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An Applications Guide for Op Amps. The general utility of the operational amplifier is derived from the fact that it is intended for use in a feedback loop whose feedback properties determine the feed-forward characteris- tics of the amplifier and loop combination. To suit it for this usage, the ideal operational amplifier would have infinite input impedance, zero output impedance, infinite gain and an open- loop 3 dB point at infinite frequency rolling off at 6 dB per octave.
Unfortunately, the unit cost—in quantity—would also be infinite. Intensive development of the operational amplifier, particu- larly in integrated form, has yielded circuits which are quite good engineering approximations of the ideal for finite cost.
Quantity prices for the best contemporary integrated ampli- fiers are low compared with transistor prices of five years ago. The low cost and high quality of these amplifiers allows the implementation of equipment and systems functions imprac- tical with discrete components. An example is the low fre- quency function generator which may use 15 to 20 opera- tional amplifiers in generation, wave shaping, triggering and phase-locking. The availability of the low-cost integrated amplifier makes it mandatory that systems and equipments engineers be famil- iar with operational amplifier applications.
This paper will present amplifier usages ranging from the simple unity-gain buffer to relatively complex generator and wave shaping cir- cuits. The general theory of operational amplifiers is not within the scope of this paper and many excellent references are available in the literature. The applications discussed will be arranged in order of in- creasing complexity in five categories: simple amplifiers, op- erational circuits, transducer amplifiers, wave shapers and generators, and power supplies.
The integrated amplifiers shown in the figures are for the most part internally compen- sated so frequency stabilization components are not shown; however, other amplifiers may be used to achieve greater operating speed in many circuits as will be shown in the text. Amplifier parameter definitions are contained in Appendix I. The Inverting Amplifier. The basic operational amplifier circuit is shown in Figure 1. The input impedance is equal to R1. The closed-loop bandwidth is equal to the unity- gain frequency divided by one plus the closed-loop gain.
The only cautions to be observed are that R3 should be cho- sen to be equal to the parallel combination of R1 and R2 to minimize the offset voltage error due to bias current and that there will be an offset voltage at the amplifier output equal to closed-loop gain times the offset voltage at the amplifier input.
For minimum error due to input bias current. Inverting Amplifier. Offset voltage at the input of an operational amplifier is com- prised of two components, these components are identified. The input offset voltage is fixed for a particular amplifier, however the contribution due to input bias current. For minimum. In this case the maximum offset voltage would be the algebraic sum of amplifier offset voltage and the voltage drop across the source resistance due to offset current.
Amplifier offset volt- age is the predominant error term for low source resistances and offset current causes the main error for high source re- sistances. In high source resistance applications, offset voltage at the amplifier output may be adjusted by adjusting the value of R3 and using the variation in voltage drop across it as an input offset voltage trim.
Offset voltage at the amplifier output is not as important in AC coupled applications. Here the only consideration is that any offset voltage at the output reduces the peak to peak linear output swing of the amplifier.
The gain-frequency characteristic of the amplifier and its feed- back network must be such that oscillation does not occur. Obviously the most critical case occurs when the attenuation of the feedback network is zero. Amplifiers which are not internally compensated may be used. As an example, the LM may. Since amplifier slew rate is dependent on compensation, the LM slew rate in the inverting unity gain connection will be twice that for the non-inverting con- nection and the inverting gain of ten connection will yield eleven times the slew rate of the non-inverting unity gain con- nection.
The compensation trade-off for a particular connec- tion is stability versus bandwidth, larger values of compensa- tion capacitor yield greater stability and lower bandwidth and vice versa. The preceding discussion of offset voltage, bias current and stability is applicable to most amplifier applications and will be referenced in later sections. A more complete treatment is contained in Reference 4. The Non-Inverting Amplifier. Figure 2 shows a high input impedance non-inverting circuit. This circuit gives a closed-loop gain equal to the ratio of the sum of R1 and R2 to R1 and a closed-loop 3 dB bandwidth equal to the amplifier unity-gain frequency divided by the closed-loop gain.
The primary differences between this connection and the in- verting circuit are that the output is not inverted and that the input impedance is very high and is equal to the differential input impedance multiplied by loop gain. In DC coupled applications, input impedance is not as important as input current and its voltage drop across the source resistance. Applications cautions are the same for this amplifier as for the inverting amplifier with one exception. The amplifier output will go into saturation if the input is allowed to float.
This may be important if the amplifier must be switched from source to source. The compensation trade off discussed for the invert- ing amplifier is also valid for this connection. Non-Inverting Amplifier. The Unity-Gain Buffer. The unity-gain buffer is shown in Figure 3. The circuit gives the highest input impedance of any operational amplifier cir- cuit. Input impedance is equal to the differential input impedance multiplied by the open-loop gain, in parallel with common mode input impedance.
The gain error of this circuit is equal to the reciprocal of the amplifier open-loop gain or to the common mode rejection, whichever is less. Unity Gain Buffer. Input impedance is a misleading concept in a DC coupled unity-gain buffer. Bias current for the amplifier will be supplied by the source resistance and will cause an error at the am- plifier input due to its voltage drop across the source resis- tance. Since this is the case, a low bias current amplifier such as the LH 6 should be chosen as a unity-gain buffer when working from high source resistances.
Bias current compen- sation techniques are discussed in Reference 5. The cautions to be observed in applying this circuit are three:. The LM may be used in this circuit with none of these problems; or, for faster operation, the LM may be chosen.
Summing Amplifier. The summing amplifier, a special case of the inverting ampli- fier, is shown in Figure 4. The circuit gives an inverted output which is equal to the weighted algebraic sum of all three in- puts.
The gain of any input of this circuit is equal to the ratio of the appropriate input resistor to the feedback resistor, R4. Amplifier bandwidth may be calculated as in the inverting am- plifier shown in Figure 1 by assuming the input resistor to be the parallel combination of R1, R2, and R3. Application cau- tions are the same as for the inverting amplifier.
If an uncom- pensated amplifier is used, compensation is calculated on the basis of this bandwidth as is discussed in the section describ- ing the simple inverting amplifier.
The advantage of this circuit is that there is no interaction be- tween inputs and operations such as summing and weighted averaging are implemented very easily.
The Difference Amplifier. The difference amplifier is the complement of the summing amplifier and allows the subtraction of two voltages or, as a special case, the cancellation of a signal common to the two inputs. This circuit is shown in Figure 5 and is useful as a computational amplifier, in making a differential to single-end- ed conversion or in rejecting a common mode signal. Difference Amplifier. Circuit bandwidth may be calculated in the same manner as for the inverting amplifier, but input impedance is somewhat more complicated.
Input impedance for the two inputs is not necessarily equal; inverting input impedance is the same as for the inverting amplifier of Figure 1 and the non-inverting input impedance is the sum of R3 and R4.
The general expression for gain is given in the figure. Compen- sation should be chosen on the basis of amplifier bandwidth. Care must be exercised in applying this circuit since input impedances are not equal for minimum bias current error.
The differentiator is shown in Figure 6 and, as the name im- plies, is used to perform the mathematical operation of differ-. The form shown is not the practical form, it is a true differentiator and is extremely susceptible to high frequency noise since AC gain increases at the rate of 6 dB per octave.
Practical Differentiator. A practical differentiator is shown in Figure 7. Here both the. R2 and C2 form a 6 dB per octave high frequency roll-off in the feedback network and R1C1 form a 6 dB per octave roll-off network in the input net-. In addition R1C1 and R2C2 form lead networks in the feed-. A gain fre- quency plot is shown in Figure 8 for clarity. Differentiator Frequency Response. The integrator is shown in Figure 9 and performs the mathe- matical operation of integration.
This circuit is essentially a. An amplitude-frequency plot is shown in Figure. For minimum offset error due to input bias current.
Integrator Frequency Response. The circuit must be provided with an external method of es- tablishing initial conditions. This is shown in the figure as S 1. When S 1 is in position 1, the amplifier is connected in unity- gain and capacitor C1 is discharged, setting an initial condi- tion of zero volts. When S 1 is in position 2, the amplifier is connected as an integrator and its output will change in ac- cordance with a constant times the time integral of the input voltage.
The cautions to be observed with this circuit are two: the am- plifier used should generally be stabilized for unity-gain op- eration and R2 must equal R1 for minimum error due to bias current.
Simple Low-pass Filter. The simple low-pass filter is shown in Figure This circuit has a 6 dB per octave roll-off after a closed-loop 3 dB point defined by f c. Gain below this corner frequency is defined by the ratio of R3 to R1.
An Applications Guide for Op Amps. The general utility of the operational amplifier is derived from the fact that it is intended for use in a feedback loop whose feedback properties determine the feed-forward characteris- tics of the amplifier and loop combination. To suit it for this usage, the ideal operational amplifier would have infinite input impedance, zero output impedance, infinite gain and an open- loop 3 dB point at infinite frequency rolling off at 6 dB per octave. Unfortunately, the unit cost—in quantity—would also be infinite.
December General Description. The LM series are complete general purpose operation-. The LM is guaranteed over a b 55 C to a C temper-. LM from 0 C to a 70 C. Y Offset voltage 3 mV maximum over temperature.
LM107 National Semiconductor, LM107 Datasheet