{"id":203,"date":"2018-11-29T04:31:30","date_gmt":"2018-11-29T04:31:30","guid":{"rendered":"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=203"},"modified":"2019-05-01T05:07:27","modified_gmt":"2019-05-01T05:07:27","slug":"applications-of-operational-amplifier","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/chapter\/applications-of-operational-amplifier\/","title":{"rendered":"Applications of Operational Amplifier"},"content":{"raw":"
\"epgp<\/a>\r\n<\/span><\/div>\r\n
\r\n\r\n\u00a0 \u00a0 Basic operational amplifier circuits used in Instrumentation<\/strong>\r\n\r\n \r\n\r\n \r\n

Op-Amps form the basic building block of various linear and non-linear analog systems. Op-Amps are used in various applications such as adder, subtractor, differentiator, integrator, comparator, zero crossing detector etc. which are discussed as follows:<\/p>\r\n \r\n\r\nAdder or Summing Amplifier<\/strong>\r\n\r\n \r\n

It is one of the most useful op-amp circuits used in analog computers. This circuit is used to add AC as well as DC signals. These are categorized as inverting summing amplifier or non-inverting summing amplifier depending on whether two or more inputs are connected at the inverting or non-inverting terminals respectively.<\/p>\r\n \r\n\r\nInverting configuration<\/em><\/strong>\r\n\r\n \r\n

The circuit diagram of inverting summing amplifier having three inputs Va, Vb and Vc is shown in figure 1. Rcomp is added to compensate for the input bias current.<\/p>\r\n \r\n\r\n\"\"\r\n

Figure 1: Circuit diagram of an inverting summing amplifier<\/p>\r\n \r\n

Writing the Kirchoff\u2019s current law at node V2, we have IA + IB + IC = IB2 + If. Using the concept of virtual ground, V1 = V2 = 0 which implies IB1 = IB2 = 0.<\/p>\r\n\r\n<\/div>\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n

Thus, the output voltage is proportional to or equal to the algebraic sum of two or more inputs with each multiplied by a constant gain factor. The negative implies that the op-amp is used in the inverting configuration. <\/span>Since, each input voltage is amplified by a different factor, the circuit is called a <\/span>scaling or<\/em> weighted amplifier.<\/em><\/p>\r\n \r\n

If RA = RB = RC = R, then equation (1) becomes<\/span><\/p>\r\n\"\"\r\n

<\/div>\r\n
This implies that the output voltage is equal to the sum of the input voltages times the gain of the circuit which is (Rf\/R). The circuit in this condition can be used to design an averaging amplifier if the ratio of Rf and R is equal to 1 divided by the number of inputs (Rf\/R) = (1\/n). In this case, the number of inputs is 3.<\/span><\/div>\r\n
\r\n\r\n\"\"\r\n\r\n \r\n\r\nwhich is the expression for Averaging amplifier<\/em>.\r\n\r\n \r\n\r\nIf R=Rf i.e the gain of the circuit is 1, ?? = \u2212 (?? + ?? + ?? )<\/span>\r\n\r\n \r\n\r\ni.e.\u00a0 Vo is negative of <\/span>sum of input voltages and works as a <\/span>summing amplifier<\/em>.<\/span>\r\n\r\n \r\n

These circuits are commonly used in analog computers and audio mixers in which the number of inputs are added or mixed to produce the desired output.<\/span><\/p>\r\n \r\n

Non-inverting configuration<\/em><\/strong><\/p>\r\n \r\n

In the non-inverting configuration, two or more voltages to be added are applied at the non-inverting input terminal of <\/span>op-amp. The circuit diagram for <\/span>an summing amplifier in <\/span>non-inverting configuration is shown in figure 2. As for the case of inverting amplifier, for special values of RA, RB <\/span>and RC, the circuit will work as an averaging amplifier and summing amplifier.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n

Figure 2: Circuit diagram of an non-inverting summing amplifier<\/p>\r\n \r\n

For values of RA=RB=RC=(R\/2), the voltage V1 at the non-inverting terminal can be obtained using the superposition theorem as<\/p>\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n

Thus, it can be inferred from equation (3) that the output voltage Vo is equal to average of all input voltages times the gain of the circuit (which can adjusted by varying the values if Rf and R1). Hence, the circuit works like an averaging amplifier<\/em>. It can be noted that in contrast to the inverting configuration, here, no sign change or phase reversal is observed between voltages at the input and output.<\/p>\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\nSubtractor<\/strong>\r\n\r\n \r\n

Since, a differential amplifier amplifies the difference between the two inputs applied to the inverting and non-inverting terminals in an op-amp, hence it can be used as a subtractor. The circuit of op-amp as a subtractor is shown in figure 3. The input signals can be scaled to the desired values by selecting appropriate values for the external resistors.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n

Figure 3: Op-amp as a subtractor<\/p>\r\n \r\n

In order to establish a relation between inputs and output, the superposition theorem is used. Let Va = 0 at first and we will calculate the output voltage due to input Vb alone (V0b).<\/p>\r\n \r\n

When Va =0, the circuit is a non-inverting amplifier having a voltage divider network composed of resistors R1 and R2 at the non-inverting terminal. Therefore, voltage at the non-inverting terminal (v1) is<\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n

Hence, the output voltage, V0 is equal to the voltage at the non-inverting input (Vb) minus the voltage at the inverting input (Va). Hence, the circuit works like a subtractor.<\/p>\r\n \r\n\r\nDifferentiator<\/strong>\r\n\r\n \r\n

The differentiator as the name implies perform the mathematical operation of differentiation which means that the output obtained from a differentiator is the derivative of the input signal. The circuit of a differentiator is given in figure 4. It may be noted that the circuit is similar to that of an inverting amplifier except the fact that the resistance at the inverting terminal (R1) is replaced by a capacitor (C1) in series with input signal. The capacitor provides a low impedance path to the ac signal and does not allow the dc signal to pass through. Therefore, if a dc voltage is applied to the input, the output of the differentiator is zero.<\/p>\r\n \r\n\r\nOutput voltage of the differentiator can be obtained by writing Kirchoff\u2019s current equation at node v2.\r\n\r\n\"\"\r\n\r\n<\/div>\r\n

Figure 4: Circuit diagram of a differentiator<\/span><\/p>\r\n\r\n

\r\n\r\n \r\n

Thus, the output voltage ( ) is proportional to the rate of change of input signal where the constant of proportionality is given by \u2212 \u00a01. The negative sign in equation (12) implies that the differentiated output is 180\u00b0 out of phase with the input. Thus, if a sine function is applied to the input of differentiator, the output will be cosine function with phase reversal. Similarly, a triangular input will produce a square wave output and a square input will produce alternating direction voltage spikes. The spiked output for square wave input is because of the fact that the input takes a finite time to rise from zero to a constant value. The input and output waveforms for the output of a differentiator are shown in figure 5.<\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n

Figure 5: Output waveforms of a differentiator when the input is (a) sine wave and (b) square wave<\/p>\r\n \r\n\r\nIt is important to point out that the differentiator circuit as shown in figure 4 does not produce the expected waveforms due to certain limitations.\r\n\r\n\"\"\r\n\r\n<\/div>\r\n \r\n

\r\n
<\/div>\r\n
<\/div>\r\n

(where, \u00a01 is the input impedance). It may be seen from the above equation that the gain of differentiator circuit increases linearly with frequency as shown in figure 6. This makes the circuit unstable. Secondly, \u00a01 decreases with an increase in frequency, so at higher frequencies, the circuit is highly susceptible to noise which may cause distortion in the output. The circuit in figure 4 is referred to as the basic differentiator circuit.<\/p>\r\n \r\n\r\nFigure 6: Variation of gain of differentiator with frequency\r\n\r\n \r\n

Let fa is the frequency at which the gain is 1 (0 dB). The value of fa can be calculated by transforming the circuit into the s-domain i.e. in figure 4, Vin and Vo are functions of S, Vin(S) and Vo(S) respectively and C1 is replaced by 1\/sC1.<\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\nThe problems of high frequency noise and stability can be overcome by adding two more components R1 and Cf as shown in figure 7. The circuit is referred to as the practical differentiator circuit due to its utility in practical applications.\r\n\r\n\"\"\r\n\r\n \r\n

Figure 7: Circuit of a basic differentiator circuit<\/p>\r\n \r\n

The frequency response of a practical differentiator is shown in figure 6 by a dashed line. For low frequencies, ??1 and ??? will be very high, therefore, (?? || ?? \u2248 ??), and the circuit reduces to that of a basic differentiator. Thus, the gain of the circuit increases linearly with frequency as for the basic differentiator for low frequencies. At high frequencies, ??1 and ??? will be low, thus, C1 will behave effectively as a short ckt and (?? || ?? \u2248 ??).<\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n

This implies that gain of the practical differentiator circuit decreases with increase in frequency at high frequencies.<\/p>\r\n \r\n

The frequency fb is called the gain limiting frequency and corresponds to the frequency at which the gain of the differentiator circuit is maximum. The value of fb can be calculated by transforming the circuit of figure 7 to the s-domain as discussed earlier.<\/p>\r\n\r\n<\/div>\r\n\"\"\r\n

\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n

The frequency fb at which the gain of the practical differentiator circuit starts decreasing with frequency (Figure 6) can be obtained by equating the denominator to zero. Therefore,<\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n

Thus, addition of R1 and Cf in the basic differentiator circuit reduces the problem of stability by preventing the increase in gain with frequency. Also, it significantly eliminates the effect of high frequency noise etc.<\/p>\r\n \r\n\r\nIn practical circuits, the value of fb and in turn, R1C1 and RfCf should be selected in such a way that\r\n\r\nfa<\/sub> < fb<\/sub> < fc\u00a0<\/sub>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (17)\r\n\r\n \r\n

where, fa and fb are as discussed earlier and fc is the unity gain bandwidth of the op-amp. For proper differentiation of the input signal, the time period T should be larger than or equal to RfC1 i.e.<\/p>\r\nT \u2265 Rf<\/sub>C1<\/sub>\r\n\r\n \r\n

Differentiator circuit is basically a high pass circuit. It is commonly used in waveshaping circuits to detect high frequency components in an input signal and rate of change detectors in FM modulators.<\/p>\r\n \r\n\r\nIntegrator<\/strong>\r\n\r\n \r\n

An integrator is a circuit that performs the mathematical operation of integration i.e. the output signal is the integral of the corresponding input signal. The circuit of an integrator is same as that of an inverting amplifier except the fact that the feedback resistor (Rf) is replaced by a capacitor Cf. The circuit of an integrator is shown in figure 8.<\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n

Figure 8: Circuit diagram of an integrator using op-amp<\/p>\r\n \r\n

In order to derive an expression for the output voltage of an integrator, Kirchoff\u2019s current equation is written at node v2 as ?1<\/sub> = ??2<\/sub> + ??<\/sub><\/p>\r\n\r\n<\/div>\r\nSince node v2 is at virtual ground, therefore ??2<\/sub> = 0, and ?1<\/sub> = ??<\/sub>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(18)\r\n

\r\n\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\nWhere, C is the constant of integration and is proportional to the value of the output voltage 0 at time t=0.\r\n\r\n \r\n

The above eqn. indicates that the output voltage is equal to the negative of the integral of the input signal with a scaling factor of (\u22121?1??).. Thus, the circuit works like an integrator. When a sinusoidal input is\u00a0applied to an integrator, the output will be cosine wave; for a square wave input, the output will be a triangular wave. The output waveforms for triangular and square inputs are shown in figure 9 where ?1<\/sub>??<\/sub> = 1 and C =0 in eqn. (19).<\/p>\r\n\r\n<\/div>\r\n\"\"\r\n\r\n \r\n

\r\n

Figure 9: Output waveforms of an integrator when the input is (a) triangular wave and (b) square wave<\/p>\r\n\"\"\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n\r\n \r\n\r\nin frequency. The frequency response of the basic integrator circuit is shown in figure 10.\r\n\r\n \r\n\r\nFigure 10: Frequency response of the basic integrator circuit\r\n

Let fb is the frequency at which the gain is 1 (0 dB). The value of fb can be calculated by transforming the circuit into the s-domain i.e. in figure 8, Vin and Vo are functions of S, Vin(S) and Vo(S) respectively and Cf is replaced by 1\/sCf.<\/p>\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n

Let us consider the circuit of a basic integrator when Vin=0. When there is no input signal, means zero frequency. In that case, capacitor Cf will offer infinite impedance (\u00a0\u00a0 = \u221e) and will work like an open circuit. The op-amp circuit behaves like an open\u2013loop amplifier. So, any offset voltage present at the inputs or the input current charging capacitor Cf will produce an error voltage at the output of integrator.\u00a0This limits the use of the above circuit in practical applications. Thus, in <\/span>practical integrator, in order to reduce the error voltage at the output, the circuit is modified by adding an extra resistor Rf in parallel to Cf as shown in figure 11.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n

Figure 11: Circuit diagram of a practical integrator<\/p>\r\n \r\n

Here, RF limits the gain at low frequencies and minimizes any spurious variations in output signal. Also, in a basic integrator, gain is not constant over any frequency range, leading to instability. The practical integrator circuit overcomes both the problems of stability and low-frequency roll-off (rate of decrease in gain at lower frequencies) in basic integrator. The frequency response of a practical integrator is shown in figure 10. At low frequencies, impedance offered by capacitor, Cf<\/sub>(???<\/sub>) will be very high. So, net impedance of the feedback circuit (??<\/sub> || ??<\/sub> \u2248 ??<\/sub> ). Therefore, the circuit will behave like an inverting amplifier with a constant gain. At higher frequencies, Cf offers a low impedance path i.e. (??<\/sub> || ??<\/sub>\u2248 ??<\/sub>)\u00a0and the gain decreases with frequency as in a basic integrator. If fa is the frequency <\/span>upto which gain is constant or gain limiting frequency, then <\/span>upto fa, the circuit works like inverting amplifier and for frequencies <\/span>f lying between fa and <\/span>fb (fa<\/sub> < f < <\/span>fb), the circuit acts <\/span>like an integrator. For calculation of <\/span>fb, the circuit of <\/span>practical integrator is transformed into s-domain as discussed earlier in this module. Here,<\/span><\/p>\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n

Generally, the value of fa (in turn R1C1 and R1Cf) should be selected in such a way that fa < fb. The input signal will be integrated properly is the time period T of the signal is larger than or equal to RfCf i.e.<\/p>\r\n

T \u2265 <\/span>RfCf\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(23)<\/span><\/p>\r\n \r\n

The ability of an op-amp to integrate a given signal makes it possible to solve differential equations. Integrators are widely used in ramp or sweep generators, in filters, analog computers, signal waveshaping circuits etc.<\/p>\r\n \r\n\r\nComparator<\/strong>\r\n\r\n \r\n

A comparator, as the name implies, compares the input signal applied at one of its inputs to that applied on other input which is called the reference signal. In this application, op-amp works in the open-loop configuration having two inputs and <\/span>a output. If the signal on inverting input is greater than that of the non-inverting input, <\/span>differential input voltage (Vid) will be negative, therefore, op-amp will go to negative saturation. On the other hand, if the input on the non-inverting terminal is greater than that on the inverting terminal, Vid will be positive resulting in positive saturation. Therefore, any given signal can be compared with <\/span>reference signal with the help of a comparator. <\/span>Comparator can be inverting or non-inverting depending on whether the signal to be compared is applied at the inverting or non-inverting terminal. The circuit diagram of a non-inverting comparator is shown in figure 11.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n

Figure 11: Circuit of a non-inverting comparator<\/p>\r\n \r\n

The fixed reference voltage (Vref) is applied to the non-inverting terminal. Let us say Vref = 1V. The ac signal to be compared is applied to the non-inverting terminal, hence the name non-inverting comparator. Diodes D1 and D2 are connected to protect the op-amp from damage due to excessive voltage across the differential inputs. In some cases, the op-amps have an in-built protection and thus, the diodes are not required. Resistor R is connected in order to limit the current through the diodes D1 and D2. When Vin in greater than Vref, the output (Vo) goes to +Vsat and when Vin is less than Vref, the output goes to \u2013Vsat. Thus, the output voltage switches from one saturation level to another whenever, Vin = Vref. A comparator converts an analog signal to digital signal. The input and output waveforms for non-inverting comparator with Vref positive and negative are shown in figure 12.<\/p>\r\n\"\"\r\n\r\n \r\n

Figure 12: Input and output waveforms for a non-inverting comparator with Vref (a) positive and (b)\r\nnegative<\/p>\r\n \r\n

Inverting comparator works in the similar way with Vref at the non-inverting signal and input signmal at the inverting terminal. The input and output waveforms for inverting comparator are shown in figure 13.<\/p>\r\n\r\n<\/div>\r\nFigure 13: Input and output waveforms for an inverting comparator with Vref (a) positive and (b) negative\r\n\r\n \r\n\r\nZero crossing detector<\/strong>\r\n\r\n \r\n

A comparator can work as a zero crossing detector provided that Vref is set to zero volts. Figure 14 shows the circuit of an inverting comparator used as zero crossing detector.<\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n

Figure 14: Circuit of an inverting comparator as zero crossing detector<\/p>\r\n \r\n\r\nThe corresponding input and output waveforms are shown in figure 15.\r\n\r\n\"\"\r\n\r\n \r\n

Figure 15: Input and output waveforms of a zero crossing detector<\/p>\r\n \r\n

The output shows that the zero crossing detector is basically a sine to square wave convertor. Output Vo is driven to negative saturation when the input sugnal crosses zero in the positive direction and it is driven to positive saturation when the input signal crosses zero in the negative direction. Thus, it may be easily inferred that in which direction does the input signal crosses zero volts. A non-inverting comparator works as a zero crossing detector in the similar way except the fact that the input and output waveforms are in the same phase.<\/p>\r\n\r\n\r\n\r\n
you can view video on Applications of Operational Amplifier<\/strong><\/td>\r\n\"\"<\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\nReferences:<\/strong>\r\n