University of Saskatchewan
EP 313 Advanced Analog Electronics and Instrumentation
Non-ideal Op-amps
Safety
The voltages used in this experiment are less than 15 V and normally do not present a risk of shock. However, you should always follow safe procedures when working on any electronic circuit. Assemble or modify a circuit with the power off or disconnected. Don ʼ t touch different nodes of a live circuit simultaneously, and don ʼ t touch the circuit if any part of you is grounded. Don ʼ t touch a circuit if you have a cut or sore that might come in contact with a live wire. Check the orientation of polarized capacitors before powering a circuit, and remember that capacitors can store charge after the power is turned off. Never remove a wire from an inductor while current is flowing through it. Components can become hot if a fault develops or even during normal operation so use appropriate caution when touching components.
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Objectives: These experiments will investigate how real op-amps differ from the ideal model and the consequences the non-ideal behaviors have for circuit operation. In each experiment, a different non-ideal aspect is studied; the experiments investigate
• bias current
• offset voltage
• bandwidth
• slew rate
• clipping
At the end of the laboratory, a student should be able to draw the equivalent circuit or describe the device parameter for common non-idealities, measure the non-idealities for a real op-amp, and explain how to mitigate the effects of the non-idealities through proper design.
Introduction: The operational amplifier is a simple device having two inputs V
+
and V
–
and an output V out
where V out
= A(V
+
– V
–
). Despite its simplicity, the op-amp is one of the most important building blocks for analog circuits. It is used in comparators, instrumentation amplifiers, integrators, differentiators, logarithmic convertors, active filters, oscillators, buffers, voltage and current sources, and many other circuits. The utility of the op-amp comes from the differential input and the very large (low-frequency) gain, in excess of 100dB.
Analysis of op-amp circuits often uses an ideal approximation, something you should have learned in your analog circuits class. The ideal op-amp has
• arbitrarily large gain,
• no current flowing into either input,
• an output that can drive any load, and
• no phase shift or any dependence on frequency.
The equivalent circuit of an ideal op-amp is particularly simple as shown in Fig. 1.

University of Saskatchewan
EP 313 Advanced Analog Electronics and Instrumentation
Non-ideal Op-amps
2
Fig. 1 Ideal op-amp (left) and the equivalent circuit (right).
Although the ideal op-amp approximation is useful for a basic analysis of circuits, none of the ideal characteristics is correct for real op-amps. Whether the deviations from ideality are important depends on the particular circuit, and it is the job of the design engineer (i.e. you) to know when the non-idealities need to be considered.
A. Input Bias Current
The inputs of the ideal op-amp draw no current, but real op-amps have a current that flows into or out of each input called the input bias current I
B
. The input stage of an op-amp is a differential amplifier, and the op-amp's inputs are each connected to the base of a transistor.
These transistors need to be biased in the operating region of the transistor's characteristic curves, and that requires a base current. This bias current is supplied by the external circuit connected to the inputs of the op-amp. The datasheet for an op-amp gives the typical and maximum input bias current.
For op-amps designed with FETs, no bias current is required since FETs are voltage-biased at the gate. However, there is always some leakage current that flows into the gate of an FET, and this current is essentially the same as the bias current for a BJT op-amp as viewed from the external circuitry. And despite the misnomer, it is still called the input bias current. FET opamps have bias currents orders of magnitude below the typical bias current of a BJT op-amp and so are good choices for designs where a large bias current causes problems. But be aware that gate leakage current is a strong function of temperature. At high temperatures, the bias current of an FET op-amp might exceed that of a BJT op-amp.
Input bias current can be measured by connecting the two inputs together and attaching a sensitive ammeter. However, we will use the op-amp itself to measure the bias current. Bias current is modeled by current sources connected to the inputs as shown in Fig. 2. For the current sources as shown in the figure, does the bias current flow into or out of the op-amp?

University of Saskatchewan
EP 313 Advanced Analog Electronics and Instrumentation
Non-ideal Op-amps
3
Fig. 2 The equivalent circuit for an op-amp with input bias currents.
When does input bias current matter? The effect of the bias current can be seen by connecting a Thevenin circuit to an input as shown in Fig. 3.
Fig. 3 Thevenin equivalent circuit connected to an input.
The bias current flows through the effective impedance of the source resulting in a voltage drop; the voltage at the input is V – I
B
R instead of V. Whether this extra voltage is a problem depends on the rest of the circuit and the design parameters. However, the effect is larger for larger R, and, in general, input bias current is more important when the source impedance is large.
Procedure: Design a non-inverting amplifier with a gain of about 10. The feedback network should have an equivalent impedance of less than 10K as seen by the – input of the op-amp
(what is the equivalent impedance?). Build the circuit using a LM741 op-amp. Use a 1M resistor to ground to simulate a high impedance source connected to the + input. Measure the output voltage (what should it be if there is no bias current?). From your measurement, estimate the bias current for the + input and compare it to the specification in the datasheets.
Repeat the experiment using a LM1458, TL072, and OP07D.
The effect of bias current can be minimized by making the impedance of the feedback network the same as the impedance of the source (why?). Using the op-amp with the largest bias current, add a resistor to the feedback network to equalize the source and feedback impedances. Does the output voltage go to zero? If not, speculate on the reason.

University of Saskatchewan
EP 313 Advanced Analog Electronics and Instrumentation
Non-ideal Op-amps
4
B. Input Offset Voltage
If the two inputs of an ideal op-amp are tied together, the output voltage should be zero. In reality, the voltage will always saturate at one of the rails. By adding a voltage source between the inputs and adjusting it, the output can be brought to zero. (Actually, because of the huge gain of the op-amp, the output can not be brought to zero but will switch between the positive and negative rails.) The voltage needed to balance the op-amp is the input offset voltage V
OS
.
The offset voltage arises because of manufacturing irregularities; if the two arms of the differential amplifier were exactly symmetric, there would be no offset voltage. The offset voltage is modeled as a voltage source connected to one of the inputs (it doesn't matter which one) as shown in Fig. 4.
Fig. 4 The equivalent circuit for an op-amp with an input offset voltage.
When does input offset voltage matter? Clearly the offset voltage adds to whatever voltage is applied to the op-amp and will produce an error at the output. Precision amplifiers in particular need to have a small offset voltage and often include a means of nulling the offset. Any circuit where the input signal is very small can be adversely affected by the offset voltage.
The effect of offset voltage can be eliminated by AC coupling (providing the offset voltage does not cause the output to saturate), but AC coupling is not possible for some designs. Some opamps provide extra pins for a variable resistor to manually eliminate the offset. But be careful, the offset voltage is temperature dependent and can drift over time so manually trimming the offset once may not be good enough. Other so-called chopper op-amps include circuitry that periodically measures the offset voltage and then automatically nulls it. In general, FET opamps have higher offset voltages than BJT op-amps, but better design and manufacturing has resulted in a steady drop in offset voltage over the last decade.
Procedure: Design a non-inverting amplifier with a gain of 100 and ground the + input. Build the circuit using the same op-amps as in the previous section and measure the output voltage.
From the measurements, calculate the input offset voltage. Consider the extent to which the input bias current affects your results.
C. Bandwidth
Designers of op-amps add capacitance to the middle section of the op-amp between the differential input amplifier and the output driver; doing this is called compensating the op-amp.
The capacitance causes the gain to decrease with frequency. The capacitance is chosen to put the polls at a low frequency, usually just a few Hertz. The datasheet will contain the Bode plot for the op-amp showing how the gain and the phase vary with frequency. Students are often surprised by compensation; after all why build an amplifier with a DC gain of 100dB only to kill the gain at even modest frequencies. The answer involves the magic of negative feedback and the stability of the amplifier. The full theory is too long for this manual but can be found in the textbook for the course.

University of Saskatchewan
EP 313 Advanced Analog Electronics and Instrumentation
Non-ideal Op-amps
5
Because of negative feedback, the gain of an op-amp amplifier will be uniform up to a certain frequency and will roll-off beyond that frequency. The frequency interval over which the amplifier is useful is its bandwidth; the highest useful frequency is usually defined where the gain is 3dB below the DC value. The bandwidth depends on the feedback in such a way that the product of DC gain and bandwidth is a constant, called the gain-bandwidth product. (This result is general and applies to many amplifiers, not just op-amps.)
Procedure: Design a non-inverting amplifier with a gain of 10. Build the circuit using a OP07D op-amp. Measure the Bode plot (gain only) and determine the bandwidth. Change your design so that the amplifier has a gain of 100. Again measure the bandwidth and verify that the gainbandwidth product is the same for both gains. Repeat the experiment using a TL072 and
LT1672.
D. Slew Rate
Compensation and certain current-limiting factors in the op-amp's design limit the rate at which the output can change. The rate of change is called the slew rate and every op-amp has a maximum slew rate. Slew rate is important for large amplitude outputs and signals with steps.
For a sine wave A sin( ω t ), the maximum rate of change occurs at the zero crossings and is equal to A ω . A larger amplitude output or higher frequency signal requires an op-amp with a greater maximum slew rate. If the output signal would exceed the maximum slew rate then the waveform becomes distorted. For a step input, the slew rate will cause the output to ramp.
Although maximum slew rate and bandwidth are related, slew rate can cause problems at frequencies well below the bandwidth.
Procedure: Design a non-inverting amplifier with a gain of about 10. Construct the circuit using a OP07D op-amp. Apply a square wave to the input, and measure the average slope of the output; this value is the slew rate. Now apply a sine wave so that the output signal has an amplitude about 80% of the supply rails. Increase the frequency until you start to notice distortion. Calculate the slew rate. Keep increasing the frequency and record your observations. Compare the frequency at which the slew rate begins to cause distortion to the bandwidth measured in the previous section. Repeat the experiment using a TL072 and
LT1672.
E. Output Voltage Limit
The output of an op-amp is limited to a certain voltage range that is determined by the power supply voltages. How close the output voltage can approach the supply rails depends on the design of the output stage of the op-amp. Some can go nearly to the rails (called rail-to-rail output) and others can not get closer than a volt or so. If the output tries to go beyond these limits then the signal clips to the maximum or minimum voltage; for most designs, clipping is bad. What is worse, clipping can destroy the device as you might discover.
Procedure: Design a unity gain voltage follower. Build the circuit using a TL072 op-amp. Apply a sine wave to the input and increase the amplitude until clipping clearly occurs. How close are the maximum and minimum voltages to the supply rails? Measure the voltage difference between the + and – inputs using the oscilloscope. What is the voltage difference in the clipping region? Why are the inputs at a different voltage? Some op-amps are destroyed if the voltage difference between + and – exceeds a certain value (often as little as 0.5 V). Repeat the experiment using a LM741 (or other cheap op-amp).