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OPERATIONAL AMPLIFIERS »
Operational amplifier models
While mention of operational amplifiers typically provokes visions of semiconductor devices built as integrated circuits on a miniature silicon chip, the first op-amps were actually vacuum tube circuits. The first commercial, general purpose operational amplifier was manufactured by the George A. Philbrick Researches, Incorporated, in 1952. Designated the K2-W, it was built around two twin-triode tubes mounted in an assembly with an octal (8-pin) socket for easy installation and servicing in electronic equipment chassis of that era. The assembly looked something like this:
The schematic diagram shows the two tubes, along with ten resistors and two capacitors, a fairly simple circuit design even by 1952 standards:
In case you're unfamiliar with the operation of vacuum tubes, they operate similarly to N-channel depletion-type IGFET transistors: that is, they conduct more current when the control grid (the dashed line) is made more positive with respect to the cathode (the bent line near the bottom of the tube symbol), and conduct less current when the control grid is made less positive (or more negative) than the cathode. The twin triode tube on the left functions as a differential pair, converting the differential inputs (inverting and noninverting input voltage signals) into a single, amplified voltage signal which is then fed to the control grid of the left triode of the second triode pair through a voltage divider (1 MΩ -- 2.2 MΩ). That triode amplifies and inverts the output of the differential pair for a larger voltage gain, then the amplified signal is coupled to the second triode of the same dual-triode tube in a noninverting amplifier configuration for a larger current gain. The two neon "glow tubes" act as voltage regulators, similar to the behavior of semiconductor zener diodes, to provide a bias voltage in the coupling between the two single-ended amplifier triodes.
With a dual-supply voltage of +300/-300 volts, this op-amp could only swing its output +/- 50 volts, which is very poor by today's standards. It had an open-loop voltage gain of 15,000 to 20,000, a slew rate of +/- 12 volts/µsecond, a maximum output current of 1 mA, a quiescent power consumption of over 3 watts (not including power for the tubes' filaments!), and cost about $24 in 1952 dollars. Better performance could have been attained using a more sophisticated circuit design, but only at the expense of greater power consumption, greater cost, and decreased reliability.
With the advent of solid-state transistors, op-amps with far less quiescent power consumption and increased reliability became feasible, but many of the other performance parameters remained about the same. Take for instance Philbrick's model P55A, a general-purpose solid-state op-amp circa 1966. The P55A sported an open-loop gain of 40,000, a slew rate of 1.5 volt/µsecond and an output swing of +/- 11 volts (at a power supply voltage of +/- 15 volts), a maximum output current of 2.2 mA, and a cost of $49 (or about $21 for the "utility grade" version). The P55A, as well as other op-amps in Philbrick's lineup of the time, was of discrete-component construction, its constituent transistors, resistors, and capacitors housed in a solid "brick" resembling a large integrated circuit package.
It isn't very difficult to build a crude operational amplifier using discrete components. A schematic of one such circuit is shown in Figure below.
A simple operational amplifier made from discrete components.
While its performance is rather dismal by modern standards, it demonstrates that complexity is not necessary to create a minimally functional op-amp. Transistors Q3 and Q4 form the heart of another differential pair circuit, the semiconductor equivalent of the first triode tube in the K2-W schematic. As it was in the vacuum tube circuit, the purpose of a differential pair is to amplify and convert a differential voltage between the two input terminals to a single-ended output voltage.
With the advent of integrated-circuit (IC) technology, op-amp designs experienced a dramatic increase in performance, reliability, density, and economy. Between the years of 1964 and 1968, the Fairchild corporation introduced three models of IC op-amps: the 702, 709, and the still-popular 741. While the 741 is now considered outdated in terms of performance, it is still a favorite among hobbyists for its simplicity and fault tolerance (short-circuit protection on the output, for instance). Personal experience abusing many 741 op-amps has led me to the conclusion that it is a hard chip to kill . . .
The internal schematic diagram for a model 741 op-amp is shown in Figure below.
Schematic diagram of a model 741 op-amp.
By integrated circuit standards, the 741 is a very simple device: an example of small-scale integration, or SSI technology. It would be no small matter to build this circuit using discrete components, so you can see the advantages of even the most primitive integrated circuit technology over discrete components where high parts counts are involved.
For the hobbyist, student, or engineer desiring greater performance, there are literally hundreds of op-amp models to choose from. Many sell for less than a dollar apiece, even retail! Special-purpose instrumentation and radio-frequency (RF) op-amps may be quite a bit more expensive. In this section I will showcase several popular and affordable op-amps, comparing and contrasting their performance specifications. The venerable 741 is included as a "benchmark" for comparison, although it is, as I said before, considered an obsolete design.
Widely used operational amplifiers
Model
Devices/ package
Power supply
Bandwidth
Bias current
Slew rate
Output current
number
(count)
(V)
(MHz)
(nA)
(V/µS)
(mA)
TL082
2
12 / 36
4
8
13
17
LM301A
1
10 / 36
1
250
0.5
25
LM318
1
10 / 40
15
500
70
20
LM324
4
3 / 32
1
45
0.25
20
LF353
2
12 / 36
4
8
13
20
LF356
1
10 / 36
5
8
12
25
LF411
1
10 / 36
4
20
15
25
741C
1
10 / 36
1
500
0.5
25
LM833
2
10 / 36
15
1050
7
40
LM1458
2
6 / 36
1
800
10
45
CA3130
1
5 / 16
15
0.05
10
20
Listed in Table above are but a few of the low-cost operational amplifier models widely available from electronics suppliers. Most of them are available through retail supply stores such as Radio Shack. All are under $1.00 cost direct from the manufacturer (year 2001 prices). As you can see, there is substantial variation in performance between some of these units. Take for instance the parameter of input bias current: the CA3130 wins the prize for lowest, at 0.05 nA (or 50 pA), and the LM833 has the highest at slightly over 1 µA. The model CA3130 achieves its incredibly low bias current through the use of MOSFET transistors in its input stage. One manufacturer advertises the 3130's input impedance as 1.5 tera-ohms, or 1.5 x 1012 Ω! Other op-amps shown here with low bias current figures use JFET input transistors, while the high bias current models use bipolar input transistors.
While the 741 is specified in many electronic project schematics and showcased in many textbooks, its performance has long been surpassed by other designs in every measure. Even some designs originally based on the 741 have been improved over the years to far surpass original design specifications. One such example is the model 1458, two op-amps in an 8-pin DIP package, which at one time had the exact same performance specifications as the single 741. In its latest incarnation it boasts a wider power supply voltage range, a slew rate 50 times as great, and almost twice the output current capability of a 741, while still retaining the output short-circuit protection feature of the 741. Op-amps with JFET and MOSFET input transistors far exceed the 741's performance in terms of bias current, and generally manage to beat the 741 in terms of bandwidth and slew rate as well.
My own personal recommendations for op-amps are as such: when low bias current is a priority (such as in low-speed integrator circuits), choose the 3130. For general-purpose DC amplifier work, the 1458 offers good performance (and you get two op-amps in the space of one package). For an upgrade in performance, choose the model 353, as it is a pin-compatible replacement for the 1458. The 353 is designed with JFET input circuitry for very low bias current, and has a bandwidth 4 times are great as the 1458, although its output current limit is lower (but still short-circuit protected). It may be more difficult to find on the shelf of your local electronics supply house, but it is just as reasonably priced as the 1458.
If low power supply voltage is a requirement, I recommend the model 324, as it functions on as low as 3 volts DC. Its input bias current requirements are also low, and it provides four op-amps in a single 14-pin chip. Its major weakness is speed, limited to 1 MHz bandwidth and an output slew rate of only 0.25 volts per µs. For high-frequency AC amplifier circuits, the 318 is a very good "general purpose" model.
Special-purpose op-amps are available for modest cost which provide better performance specifications. Many of these are tailored for a specific type of performance advantage, such as maximum bandwidth or minimum bias current. Take for instance the op-amps, both designed for high bandwidth in Table below.
High bandwidth operational amplifiers
Model
Devices/ package
Power supply
Bandwidth
Bias current
Slew rate
Output current
number
(count)
(V)
(MHz)
(nA)
(V/µS)
(mA)
CLC404
1
10 / 14
232
44,000
2600
70
CLC425
1
5 / 14
1900
40,000
350
90
The CLC404 lists at $21.80 (almost as much as George Philbrick's first commercial op-amp, albeit without correction for inflation), while the CLC425 is quite a bit less expensive at $3.23 per unit. In both cases high speed is achieved at the expense of high bias currents and restrictive power supply voltage ranges. Some op-amps, designed for high power output are listed in Table below.
High current operational amplifiers
Model
Devices/ package
Power supply
Bandwidth
Bias current
Slew rate
Output current
number
(count)
(V)
(MHz)
(nA)
(V/µS)
(mA)
LM12CL
1
15 / 80
0.7
1000
9
13,000
LM7171
1
5.5 / 36
200
12,000
4100
100
Yes, the LM12CL actually has an output current rating of 13 amps (13,000 milliamps)! It lists at $14.40, which is not a lot of money, considering the raw power of the device. The LM7171, on the other hand, trades high current output ability for fast voltage output ability (a high slew rate). It lists at $1.19, about as low as some "general purpose" op-amps.
Amplifier packages may also be purchased as complete application circuits as opposed to bare operational amplifiers. The Burr-Brown and Analog Devices corporations, for example, both long known for their precision amplifier product lines, offer instrumentation amplifiers in pre-designed packages as well as other specialized amplifier devices. In designs where high precision and repeatability after repair is important, it might be advantageous for the circuit designer to choose such a pre-engineered amplifier "block" rather than build the circuit from individual op-amps. Of course, these units typically cost quite a bit more than individual op-amps.



Operational Amplifier Circuits
We have built voltage and current amplifiers using transistors. Circuits of this kind with nice properties (high gain and high input impedance, for example), packaged as integrated circuits (ICs), are called operational amplifiers or op amps. They are called ``operational'' amplifiers, because they can be used to perform arithmetic operations (addition, subtraction, multiplication) with signals. In fact, op amps can also be used to integrate (calculate the areas under) and differentiate (calculate the slopes of) signals.
\includegraphics{lab4-opamp.eps}
Figure 22: A circuit model of an operational amplifier (op amp) with gain $A$and input and output resistances $R_{in}$and $R_{out}$.
A circuit model of an operational amplifier is shown in Figure 22. The output voltage of the op amp is linearly proportional to the voltage difference between the input terminals $v_+ - v_-$by a factor of the gain $A$. However, the output voltage is limited to the range $-V_{CC} \leq v \leq V_{CC}$, where $V_{CC}$is the supply voltage specified by the designer of the op amp. The range $-V_{CC} \leq v \leq V_{CC}$is often called the linear region of the amplifier, and when the output swings to $V_{CC}$or $-V_{CC}$, the op amp is said to be saturated. The output ranges of the amplifiers we built as part of Lab 3 were similarly limited by the supply voltage.
An ideal op amp has infinite gain ($A = \infty$), infinite input resistance ( $R_{in} = \infty$), and zero output resistance ($R_{out} = 0$). You should use these two assumptions to analyze the op amp circuits covered in the assignments below. A consequence of the assumption of infinite gain is that, if the output voltage is within the finite linear region, we must have $v_+ = v_-$. A real op amp has a gain on the range $10^3$-$10^5$ (depending on the type), and hence actually maintains a very small difference in input terminal voltages when operating in its linear region. For most applications, we can get away with assuming $v_+ \approx v_-$.
\scalebox{1.2}{ \includegraphics{lab4-opschem.eps} }
Figure 23: (a) Schematic symbol for an op amp. (b) Connection diagram for the LM741 and LF411 8 pin dual inline packages (DIPs). We will not make use of the null (LM741) / balance (LF411) pins. Pins labeled NC are not connected to the integrated circuit.
We will use two operational amplifiers in our laboratory exercises, the LM741, a general purpose bipolar junction transistor (BJT) based amplifier with a typical input resistance of 2 M$\Omega $, and the LF411, with field effect transistors (FETs) at the inputs giving a much larger input resistance ( $10^{12}~\Omega$). Detailed data sheets for these devices are available for dowload at the National Semicondictor web site (www.national.com ). Of the two, the LF411 comes closest to satisfying our two assumptions associated with ideal op amp behavior. It costs more than the LM741 (a whopping $0.61 vs. $0.23 as of spring 2001). The schematic symbol for an op amp and the connection diagram for the chips, called dual inline packages (DIPs), we will be using are shown in Figure 23.
Assignment
The inverting amplifier (4.1) and Schmitt trigger (4.8) are mandatory for everyone. Of the remaining circuits, choose at least 4. Whether you use a LM741 or LF411 op amp is up to you, but in at least one circuit, compare the two. For all circuits and both kinds of op amp, $V_{CC} = 15$ V.

Inverting Amplifier
\includegraphics{lab4-inv.eps}
Figure 24: Inverting amplifier circuit.
An inverting amplifier circuit is shown in Figure 24.
  1. Show that the gain of the amplifier is
\begin{displaymath} A = -\frac{R_f}{R_1}. \end{displaymath}
(18)

  2. Build the circuit, and check your prediction experimentally for gains of 10 and 100.
  3. Measure the bandwidth (the difference between the upper and lower 3 dB points) of the amplifier for each gain. The product of the gain and bandwidth should be constant. Is it?
  4. Check the linearity of the amplifier for each gain over its useful frequency range.
  5. Measure the input impedance of the amplifier by placing various resistors in series with the source. Explain your result.

Noninverting Amplifier
\includegraphics{lab4-noninv.eps}
Figure 25: Noninverting amplifier circuit.
A noninverting amplifier circuit is shown in Figure 25.
  1. Show that the gain of the amplifier is
\begin{displaymath} A = \frac{R_1 + R_f}{R_1}. \end{displaymath}
(19)

  2. Build the circuit, and check your prediction experimentally for gains of 10 and 100.
  3. What is the input impedance of the amplifier?

Voltage Follower
\includegraphics{lab4-follow.eps}
Figure 26: Voltage follower circuit.
A voltage follower circuit is shown in Figure 26.
  1. What's the point?
  2. What is the input impedance of the amplifier?
  3. Build the circuit, and use it to improve the input impedance of an inverting amp.

Differential Amplifier
\includegraphics{lab4-differential.eps}
Figure 27: Differential amplifier circuit.
A differential amplifier circuit is shown in Figure 27.
  1. Show that the output signal of the amplifier is
\begin{displaymath} V_{out} = -\frac{R_2}{R_1} (V_1 - V_2). \end{displaymath}
(20)

  2. Build the circuit, and check your prediction experimentally for a gain of 10.
  3. Measure the input impedance of the amplifier by placing various resistors in series with the source. To measure the impedance of one terminal, drive it with a small signal through a resistor and ground the other. Explain your result.

Summing Amplifier
\includegraphics{lab4-sum.eps}
Figure 28: Summing amplifier circuit.
A summing amplifier circuit is shown in Figure 28.
  1. Show that the output signal of the amplifier is
\begin{displaymath} V_{out} = -R_f \left( \frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3} \right) \end{displaymath}
(21)

  2. Build the circuit, and check your prediction experimentally for a gain of 10.
  3. Measure the input impedance of the amplifier by placing various resistors in series with the source. To measure the impedance of one terminal, drive it with a small signal through a resistor and ground the other. Explain your result.

Integrator
\includegraphics{lab4-integrator.eps}
Figure 29: Integrator circuit.
An integrator circuit is shown in Figure 29.
  1. Show that the output signal of the amplifier is
\begin{displaymath} V_{out} = -\frac{1}{RC} \int V_{in} dt. \end{displaymath}
(22)

  2. Build the circuit with $R = 10$ k$\Omega $, $C = 0.1$ $\mu$F and use square and sinusoidal wave forms to test the predicted behavior. Also place a $100$ M$\Omega $ resistor in parallel with the capacitor. This resistor drains charge to avoid saturation due to very low frequency or DC signals.

Differentiator
\includegraphics{lab4-diff.eps}
Figure 30: Differentiator circuit.
A differentiator circuit is shown in Figure 30.
  1. Show that the output signal of the amplifier is
\begin{displaymath} V_{out} = -RC \frac{dV_{in}}{dt}. \end{displaymath}
(23)

  2. Build the circuit with $R = 10$ k$\Omega $, $C = 0.1$ $\mu$F and use triangle and sinusoidal wave forms to test the predicted behavior.

Schmitt Trigger
\includegraphics{lab4-schmitt.eps}
Figure 31: Schmitt trigger circuit. $V_{out}$and $V_{in}$are relative to ground, or some reference between $-V_{CC}$and $+V_{CC}$.
A Schmitt trigger circuit is shown in Figure 31. The analysis is not difficult. It is, however, tedious. The $R_1$, $R_2$voltage divider sets the rough neighborhood of the trigger thresholds. $R_3$controls the hysteresis of the switch (the difference between the ``turn on'' and ``turn off'' thresholds). The feedback resistor $R_f$should be a factor 10-100 larger than the voltage divider resistors. Otherwise, it drags the thresholds apart.
  1. Predict the ``turn on'' and ``turn off'' thresholds for $R_1 = 1$ k$\Omega $, $R_2 = 2.2$ k$\Omega $, $R_3 = 2.2$ k$\Omega $, and $R_f = 100$ k$\Omega $. Rather than finding a general expression, it's fine to consider this particular case. For the analysis, assume a maximal output voltage swing of $\pm 13$ V. This actually varies with each op amp, but should not be far from the truth.
  2. Build the circuit, using the resistance values given above. Measure the input thresholds of the trigger and compare with your predictions. 

imple 741 Circuit Designs Just For You
IC 741 is one of the most versatile and multipurpose op-amp and can be wired up in numerous different ways. Let’s study some of the important 741 opamp circuit design configurations:
Inverting DC Amplifier Circuit Using IC 741, Image
Inverting DC Amplifier: Sometimes it becomes important for amplifying DC voltages, the diagram shows how the IC can be wired up into an inverting DC amplifier circuit. As the name informs a DC input to the IC will be amplified at its output but will be just the opposite with polarity. VR1 may be used for adjusting the gain of the amplifier.
Non-Inverting DC Amplifier Circuit Using IC 741, Image
Non-inverting DC Amplifier: This configuration is similar to the above circuit, the only difference being the output response, which is always equal to the polarity of the fed input voltage.
Inverting AC Amplifier Circuit Using IC 741, Image
Inverting AC Amplifier: The figure shows how the basic inverting DC mode of the IC can be simply modified into an inverting AC amplifier design. This circuit is intended to be used with AC or oscillating input signals, primarily for amplifying minute frequencies. C1 and C2 form the input and the output coupling capacitors. Again here the gain may be varied using the pot VR1.
Non-Inverting AC Amplifier Coupled, Circuit Using IC 741, Image
Non-Inverting AC Amplifier: The circuit is similar to the above explained design; the only difference being the output of the circuit provides oscillations in phase with the input whereas the previous design produces oscillations with opposite phase to that of the input.
Tone Control Active Circuit Using IC 741, Image
Active Tone Control: The opamp IC741 can be very effectively used for processing audio frequencies and customizing them as per one’s own choice. Folks who prefer more bass in music may achieve it by just adjusting the bass control shaft whereas those who appreciate extra treble with music may do the same through another similar control reserved for the purpose.
The circuit diagram shows how by adding just a few passive components with the IC 741 a neat little active tone control circuit can be built. For the given values, the circuit provides a bass boost of 12.5 dB and a cut of 10.5 dB at around 100 Hz. The treble chill is of 8.8 dB with a cut of 9.8 dB at around 10 kHz, with respect to the set gain of the device at 1 kHz. The circuit also features high input impedance and low output impedance.
Regulated Power Supply Circuit Using IC 741, Image
The final diagram of this article shows a classic regulated voltage DC power supply using 741 opamp circuit design. A cheap zener / resistor voltage reference is used to provide a reasonably stable reference to the non-inverting input of the IC. The pot VR 1 is used to set the output voltage right from zero to a maximum of 15 volts continuously. A Darlington pair transistor is used at the output to enhance high current delivering capacity. However another transistor T3 has also been incorporated to check the above current if it tends to drift beyond limit. The control limit may be set by varing the value


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