Ramp Generator

4QD-TEC: Electronics Circuits Reference Archive Waveform generator circuits There are many different types of waveform generator circuits for many different uses. Here are some which I've collected. I leave it up to you to find uses for them!

Dual Ramp Generator

The first circuit is a dual ramp generator where the positive and negative ramps are generated separately. This circuit was used as a ramp generator for a transistor curve tracer: the positive going ramp was used for testing NPN transistors and the negative ramp for testing PNP transistors. The two ramp outputs are at A and B. The A output sits at -12v whilst the B output is ramping and then it ramps positive while the B output sits at +12v. The two waveforms are shown below the circuit and ramp lengths are determined by the integrator (-ve feedback) capacitors and the 'set' presets. For transistor testing this is nice since each ramp is 50% of the duty cycle so the transistor gets a chance to rest between ramps. If the output is selected with respect to +ve or negative (which requires an isolated supply) the polarity can be switched as shown in the bottom right of the diagram.

Three phase oscillator

The second circuit is a 3 phase squarewave oscillator, or tristable. Its operation should be reasonably obvious and it is like a simple bistable oscillator with 3 stages.

Quadrature (sine/cosine) voltage controlled oscillator

This is a voltage controlled oscillator with a difference: it gives a quadrature output which is shaped as shown in the diagram, with an output which approximates to a sine/cosine waveform. If you have difficulty understanding it this is because it does not use standard op-amps but an LM3900 which is a Norton op-amp - it works on differential currents, not on differential voltages. The LM3900 is a

very versatile op-amp which has some very special advantages over standard op-amps but is not nearly as commonly used: I suspect that few students are taught about it so few consider using it.

free run ramp uses 555

ramp function gen

RCA CD4004T IC, internally connected as ripple counter, provides flip-flop outputs corresponding to number of binary bits loaded into single input 1. Frequency range of counteris DC to 2.5 MHz, making it ideal for low-frequency operation. With R-2R ladder connected to flip-flop outputs, input square wave gives digitally stepped ramp at ladder output, with ramp frequency equal to 1/128 of input frequency.-W. E. Peterson, Digital Ramp Generator, EEEA Magazine, Jan. 1971, p 64-65.

The IEEE Student Branch at ENSEEIHT has been officially formed the 3rd of May 2000. But the activities have begun when the application forms had been sent to IEEE some months earlier. This report summarizes the projects realized during this longer period (i.e., about six months). For the first year, the main activities are in the microwave field.

Number of student members in the Branch The number of student members involves in the branch was twenty-two. This group is composed by eleven PhD students, one DEA and ten engineers student (in their last year of engineering studies). Web Site (Tan Hoa Vuong, PhD student) One of the first activity of the branch was to design a temporary web page located at the following address: http://www.enseeiht.fr/larecherche/main.html.fr. Up to now this page

presents the members and the main projects of year 2000. In the year 2001, the design of a new web with more information site will be performed. Engineering Projects These projects are intended to put the student members in an engineering work with a deadline (about six months of work). The work is composed by a bibliography study (the state of the art of one subject by exploring the IEEE reviews in our Electrical Engineering Laboratory), then a design of the structure and finally, if the simulations are satisfactory, a practical realization and validation. During the year 2000, three projects have been investigated : the design of a low cost spectrum analyzer, the design (and realization) of a GPS antenna and the design electromagnetic environment sensor : 1- Low cost spectrum analyzer The subject of this project is the design of a low cost spectrum analyzer with in the bandwidth of 0 to 350 MHz. It could cover several years: each unit of the synoptic (figure 1) will be designed separately. Before the realization of all units, integrated circuits will replace them. The first work was to elaborate the synoptic of the system. Then the first unit to be designed was the ramp generator ("générateur de rampe" in the figure 1)

Figure 1 : Synoptic of the low cost spectrum analyzer. The figure 1 represents the synoptic of the system. The input signal is applied to a low-pass filter with a cut-off frequency of 350 MHz (which corresponds to the maximum frequency of the spectrum analyzer). Then the signal is mixed with a VCO one, which sweeps across 450 MHz to 800 MHz. After the mixer, the signal has a frequency of 450 MHz and he is filtered with a narrow band-pass filter in order to remove the harmonics created by the VCO. Then, a logarithmic amplifier is used so as to visualize a dB y-axe on the oscilloscope. On the x-input, we apply the "rampe" (ramp) which control the VCO.

Figure 2 : Electrical circuit of the ramp generator. The principle of the ramp generator is the creation of a generator of functions (figure 2). At the output of the first operational amplifier we obtain a square signal and at the output of the second operational amplifier, we have a triangular signal. The last operational amplifier is used to put an offset voltage in order to obtain a signal not centered on 0 V. The minimal and maximal voltage of the ramp is calculated from the needed frequency of the VCO, i.e. between 2V and 14V. Furthermore, the generation frequency of the triangle signal must be the lowest so as to visualize the signal on the oscilloscope. The frequency range is between 30 Hz and 75 Hz (this variation is realized by the R13 potentiometer. And the R12 component allows to add an offset on the signal. The realization of this function uses double operational amplifier (TL082), and we measure the following results: f = 33.56Hz Vmax = 13.67V Vmin = 2.73V Vpp = 10.94V f = 73.53Hz Vmax = 13.67V Vmin = 2.73V Vpp = 10.94V A practical realization of the spectrum analyzer is under way. 2- GPS antenna The aim of this project is double: to elaborate a complete state of the art on antennas for GPS applications (spiral, planar, etc.) and to design a planar antenna with the following specifications : resonance frequency : 1.5754 GHz right handed circular polarization VSWR 10 dBi

To design the patch antenna, we use Depron (r = 4.32 and substrate thickness : 1.52mm) as substrate. So, with this dielectric and the resonance frequency given above, the theoretical square patch dimension (without excitation ports) is 90mm. To excite the metallic patch, three methods have been investigated : by coaxial line, by microstrip line and by electromagnetic coupling. The latter method was adopted (it facilitates the feeding of patch array and improve the circular polarization). To obtain the circular polarization, a Wilkinson power divider was designed. The /2 phase shift between the two output ports was achieved. To calculate the dimension of the iris coupling we use the following well-known relationship : L = 6w + e where w designates the width of the exciting line, e denotes the dielectric thickness and l is the length of the iris. To obtain the required resonance frequency at 1.5754 GHz (in presence of the iris coupling), the dimension of the patch has been reduced to 87mm. A practical realization is under way. 3- Electromagnetic environment sensor The aim of this project is the design of a sensor to characterize the electromagnetic environment around an airplane (typically, the electromagnetic pollution has a frequency between 10 GHz to 40 GHz). This sensor must be placed above an electronic level, which will treat the signal picked up by the antenna. The maximum surface of the antenna is 3 x 1 cm2 and it must have low consumption. The state of the art has been concluded by the selection of two kind of structures: a spiral antenna or a planar antenna. The spiral antenna, for the considered frequency, needed too much space, so a deeper study was made on planar patches. To increase the antenna sensitivity, we associate eight patches (the dimensions of each patch are 2mm x 3mm). The numerical simulations have been performed and show a very low gain. The patch antenna structure is difinitively not adapted to our problem. The design of a wire antenna is underway. Research projects The duration of these projects was short (about 3 months). These projects consist in the use of numerical methods in order to characterize new structures or to modify these methods. During the year 2000, two projects gave interesting results: the characterization of a circular iris and the real time modification of the topology of a planar circuit. 1- Characterization of a circular iris In this project, we study a new coupling iris. It is composed by four circular holes. It must replace the classical cross iris. This new iris is easy to manufacture and it is less sensitive to mechanical errors.

In a first part, we examine the influence of the hole positions on the coupling coefficient. We study two holes parallel to the electric field polarization, then two holes orthogonal to the polarization and finally the four holes. After modeling of the circular irises (two and four irises), we can study the influence of the holes position on the coupling coefficient. The results show that the two parallel holes have a greater influence than the orthogonal ones. This observation allows us to study separately the coupling coefficient of each polarization. 2- Real-time modification of the topology of planar circuits In this project, we plan to modify programs based on a recent iterative method in order to let the possibility to modify the circuit during the simulation. The idea is, when the convergence is reached, the user can add or remove metallic part of the circuit, the simulation of this new circuit uses the result of the former one (which is topologically near) to obtain faster results. After the modification of the programs, a classical case was studied: a bend in a microstrip line. The results show that the computation time is reduced in comparison to a direct simulation.

LINEAR RAMP

2N388 TIX882 TIX883 Output voltage varies linearly with frequency within 98%, while peak voltage is constant of 0.6 v. Thermistor R1 provides temperature stability and source follower Q6 reduces loading.D. D. Brooks and C. F. Johnson, Sawtooth Generator Uses FET as Constant Current Source, Electronics, 38:18, p 87.

A constant amplitude triangular-wave generator is shown in Figure 1. This circuit provides a variable frequency triangular wave whose amplitude is independent of frequency.

Figure 1. Triangular-Wave Generator The generator embodies an integrator as a ramp generator and a threshold detector with hysterisis as a reset circuit. The integrator has been described in a previous section and requires no further explanation. The threshold detector is similar to a Schmitt Trigger in that it is a latch circuit with a large dead zone. This function is implemented by using positive feedback around an operational amplifier. When the amplifier output is in either the positive or negative saturated state, the positive feedback network provides a voltage at the non-inverting input which is determined by the attenuation of the feedback loop and the saturation voltage of the amplifier. To cause the amplifier to change states, the voltage at the input of the amplifier must be caused to change polarity by an amount in excess of the amplifier input offset voltage. When this is done the amplifier saturates in the opposite direction and remains in that state until the voltage at its input again reverses. The complete circuit operation may be understood by examining the operation with the output of the threshold detector in the positive state. The detector positive saturation voltage is applied to the integrator summing junction through the combination R3 and R4 causing a current I+ to flow.

Figure 2. Threshold Detector with Regulated Output The integrator then generates a negative-going ramp with a rate of I+/C1 volts per second until its output equals the negative trip point of the threshold detector. The threshold detector then changes to the negative output state and supplies a negative current, I−, at the integrator summing point. The integrator now generates a positive-going ramp with a rate of I−/C1 volts per second until its output equals the positive trip point of the threshold detector where the detector again changes output state and the cycle repeats. Triangular-wave frequency is determined by R3, R4 and C1 and the positive and negative saturation voltages of the amplifier A1. Amplitude is determined by the ratio of R5 to the combination of R1 and R2 and the threshold detector saturation voltages. Positive and negative ramp rates are equal and positive and negative peaks are equal if the detector has equal positive and negative saturation voltages. The output waveform may be offset with respect to ground if the inverting input of the threshold detector, A1, is offset with respect to ground. The generator may be made independent of temperature and supply voltage if the detector is clamped with matched zener diodes as shown in Figure 2. The integrator should be compensated for unity-gain and the detector may be compensated if power supply impedance causes oscillation during its transition time. The current into the integrator should be large with respect to Ibias for maximum symmetry, and offset voltage should be small with respect to Vout peak.

A spectrum analyzer (for our purposes) is basically a device which displays radio activity within a certain range of frequencies. It does this by synchronizing the horizontal sweep of an o-scope with the swept tuning of a radio receiver. In this project's case, the synchronizing signal is a ramp signal generator, and the receiver is the VCO-controlled receive circuit of a CB. The horizontal trace of the scope is controlled by the ramp signal, which is also controlling the frequency of the VCO in the CB (The VCO is what actually "tunes" the CB radio). When the vertical trace of the o-scope is tied to the CB's detector output, we have a DC voltage generated for every signal present, and those voltages are spaced equally for each chanel that has activity. As for accuracy and specific measurements, this setup is probably not going to do what you need, but for seeing what activity might be present in the 10 or 11 meter bands, this is just dandy. Besides, its a real kick to know that you built it yourself out of basically junk. Another big plus is that it can be built in less than an hour if you're good at breadboarding, reading schematics, and tracking down specific parts in a CB. For those of you who like to tinker, here's how to do it. You will need an o-scope with X-Y capability, and any AM-mode, PLL-controlled CB with a working receiver. It would help to have a CB to which you can get the schematic, because you will need to be able to identify the VCO control point, as well as the detector circuit. Basic steps are as follows: 1. Build a ramp generator capable of at least 4 volts peak-to-peak output (more than 4 is ok, but at least 4 is recommended to give the VCO a decent range) . 2. Tie the output of the ramp generator to the X input of the scope. 3. Tie the output of the generator to the control voltage input of the CB's VCO, after unhooking the VCO from the PLL chip, and eliminate any filtering caps on the VCO control voltage line. The filter caps need to be removed to allow the fast tuning needed here.

4. Tie the Y input of the scope to the output of the AM detector. You will need to invert the scope input if the DC level out of the detector is negative, or your signal levels will be showing upside down on the scope (kinda neat, actually, if you like the strange and unusual. I set mine up to show frequencies in reverse order AND upside down just for kicks. You can't do that with those high-dollar analyzers I'll bet!). You will need to play with the ramp generator frequency to get the best results. I found that from 10 to 60 hz did pretty well. The faster the ramp, the more the individual signals tended to run together on the display. A cb with a faster-responding VCO will make for a sharper display and better resolution, which will allow faster ramp speeds without loss of display sharpness. You will also need to play with the settings of the two scope inputs in order to get a usable display. I found that the X input did well at anywhere from 1 VPD to .2VPD, and the Y input I ran at 1VPD, with variations in the calibration on both inputs. The horizontal position control ended up being maxed out on my scope by the time I was happy with the results. Here are a couple pictures of the one I threw together at the project's start:

Below is a schematic of the basic signal generator used in the project.

GROUND-REFERENCED RAMP-AND-PEDESTAL CONTROL

1N4004 1N4001 Q2015L5 Need for transformer is eliminated by applying alternate half-cycles to inverting and noninverting inputs of section 3 of LM3900 quad opamp, so full-wave-rectified waveform is referenced to ground. Comparator opamp 1 discharges timing capacitor at zero line voltage and synchronizes circuit with line frequency. Buffer opamp 2 scales input and provides linear pedestal for capacitor. Opamp 4 is comparator serving as output driver whose output is high when capacitor is charged to level selected by high-end trimming pot. Output is sufficient for optoisolators and logic triacs.-J.C. Johnson, Ramp-And-Pedestal Phase Control Uses Quad Op Amp, EDN Magazine, June 5, 1977, p 208 and 211.

Voltage-ratio-to-frequency-converter

The circuit accepts two positive-voltage inputs VN and Vv and provides a TTL-compatible output pulse train whose repetition mte is proportional to the ratio VN/ V0. Full-scale output frequency is about 100 Hz, and linearity error is below 0.5 percent. The outputF, equals KVn/Vd, where K = 1/(4R2C1) provided R1 = R3. Op amp IC1A alternately integrates VN/2 and -VN/2, producing a sawtooth output that ramps between the Vv level and ground. When transistor Ql is on, for example, IC1A integrates -VN/2 until its output equals Vv.

This circuit generates simultaneously, a triangle and a square waveform. It is self starting and has no latch up problems. IC1 is an integrator with a slew rate determined by CT and RT and IC2 is a Schmitt trigger. The output of IC1 ramps up and down between the hysteresis levels of the Schmitt, the output of which drives the integrator. By making RT variable, it is possible to alter the operating frequency over a 100 to 1 range.

The quad operational amplifier circuit yields full 0 to 100 percent pulse width control. The controller uses an LM3900 requires only a single supply voltage of 4-30 V. The pulse repetition frequency is set by a 1 kHz oscillator amplifier that integrates AI. The oscillator feeds the Az ramp generator, which generates a linear ramp voltage for each pulse oscillator. The ramp signal feeds the inverting input of comparator A3, the control voltage feeds speed non-inverting input. Thus, the output of the comparator is a 1 kHz pulse train, pulse width that changes linearly with control voltage.

555 ramp generator PARTS AND MATERIALS          

Two 6 volt batteries One capacitor, 470 µF electrolytic, 35 WVDC (Radio Shack catalog # 272-1030 or equivalent) One capacitor, 0.1 µF, non-polarized (Radio Shack catalog # 272-135) One 555 timer IC (Radio Shack catalog # 276-1723) Two PNP transistors -- models 2N2907 or 2N3906 recommended (Radio Shack catalog # 276-1604 is a package of fifteen PNP transistors ideal for this and other experiments) Two light-emitting diodes (Radio Shack catalog # 276-026 or equivalent) One 100 kΩ resistor One 47 kΩ resistor Two 510 Ω resistors Audio detector with headphones

The voltage rating on the 470 µF capacitor is not critical, so long as it generously exceeds the maximum power supply voltage. In this particular circuit, that maximum voltage is 12 volts. Be sure you connect this capacitor in the circuit properly, respecting polarity!

CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 13: "Capacitors" Lessons In Electric Circuits, Volume 4, chapter 10: "Multivibrators"

LEARNING OBJECTIVES   

How to use the 555 timer as an astable multivibrator A practical use for a current mirror circuit Understanding the relationship between capacitor current and capacitor voltage rate-of-change

SCHEMATIC DIAGRAM

output voltage linearly varies with frequency

linear output ramp

There is no such thing as too many introductory articles on operational amplifiers (opamps). Of course, when this story was written for Electronics World back in 1967, opamp were relatively new to the scene. Prior to the advent of opamps, circuit design for controllers, filter, comparators, isolators, and just plain old amplification was much more involved. Opamps suddenly allowed designers to not worry as much about biasing, variations in power supply voltages, and other annoyances, and instead focus on function. Even from the very beginning with the μa741 operational amplifier, the parameters came close to those of an ideal device: infinite input impedance, zero output impedance, perfect isolation between ports, and infinite bandwidth. OK, the bandwidth spec was more constrained compared to the other three, but still, with frequencies being what they were compared to today, it was close enough. Opamps allowed engineers to design with the simplicity of LaPlace equations.

See all the available Electronics World articles.

The Operational Amplifier Circuits & Applications

By Donald E. Lancaster These highly versatile controllable-gain modular or integrated-circuit packages have been used in computer and military circuits. New price and size reductions have opened commercial and consumer markets. Here are complete details on what is available and how the devices are used.

Typical modular package and TO-5 style IC operational amplifiers.

Once exclusively the mainstay of the analog-computer field, operational amplifiers are now finding diverse uses throughout the rest of the electronics industry. An operational amplifier is basically a high-gain, d.c.-coupled bipolar amplifier, usually featuring a high input impedance and a low output impedance. Its inherent utility lies in its ability to have its gain and response precisely controlled by external resistors and capacitors. Since resistors and capacitors are passive elements, there is very little problem keeping the gain and circuit response stable and independent of temperature, supply variations, or changes in gain of the op amp itself. Just how these resistors and capacitors are arranged determines exactly what the operational amplifier will do. In essence, an op amp provides "instant gain" that may be used for practically any circuit from a.c., d.c., and r.f. amplifiers, to precision waveform generators, to high- "Q" inductorless filters, to mathematical problem solvers.

Fig. 1. (A) Op-amp symbol. (B) Block diagram of typical op amp.

Fig. 2. Characteristics of the Fairchild μA702C. Price: $9.00.

Fig. 3. Characteristics of Motorola's MC1430. Price: $12.00.

Fig. 4. The RCA CA3030 operational amplifier. Unlabeled terminals are used for frequency-compensation. Price: $7.50. Note that the prices given here and above are for singleunit quantities and these prices are subject to change.

Op amps used to be quite expensive, but many of today's integrated circuit versions now range from $6 to $20 each and less in quantity. Due to price breaks that have occurred very recently, the same benefits now available to the analog computer, industrial, and military markets are now extended to commercial and consumer circuits. One obvious application will be in hi-fi preamps where a single integrated circuit can replace the bulk of the low-level transistor circuitry normally used. Fig. 1A shows the op-amp symbol. An op amp has two high-impedance inputs, the inverting input and the noninverting input, as indicated by a "-" or a "+" on the input side of the amplifier. The inverting input is out-of-phase with the output, while the non-inverting input is in-phase with the output. The amplifier has an open-loop gain A, which may range from several thousand to several million. On closer inspection, we see three distinct parts to any operational amplifier's internal circuitry, as shown in Fig. 1B. A high-input-impedance differential amplifier forms the first stage, with the inverting input going to one side and the non-inverting input the other. The purpose of this stage is to allow the inputs to differentially drive the circuit and also to provide a high input impedance. There are several possibilities for this input stage. If an ordinary matched pair of transistors (or the integrated circuit equivalent) is used, an input impedance from 10,000 to 100,000 ohms will result, combined with low drift, low cost, and wide bandwidth. By using four transistors in a differential Darlington configuration, the input impedance may be nearly one megohm. Drift and circuit cost are traded for this benefit. Field-effect transistors are sometimes used, yielding input impedances of 100 megohms, but often with limited bandwidths. FET integrated-circuit operational amplifiers are not yet available, limiting this technique to the modular-style package at present. One or two novel techniques allow extreme input impedances, but presently at very high cost. One approach is to use MOS transistors with their 1013-ohm input impedance; a second is to use a varactor diode parametric amplifier arrangement on the input. The input differential amplifier is followed by ordinary voltage-gain stages, designed to bring the total voltage gain up to a very high value. Terminals are usually brought out of the voltage-gain stage to allow the frequency and phase response of the op amp to be tailored for special applications. This is usually done by adding external resistors and capacitors to these terminals. Since an operational amplifier is bipolar, the output can swing either positive or negative with respect to ground. A dual power-supply system, one negative and one positive, is required. The final op-amp stage is a low-impedance power-output stage, which may take the form of a single emitter-

follower, a push-pull emitter-follower, or a class-B power stage. This final circuit serves to make the output loading and the over-all gain and frequency response independent. It also provides a useful level of output power. THE MATH BEHIND THE OP AMP The gain of an operational-amplifier circuit is always chosen be much less than the open-loop gain of the amplifier itself. This allows the circuit response to be precisely determined by the external feedback and input network impedances. Feedback is almost ways applied to the inverting (-) input. This is negative feedback for any change in output tries to produce an opposing change in the input. The feedback and input network impedances are normally chosen such that they are much larger than the op amp's output impedance, much smaller than the op amp's input impedance, and such that the gain they require for proper operation is much less than the amp's gain. If these assumptions are met, the ratio of input to output voltage (the gain of the circuit) will be given by:

Circuit Gain = For instance, the op-amp circuit of Fig. 5B has an input impedance of 1000 ohms and a feedback impedance of 10,000 ohms Its gain will be - 10k/1k = - 10. Any of the op amps of Figs. 2, 3, or 4 may be used for this circuit. Some circuit analysis will show that the inverting input is always very near ground potential, and this point is then called a virtual ground insofar as the input signals and output feedback are concerned. Thus the input impedance to the circuit will exactly equal the input network impedance. When capacitors are used in the networks, the phase relationships between current and voltage must be taken into account. These differences in phase allow such operations as differentiation, integration, and active network synthesis. But isn't an op amp a d.c. amplifier and don't d.c. amplifiers drift and have to be chopper-stabilized or otherwise compensated? This certainly used to be true of all amplifiers, but today such techniques are reserved for extremely critical circuits. The reasons for this lie in the input differential stage. It is now very easy to get an integrated circuit differential amplifier stage to track within a millivolt or so over a wide temperature range. This is due to the identical geometry, composition, and temperature of the input transistors. Matched pairs of ordinary transistors can track within a few millivolts with careful selection. FET's offer still drift performance, as one bias point may be selected that is drift-free with respect to temperature over a very wide range. Thus, chopper-stabilized systems are rarely considered today for most op-amp applications. There are three basic op-amp packages available today. The first type consists of specialized units used only for precision analog computation and critical instrumentation circuits. These are priced into the hundreds and even thousands of dollars for each category, and are not considered here. The second type is the modular package, and usually consists of a black plug-in epoxy shell an inch or two on a side. Special sockets are available to accommodate the many pins that protrude out the case bottom. The third package style uses the integrated circuit. Here the entire op amp is housed in a flat pack, in-line epoxy, or TO-5 style package. (See lead photograph.) Generally speaking, the modular units are being replaced in some cases by the integrateds, but at present, each package style offers some clear-cut advantages. Table 1 compares the two packages. The IC versions offer low cost, small size, and very low drift, while the modular versions offer higher input impedances, higher gain, and higher

output power capability. Three low-cost readily available IC op amps appear in Figs. 2, 3, and 4. Here, their schematics and major performance characteristics are compared. Devices similar to these at even lower cost may soon be available. A directory of op amp makers is given in Tables 2 and 3.

Table 2. Listing of modular-type operational-amp manufacturers.

Table 3. Listing of integrated-circuit op-amp manufacturers.

Industrial Op-Amp Applications We can split the op-amp applications into roughly three categories: the industrial circuits, the computer circuits, and the active network synthesis circuits. The industrial circuits are "ordinary" ones, which will carryover into the consumer and commercial fields with little change. The boxed copy (facing page) sums up the mathematics. An operational amplifier is often used in conjunction with two passive networks, an input network, and a feedback network, both of which are normally connected to the inverting input. The gain of the over-all circuit at any frequency is given by the equation shown. It is simply the ratio of the feedback impedance to the input impedance at that frequency. For the circuits shown, a low impedance path to ground must exist for all input sources to allow a return path for base current in the two input transistors. Fig. 5A shows an inverting gain-of-100 amplifier useful from d.c. to several hundred kHz. The basic equation tells us the gain will be -10,000/100 = -100. The 100-ohm resistor on the "+" input provides base current for the "+" transistor and does not directly enter into the gain equation. It may be adjusted to obtain a desired drift or offset characteristic. The higher the gain of the op amp, the closer the circuit performance will be to the calculated performance. In the of-100 amplifier, if the op amp gain is 1000, the gain error will be roughly 1 %. The exact value of the gain also depends upon the precision to which the input and feedback components are selected.

Choosing different ratios of input and feedback impedances gives us different gains. Fig. 5B shows a gain-of-10 amplifier with a d.c. to 2 MHz frequency response and a 1000-ohm input impedance.

Table 1. Comparison between integrated operational amplifiers and modular-type operational amplifiers.

We might ask at this point what we gain by using an op amp in this circuit instead of an ordinary single transistor circuit. There are several important answers. The first is that the input and output are both referenced to ground. Put in zero volts and you get out zero volts. Put in -400 millivolts and you get out +4 volts. Put in 400 millivolts you get out -4 volts. Secondly, the output impedance is very low and the gain will not change if you change the load the op amp is driving, as long as the loading is light compared to the op amp's output impedance. Finally, the gain is precisely 10, to the accuracy you can select the input and feedback resistors, independent of temperature and power-supply variations. It is this precision and ease of control that makes the operational amplifier configuration far superior to simpler circuitry. If the output is connected to the "-" input and an input directly drives the "+" input, the unity-gain voltage follower of Fig. 5C results. This configuration is useful for following precision voltage references or other voltage sources that may not be heavily loaded. The circuit is superior to an ordinary emitter-follower in that the offset is only a millivolt or so instead of the temperature-dependent 0.6-volt drop normally encountered, and the gain is truly unity and not dependent upon the alpha of the transistor used.

Fig. 5. Industrial op-amp circuits. (A) Gainof-100 inverting amplifier. (B) Gain-of-10 inverting amplifier. (C) Unity-gain high input Z amplifier. (D) Band-stop amplifier. (E) Band-pass amplifier. (F) Precision ramp or linear saw-tooth generator. (G) Detector with low offset. (H) Logarithmic amplifier. (I) Voltage comparator. (J) Sine-wave oscillator.

By making the gain of the op amp frequency-dependent, various filter configurations are realized. For instance, Fig. 5D shows a band-stop amplifier. For very low and very high frequencies, the series RLC circuit in the feedback network will be a very high impedance and the gain will be -10,000/1000 = -10. At resonance, the series RLC impedance will be 100 ohms and the gain will be -100/1000 = -0.1. The gain drops by a factor of 100:1 or 40 deci\bels at the resonant frequency. The selection of the LC ratio will determine bandwidth, while the LC product will determine the resonant frequency. Fig. 5E does the opposite, producing a response peak at resonance 100 times higher than the response at very high or very low frequencies, owing to the very high impedance at resonance of a parallel LC circuit. More complex filter structures may be used to obtain any reasonable filter function or response curve. Audio equalization curves are readily realized using similar techniques. Turning to some different applications, Fig. SF shows a precision ramp generator. Operation is based upon the current source formed by the reference voltage and 1000-ohm resistor on the input. In any op-amp circuit, the current that is fed back to the input must equal the input current, for otherwise the"-" input will have a voltage on it, which would immediately be amplified, making the input and feedback currents equal. A constant current to a capacitor linearly charges that capacitor, producing a linear voltage ramp. The slope of the ramp will be determined by the current and the capacitance, while the linearity will be determined by the gain of the op amp. A sweep of 0.1-percent linearity is easily achieved. The output ramp is reset to zero by the switch and the 10-ohm current-limiting resistor. For synchronization, S may be replaced by a gating transistor. A negative input current produces a positive voltage ramp at the output. Note that the sweep linearity and amplitude is independent of the output loading as long as the load impedance is higher than the output impedance of the op amp. Ramps like this are often used in CRT sweep waveform generation, analog-to-digital converters, and similar circuitry. Silicon diodes normally have a 0.6-volt offset that makes them unattractive for detecting very low signal levels. If a diode is included in the feedback path of an operational amplifier, this offset may be reduced by the gain of the circuit, allowing low-level detection. Fig. 5G is typical. Here the gain to negative input signals is equal to unity, while the gain to positive input signals is equal to 100. The diode threshold will be reduced to 0.6 volt/100 = 6 millivolts. Another diode op-amp circuit is that of Fig. 5H. Here the logarithmic voltage-current relation present in a diode makes the feedback impedance decrease with increasing input signals, reducing the circuit gain as the input current increases. The net result is an output voltage that is proportional to the logarithm of the input, and the circuit is a logarithmic amplifier. This configuration only works on negative-going inputs and is useful in compressing signals measuring decibels, and in electronic multiplier circuits where the logarithms of two input signals are added together to perform multiplication. An operational amplifier is rarely run "wide open", but Fig. 51 is one exception. Here the op amp serves as a voltage comparator. If the voltage on the "-" input exceeds the "+" input voltage, the op amp output will swing as negative as the supply will let it, and vice versa. A difference of only a few millivolts between inputs will shift the output from one supply limit to the other. Feedback may be added to increase speed and produce a snap action. One input is often returned to a reference voltage, producing alarm or a limit detector. Op amps may also be used in groups. One example is the low-distortion sine-wave oscillator of Fig. 5J, in which three

op amps generate a precision sine wave. Both sine an cosine outputs, differing in phase by 90° are produced. An external amplitude stabilization circuit is required, but not shown. Output frequency is determined solely by resistor and capacitor values and their stability. Computer Circuits The analog computer industry was the birthplace and once the only home of the operational amplifier. In fact the name comes from the use of op amps to perform mathematical operations. Many of these circuits are of industrywide interest and use. Perhaps the simplest op-amp circuit is the inverter. This is an op amp with identical input and feedback resistors Whatever signal gets fed in, minus that signal appears the output, thus performing the sign-changing operation. Addition is performed by the circuit of Fig. 6A. Here the currents from inputs E1, E2, and E3 are summed and the negative of their sum appears at the output. Since the negative input is always very near ground because of feedback, there is no interaction among the three sources Resistor R is adjusted to obtain the desired drift performance. By shifting the resistor values around, the basic summing circuit may also perform scaling and weighting operations. For instance, a 30,000-ohm feedback resistor would produce an output equal to minus three times the sum of the inputs; a smaller feedback resistor would have the opposite effect. By changing only one input resistor without changing the other, one input may be weighted more heavily than the other. Thus, by a suitable choice of resistors, the basic summing circuit could perform such operations as EOUT= -0.5 (E1 + 3E2 + 0.6E3). Subtraction is performed by inverting one input signal and then adding. Two very important mathematical operations are integration and differentiation. Integration is simply finding the area under a curve, while differentiation involves finding the slope of a curve at a given point. The op-amp integration circuit is shown in Fig. 6B, while the differentiation circuit is shown in Fig. 6C. The integrator also serves as a low-pass filter, while the differentiator also serves as a high-pass filter, both with 6 dB/octave slopes. The differentiator circuit's gain increases indefinitely with frequency, which obviously brings about high-frequency noise problems. The circuit cannot be used as shown. Fig. 6D shows a practical form of differentiator in which a gainlimiting resistor and some high-frequency compensation have been added to limit the high-frequency noise, yet still provide a good approximation to the derivative of the lower frequency inputs. These two circuits are very important in solving advanced problems, particularly mathematics involving differential equations. Since most of the laws of physics, electronics, thermodynamics, aerodynamics, and chemical reactions can be expressed in differential-equation form, the use of operation amplifiers for equation solution can be a very valuable and powerful analysis tool.

Fig. 7. Operational amplifiers in active network synthesis. (A) One form of active filter. (B) A twin-T network is identical to an LC parallel resonant circuit except for the "Q". (C) Circuit to realize "Q" of 14 without using an inductor.

Active Network Synthesis Perhaps the newest area in which operational amplifiers are beginning to find wide use is in active network synthesis. There is increasing pressure in industry to minimize the use of inductors. Inductors are big, heavy, expensive, and never obtained without some external field, significant resistance, and distributed capacitance. Worst of all, no one has yet found any practical way to stuff them into an integrated-circuit package. If we can find some circuit that obeys all the electrical laws of inductance without the necessity of a big coil of wire and a core, we have accomplished our purpose. Operational amplifiers are extensively used for this purpose. One basic scheme is shown in Fig. 7 A. If two networks are connected around an op amp as shown, the gain will equal the ratio of the transfer impedances of the two networks. Since we are using three-terminal networks, and since the op amp is capable of adding energy to the circuit, we can do many things with this circuit that are impossible with two-terminal passive resistors and capacitors. Fig. 7B shows an interesting three-terminal network called a twin-T circuit. It exhibits resonance in the same manner as an ordinary LC circuit does. It has one limitation - its maximum "Q" is only 1/4. If we combine an op amp with a parallel twin- T network, we can multiply the "Q" electronically to any reasonable level. A gain of 40 would bring the "Q" up to 10. We then have a resonant "RLC" circuit of controllable center frequency and bandwidth with no large, bulky inductors required even for low-frequency operation. One example is shown in Fig. 7C where an operational amplifier is used to realize a resonant effect and a "Q" of 14 at a frequency of 1400 Hz. As the desired "Q" increases, the tolerances on the components and the gain become more and more severe. From a practical standpoint, value of "Q" greater than 25 are very difficult to realize at the present time. Note that the entire circuit shown can be placed in a space much smaller than that occupied by the single inductor it replaces.

Fig. 6. Computer operational-amplifier circuits. (A) Addition. (B) Integration. (C) Differentiation. (D) Practical operational-amplifier differentiator.