Precision voltage follower
PARTS AND MATERIALS
Operational amplifier, model 1458 or 353
recommended (Radio Shack catalog # 276-038 and 900-6298,
Three 6 volt batteries
One 10 kΩ potentiometer, linear taper
(Radio Shack catalog # 271-1715)
Lessons In Electric Circuits, Volume
3, chapter 8: "Operational Amplifiers"
In the previous op-amp experiment, the
amplifier was used in "open-loop" mode; that is, without any
feedback from output to input. As such, the full
voltage gain of the operational amplifier was available,
resulting in the output voltage saturating for virtually any
amount of differential voltage applied between the two input
terminals. This is good if we desire comparator operation,
but if we want the op-amp to behave as a true amplifier,
we need it to exhibit a manageable voltage gain.
Since we do not have the luxury of
disassembling the integrated circuitry of the op-amp and
changing resistor values to give a lesser voltage gain, we
are limited to external connections and componentry.
Actually, this is not a disadvantage as one might think,
because the combination of extremely high open-loop voltage
gain coupled with feedback allows us to use the op-amp for a
much wider variety of purposes, much easier than if we were
to exercise the option of modifying its internal circuitry.
If we connect the output of an op-amp to its
inverting (-) input, the output voltage will seek whatever
level is necessary to balance the inverting input's voltage
with that applied to the noninverting (+) input. If this
feedback connection is direct, as in a straight piece of
wire, the output voltage will precisely "follow" the
noninverting input's voltage. Unlike the voltage follower
circuit made from a single transistor (see chapter 5:
Discrete Semiconductor Circuits), which approximated the
input voltage to within several tenths of a volt, this
voltage follower circuit will output a voltage accurate to
within mere microvolts of the input voltage!
Measure the input voltage of this circuit
with a voltmeter connected between the op-amp's noninverting
(+) input terminal and circuit ground (the negative side of
the power supply), and the output voltage between the
op-amp's output terminal and circuit ground. Watch the
op-amp's output voltage follow the input voltage as you
adjust the potentiometer through its range.
You may directly measure the difference, or
error, between output and input voltages by
connecting the voltmeter between the op-amp's two input
terminals. Throughout most of the potentiometer's range,
this error voltage should be almost zero.
Try moving the potentiometer to one of its
extreme positions, far clockwise or far counterclockwise.
Measure error voltage, or compare output voltage against
input voltage. Do you notice anything unusual? If you are
using the model 1458 or model 353 op-amp for this
experiment, you should measure a substantial error voltage,
or difference between output and input. Many op-amps, the
specified models included, cannot "swing" their output
voltage exactly to full power supply ("rail") voltage
levels. In this case, the "rail" voltages are +18 volts and
0 volts, respectively. Due to limitations in the 1458's
internal circuitry, its output voltage is unable to exactly
reach these high and low limits. You may find that it can
only go within a volt or two of the power supply "rails."
This is a very important limitation to understand when
designing circuits using operational amplifiers. If full
"rail-to-rail" output voltage swing is required in a circuit
design, other op-amp models may be selected which offer this
capability. The model 3130 is one such op-amp.
Precision voltage follower circuits are
useful if the voltage signal to be amplified cannot tolerate
"loading;" that is, if it has a high source impedance. Since
a voltage follower by definition has a voltage gain of 1,
its purpose has nothing to do with amplifying voltage, but
rather with amplifying a signal's capacity to deliver
current to a load.
Voltage follower circuits have another
important use for circuit builders: they allow for simple
linear testing of an op-amp. One of the troubleshooting
techniques I recommend is to simplify and rebuild.
Suppose that you are building a circuit using one or more
op-amps to perform some advanced function. If one of those
op-amps seems to be causing a problem and you suspect it may
be faulty, try re-connecting it as a simple voltage follower
and see if it functions in that capacity. An op-amp that
fails to work as a voltage follower certainly won't work as
anything more complex!
Schematic with SPICE node numbers:
Netlist (make a text file containing the
following text, verbatim):
vinput 1 0
rbogus 1 0 1meg
e1 2 0 1 2 999meg
rload 2 0 10k
.dc vinput 5 5 1
.print dc v(1,0) v(2,0) v(1,2)
An ideal operational amplifier may be
simulated in SPICE using a dependent voltage source (e1
in the netlist). The output nodes are specified first (2
0), then the two input nodes, non-inverting input first
(1 2). Open-loop gain is specified last (999meg)
in the dependent voltage source line.
Because SPICE views the input impedance of a
dependent source as infinite, some finite amount of
resistance must be included to avoid an analysis error. This
is the purpose of Rbogus: to provide DC path to
ground for the Vinput voltage source. Such
"bogus" resistances should be arbitrarily large. In this
simulation I chose 1 MΩ for an Rbogus value.
A load resistor is included in the circuit
for much the same reason: to provide a DC path for current
at the output of the dependent voltage source. As you can
see, SPICE doesn't like open circuits!