# Analog Circuits Laboratory EXPERIMENT 1: Operational

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University of California, Santa Cruz
Electrical Engineering Department
Analog Circuits Laboratory
EXPERIMENT 1: Operational Amplifiers
I. DESCRIPTION AND OBJECTIVES
This laboratory presents a basic practical summary of operational amplifiers (op-amps) and will
provide the opportunity to become familiar with their behavior from ideal and non-ideal
perspectives. Effects of non-linear circuit operation will be observed in both the time and
frequency domains.
II. GENERAL DISCUSSION
An op-amp is a three-port device having two inputs and one output. It was invented to simplify
the design of inverting and non-inverting DC amplifiers by the simple control of external
negative feedback. This deceptively simple building block is to analog electronics what Nand or
Nor gates are to digital electronic circuits: it reduces analog circuit design to a simple problem of
determining suitable external feedback and interconnecting networks without the complication of
having to know what’s going on inside the op-amp itself. Treating the op-amp as ideal is often
all that is necessary to use it in practice – provided we skillfully appreciate the limitations
imposed by basic device parameters that would typically include:
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non-infinite open-loop gain
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frequency response expressed by slew rate, , single-pole roll-off frequency,
related gain-bandwidth product, GBP.
non-infinite input port resistances and non-zero output resistance.
power-supply limiting or railing due to finite power supply voltages.
internal wideband zero-mean noise generation.
non-zero DC bias currents.
,and its
Although the op-amp is employed in a truly impressive array of many different circuits, all
are based in part on one or both of the following two fundamental circuit configurations: the
inverting and non-inverting DC amplifiers. You will gain an appreciation of the power of the
op-amp as a basic building block along with some of its inherent limitations through
experimental investigation of these two basic circuits.
Op-amp circuits may be linear or non-linear, depending on what they’re designed to do. We
will look at various non-linear effects when the input signal is a sinusoid by observing the input
and output on a dual-trace oscilloscope; frequency domain effects will be observed with a
spectrum analyzer. These instruments will both be thoroughly discussed in lab.
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III. NON-INVERTING CONFIGURATION
Construct the non-inverting circuit shown in Fig. 1. using an LM324 Quad op-amp.
10k. Determine the following for
and
:
should be
Observe power-supply limiting and log what these voltage rails are. Measure and accurately plot
the amplitude and phase response vs. frequency. Frequency should be measured with a counter,
amplitude in
from a DVM. Measure the slew rate. Observe two types of non-linear
behavior: power supply clipping and slew-rate limiting, and note the effects that each of these
has separately on an applied sinusoid in both the time and frequency domains. Observe timedomain signals with an oscilloscope and frequency domain signals with a spectrum analyzer.
Figure 1. Basic non-inverting op-amp configuration.
Note: Re-draw this schematic in your engineering notes and make any experimental scribbles or annotations there.
From your linear frequency response data, construct a simple Bode Plot showing both plots for
the two different circuit gains. Discuss the meaning of the gain-bandwidth product relationship
and verify it from your data. Discuss your results for slew-rate. Numeric data should be
discussed with realistic precision using only as many significant figures as your data warrants.
Finally, discuss the two types of non-linearity you observed and their consequences.
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General Recommended Procedure:
1. Don’t mindlessly take data unless you have a good idea of what should be observed. You can
analyze things before doing the lab or as you go along. Put everything in your engineering
notes. Be sure to accurately measure all resistors before putting them in the circuit. Use the
ideal op-amp model to determine the expected closed-loop gains expressing them in both
10[V] before connecting them to
your circuit. These don’t have to be precise, but accurately measure and log what they
actually turn out to be. Use the data sheet to estimate the supply rails and slew-rate.
2. Before taking refined measurements, verify circuit operation by sweeping the signal generator
over a 10 or 100:1 frequency range while observing both the input and output simultaneously
on the oscilloscope; use dual-trace mode for this. This will give you a good idea of where the
cutoff frequency is, whether the circuit is working, and what frequencies to include in your
actual measured data. Remember, the cutoff frequency is defined as that frequency where
the gain has dropped by –3dB and the phase-shift is –45 degrees. Since the gain can more
accurately be measured using a DVM, use it rather than time delay to actually find the
frequency by observing the AC RMS voltage (this is the only AC voltage that can be
measured by the DVM). The observed phase shift on the oscilloscope should be close to –45
degrees in any case.
3. Slew-rate is best measured by changing the input to a square-wave and looking at the output
voltage slope over some convenient time interval. Adjust the frequency from the generator to
suitably observe this. Be sure the op-amp is not railing. Once you know where slew-rate
limiting begins, the effects of this non-linear behavior can also be observed by changing to a
sine-wave input.
4. Observe and measure the non-linear effects of clipping (power-supply limiting) using a low
sinusoidal frequency to avoid the possibility of slew-rate limiting occurring at the same time.
5. Investigate other phenomena you find interesting if you like and include them in your report.
IV. INVERTING CONFIGURATION
Modify your circuit to implement an inverting amplifier using the same resistors, and repeat the
measurements taken earlier for the non-inverting configuration . Be sure to use one of the other
op-amps in the LM324 to remove any effects of the lab generator’s 50 Ohm source impedance
from changing the effective gain of your circuit. Discuss all differences you observe between the
non-inverting and inverting configurations.
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V. QUESTIONS
1. Some op-amps are not unity-gain stable. Investigate and explain what this means.
2. The LM324 is capable of single-supply operation. Explain what this is and show how to use
the LM324 as an audio amplifier using a single-supply having a gain of +24dB. This circuit
will require the use of blocking capacitors. Explain what they are, why they’re used and what
the effects of having them in this circuit are.
3. Is there a relationship between an op-amp’s slew-rate and its frequency response? Explain.
4. When an op-amp is configured to behave as a voltage-follower, its closed-loop gain is
.
Why is this a useful circuit? Can this configuration show gain of any type at all (refer to our
textbook, Ch-1)?
5. Your measurement of cutoff frequency assumes a low-pass filter model having only a single
dominant pole in its transfer function. Actual op-amps typically have more complicated
transfer functions with more poles than this. Why are we justified in using the so-called
dominant-pole model ? What would happen to the measured phase shift if the -3dB corner
frequency actually was caused by two or more internal poles very close together in frequency?
6. The LM324 is not a “rail-to-rail” op-amp. Investigate what this means and confirm from your
data that the LM324 is indeed not a true “rail-to-rail” device.
7. When using a device like the LM324, why are the supply rails bypassed with 100nF
capacitors? Adding these bypass capacitors is considered a standard of good engineering
practice. Develop a simple theoretical model showing why they are typically necessary and
what is being “bypassed.”
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