5

Complex Circuits

As you learn to read and draw schematic diagrams, don’t get discouraged by occasional difficulties. You might think, “Anyone can learn to read schematics of simple circuits, like those that have a transistor or two, a few capacitors, and a few resistors. But it’ll take years before I can decipher complex schematics.” Not so! You must put some effort into the learning process, but you can always break a complicated system down into simple circuits.

Identifying the Building Blocks

Even a system whose diagram looks overwhelming at first glance comprises smaller circuits interconnected in a straightforward way. A system with six diodes, ten inductors, ten transistors, and dozens of resistors and capacitors might resolve into four or five simple circuits, each containing only a few components. If you look at the entire system schematic all at once, you might as well try to eat a jumbo hamburger in a single swallow. With the diagram, as with the burger, you face an easier task if you assimilate the thing in little bites or pieces.

Figure 5-1 shows a “crystal radio” receiver built with an antenna, a tapped air-core inductor, a variable capacitor, an RF diode, and a fixed capacitor. The term “crystal” derives from the original construction of RF diodes in the early 1900s. In order to get a one-way current gate to act as a signal detector (or demodulator), radio experimenters placed a strand of fine wire called a cat’s whisker into contact with a chunk of crystalline lead sulfide called galena. Today, semiconductor diodes process RF signals in the same way as “crystals” once did, even though modern RF diodes don’t look like the old galena-and-cat’s-whisker contrivances.

FIG. 5-1   Schematic of the tuned circuit and detector stages of a “crystal radio” receiver. This circuit produces a weak audio-frequency (AF) signal.

You can’t call the circuit of Fig. 5-1 “complicated,” but it performs some sophisticated tricks. Aside from the antenna (an external component such as a length of wire running outdoors under a window sash to a tree) and a sensitive earphone or headphone that you can connect at the output terminals to hear radio stations (however faintly), this circuit contains only four components: the coil, the diode, and two capacitors.

You can connect an amplifier to the output of the “crystal radio” to boost the audio-frequency (AF) volume to the point where it can drive a headset to a comfortable listening level. Figure 5-1 doesn’t include a headset at the output. To accomplish that feat, you’ll need another circuit, along with a battery or other source of DC power to make the AF output signal strong enough.

Figure 5-2 shows another fairly simple schematic: an AF amplifier that employs a single NPN bipolar transistor. In addition to the transistor, this circuit has four resistors and three capacitors for a total of eight components. It needs a source of DC power such as a battery (not shown), which provides 12 V. This circuit accepts a low-level AF signal (the output of a “crystal radio,” for example) at the input terminals and boosts the power to a level strong enough to make audible sound come out of a headset. An experienced engineer might need a couple minutes to scribble the schematic and a couple of hours to build and test the circuit, “tweaking” the component values to get the best possible performance.

FIG. 5-2   An AF preamplifier circuit that can work with the “crystal radio” to produce a signal strong enough to drive a headset.

Because the circuit of Fig. 5-2 takes a weak signal and boosts it to a reasonable (but not very powerful) level, it’s sometimes called a preamplifier. If you want to drive a speaker so that all the students in a classroom can hear the sound, you’ll need more amplification. You can get that extra AF boost with one or more additional amplifiers connected to the output of the preamplifier.

Figure 5-3 is a schematic of a circuit that looks, at first glance, more complicated than either Fig. 5-1 or Fig. 5-2. But as you examine Fig. 5-3 for a minute, you’ll see that it’s nothing more than the composite of the “crystal radio” (Fig. 5-1) and the AF preamplifier (Fig. 5-2). The components are re-numbered generally going from left to right, the direction of signal flow through the system. (You should never duplicate a component designator within a single schematic.) In Fig. 5-3, the connection between the original “crystal radio” and the preamplifier corresponds to the short, horizontal line that goes from the dot above C2 to the left-hand side of C3.

FIG. 5-3   Combination of “crystal radio” tuned circuit, detector, and AF preamplifier stages. Some component designators are updated from Fig. 5-2.

Now that you can envision the two building blocks that make up the circuit of Fig. 5-3, the whole diagram looks elementary, wouldn’t you say? You can follow the signal as it passes through the “crystal radio” and then through the AF preamplifier. The entire process, from the RF signal arriving at the antenna to the AF energy appearing at the output, takes place in a tiny fraction of a second.

The circuit of Fig. 5-3 produces a stronger signal than the feeble output of the “crystal radio” alone, which gets its power only from RF current that flows in the antenna. Nevertheless, even the amplified AF output from the circuit of Fig. 5-3 isn’t strong enough to provide a comfortable listening volume in a loudspeaker. It offers some sound power if you connect a headset to it, but not much. In order to further boost the AF signal level, you’ll need a substantial power amplifier.

Figure 5-4 shows a two-transistor ensemble that can produce respectable sound power. It’s called a push-pull amplifier. The top transistor amplifies half the AF waveform and the bottom transistor amplifies the other half. Imagine that Q1 “pushes” and Q2 “pulls” so when you combine their outputs, you get a magnified version of the entire input waveform. The push-pull amplifier can take the weak AF signal from a low-level amplifier (such as the circuit of Fig. 5-3) and boost it enough to make some loud sound come out of a speaker!

FIG. 5-4   An AF power amplifier circuit suitable for driving a speaker.

If the input signal doesn’t contain much power, then the circuit of Fig. 5-4 won’t get enough drive (input power) to produce a decent output signal. The circuit of Fig. 5-3 (the AF preamplifier) can provide enough “oomph” to adequately drive a push-pull AF power amplifier such as the one diagrammed in Fig. 5-4. The circuit of Fig. 5-1 (the “crystal radio” alone) can’t.

If you combine the circuits of Figs. 5-3 and 5-4 in cascade (one after the other), you get a complete AM radio receiver that will produce respectable sound from a speaker. Figure 5-5 shows the entire three-transistor AM radio receiver in a single schematic. Again, we’ve had to change some of the component designators that appeared in previous diagrams, so they increase generally as you go from the original input at the antenna to the final output at the speaker, taking pains to ensure that you don’t inadvertently give two different components the same name.

FIG. 5-5   Complete radio receiver circuit. Some of the component designators in the AF power amplifier stage are updated from Fig. 5-4. This schematic includes the speaker.

The evolution of an electronic system breaks down into a well-defined sequence. First, the individual components (resistors, capacitors, diodes, and so on) combine to form simple circuits. Second, those simple circuits combine to make complex devices or, in some cases, the whole system. Third, if the design is sophisticated, the complex circuits combine to form the complete system.

Several different devices (some of them simple and others not so simple) can combine to form a large system. An amateur radio station offers a good example. It might have a transceiver (transmitter/receiver in a single box), an antenna tuner, a personal computer, an interface unit that goes between the computer and the transceiver, a microphone that lets you transmit voice signals, a speech processor that goes between the microphone and the transceiver, a key that lets you transmit in Morse code if you want, a headset, a speaker, and a power supply that converts utility AC into the DC from which the whole system gets the various forms of electricity that it needs in order to function.

Page Breaks

Figure 5-5 is a “respectably complicated” diagram. You can draw the system in a two-level format with the detector and preamplifier on top, and the audio power amplifier on the bottom. A long, tortuous line, broken in the middle by C5, represents the connection between the preamplifier output and the power amplifier input. There’s nothing technically wrong with this diagram, but some people would rather see it all on one level. In order to render the diagram that way, you could make it extremely small, or else draw it sideways on the page. You could even produce it on a foldout page (the sort of thing that they do in those upscale print magazines when they want to show you something spectacular).

You have yet another alternative, though! You can split the diagram into multiple pages. You need not use that approach with the schematic of Fig. 5-5, but when you get to extremely complicated systems such as amateur radio transceivers, television sets, or computers, you might want to take advantage of that option. Figure 5-6 shows how you can use this technique with the diagram of the radio receiver from Fig. 5-5. Figure 5-6A puts the tuner, detector, and AF preamplifier right-side-up on a single page along with an output designator that appears as an X inside an arrow that points off the page toward the right. Figure 5-6B shows the push-pull AF power amplifier with an input designator comprising an X inside an arrow that points off the page toward the left.

FIG. 5-6A   Tuner, detector, and AF preamplifier stages in the radio receiver. The wedge X represents an extension to drawing B.

FIG. 5-6B   The AF power amplifier and speaker in the radio receiver. The wedge X represents an extension from drawing A.

Let’s follow the signal through Fig. 5-6A. A radio wave in free space causes RF current to flow in the antenna, and also through inductor L1. Capacitor C1 causes the inductor/capacitor combination (called an LC circuit, where an italic L stands for “inductance” and an italic C stands for “capacitance”) to resonate at the frequency of the RF signal that you want to hear. Diode D1 detects (demodulates) the signal, splitting the AF and RF portions apart. Capacitor C3 passes the AF portion of that signal along to the base of transistor Q1. Capacitor C2 shunts (short-circuits) the RF portion of the diode’s output to ground, because the circuit doesn’t need the RF energy anymore; its presence could, in fact, cause trouble in the following stages! Transistor Q1 acts as an amplifier for the weak AF signal at its base. Resistors R1, R2, R3, and R4 ensure that Q1 gets optimum DC voltage (called bias), so that it will produce the greatest possible AF gain. Capacitor C4 keeps the emitter at AF signal ground while allowing some DC voltage to exist there. The AF output signal, along with some DC from the power supply (+12 V), goes off the page through the rightward-pointing arrow marked X.

Now let’s look at Fig. 5-6B and follow the signal after it comes in from Fig. 5-6A. The AF energy, along with some DC, appears at the leftward-pointing arrow marked X. Capacitor C5 blocks the DC so that only the AF current can reach potentiometer R8.

The full AF voltage appears across the entire resistance of R8. The arrow touching the zig-zag symbolizes the potentiometer wiper or slider, which “picks off” AF voltages that can range from zero (all the way to the right-hand end of the zig-zag, at ground) to the maximum possible (all the way to the left-hand end of the zig-zag, at C5). The slider signal causes AF current to flow in the primary of transformer T1. From there, the signal flows as described in “Follow the flow” for Fig. 5-4. The only difference between this situation and that one is the numbering of the component designators. You can also add a speaker to the output of T2, as you did in Fig. 5-5.

Some More Circuits

Figure 5-7 shows an antenna matching circuit known as an L network. In this case, the letter L refers to the general layout of the components in the diagram, not to the inductor in the circuit. (Actually, to make the coil and capacitor in Fig. 5-7 take the shape of an uppercase L in the layout, you’ll have to rotate the page 90 degrees clockwise and then hold it up to a mirror! But you get the general idea, right?)

FIG. 5-7   An L network comprising an inductor and a variable capacitor.

Figure 5-8 shows another type of antenna matching network, which comprises the circuit from Fig. 5-7 with an extra capacitor added at the input end. Engineers call this type of circuit a pi network because its components, in the schematic layout, resemble the shape of the upper case Greek letter pi (π).

FIG. 5-8   A pi network comprising an inductor and two variable capacitors.

Figure 5-9 shows a circuit that’s more complicated than the ones in Figs. 5-7 and 5-8, but in a sense contains them both put together. When you follow a pi network with an L network, you get a pi-L network. The advantage of a circuit like the one in Fig. 5-9, compared to those in the previous two diagrams, lies in its ability to make RF transmitters work with antennas that otherwise wouldn’t accept power. Those two extra components can go a long way!

FIG. 5-9   A pi-L network comprising two inductors and three variable capacitors.

If you’re old enough, you’ll remember the days when you had to learn the International Morse code (often simply called “the code”) to get an amateur radio operator’s license. That mandate has passed into history, but some amateur radio operators still enjoy communicating this way. If you want to do that, you must learn to “read” and “speak” in the code. To that end, you can build a code practice oscillator such as the one diagrammed in Fig. 5-10. It’s an AF oscillator that you can switch on and off with a straight key or telegraph key, labeled “Key” in the figure. (Because a telegraph key technically constitutes an SPST switch, you could label it S1.)

FIG. 5-10   An AF code-practice oscillator using two PNP bipolar transistors. The values of Rx and Cx determine the frequency.

When you first examine Fig. 5-10, you might wonder why an AF oscillator circuit needs so many components. Can’t you build a simple AF amplifier like the preamplifier or power amplifier discussed earlier, and feed some of the output back to the input? Well, yes, you can do that; but if you want a decent “tone” to come out of your code practice oscillator, you’ll get superior results with a circuit like the one in Fig. 5-10. It’s called a twin-T oscillator because of the T-shaped configurations including the resistors marked Rx and the capacitors marked Cx. The twin-T oscillator produces a musical note that’s pleasing to the ears and has a predictable and stable pitch (frequency).

The circuit of Fig. 5-10 uses a 9-V battery as its power source. In this example, the transistors are of the PNP type, so the collectors get a negative voltage while the positive battery terminal goes straight to ground. This circuit therefore constitutes a positive-ground system.

You might want to build a power supply from the AC utility mains rather than relying on a battery. If you want to do that, you’ll need to design the supply so that it produces a negative voltage with respect to ground. Figure 5-11 shows a power supply that can provide pure, constant –9VDC. It’s almost the same circuit as the one you saw back in Fig. 4-13, with the following exceptions:

FIG. 5-11   A regulated –9 VDC power supply that can power the code-practice oscillator of Fig. 5-10. Note the positive ground for use with PNP transistors.

•   All the diodes go in the opposite direction (including the Zener diode).

•   The electrolytic capacitor has the opposite polarity.

•   The circuit produces a lower DC output voltage.

Figure 5-12 shows a complete AF code practice oscillator system that can operate from the AC utility mains. It combines the power supply of Fig. 5-11 with the oscillator of Fig. 5-10. As with the radio receiver schematic of Fig. 5-5, you connect the power supply output to the oscillator in Fig. 5-12 with a single line (but not as long as the one in Fig. 5-5). Figure 5-12 also shows a volume control (R6) and a pair of headphones.

FIG. 5-12   Combination of the regulated power supply and code practice oscillator. Note the addition of the volume control and headphones.

You might want to boost the twin-T oscillator output so that the AF power will drive a loudspeaker, letting you send Morse code to a classroom full of students! A push-pull AF amplifier, such as the one you used for the radio receiver except with PNP rather than NPN transistors, will do this job. Then you’ll get a system with three essential circuits: a power supply, an oscillator, and an amplifier. Figures 5-13A, B, and C show the complete system schematic spread across three different pages.

FIG. 5-13A   A regulated power supply for a classroom code-practice system. The wedge X represents an extension to illustrations B and C.

FIG. 5-13B   A twin-T audio oscillator for a classroom code-practice system. The wedge X represents an extension from illustration A on the previous page. The wedge Y represents an extension to illustration C.

FIG. 5-13C   An AF power amplifier for a classroom code-practice system. Note the PNP transistors, consistent with the negative power-supply voltage (positive-ground system). The wedge X represents an extension from illustration A on the previous page. The wedge Y represents an extension from illustration B.

Figure 5-14 shows a simple LC circuit that resembles the L network of Fig. 5-7, but the inductor and capacitor have changed places, the capacitor is fixed rather than variable, and the inductor has a powdered-iron core instead of an air core. In addition, this circuit performs a different function than the other one does. The circuit in Fig. 5-7 works mainly to tune an antenna system or to match the output of a transmitter to a particular antenna. The circuit in Fig. 5-14 is designed to let signals get through (or not) depending on their frequency. It’s called a highpass filter because it lets signals pass more easily as the frequency increases. The exact frequency at which high attenuation (lots of signal loss) changes to low attenuation (little or no signal loss) depends on the values of the capacitor and inductor.

FIG. 5-14   A simple frequency-sensitive filter circuit.

Figure 5-15 shows a more complicated LC circuit that comprises two filters in cascade. The first filter, made up of the series-connected capacitor C1 and the parallel-connected inductor L1, has the same design as the one in Fig. 5-14. The second filter, made up of the series-connected inductor L2 and the parallel-connected capacitor C2, forms a lowpass filter. It works in the opposite manner from a highpass filter, letting signals get through more easily as the frequency goes down.

FIG. 5-15   A complex frequency-sensitive filter comprising two simple, but different, filters connected in cascade.

When you follow a highpass filter with a lowpass filter, and if you choose the cutoff frequencies (or transition points) so that the highpass filter cutoff frequency lies below the lowpass filter cutoff frequency, you get a bandpass filter, which a signal can pass through easily when its frequency lies between the two cutoffs. If the frequency lies outside the “zone of easy passage,” it gets greatly attenuated.

If you know how one of the circuits in a repetitive system operates, then you know, by extension, how all the circuits work. A problem that develops in one circuit might also arise in any of the others. For example, suppose that you learn (by testing) that an oscillator has changed frequency because of a defective resistor in the base circuit. If another oscillator of the same configuration develops the same malfunction, you can consult the schematic, locate the second base resistor, and conduct some tests to see if it, too, has gone bad. Without the schematic, you’d have a difficult time locating the rogue resistor.

If you break a gigantic, malfunctioning system down into multiple complex circuits, you can figure out which circuit might be responsible for the problem. You can then split the complex circuit into simple ones and figure out which circuit is most likely the culprit. Within that rogue circuit, you can examine the components one at a time. If you follow such a process of elimination with the help of schematics, you can repair the equipment with less trouble than you’d go through if you didn’t have the diagrams. Whenever you go through this process, an engineer would say that you troubleshoot to the component level.

Many electronic system failures arise from a problem with a single component. Sometimes this glitch will cause other components to go bad, too. Once in a while you’ll discover two or more defective components causing a single problem. You must familiarize yourself with the system, and then, after you’ve studied and understood the system’s normal operating state, you can use a schematic to get a good idea of where future troubles might arise. By following this procedure whenever malfunctions occur, you can identify the most suspect individual component(s). Then you need only find those component(s) in the physical system, get into the equipment with the appropriate test instrument, and check the suspect component(s) one by one.

Getting Comfortable with Large Schematics

No matter how much you enjoy electronics, you can’t expect to sit down as a beginner and read complicated schematics with ease. You need to climb a learning curve. First of all, you must make certain that you know every schematic symbol that you expect to see. Complex schematics can serve as a great learning tool, because they contain lots of symbols, some of which you probably won’t know at first. You can use these diagrams to help you learn the symbols.

Once you feel comfortable with the individual symbols, put away the complex schematics and start looking over diagrams of simple, common circuits. You’ll find lots of them in magazines for electronics enthusiasts. (You’ll also find plenty of simple projects and related diagrams in Electricity Experiments You Can Do at Home, published by McGraw-Hill.) Don’t limit your studies to one type of schematic, such as those that portray only amplifiers. Check into oscillators, power supplies, solid-state switches, RF circuits, AF circuits, and anything else you can find. You’ll discover similarities among different types of circuits, sometimes with no significant differences other than a few changes in component values. When you can identify an amplifier or oscillator or detector by looking at its schematic, then you’ll know that you’ve made progress.

Your next step will include devices that combine a few of the simple circuits you’ve previously studied. Sometimes you’ll see additional components that electrically match the output of one circuit to the input of another. Choose books and publications that offer both theoretical and practical discussions of the circuit that the schematic depicts. Even better, build some simple circuits in a home workshop.

You might get a surprise when you see how your first “homebrew” electronic circuit looks in real life when compared with the schematic. Your study will continue from this point by examining the functional circuit and noting the relationship of the physical components to those in the schematic. You can expand your electronics knowledge by experimenting with these circuits (substituting different components, for example). You might find a way to make the circuit work better than it originally did. Note the improvements that you make, and draw a new schematic that reflects them all. If you didn’t make many changes, you can pencil in the changes on the schematic from which you built the original circuit.

When you feel comfortable building simple circuits from schematics, you might want to combine two or more circuits to make a more sophisticated device. Take two schematics from a “projects” book and combine them on paper. You’ll have to draw your own schematic to serve as a plan for the building procedure. You might know enough by this time to design and build a circuit that can interface the two (connect the output of the first circuit to the input of the second one so they both work at their best). When you combine circuit-building with the task of learning to read and create schematics, you’ll improve your electronics knowledge more easily than you can do by merely looking at, and drawing, the diagrams.

Before you know it, you’ll have a solid knowledge of schematics and circuit-building. The circuits that you once imagined as complicated will seem elementary. Nevertheless, you should remain inquisitive. You might feel the temptation to stay with the types of circuits that you know best, and not venture into new territory. Don’t let laziness get the better of you! As soon as you reach one stage of comfort, move on to more difficult diagrams. Keep building more complex projects. Of course, this practice can grow expensive if you overdo it, so if you can’t build everything in sight, keep reading schematics and deciphering diverse circuit components anyway.

You’ll forever stay amazed at what you know and what you don’t know. For instance, many electronics neophytes imagine that a commercial AM radio transmitter must be a highly complex system. Most electronics novices are astonished to learn that the AM transmitter is less complicated than an old-fashioned transistorized pocket receiver that you might use to intercept the broadcasts. A commercial radio transmitter is a rather simple system, even if it’s as big and massive as your car. The transmitter size directly correlates with the component size, which in turn directly relates to the amount of power that the system consumes. The power-supply transformer for a commercial transmitter, all by itself, might weigh as much as your home refrigerator! This and other components make the commercial broadcast transmitter large and heavy. The power-supply transformer for a small amateur radio transmitter will likely mass less than a kilogram. Nevertheless, both transformers will look the same in schematics.

The most massive pieces of equipment are rarely the most complicated ones, both electronically and schematically. The tiny units that you can hold in the palm of your hand often take the prize for schematic complexity when you break them down to the component level. A tablet computer offers an excellent example. The integrated circuits (ICs or chips) inside such a system can contain millions of individual diodes, transistors, capacitors, and resistors. For this reason, an electronics novice should not shy away from any particular circuit, device, or system just because its size suggests complexity. You might be wrong, but even if you’re right, every schematic will contain portions that you can comprehend.

After you’ve gotten past the intermediate stage of learning schematics, then you can tackle complex circuits, devices, and systems. You can break them down into multiple-circuit stages or devices, and ultimately into simple circuits. Try to obtain schematics of a complex nature that offer a complete and detailed explanation of how the circuits work.

Recall the block diagram of Fig. 2-2, the strobe light circuit that you saw in Chapter 2. Compare it to Fig. 5-16, a schematic that shows all the individual components. The whole diagram is tilted on its side, allowing it to fit on the page neatly. The circuit gets powered with 120 VAC, which enters at the left side of the schematic (after you rotate the page to make the diagram appear right-side up). The three terminals of the AC line take three separate paths along color-coded wires. A black wire goes to the fuse, a white wire goes to the power supply and timing components, and a green wire, coming from the “third prong” of the plug, goes to a substantial earth ground.

FIG. 5-16   Schematic of the strobe light circuit originally shown in the block diagram of Fig. 2-2. In order to fit it on a single page, the entire diagram has been rotated counterclockwise by a quarter turn (90 degrees).

Figures 5-17A and B show the same circuit as Fig. 5-16 does, except that the diagram is split into two sections so that it can all go right-side-up. The first part (Fig. 5-17A) shows the power supply and some of the timing circuitry. The second part (Fig. 5-17B) shows the frequency-adjusting potentiometer R4 along with the rest of the timing circuitry, the switching device, and the transformer that provides the strobe light with the voltage that it needs. The three right-pointing wedges in Fig. 5-17A connect directly to their left-pointing counterparts in Fig. 5-17B.

FIG. 5-17A   The plug, fuse, and rectifier portions of the strobe light circuit. Wedges X, Y, and Z represent extensions to illustration B.

FIG. 5-17B   The timing and transformer portions of the strobe light circuit. Wedges X, Y, and Z represent extensions from illustration A.

Op Amp Circuits

Now turn your attention back to Chapter 3 and re-read the section on op amps. After you’re finished, let’s take a look at a few real-world circuits that use these venerable little chips. All of these circuits are designed to work in the AF range.

Figure 5-18 shows an op amp wired up as a non-inverting broadband amplifier. The signal comes into the non-inverting input while negative feedback flows through the inverting input. You can add a resistor between the non-inverting input and ground, as shown in this schematic, to limit the input impedance and provide some extra stability to the amplifier. (You need not include this resistor if external components determine the input impedance, or if you want to keep the input impedance as high as possible.) In any non-inverting broadband amplifier, the output wave emerges in phase coincidence with the input wave over a wide range of frequencies. You connect a fixed resistor between the inverting input and ground, and another resistor, which can have either fixed or variable value, between the output and the inverting input.

FIG. 5-18   A variable-gain, broadband AF amplifier circuit that uses an op amp. This circuit produces its output signal in phase coincidence (“right-side up”) with respect to the input signal.

Figure 5-19 shows an op amp serving as an inverting broadband amplifier. You’ll find this arrangement in many of the same scenarios as you see non-inverting amplifiers. It resembles the circuit of Fig. 5-18, except that the input signal goes to the inverting input rather than the non-inverting input. You can add a resistor between the input terminal and ground to limit the input impedance and enhance the stability, just as you can do with a non-inverting amplifier. (You won’t need this resistor if external components determine the input impedance, or if you want to maximize the input impedance.) In an inverting amplifier, the output wave emerges in phase opposition with respect to the input wave. You can connect either a fixed resistor or a potentiometer between the output and the inverting input, exactly as you would do with the circuit of Fig. 5-18.

FIG. 5-19   Another variable-gain, broadband AF amplifier circuit using an op amp. This circuit produces its output signal in phase opposition (“upside down”) with respect to the input signal.

An inverting differentiator is a circuit whose instantaneous output level varies in proportion to an upside-down version of the rate of change in the input signal level as a function of time. This arrangement produces an output signal with the same frequency as that of the input signal, although the waveform might (and often does) differ. Figure 5-20 shows a schematic of an op amp wired up as an inverting differentiator. This circuit provides some gain.

FIG. 5-20   An op amp circuit that inverts and differentiates a signal and provides some gain.

An inverting integrator is a circuit whose instantaneous output level varies in proportion to an upside-down version of the accumulated input signal level as a function of time. The output signal might have the same frequency as the input signal, but not necessarily. (In some cases, the output differs drastically from the input!) Figure 5-21 shows a schematic of an op amp wired up as an inverting integrator. As with the circuit of Fig. 5-20, this arrangement provides some gain.

FIG. 5-21   An op amp circuit that inverts and integrates a signal and provides some gain.

If you connect specialized groups of resistors and capacitors together with op amps, you can create frequency-sensitive AF filters that can also provide amplification. Engineers call them active filters because they need a source of DC electricity (such as a battery) in order to work. All the way back in Chapter 3, you saw four gain-versus-frequency graphs showing:

•   A lowpass response that favors low frequencies (Fig. 3-47A).

•   A highpass response that favors high frequencies (Fig. 3-47B).

•   A resonant peak that has maximum gain at a single frequency (Fig. 3-47C).

•   A resonant notch that has minimum gain at a single frequency (Fig. 3-47D).

Figure 5-22 shows how you can wire up an op amp to produce a lowpass response. The values of resistor R and capacitor C determine the cutoff frequency (where the voltage gain is -3 dB, representing roughly 70.7 percent of maximum). The cutoff frequency drops if you:

FIG. 5-22   An op amp wired up to serve as a lowpass filter. The values of resistor R and capacitor C determine the cutoff frequency. This circuit provides some gain.

•   Increase the resistance but leave the capacitance constant.

•   Increase the capacitance but leave the resistance constant.

•   Increase both the resistance and the capacitance.

The cutoff frequency rises if you:

•   Decrease the resistance but leave the capacitance constant.

•   Decrease the capacitance but leave the resistance constant.

•   Decrease both the resistance and the capacitance.

Figure 5-23 is a schematic of an op amp, a resistor R, and a capacitor C connected to produce a highpass response. As with the lowpass filter, the cutoff frequency drops if you:

FIG. 5-23   An op amp wired up to serve as a highpass filter. The values of resistor R and capacitor C determine the cutoff frequency. This circuit provides some gain.

•   Increase the resistance but leave the capacitance constant.

•   Increase the capacitance but leave the resistance constant.

•   Increase both the resistance and the capacitance.

The cutoff frequency rises if you:

•   Decrease the resistance but leave the capacitance constant.

•   Decrease the capacitance but leave the resistance constant.

•   Decrease both the resistance and the capacitance.

In order to calculate the cutoff frequency f (in hertz) of the lowpass filter of Fig. 5-22 or the highpass filter of Fig. 5-23, you need to know the resistance R in ohms and the capacitance C in farads. Then you can use the formula

f = 1 / (2πRC)

where π represents the ratio of a circle’s circumference to its diameter (approximately 3.14159). This formula will also work if you express R in megohms and C in microfarads. (The frequency f will still come out in hertz.)

Figure 5-24 is a schematic of an op amp, two resistors R1 and R2, and two capacitors C1 and C2 connected to produce a resonant peak response. The resonant peak (maximum gain) frequency drops if you:

FIG. 5-24   An op amp wired up to serve as a resonant peak filter. The values of resistors and capacitors R1, R2, C1, and C2 determine the resonant frequency.

•   Increase the resistances but leave the capacitances constant.

•   Increase the capacitances but leave the resistances constant.

•   Increase both resistances and both capacitances.

The resonant peak frequency rises if you:

•   Decrease the resistances but leave the capacitances constant.

•   Decrease the capacitances but leave the resistances constant.

•   Decrease both resistances and both capacitances.

To calculate the resonant peak frequency f (in hertz), you need to know the resistance values R1 and R2 in ohms and the capacitance values C1 and C2 in farads. Then you can use the formula

f = 1 / [ 2π (R1 R2 C1 C2)^1/2 ]

This formula will also yield f in hertz if you express both resistances in megohms and both capacitances in microfarads.

Figure 5-25 is a schematic of an op amp, four resistors R1 through R4, and two capacitors C1 and C2 connected to produce a resonant notch response. In this circuit, resistances R1 and R2 govern the gain at frequencies above and below that of the notch. Resistances R3 and R4 should equal each other; let’s call that resistance R. In addition, capacitances C1 and C2 should equal each other; let’s call that capacitance C.

FIG. 5-25   An op amp wired up to serve as a resonant notch filter. The values of resistors and capacitors determine the resonant frequency. In this circuit, R3 = R4; you can call this resistance R. Also, C1 = C2; you can call this capacitance C.

The resonant notch (or minimum gain) frequency drops if you:

•   Increase R but leave C constant.

•   Increase C but leave R constant.

•   Increase both R and C.

The resonant notch frequency rises if you:

•   Decrease R but leave C constant.

•   Decrease C but leave R constant.

•   Decrease both R and C.

To calculate the resonant notch frequency f (in hertz), you need to know R and C, as defined above, in ohms and farads respectively. Then you can use the formula

f = 1 / (2πRC)

This formula will also yield f in hertz if you express both R3 and R4 in megohms and both C3 and C4 in microfarads.

Summary

Reading and drawing schematics often involve breaking down complex circuits into simple ones. Then you can look at the system’s parts and how they relate to each other, rather than try to imagine the whole thing as a single appliance. As you study a complex schematic, the relationships among the circuits will grow apparent. Once in awhile, you’ll see all of a system’s “secrets” revealed at once: an “Aha” moment!

Learning to read and write schematics is a lot like learning to receive and send the old Morse code. “The code” is a language of audible symbols, just like a schematic is a language of printed symbols. Once you learn either language, you can use it to communicate; Morse code communicates words and sentences, while schematics communicate principles and concepts.

Using Morse code as a further example, a long sequence of dots and dashes will mean nothing unless you can break the data down into words. As your proficiency increases, you’ll stop hearing the individual dots and dashes (or, as some people say, “dits” and “dahs”) and hear letters of the alphabet instead. As you keep practicing, you’ll start to hear entire words. Eventually, if you keep at it long enough (and especially if you get fond of the code for its own sake, communicating with it for hours on end, as I have done over the years as a ham radio operator), you’ll hear whole phrases and sentences.

Reading and writing schematics takes you through a similar pattern of development. At first you’ll see individual component symbols. Later, you’ll find simple circuits hidden within complex circuits. Then you’ll identify and analyze those complex circuits. Finally, you’ll envision entire systems. This knowledge might come slowly, but your proficiency will improve every time you practice if you keep pushing yourself (gently, of course) into new knowledge zones.