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Opamps (operational amplifiers) are a particular class of integrated circuit comprising a directlycoupled highgain amplifier with overall response characteristics controlled by feedback. The opamp gets its name from the fact that it can be made to perform numerous mathematical operations. An opamp is the basic building block in many analog systems and is also known as a linear integrated circuit because of its response.
It has an extremely high gain (theoretically approaching infinity), the actual value of which can be set by the feedback. The introduction of capacitors or inductors in the feedback network can give gain varying with frequency and thus determine the operating condition of the whole integrated circuit. The basic opamp is a threeterminal device with two inputs and one outputFig. 1. The input terminals are described as "inverting" and "noninverting." At the input there is a virtual "short circuit," although the feedback keeps the voltage across these points at zero so that no current flows across the "short." The simple circuit equivalent is also shown in Fig. 1, when the voltage gain is given by a ratio of the impedances Z2/Z1. OPAMP PARAMETERS The ideal opamp is perfectly balanced so that if fed with equal inputs, output is zero, i.e. VIN 1 = VIN 2 gives VOUT = 0 In a practical opamp the input is not perfectly balanced so that unequal bias currents flow through the input terminal. Thus an in put offset voltage must be applied between the two input terminals to balance the amplifier output. The input bias current (IB) is one half the sum of the separate currents entering the two input terminals when the output is balanced, i.e., V_OUT = 0. It is usually a small value, e.g., a typical value is 1B = 100 nA. The input offset current (I_io) is the difference between the separate currents entering the input terminals. Again it is usually of a very small order, e.g., a typical value is I_io = 10 nA. The input offset voltage V_io is a voltage which must be applied across the input terminal, to balance the amplifier. Typical value, V_io = 1 mV. Both I_io and V_io. are subject to change with temperature, this change being known as I_Iio drift and V_io. drift, respectively. The Power Supply Rejection Ratio (PSRR) is the ratio of the change in input offset voltage to the corresponding change in one power supply voltage. Typically this is of the order of 10 20 µV /V. Other parameters which may be quoted for opamps are: Openloop gainusually designated A_d. Commonmode rejection ratiodesignated CMRR. This is the ratio of the difference signal to the commonmode signal and represents a figure of merit for a differential amplifier. This ratio is expressed in decibels (dB). Slew rateor the rate of change of amplifier output voltage under largesignal conditions. It is expressed in terms of V/uS. Some examples of the versatility of the opamp are given in the following simple circuits:
AMPLIFIER OR BUFFER Figure 2 shows the circuit for an inverting amplifier, or inverter. The gain is equal to: Av = R2/R1 Notice that if the two resistances are equal (i.e., R1 = R2), the gain is negative one, meaning that the circuit works as a phase inverting voltage follower. The output will be the same as the input, except the polarity will be reversed. In fact, for unity gain, the resistors can be eliminated and re placed with direct connections, as illustrated in Fig. 3. This works because in this circuit R1 = R2 = 0. R3 is usually eliminated in the inverting voltage follower circuit. If R1 is smaller than R2, the input signal will be amplified at the output. For example, if R1 is 2.2 KO and R1 is 22 Ko, the gain will be: Av = 22,000/2,200 =10 The minus sign indicates phase inversion. The output polarity is reversed from the input. The same circuit can also attenuate (reduce the level of) the input signal by making R1 larger than R2. For example, if R1 is 120 Ko, and R2 is 47 KO, the circuit gain will be approximately: Av = 47,000/120,000 = 0.4
Once again, the output's polarity is the opposite of the input's polarity. The value of R3 is not terribly critical, but it should be approximately equal to the parallel combination of R1 and R2. That is: R3 = (R1 x R2)/(R1 + R2) To illustrate this, let's return to our earlier example, in which R1 = 2.2 KO and R2 = 22 KO. In this case, the value of R3 should be about: R3 = (2200 x 22000)/(2200 + 22000) = 48,400,000/24,200 = 2000 ohm Since the exact value is not critical, we can use the nearest standard resistance value for R3. In this example, either a 1.8 KO or a 2.2 Ko resistor may be used. In some applications, the phase inversion produced by the circuit shown in Fig. 2 may be undesirable. To have the opamp work as a noninverting amplifier (buffer), the connections are made as shown in Fig. 4. In this circuit, the gain is defined as: Av = 1 + R2/R1 The output is in phase (same polarity) with the input. Notice that the gain must always be at least 1 (unity). The noninverting circuit can not be used for signal attenuation. If R2 is considerably larger than R1, the gain will be relatively large. […] gain works out to: Av = 1 + 470,000/10,000 = 1 + 47 = 48 If, on the other hand, R1 is considerably larger than R2, the gain will be just slightly greater than unity. For instance, if R1 = 100 K ohm and R2 = 22 KO the gain will be: Av = 1 + 22,000/100,000 = 1 + 0.22 = 1.22 If the two resistances are equal (R1 = R2), the gain will al ways be 2. Try a few examples using the gain equation to prove this to yourself. A special case is when both resistances are made equal to 0. That is, the resistors are replaced by direct connections, as shown in Fig. 5. Here, the gain is exactly unity. This is in keeping with the gain formula: Av = 1 + R2/R1 = 1 + 0/0 = 1 + 0 = 1 The output is identical to the input. This noninverting volt age follower circuit is used for buffer, isolation, and impedance matching applications.
ADDER An opamp can be used to add multiple input voltages. Input signals V1, V2, . .. Vn are applied to the opamp through resistors R1, R2, . .. Rn, as shown in Fig. 6. The output signal is then a combination of these signals, giving the sum of the inputs. The actual performance of the opamp as an adder can be calculated with this formula: VOUT = Ro ((V1/R1) + (V2/R2) . . . + (Vn/Rn)) Note the minus sign. This indicates that the output is inverted (the polarity is reversed). That is, this circuit is an inverting adder. By changing the connections to the inverting and noninverting inputs of the opamp, as shown in Fig. 7, the circuit can be converted to a noninverting adder. If all of the input resistors have equal values, the output equation can be simplified to: VOUT = Ro ((V1 + V2 . . . + Vn)/R) DIFFERENTIAL AMPLIFIER A basic circuit for a differential amplifier is shown in Fig. 8. Component values are chosen so that R1 = R2 and R3 = R4. Performance is then given by: V_OUT = V_IN 2 V_IN 1 Provided the opamp used can accept the fact that the impedance for input 1 and input 2 is different (impedance for input 1 = R1; and impedance for input 2 = R1 + R3). ADDER/SUBTRACTOR
Connections for an adder/subtractor circuit are shown in Fig. 9. If R1 and R2 are the same value; and R3 and R4 are also made the same value as each other, then: V_OUT = V3 + V4 V1 V2 In other words, inputs to V3 and V4 give a summed output (V_out = V3 + V4). Inputs V1 and V2 subtract from the output voltage. Values for R1, R2, and R3 and R4 are chosen to suit the opamp characteristics. R5 should be the same value as R3 and R4; and R6 should be the same value as R1 and R2.
MULTIPLIER The circuit shown in Fig. 10 can be used to perform simple multiplication. Note that this is the same circuit as Fig. 2. For accurate results, precision resistors of the specified values for R1 and R2 should be used to give a constant gain (and thus multiplication of input voltage in the ratio R2/R1). Note that this circuit inverts the phase of the output. The output voltage will be equal to: VOUT = (VIN x Av) ...where VOUT is the output voltage, VIN is the input voltage, and Av is the gain as defined by R1 and R2. If a variable resistance (potentiometer) is used for R2, as shown in Fig. 11, the multiplication constant can be varied. A calibration dial with markings for various typical gains should be placed around the control shaft. This dial can be calibrated to read out the multiplication constant directly. INTEGRATOR Theoretically, at least, an opamp will work as an integrator with the inverting input connected to the output via a capacitor. In practice, a resistor needs to be paralleled across this capacitor to pro vide de stability as shown in Fig. 12. This circuit integrates input signal with the following relation ship applying: VOUT R1 1 C J VIN dt * The value of R2 should be chosen to match the opamp characteristics so that: VOUT = R2 VIN R1
DIFFERENTIATOR The differentiator circuit has a capacitor in the input line connecting to the inverting input, and a resistor connecting this input to output. Again this circuit has practical limitations, so a better configuration is to parallel the resistor with a capacitor as shown in Fig. 13. The performance of this circuit is given by: VOUT = R2 C1 dVIN dt LOG AMPLIFIERS The basic circuit (Fig. 14) uses an NPN transistor in conjunction with an opamp to produce an output proportional to the log of the input: VOUT =k log 10 VIN RI. The lower diagram shows the "inverted" circuit, this time using a PNP transistor, to work as a basic antilog amplifier. The capacitor required is usually of small value (e.g., 20 pF). LOG MULTIPLIERS
Logarithmic working of an opamp is extended in Fig. 15 to give a log multiplier. Input X to one log amplifier gives log X out put; and input Y to the second log amplifier gives log Y output. These are fed as inputs to a third opamp to give an output log X Y. If this output is fed to an antilog amplifier, the output is the inverted product of X and Y (i.e., X. Y). LOG DIVIDER The circuit shown in Fig. 16 is just the opposite of the one in Fig. 15. Here log and antilog amp stages are used to perform division on the two input signals. The output is proportional to x/y. AUDIO AMP The opamp is primarily a dc amplifier, but it can also be used for ac applications. Figure 317 shows a simple audio amplifier. More audio amplifier circuits will be presented in Section 4. MIXER This circuit (Fig. 18) is a variation on the audio amplifier. Note the similarity to the adder circuit shown in Fig. 6. The various input signals are combined, or mixed. The level of each input signal can be adjusted via its input potentiometer. This allows the user to control the relative proportions of the various input signals in the output. SIGNAL SPLITTER The signal splitter circuit shown in Fig. 19 is just the reverse of a mixer. A single output signal is split off into multiple identical outputs to feed different inputs. This circuit is used to isolate the various signal paths from each other. Each output line has its own individual potentiometer to set the desired level. VOLTAGETOCURRENT CONVERTER The circuit configuration shown in Fig. 20 will result in the same current flowing through R1 and the load impedance R2, the value of this current being independent of the load and proportional to the signal voltage, although it will be of relatively low value be cause of the high input resistance presented by the noninverting terminal. The value of this current is directly proportional to VIN/R1.
CURRENTTOVOLTAGE CONVERTER This configuration (Fig. 21) enables the input signal current to flow directly through the feedback resistor R2 when the output voltage is equal to IIN x R2. In other words, input current is converted into a proportional output voltage. No current flows through R2, the lower limit of current flow being established by the bias circuit generated at the inverting input. A capacitor may be added to this circuit, as shown in the dia gram, to reduce "noise." CURRENT SOURCE Use of an opamp as a current source is shown in Fig. 22. Resistor values are selected as follows: R1 = R2 R3 = R4 + R5 Current output is given by: IOUT R3 VIN R1 R5
MULTIVIBRATOR An opamp can be made to work as a multivibrator. Two basic circuits are shown in Fig. 23. The one on the top left is a free running (astable) multivibrator, the frequency of which is determined by: f 1 2C R1 loge 2R3 + 1 R2 The lower right hand diagram shows a monostable multivibrator circuit which can be triggered by a square wave pulse input. Component values given are for a CA741 opamp. See also separate section on "Multivibrators."
SQUARE WAVE GENERATOR A practical square wave generator circuit built around an opamp is shown in Fig. 24. This is perhaps the simplest possible square wave generator circuit. Besides the opamp itself, only three external resistors and a single capacitor are required. Resistor R1 and capacitor C1 are the primary components in defining the time constant (output frequency) of the circuit. But the output frequency is also affected by the positive feedback network made up of R2 and R3. The general equations are rather complex, but they can be simplified for specific R3/R2 ratios. For instance: or: If R3/R2 = 1.0 then F ... 0.5/(R1/C1) If R3/R2 . 10 then F . 5/(R1/C1) For most applications, the most practical approach is to use one of these standard ratios, and adjust the values of R1 and C1 to generate the desired frequency. Standardized values can be used for R2 and R3. For example, if R2 = 10K and R3 = 100K, the R3/R2 ratio will be 10, so: F = 5/(R1/C1) Generally, we will know the desired frequency and will need to select the appropriate component values. The easiest approach is to first select a likely value for C1, and then rearrange the equation to solve for the value of R1: R1 = 5/(FC1) Let's try a typical example. We want to generate a 1200 Hz square wave signal. If we use a 0.22 µF capacitor for C1, the value of R1 should be: R1 = 5/(1200 x 0.00000022) = 5/0.000264 = 18,940 it For most applications, a standard 18K resistor could be used. This circuit can be made even more useful and versatile by adding a potentiometer in series with R1, as shown in Fig. 25. This allows the output frequency to be manually changed. The same equations are used for this circuit, except the value of R1 is equal to the series combination of fixed resistor R1a, and the adjusted value of potentiometer R1b; R1 = R1a + R1b The fixed resistor is included to prevent the value of R1 from ever becoming zero. The fixed value of R1a and the maximum resistance of R 1b sets the range of output frequencies. VARIABLE PULSE WIDTH GENERATOR A square wave is perfectly symmetrical. That is, it is in its high state for exactly one half of each cycle, as illustrated in Fig. 26. The ratio of the high level time to the total cycle time is called the duty cycle of the signal. The duty cycle of a square wave is, by definition, 1:2. Closely related to square waves are rectangle waves and pulse waves. These waveforms also switch between a high and a low state, but have different duty cycles. The terms "rectangle wave" and "pulse wave" are used somewhat interchangeably, although usually, a pulse wave is considered to have a relatively short high level time. Figure 27 shows a rectangle wave with a duty cycle of 1:3. The output level is high for one third of each cycle. The rectangle wave illustrated in Fig. 28 has a duty cycle of 1:4. We can convert the squarewave generator described in the preceding section into a rectangle wave generator by adding just two components. The revised circuit is shown in Fig. 29. On negative halfcycles, diode D1 blocks flow of current through R4. The time constant is comprised of R1 and C1: T1 = 5/(2C1 R1)
On positive halfcycles, however, the diode conducts and the time constant is defined by C1 and the parallel combination of R1 and R4: T2 = 5/(201 ((R1 R4)/(R1 + R4))) The length of the total cycle is simply the sum of the two halfcycle time constants: Tt = T1 + T2 The output frequency is the reciprocal of the total time constant of the complete cycle: F = 1/Tt
Since the time constant will be different for the high and low level portions of the cycle, the duty cycle will be something other than 1:2. The output waveform becomes asymmetrical. Either R1 or R4, or both, may be made variable, but bear in mind that changing either of these resistances affects both the out put frequency and the duty cycle. SINE WAVE OSCILLATOR The simplest of all ac signals is the sine wave, which is illustrated in Fig. 30. This is a very pure signal with no harmonic con tent at all. A sine wave consists of only a single fundamental frequency. Actually, it is quite difficult to generate a truly pure, distortion free, sine wave. Fortunately, we can come close to the ideal with an oscillator circuit built around an opamp. A typical sine wave oscillator circuit using an opamp is shown in Fig. 31. The feedback network is a twinT circuit, which functions as a bandreject (or notch) Filter. Resistors R1 and R2 along with capacitor C1 form one T. The other T is made up of C2, C3, R3, and R4. It is upside down in the schematic. For this circuit to function properly, the component values must have the following relationships: R2 = R1 R3 = R1/4 R4 = R1/2 (approximate) C1 = 2C2 C3 = C2 The output frequency is determined by this formula: F = 1/(6.28 R1 C2)
The twinT feedback network is detuned slightly by adjusting the value of R4. This will usually be a miniature trimmer potentiometer. The potentiometer is set for its maximum resistance, then slowly decreased, until the circuit just begins to break into oscillation. If the resistance is set low, the sine wave will be distorted at the output.
SCHMITT TRIGGER A Schmitt trigger is known technically as a regenerative comparator. Its main use is to convert a slowly varying input voltage into an output signal at a precise value of input voltage. In other words it acts as a voltage "trigger" with a "backlash" feature, called hysteresis. The opamp is a simple basis for a Schmitt trigger (see Fig. 32). The triggering or trip voltage is determined by: V trip VOUT R1 R1 + R2 The hysteresis of such a circuit is twice the trip voltage. Another Schmitt trigger circuit is shown in Fig. 33, the triggering point being approximately onefifth of the supply voltage, i.e., there is a "triggered" output once the dc input reaches onefifth the value of the supply voltage. The supply voltage can range from 6 to 15 volts, thus the trigger can be made to work at any thing from 1.2 to 3 volts, depending on the supply voltage used. The actual triggering point can also be adjusted by using different values for R4, if required.
Once triggered, the output will be equal to that of the supply voltage. If output is connected to a filament bulb or LED (with bal last resistor in series), the bulb (or LED) will light once the input voltage has risen to the triggering voltage and thus indicate that this specific voltage level has been reached at the input.
CAPACITANCE BOOSTER The circuit shown in Fig. 34 works as a multiplier for the capacitor C1, i.e., associated with a fixed value of C1 it gives an effective capacitance Ce which can be many times greater. The actual multiplication ratio is R 1/R2 so that making R1 ten times greater than R2, say, means that the effective capacitance of this circuit would be 10 x C1. As far as utilization of such a multiplier is concerned, the circuit now also contains resistance (R2) in series with the effective capacitance. FILTERS Opamps are widely used as basic components in filter circuits. Two basic circuits are shown in Fig. 35. (See also separate section on Filters.)

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