# Op Amp Circuits. Inverting and Non-inverting Amplifiers, Integrator, Differentiator

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1 M.B. Patil, IIT Bombay 1 Op Amp ircuits Inverting and Non-inverting Amplifiers, Integrator, Differentiator Introduction An Operational Amplifier (Op Amp) is a versatile building block used in a variety of applications in electronics. Op amps make circuit design simple and robust. An op amp chip has a complex internal circuit (see Fig. 1), but from the user s perspective, it can be treated by a simple equivalent circuit, making the design process very simple and straightforward, as compared to using discrete transistors. Actual ircuit V Q12 Q9 Q8 Q Q1 Q3 Q4 Q2 1 Q19 Q18 Q15 Q Q14 Q2 OUT Symbol V V EE OUT Q7 Q16 Q23 Q11 4 Q1 Q5 1 Q Q17 8 Q22 Q24 V EE offset adjust Figure 1: Internal circuit of Op Amp 741 Power supply Fig. 2 shows the most commonly used configuration for providing power supply to an op amp. The +V and V terminals of the op amp are connected to +V and V where V is typically 1 to 15V. For example, the +V terminal may be connected to +15V, and the V terminal to 15V. The voltages +15V and 15V here are with respect to the ground of the power supply which we will use in the lab. Note that the Op Amp 741 (see Fig. 1) does not have a ground terminal of its own.

2 M.B. Patil, IIT Bombay 2 In op amp circuit diagrams, the ±V connections are often not shown explicitly, but we must always remember that an op amp circuit will not work if the power supply is not provided. While testing the circuit, it is a good idea to first check whether the ±V terminals of the op amp are indeed getting ±V. non inverting input inverting input V V EE output V V Linear and saturation regions Figure 2: onnecting power supply to an op amp An op amp exhibits a very large gain (of the order of 1 5 ) A V =, where =V + V. The maxmimum and minimum values of are limited to ±V sat (the saturation voltage), where V sat is about 1V smaller than V. As an example, consider V sat =1V (see Fig. 3(a)). When saturation linear saturation 1 (a) V sat 1 (b) Vo (V) 5 Vo (V) 5 saturation linear 5 1 slope=a V V sat 5 1 saturation (mv) (V) Figure 3: Typical versus =V + V relationship for an op amp: (a)expanded scale, (b)compressed scale. > 1V 1 =.1mV, =1V. Similarly, when V 5 i < 1V 1 =.1mV, = 1V. These two 5 regions are referred to as saturation. For an input voltage between these two limits, i.e.,.1mv < <.1mV, changes linearly with, and this region is referred to as the linear region. The exact values of these limits will of course change with V sat and the gain A V of the op amp, but it is clear that the linear region is very narrow indeed. When the versus

3 M.B. Patil, IIT Bombay 3 relationship is plotted on comparable scales, the linear region appears as a vertical line (see Fig. 3(b)). In other words, when the op amp operates in the linear region, we can say that V + V V, i.e., V + V. Input resistance From Fig. 1, we see that the current entering the inverting or the non-inverting terminal of the op amp is a base current of a BJT (or the gate current of an FET for op amps with FET input devices), which is generally small much smaller than the other currents in the external circuit. To an excellent approximation, therefore, we can say that the input currents of the op amp can be neglected or that the op amp has an infinite input resistance. To summarise, we can make the following assumptions for an op amp operating in the linear region. (a) V + V or V + and V are virtually the same. (b) i + =i =, wherei + andi arethecurrentsenteringthenon-invertingandinvertinginput terminals of the op amp, respectively. In the following, we will consider op amp circuits in which the op amp operates in the linear region. Inverting amplifier Fig. 4 shows the inverting amplifier circuit. 2 i Figure 4: Inverting amplifier circuit SinceV + =V,V V + =V,and = =. Sincethecurrententeringtheinverting terminal can be neglected, must flow through 2, and therefore = V 2 = 2 = 2. (1) Since and are out of phase (because of the negative sign in Eq. 1), the circuit is called an inverting amplifier. The amplifier has a gain (magnitude) of 2 / which can be changed

4 M.B. Patil, IIT Bombay 4 simply by choosing appropriate values of and 2, which is much simpler than designing a common-emitter or common-source amplifier, for example. Note also that Eq. 1 does not depend on whether or not a load resistance is connected or its value, and that surely makes the amplifier design simpler. We should keep in mind the following practical considerations (which may also apply to other op amp circuits). (a) Saturation: Since the op amp output is limited to ±V sat, the output voltage waveform gets clipped if the expected output voltage (i.e., gain times the input voltage) exceeds these limits, as shown in Fig. 5. V m =2V f =1kHz 2 1k 15 1k t (msec) Figure 5: Effect of op amp saturation in inverting amplifier (representative example). (b) ealistic i and o : In the above analysis, we have assumed the op amp to be ideal, with an infinite input resistance i and zero output resistance o. In practice, i could be of the order of a few MΩ, and o could be a few ohms. For Eq. 1 to hold, we require that and 2 should be small compared to i and large compared to o. Keeping these limits in minds, and 2 are typically chosen to be in the 1kΩ to 5kΩ range. (c) Frequency response: Eq. 1 says nothing at all about the frequency response of the amplifier, implying that the amplifier will follow Eq. 1 for an input signal with very low frequencies (including D) to very high frequencies. In reality, the frequency response of an op amp is limited and is given by A(jω) = A V 1+jω/ω c. (2) For Op Amp 741, A V 1 5, and f c =1Hz (ω c =2πf c ). With Eq. 2, we get the following expression for the gain of the inverting amplifier. (s) (s) = 2 1, ω 1+s/ω c c = A Vω c. (3) 1+ 2 /

5 M.B. Patil, IIT Bombay 5 The gain now depends on the signal frequency, as shown in Fig. 6. Note that Eq. 1 holds only at low frequencies. At higher frequencies, the gain starts dropping. Higher the gain, lower is the cut-off frequency of the amplifier k 1k Gain (db) 2 25k 1k 2 =5k f(hz) Figure 6: Gain of inverting amplifier versus frequency (representative example). (d) Slew rate: In a real op amp, the maximum rate at which the output voltage can rise (or fall) is limited by the slew rate. For Op Amp 741, the slew rate is.5v/µsec. The slew rate limitation can casue distortion in the output voltage waveform. For example, with a sinusoidal input voltage to the inverting amplifier, we expect a sinusoidal output voltage. d However, if the expected is larger than the slew rate, the output voltage waveform dt becomes triangular (see Fig. 7). V m =1V f =25kHz 2 1k 1 (expected) 1k t(µsec) Figure 7: Slew rate limitation in the inverting amplifier (representative example). If we want to plot gain versus frequency for the inverting amplifier, we must keep in mind the slew rate limitation and keep the magnitude of the input sinusoid sufficiently small in

6 M.B. Patil, IIT Bombay 6 thefrequency range ofinterest. In other words, we need to check that theoutput waveform is sinusoidal at the highest frequency of interest. Non-inverting amplifier Fig. 8 shows the non-inverting amplifier circuit. 2 Figure 8: Non-inverting amplifier circuit Since V + =, we have V V + =. The current is therefore = =. Since the input current of the op amp is negligibly small, the current through 2 is also equal to. The output voltage is given by ( ) Vi = V 2 = 2 = (4) The output voltage is in phase with the input voltage, and the circuit is therefore known as the non-inverting amplifier, its gain being 1+ 2 /. Integrator Fig. 9 shows the integrator circuit. V i Figure 9: Integrator circuit Asintheinvertingamplifier, wehaveavirtualgroundatv sincev V + =V.Thecurrent i, which also flows through the capacitor, is =. Since i= dv, we have dt dv = i dt = V = 1 dt. (5)

7 M.B. Patil, IIT Bombay 7 Finally, the output voltage can be related to the input voltage as = V V = V = 1 dt. (6) Integrator: Practical implementation Fig. 1 shows the integrator circuit with a more realistic op amp model, including the bias currents [i.e., the base currents of transistors Q 1 and Q 2 (see Fig. 1) in Op Amp 741]. i 2 i 2 V V eal Ideal eal Ideal I B I + B I B I + B (a) (b) Figure 1: (a) An integrator with a realistic op amp model, (b) improved integrator circuit. As mentioned earlier, the bias currents are generally small and can be neglected, as we have done for the inverting and non-inverting amplifier circuits. In the integrator, however, the bias currents are a cause for concern for the following reason. onsider = in the circuit of Fig. 1(a). Let the capacitor voltage be initially zero. In this situation, we would expect the output voltage to remain V. However, the bias current I B flows through the capacitor, and it charges the capacitor. Even though I B is a small current, it results in a continuous increase in the capacitor voltages, eventually driving the op amp into saturation. To prevent this undesirable situation, we can provide a D path to the bias current in the form of the resistor shown in Fig. 1(b). In steady state, the bias current causes a voltage drop I B across the resistor. The output voltage is now =V V = I B which can be made negligibly small by choosing an appropriate value of. Note that should not be made so small that it interferes with the functioning of the circuit as an integrator. In other words, must be large as compared to 1/jω (in magnitude) at the frequency of interest.

8 M.B. Patil, IIT Bombay 8 Differentiator Fig. 11(a) shows the differentiator circuit. i 2 V i (a) Figure 11: Differentiator circuit: (a) basic operation, (b) practical configuration As in the inverting amplifier, we have V V + =V. The voltage across the capacitor is V = =, and the capacitor current is dv dt. Since the current i can be neglected, we have The output voltage is and the circuit works as a differentiator. i 2 = = dv dt (b) = d dt. (7) = V i 2 = d dt = d dt, (8) There is a practical difficulty in using a differentiator in the above form. The A gain of the circuit is A = /(1/jω) = jω, which keep increasing with increasing frequency and makes the circuit oscillate. The high-frequency gain can be reduced by adding a small capacitance in the feedback path (see Fig. 11(b)). The gain now becomes A= jω 1+jω and is limited at high frequencies 1, thus stabilising the circuit operation. eferences 1.. A. Gayakwad, Op-amps and linear integrated circuits, Prentice Hall, 2. 1 In addition, we also need to consider the frequency response of the op amp, see [1].

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