IN THIS CHAPTER

check Getting familiar with op-amps

check Exploring how feedback circuits work with op-amps

check Looking at summing amplifiers and comparators

check Exploring several popular op-amp packages

Did you ever play Operation, the game in which you had to use electrified tweezers to remove plastic body parts from little holes in a body? The edges of the holes were metal conductors, so if you touched the edge of the hole with the tweezers while trying to remove the plastic piece inside, a buzzer would sound, and the patient’s nose (which was a red light bulb) would light up.

I was never very good at it, because it required nerves of steel and precise control of the tweezers. The slightest jiggle of the tweezers was amplified into a flashing light, a loud buzzer, and the mocking laughter of my brother, who was a much better Operation surgeon than I was.

An operational amplifier (op-amp for short) is kind of like the game Operation. Well, actually, it isn’t really, except for the part about the slightest variations in the input (your hand holding the tweezers) being amplified into a huge variation in the output (the flashing red nose, the jarring buzzer, and the ridicule of your brother).

Op-amps are among the most common types of integrated circuits — probably second in popularity only to the 555 timer chip, described in the previous chapter. In this chapter, you learn what an op-amp is and how to build several useful circuits with it. So put on your scrubs, and let’s start the operation!

Looking at Operational Amplifiers

An op-amp is a super-sensitive amplifier circuit that’s designed to amplify the difference of two input voltages. Thus, an op-amp has two inputs and one output. The output voltage is often tens or even hundreds of thousands of times greater than the difference in the input voltages. Thus, a very small difference in the two input voltages — perhaps a few hundredths or even a few thousandths of a volt — can result in a large output voltage.

Although an op-amp is a type of integrated circuit, op-amps were invented long before integrated circuits. Op-amp circuits are a natural for integrated circuits, however, so it wasn’t long after the introduction of the first integrated circuits that IC versions of op-amps became available. Today, op-amps are among the most popular types of integrated circuits.

The name operational amplifier may be a bit confusing. Originally, the op-amp circuit was created for use as an amplifier in telephone distribution systems. Later, computer engineers discovered that the circuit could easily be adapted to do mathematical operations such as addition, subtraction, multiplication, and division. It was around that time that the term operational amplifier was coined, because the circuits are amplifiers that can perform (mathematical) operations. (For more information, see the nearby sidebar “How the op-amp came to be .”)

Internally, the simplest op-amps consist of several dozen transistors, and more complicated varieties have many more. In this chapter, I completely ignore the internal circuitry of an op-amp and treat it as what it is: a handy device you can use without understanding how it works. You can thank the engineers who, many decades ago, worked out all the internal details that make an op-amp do its magic.

The standard schematic symbol for an op-amp is a triangle, as shown in Figure 3-1 . As you can see, the two inputs are on the left side of the triangle, the output is on the right, and the power supply connections for the circuit are on the top and bottom of the triangle.

FIGURE 3-1: Schematic symbol for an op-amp.

Many types of op-amp chips are manufactured today, but all have the five connections shown in Figure 3-1 . The following paragraphs describe the function of each of these connections:

and : The power supply for an op-amp is provided via two pins usually labeled and . (These pins may be labeled and instead, but their functions are the same.) Most op-amps require both a positive and a negative voltage power supply, with voltages usually ranging from to . This type of power supply is called a split supply. The indicates that both positive voltage and negative voltage are required. , for example, means that both and are required.

You can easily build a split supply by using two batteries connected end to end, as shown in Figure 3-2 . Here, two 9 V batteries are connected to create a supply. Note that the and are measured relative to ground, which is accessed between the two batteries.

Note that some op-amps don’t require split-voltage power supplies. Op-amps that use single power supplies have a ground terminal instead of a terminal.
V_out : The output of the op-amp is taken from the V_out terminal. The voltage at the output terminal can be positive or negative, depending on the voltage difference between the two input terminals. The maximum voltage is usually a few volts less than the supply voltage at the and terminals. Thus, if the power supply for an op-amp is , the maximum output will be around or 8 V.

Most op-amps can handle only a small amount of current through the output terminal — usually, in the neighborhood of 25 mA or less. As Figure 3-3 shows, the output is passed through an external resistance, designated R_L . The other end of this resistance is connected to ground. Thus, the output current that flows through the op-amp must eventually end up at ground.

Note that the load resistance isn’t necessarily in the form of a simple resistor; it can be any other circuit that provides some load resistance, such as the base-emitter circuit of a transistor or even input of another op-amp.
and : The two inputs of an op-amp are the and terminals. These terminals are sometimes identified by + and – signs inside the triangle. The inputs are called differential inputs because the output voltage, which appears on the V_out terminal, depends on the difference between the voltage of the + and – terminals.

For most op-amps, the maximum allowable input voltage is a bit less than the maximum power supply voltage. is a typical limit. Remember, though, that the difference between the two input voltages is what an op-amp amplifies. In many cases, the two input voltages are very close, so the difference is very small.

I’ve said it already, but it’s worth repeating: The polarity of the op-amp output depends on the polarity of the difference between the and inputs. Thus, if is greater than , the output will be a positive voltage, but if is less than , the output will be a negative voltage.

In many op-amp circuits, one input is connected to ground. If the input is grounded, the output polarity is always the opposite of the polarity of the input voltage on the terminal. In other words, negative voltage on will give positive voltage on V_out , and positive voltage on will give negative voltage on V_out . For this reason, the input is often called the inverting input because its polarity is inverted in the output.

If, on the other hand, the input is connected to ground, the polarity of the output is the same as the polarity of the input voltage applied to . Thus, if is positive, V_out will be positive; if is negative, V_out will be negative. For this reason, the input is called the noninverting input because its polarity is the same in the output — that is, the input voltage is not inverted.

FIGURE 3-2: A split supply for an op-amp.

images — FIGURE 3-2: A split supply for an op-amp.

FIGURE 3-3: The output from an op-amp passes to ground through a load resistance.

HOW THE OP-AMP CAME TO BE

The modern operational amplifier dates way back to the early 1930s, when Bell Telephone was just starting to run telephone cables throughout the country. In the early days of the telephone, engineers had a difficult problem with phone lines that ran more than a few thousand feet. Long phone lines needed amplifiers to give their signals a boost, but the amplifiers available at the time were very fidgety — too sensitive to weather (temperature and humidity) and unable to work consistently over the range of voltages used in early phone lines.

A Bell engineer named Harry Black was working on the amplifier problem in 1934 when an idea struck him as he was riding the ferry home from work. This idea was a stroke of genius that seems obvious decades later. Instead of trying to design an amplifier that would have the exact amplitude gain needed for the job, Black’s idea was to use an amplifier that had far more gain than was needed — thousands of times more gain, in fact — and then feed some of the output back into the input through a resistor. This feedback circuit would reduce the overall gain of the amplifier based on the amount of resistance in the circuit.

The circuit didn’t gain the name operational amplifier until the computer age began a decade or so later, and computer researchers figured out how to use the amplifier’s unique characteristics to perform basic mathematical operations like addition, subtraction, multiplication, and division on the input voltages. Eventually, digital computers replaced the analog computers built from op-amps. Op-amps still play an important role in computers today, however, primarily to provide an interface with real-world input measuring devices such as voltage sensors and moisture detectors.

The original op-amp circuits were built with vacuum tubes. They were large, required several hundred volts to operate, and generated substantial heat. When transistors replaced vacuum tubes in the 1950s, op-amps became smaller, and when integrated circuits were invented in the 1960s, op-amps were among the first chips to be designed.

Understanding Open Loop-Amplifiers

As its name suggests, one of the most basic uses of an op-amp is as an amplifier. If you connect an input source to one of the input terminals and ground the other input terminal, an amplified version of the input signal appears on the out terminal.

An important concept in op-amp circuits is voltage gain, which simply represents the amount by which the difference between the two input voltages is multiplied to produce the output voltage. If the input voltage difference is 2 V and the output voltage is 12 V, for example, the voltage gain of the amplifier is 6.

If you simply apply an input signal to the V_– terminal of an op-amp as shown in Figure 3-4 , the circuit is called an open loop-amplifier. The reason it’s called this will become more apparent when you get to the next section. For now, just realize that this type of circuit goes by the name open loop.

FIGURE 3-4: A op-amp configured as an open loop-amplifier.

In the open loop op-amp circuit, the images input is connected to ground, and an input signal is placed on the images input. In this arrangement, the voltage to be amplified is the same as the voltage of the images input. Although Figure 3-4 shows the input as alternating current, the open loop op-amp circuit works for direct current as well.

The voltage gain in an open loop op-amp circuit is extraordinarily high — on the order of tens or even hundreds of thousands. Suppose that you’re using an op-amp whose open loop voltage gain is 200,000 and that the power supply is images . In that case, an input voltage of images will result in an output voltage of images . An input voltage of images will give you an output voltage of 8 V.

The output voltage can never exceed the power supply voltage. In fact, the maximum output voltage usually is about 1 V less than the power supply voltage. So if you’re using a pair of 9 V batteries to provide a power supply, the maximum output voltage is . As a result, the most that an open loop op-amp circuit with an open loop gain of 200,000 can reliably amplify is 0.00004 V. If the input voltage difference is any larger than 0.00004 V, the op-amp is said to be saturated, and the output voltage will go to the maximum.

I guarantee that no matter how much money you invested in a top-quality voltmeter, it isn’t sensitive enough to measure voltages that small. Physicists at Cal Tech may be able to measure voltages that size, but for all practical purposes, 0.00004 V is the same as 0 V.

As a result, one of the basic features of an open loop op-amp circuit is that if the input voltage difference is anything other than zero, the op-amp will be saturated, and the output voltage will be the same at its maximum. So if the maximum output voltage is images , the output will be one of only three voltages: images , 0 V, or images .

Open loop op-amp circuits may not sound very useful, but actually, they have many useful applications. You see one example in “Using an Op-amp as a Voltage Comparator ,” later in this chapter.

THE IDEAL OP-AMP

If you read about op-amps on the web or in an electronics book, you’ll undoubtedly come across the term ideal op-amp. An ideal op-amp is a hypothetical op-amp with certain characteristics that real op-amps strive to achieve. Real op-amps come very close to the ideal op-amp, but no op-amp in existence actually achieves the perfection of an ideal op-amp. So you see, in many ways, op-amps are almost human.

Depending on which list you read, an ideal op-amp has anywhere between two and seven characteristics, the most important of which are

Infinite open loop gain: Several times in this chapter, I mention that the open loop gain in an op-amp is very large — on the order of tens or even hundreds of thousands. In an ideal op-amp, the open loop gain is infinite, which means that any voltage differential on the two input terminals will result in an infinite voltage on the output. In real op-amps, the output voltage is limited by the power supply voltage. Because the output voltage can’t be infinite, the gain can’t be infinite either.
Infinite input impedance: Impedance represents a circuit’s opposition to current flow, whether the current is alternating or direct. In an ideal op-amp, the impedance of the two input terminals is infinite, which means that no current enters the op-amp from the inputs. The inputs are able to see and react to the voltage, but that voltage is unable to push any current into the op-amp. What that means in practice is that the op-amp has no effect on the input voltage. In an actual op-amp, a small amount of current — usually, a few milliamps or less — does leak into the op-amp’s input circuits.
Zero output impedance: In an ideal op-amp, the output circuitry has zero internal impedance, which means that the voltage provided from the output is the same regardless of the amount of load placed on it by the circuit to which the output is connected. In reality, most op-amps have an output impedance of a few ohms, which means that the actual voltage provided by the output terminal will vary a small amount depending on the load connected to the output.
Zero offset voltage: The offset voltage is the amount of voltage at the output terminal when the two inputs are exactly the same. If you connect both inputs to ground, for example, there should be exactly 0 V at the output. In reality, real world op-amps have a very small voltage on the output even when both inputs are grounded, connected to each other, or not connected to anything at all. For most op-amps, this offset voltage is just a few millivolts.
Infinite bandwidth: The term bandwidth refers to the range of alternating current frequencies within which an op-amp can accurately amplify. In an ideal op-amp, the frequency of the input signal has no effect on how the op-amp behaves. In real-world op-amps, the op-amp doesn’t perform well above a certain frequency — typically, a few megahertz (millions of cycles per second).

The characteristics are often summed up with the following two “golden rules” of op-amps:

The output attempts to do whatever is necessary to make the voltage difference between the inputs zero.

This rule, which applies only to closed-loop-amplifier circuits, means that the feedback sent from the output to the input causes the two input voltages to become the same.
The input draws no current.

This rule means that the input terminals look at the voltage placed across them but don’t allow any current to flow into the op-amp.

Although no actual op-amp is able to live up to the standards of the ideal op-amp, most come pretty close. Close enough, in fact, that you can safely design an op-amp circuit as if the op-amps were ideal. In particular, the two golden rules apply: The feedback will equalize the input voltages, and the op-amp draws no current from the input.

Looking at Closed Loop-Amplifiers

As I explain in the preceding section, open loop op-amp circuits aren’t very useful as amplifiers because they’re so easily saturated. To make an op-amp useful as an amplifier, you must use it in a feedback circuit, which reduces the gain to a more manageable amount so that input voltages that are usable (and even measurable!) can be amplified reliably.

I’m sure that you’re already familiar with the concept of feedback. You’ve probably sat in an auditorium listening to someone talk into a public-address system when suddenly a piercing screech came out of the speakers. That screech was feedback. In the case of the public-address system, the microphone picked up some of the output from the speakers and sent it back through the amplifier again. The result was an annoying high-pitched squeal.

Not all feedback is bad, though. In an op-amp amplifier circuit, feedback is used to reduce the enormous open loop-amplification gain to a more manageable gain, such as 10. To do this, the output signal is fed back into the input via the images terminal. A resistor is used to reduce the voltage that is fed back to the input. This type of circuit is called a closed loop-amplifier because a closed circuit path exists between the output and the input. (Now you understand why an op-amp circuit without the feedback loop is called an open loop-amplifier. )

The most common op-amp configuration is called an inverting amplifier because the voltage of the output is opposite the voltage of the input. Figure 3-5 shows a basic inverting amplifier circuit.

FIGURE 3-5: An op-amp configured as an inverting amplifier.

In an inverting amplifier circuit, the input signal works its way through a resistor on its way to the images input, and the output is looped back into the images input through a second resistor. In Figure 3-5 , these resistors are designated R1 and R2. You can easily calculate the overall voltage gain of the circuit by using this formula:

Here, the gain is designated A_CL (CL stands for closed loop ).

If R1 is images and R2 is images , the voltage gain of the circuit will be images . Then if the input voltage is images , the output voltage will be images .

Note that the negative sign is required because Figure 3-5 is an inverting amplifier circuit, so positive inputs give negative outputs, and vice versa.

A closed loop-amplifier can also be designed as a noninverting amplifier in which the output voltage is not reversed. To do that, you simply reverse the inputs, as shown in Figure 3-6 . Instead of connecting the input voltage to images through a resistor and grounding images , you ground images through a resistor and connect the input voltage to images . The feedback circuit is the same; the output is connected to the images input through resistor R1.

FIGURE 3-6: An op-amp configured as a noninverting amplifier.

The formula for calculating the gain for a noninverting amplifier is a little different from the formula for an inverting amplifier:

If R1 is images and R2 is images , the gain is 11. Thus, an input voltage of images will result in an output voltage of images .

DELVING DEEPER INTO FEEDBACK

If you’re interested in understanding how the feedback circuit works, remember the rule that I describe in the section “Understanding Open Loop-Amplifiers ”: If the input voltage is anything other than zero, the op-amp will be saturated, and the output voltage will be the maximum allowed. The purpose of the feedback circuit is to return some of the output voltage to the inverting input, which results in the input-voltage difference’s being driven toward zero. As the voltage approaches zero, the op-amp’s gain begins to drop to a useful range.

Suppose that the input voltage difference in an inverting op-amp circuit is images . This difference results in the op-amp’s becoming saturated, so images appears at the output. A portion of the negative voltage that depends on the voltage divider created by R1 and R2 is returned to the images input, which has the effect of reducing the input voltage. That results in a smaller voltage difference, but not small enough to prevent the op-amp from still being saturated.

Remember, however, that the feedback loop is just that: a loop. As more and more of the saturated output voltage gets fed back through the loop, the input voltage difference gets closer to zero. When it gets oh-so-close to zero, the output voltage drops to a range between zero and the maximum voltage.

The best feature of the closed loop-amplifier circuit is that the two resistors, which are outside the op-amp IC, give you precise control of the amount of gain that the circuit will ultimately have. All you have to do to get any gain you want (within the limits of the op-amp) is choose the right resistor values.

Using an Op-Amp as a Unity Gain Amplifier

A unity gain amplifier is an amplifier circuit that doesn’t amplify. In other words, it has a gain of 1. The output voltage in a unity gain amplifier is the same as the input voltage.

You may think that such a circuit would be worthless. After all, isn’t a simple piece of wire a unity gain circuit? Sure, but a unity gain amplifier provides one important benefit: It doesn’t take any current from the input source. (Remember, that’s one of the Golden Rules of the ideal op-amp.) Therefore, it completely isolates the input side of the circuit from the output side of the circuit. Op-amps are often used as unity gain amplifiers to isolate stages of a circuit from one another.

Unity gain amplifiers come in two types: voltage followers and voltage inverters. A follower is a circuit in which the output is exactly the same voltage as the input. An inverter is a circuit in which the output is the same voltage level as the input but with the opposite polarity.

If you think about it for a moment, you might be able to come up with the circuit for unity gain followers and inverters on your own. The formula for calculating the gain of both an inverting amplifier and a noninverting amplifier requires you to divide R1 by R2, so all you have to do is choose resistor values that will result in a gain of 1.

The following sections explain how to create unity followers and unity inverters.

Configuring a unity follower

A unity gain follower is simply a noninverting amplifier with a gain of 1. Recall that the formula for calculating the value of a noninverting amplifier is this:

To create a unity gain follower, you just omit R2 and connect the output directly to the inverting input, as shown in Figure 3-7 . Because R2 is zero, the value of R1 doesn’t matter, because zero divided by anything equals zero. So R1 is usually omitted as well, and the images input isn’t connected to ground.

FIGURE 3-7: An op-amp configured as a unity gain follower.

Configuring a unity inverter

The formula for calculating gain for an inverting amplifier is this:

In this case, all you have to do is use identical values for R1 and R2 to make the amplifier gain equal to 1. Figure 3-8 shows a unity gain inverter circuit using images resistors.

FIGURE 3-8: An op-amp configured as a unity gain inverter.

Using an Op-Amp as a Voltage Comparator

A voltage comparator is a circuit that compares two input voltages and lets you know which of the two is greater. Suppose that you have a photocell that generates 0.5 V when it’s exposed to full sunlight, and you want to use this photocell as a sensor to determine when it’s daylight. You can use a voltage comparator to compare the voltage from the photocell with a 0.5 V reference voltage to determine whether or not the sun is shining.

It’s easy to create a voltage comparator from an op-amp, because the polarity of the op-amp’s output circuit depends on the polarity of the difference between the two input voltages. Figure 3-9 shows the basic circuit for an op-amp voltage comparator.

FIGURE 3-9: An op-amp configured as a voltage comparator.

In the voltage-comparator circuit, first a reference voltage is applied to the inverting input ( images ); then the voltage to be compared with the reference voltage is applied to the noninverting input. The output voltage depends on the value of the input voltage relative to the reference voltage, as follows:

Input Voltage	Output Voltage
Less than reference voltage	Negative
Equal to reference voltage	Zero
Greater than reference voltage	Positive

Note that the voltage level for both the positive and negative output voltages will be about 1 V less than the power supply. Thus, if the op-amp power supply is images , the output voltage will be images if the input voltage is greater than the reference voltage, 0 V if the input voltage is equal to the reference voltage, and images if the input voltage is less than the reference voltage.

You can modify the circuit to eliminate the negative voltage if the input is less than the reference by sending the output through a diode, as shown in Figure 3-10 . In this circuit, a positive voltage appears at the output if the input voltage is greater than the reference voltage; otherwise, no output voltage exists.

FIGURE 3-10: Using a diode in a voltage-comparator circuit.

To create a voltage comparator that creates a positive voltage output if the input voltage is less than a reference voltage, use the circuit shown in Figure 3-11 . Here, the input voltage is applied to the inverting ( images ) input, and the reference voltage is applied to the noninverting ( images ) input.

FIGURE 3-11: A voltage comparator that tests for a voltage that’s less than a reference voltage.

The final voltage-comparator circuit you should know about is the window comparator, which lets you know whether the input voltage falls within a given range. A window comparator requires three inputs: a low reference voltage, a high reference voltage, and an input voltage. The output of the window comparator will be a positive voltage only if the input voltage is greater than the low reference voltage and less than the high reference voltage. If the input voltage is less than the low reference voltage, the output will be zero. Similarly, if the input voltage is greater than the high reference voltage, the output will also be zero.

You need two op-amps to create a window comparator, as shown in Figure 3-12 . As you can see in the figure, one op-amp is configured to produce positive output voltage only if the input is greater than the low reference voltage (V_REF(LOW) ). The other op-amp is configured to produce positive output voltage only if the input is less than the high reference voltage (V_REF(HIGH) ).

FIGURE 3-12: Two op-amps can be used to create a window comparator.

The input voltage is connected to both op-amps; the output voltage is sent through diodes to allow only positive voltage and then combined. The resulting output will have positive voltage only if the input voltage falls between the low and high reference voltages.

Notice in Figure 3-12 that the power supply connections aren’t shown separately for each op-amp in the circuit. It’s common to omit the power supply connections when multiple op-amps are used in a single circuit. If the power supply connections were shown for all the op-amps, the power supply connections would complicate the schematic unnecessarily. I don’t know about you, but I don’t need any unnecessary complications in my life. I have enough necessary complications as it is.

Adding Voltages

An op-amp can be used to add or subtract two or more voltages. A circuit that adds voltages is called a summing amplifier. A summing amplifier has two inputs and an output whose voltage is the sum of the two input voltages but with the opposite polarity. If one of the inputs is images and the other is images , for example, the output voltage will be images .

Figure 3-13 shows a basic circuit for a summing amplifier. For the summing amplifier to work, resistors R1, R2, and R3 should all be the same value.

FIGURE 3-13: A basic summing amplifier circuit.

If all the resistors in a summing amplifier are the same, the output voltage will be the sum of the input voltages. This is the usual way to configure a summing amplifier, though you can vary the resistor values if you want.

If the resistors have different values, each of the input voltages is weighted according to the value of the resistor on its input circuit, which has the effect of multiplying each input voltage by a certain value before the voltages are summed. The exact value by which each input is multiplied depends on the mix of resistors you use.

If R1 is images and R2 is images , for example, the input voltage applied through the images resistor will be multiplied by 10 before being added to the voltage applied through the images resistor. Thus, if the input at R1 is images , and the input at R2 is images , the output voltage will be images . (For this formula to work, R3 must also be images .)

The actual formula for calculating the output voltage based on the input voltages and the resistor values is this:

I’ll leave it to you to work out the math for various combinations of resistor values and input voltages. Here, though, are a few examples that should give you an idea of how the circuit will behave when R1 is images and both R2 and R3 are images :

One drawback of the summing amplifier is that it inverts the polarity of the input, but you can easily feed the output of a summing amplifier into the input of a unity gain inverter, as shown in Figure 3-14 . Here, the second op-amp inverts the polarity of the output from the summing amplifier, which has the effect of returning the output voltage polarity to the polarity of the original inputs. (For more information about the voltage-inverter portion of this circuit, refer to “Using an Op-Amp as a Unity Gain Amplifier ,” earlier in this chapter.)

FIGURE 3-14: A summing amplifier can be combined with a voltage inverter to preserve the input polarity.

One common use for a summing amplifier circuit is as an audio mixer. When this type of circuit is used as an audio mixer, each input is connected to a microphone. The summing amplifier combines all the microphone inputs by adding the voltages from each microphone, and the resulting output is sent on to another amplifier stage.

The resistors in each input circuit are often potentiometers, which allows you to vary the signal level from each input source. When you increase the resistance on one of the input circuits, less of that input is represented in the output mix — especially useful if one of your singers is a bit off key.

A summing amplifier circuit can be extended with additional inputs. Figure 3-15 shows a circuit with four inputs that uses potentiometers to control the level of each input. You can add as many inputs as you want, but you need to ensure that the total combined voltage from all inputs doesn’t exceed the power supply voltage (minus a volt or two).

FIGURE 3-15: A simple audio mixer with four inputs.

One final variation of the summing amplifier circuit is used in conjunction with a second op-amp configured as an inverter. This configuration preserves the polarity of the input voltages.

Working with Op-Amps