change (59.2 mV) wa
s indicated as one unit on the readout, for example, one volt
.
A
n
offset control for calibration of the zero point

would also help

to make the output
indicate

the

pH

of the solution
.

Concept Question 1

If the voltage coming from a glass electrode was monitored using an
oscilloscope with a 1 M

input impedance, how much smaller would the observed sign
al be?
(
Treat it as a
voltage div
ider where the
voltage to be measured is applied across the 100 M

of
the pH
electrode

and the scope resistance is after that.
)

Circuit Exercise 1

circuit

below using

the

high impedance
3140
op amp
for
the input stage

(from the pH meter)

and a 741 for
.
The output, when
calibrated
,

will be one volt per pH unit.
In this circuit potentiometer Pl adjusts the offset and P2
sets
the slope
.
It is hard to get this circuit to work well, because the high output impedance
of the
glass
electrode and the

high gain tends to “pick up” external fields
.
It may help to use some kind
of shielding around the connections and to stand back from the circuit for a few minutes while
the outp
ut stabilizes for each solution.

Concept Question
2

Referring to the schematic, what type of
amplifier

(from last lab) is the
3140 used in?

And what type of
amplifier

is the 741 used for?

Before applying power, connect the electrode
(
s
)

to the circuit, immerse in a pH = 7 buffer, and
set the DMM for the

20 V range
.
Activate the power sup
of 7.0
±0.1

V on the DMM (P2 should be at about mid
-
range)
.
Rinse the electrodes in water and
immerse them in a buffer of pH = 4, adju
st P2 for a reading of 4.0 ±0.1

V. Repeat the calibration
at least once
.

Measure the pH of the pH 4, 7, and 10 buffers and record below
.
Comment on the reliability of
the three measurements.

Measure the pH of
tap water

and record below.

If you wanted to create an auto
-
titrator, you
voltage

with a PMD

and
feed the output directly into a graphical display
.

What else would you need to complete the auto
-
titrator
? (Q
ualitatively

you don’t have to know
how to build one yet
.
)

Active
Band
P
ass

Filter
/ Photometer

When we worked with RC filters earlier, we noted that it would be possible to make better filters
using
active

elements
.
The next circuit uses an op amp to
produce

a filter with characteristics
that

are superior to those made with only
passive

elements
.
The combination of RC filters

(more than
one)

and an op amp shown below has high gain over a narrow frequency range
, with small gain
elsewhere
.
I
t is called a
band pass

filter

and can be used to focus

on signals with a particular
frequency (often one that we control
).
We’ll use it with a photo cell to

build a photodetector that
selectively measures one light source, while

ignoring any other light sources nearby
.
If we are
successful at that, we’ll buil
d a rudimentary absorption spectrometer and see how well it works
.

Circuit Exercise 2

Set up the
band pass filter

circuit shown below and drive it with the
function generator to characterize it
.
We’ll hook up the photocell

and source after we’re
conf
ident that this piece works.

Record the input and output
voltages (peak to peak)

for sine waves over the following frequency
range
.
Input amplitude
should

pp
.
Also note

the

phase

shift

in the usual way
,
although you may want to characterize the shift as a
(
i.e.
,

of

or
behind the input) instead of as a full 360 shift.

Locate the frequency (
f
0
) that gives the
maximum output voltage.

Estimate the Qual
i
ty factor Q for the filter
.
Q =
f
0
/

f
, where
f
0

is the center frequ
e
ncy and

f

is
the frequency difference between the

3 db points on either side (approximately the FWHM.)

Take a guess at the changes you would h
ave to make to get a filter with a pass band centered at
100 Hz
.
(If you’ve got time, you
might

try it out.)

Power one of the monolithic LEDs (any color) with the function generator
.
Try a 100
Ω current
limiting resistor in series with the LED
.
If that is
n’t bright enough, try a smaller resistor
.
That
Frequency
lnput/volts
Output/volts
Phase
400 Hz
600 Hz
800 Hz
1 kHz
1.1 kHz
1.2 kHz
1.3 kHz
1.4 kHz
1.8 kHz
3 kHz
will be the
source

.
Put a photocell in series with a resistor of about the same
value (make a light
-
dependent ½ voltage divider) and power it with the 5 VDC power supply
.
This is the
detector
.
Point the photocell at the LED, leaving enough space between for a 1 cm
cuvette
.
Try to monitor the outpu
t of the detector directly with the scope (you
should

monitor the
output of the FG that’s driving the LED

with the other probe and use this t
o trigger the scope
)
.

Describe what you see
.

Connect the output of the detector circuit to the bandpass filter and monitor the output of the
bandpass
circuit
with the scope
.
Assuming that you

can

see the modulated signal
,

verify that
there is a dependen
ce of the output signal magnitude on the modulation frequency
.
Maximize the
signal
.
If you can detect something that you think is proportional to light before the bandpass
filter, measure that too
.

Describe the waveform you see

after the bandpass filter
.

Obtain a cuvette (plastic is fine) and a solution that you think will absorb at the wavelength of
.
Acid
-
base indicators or food colors both work, since they come in a variety of colors
and absorb strongly
. Keep in mind the complementarity of
color and absorption
.
Construct a
calibration curve of absorbance vs. concentration
.
This system is probably going to be very
alignment sensitive, so the best
way to do this might

be to use double sided tape to hold the
cuvette rigidly in place
, and then

u
se a Pasteur pipette to fill and empty liquid from the cuvette
.
Don’t forget to measure a blank

(water only)

and the signal with no light (if there is one)
.

What part of the waveform are you measuring? What is proportional to light intensity at the
dete
ctor?

.
Don’t forget to include the slope, intercept, and correlation
coefficient
.
If you measured the unfiltered signal, show the curve for that too.

Comment on the values of the slope, intercept, and correlation coeffic
ient (linearity!) for the
graph(s).

Why
doesn’t this

“spectrometer” require a monochromator
? (These instruments are sometimes
called photometers.)

Why doesn’
t
this photometer require a light
-
tight box

like most of them have
?

(Assuming it
worked

without one
.)

Bridging the Analog/Digital Divide
-

The Comparator

Now that we have started to think about the

land of

digital

,
we’ll also

introduce you to a circuit
that
derives a

simple

digital

response
from a
n

analog

signal, the
comparator
.
A comparator
gives a
yes

or
no

response
to the question “is

an inpu
t voltage
smaller

th
an a provided referenc
e
voltage?”

S
pecialized comparators are better than the op amp analogs that we will
build
, but their
princ
iple of operation is the same
.
The

311
(which we’ll see in the next exercise)
is a popular
comparator chip that has a high impedance op amp front end

(input)

and an open collector
bipolar transistor back end

(output
).
This allows the input to trigger any output

voltage

that you
want
, consistent

with a standard bipolar tra
n
sistor switch circuit
.

In
a comparator
,

the voltage

input

is connected directly to the inverting input of an op amp, while
the reference voltage is connected to the
non
-
inverting input
.
No feedback loop is provided
.
Assume th
at the input voltage is bigger than the reference voltage
.
From the golden rules you
know that the ou
t
put will do everything in its power to try to make the voltages at the two inputs
equal
, usually by trying to supply negative voltage to the inverting inp
ut
.
I
n this case, it is
unable

to make any changes to the in
puts because of
the lack of feedback
.
Frustrated, the ou
t
put swings
to the
negative
rail (and hopefully stays there
)
and

the
-
15 V is the answer to our question,
no
.

Now assume that
the voltage at the inverting input drops below that at the non
-
inverting input, at
which time
the output swings to the other rail
:

+ 15 V =
yes
.
That’s ho
w digital works

only two
voltages allowed, one is called

yes

or 1 and the other is called

no

or
0
.
The problem with
using the comparator is, “what if the two voltages are very close to one another and are both
pretty noisy?” The op amp

s output suffers from indecision and tends to go out of control
,
oscillating rapidly from one rail to the other
.
Th
is is a bad thing, so the comparator is one of the
few cases you will see where we will
use

positive feedback

(a feedback loop to the non
-
inverting
input)
.
What you end up with is the op amp deciding that it needs to respond and in responding it
will ten
d
to aggravate the situation, m
oving the “low” input even lower (or vice versa)
accelerating the circuit towards the correct decision.

Circuit Exercise 4

the simple comparator below and drive it with the function
generator
using a

sine wave
that
crosses ground

(the reference voltage
).
This circuit doesn’t
benefit from positive feedback
, but it usually works just fine
.
We could call this a zero
-
crossing
detector
.

Rationalize the output pattern

as I did above
.
(What is the output “trying” to
do.)

Do you see any

funny

behavior at the edges of the square wave? (Try changing the frequency a
bit to see if you can induce oscillations
).
Usually you can’t
.
The reason we still use 741s in this
lab is that they are really stable, perhaps bordering
on sluggish
.
It’s hard to get them to go fast,
but it’s equally hard to get them to “freak out” on fast changes
.

If you want to see the “funny” behavior, you can try a faster op amp, like the 3140 or the 355, we
have those in the lab
.
If you do, describe

what you got and what you did to get it.

Now add the following resistors to the circuit to provide positive feedback.

Are the transitions sharper?
Are they at the same voltages as before?

Again walk through the analysis of this circuit, describing wha
t the output is “trying” to do in
response to different values of the input
.
Think about what determines the reference value
.
(Hint:
it is easiest to start with a presumed value of the input and follow that result through the circuit,
and then let that val
ue change
).

This is a tricky one

ask for help if you’re struggling.

This circuit makes use a concept called
hysteresis
, which we will see again when we talk about
the Schmitt trigger in the digital section
.
In this context, hysteresis just means that where the
thing switches in one
signal
direction (inverting input coming down with respect to non
-
inverting) is different from where it switches in the other direction
.
T
his helps make the system
more immune to n
oise.

Real World Example

This lab has been all about real world examples
, so we don’t need to use our imagination to come
up with one
.

Which
circuits

were DC measurements and which

were inherently time dependent?

What other characteristics can you id
entify about the signal sources and the nature of the output
for the various circuits?

Often the first step to optimizing an instrument is thinking carefully
about the characteristics of the signal itself.

Revised 6/12/13 DBA