12 Operational amplifiers

Vinay Gupta

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    1. Introduction

 

 

The electrical signals produced at the output of most transducers have a low voltage or power level and cannot be transmitted directly over large distances. Thus, instrumentation amplifiers are required to increase the amplitude and supply the power required to drive the output devices. Instrumentation amplifiers are also needed to provide impedance matching and isolation. Amplifiers are also used to process the quantity to be measured i.e to perform mathematical operations such as addition, subtraction, integration, differentiation etc. before it is processed. The basic integrated circuit used in the amplification of electronic signal is the operational amplifier

 

2. Operational amplifiers

 

An operational amplifier, abbreviated as ‘op-amp’ is a direct coupled, high gain differential amplifier that uses voltage shunt feedback to provide a stabilized voltage gain. It is called as ‘operational’ as it was used originally to perform the basic mathematical operations such as addition, subtraction, integration, differentiation etc. And the word ‘amplifier’ specifies its capability of providing the voltage gain. Now-a-days, op-amps are used for a variety of other applications such as ac and dc signal amplification, active filters, oscillators, comparators, regulators etc. An op-amp can amplify both the dc as well as ac signals in a wide range of frequency varying from few Hz to MHz. Since an op-amp is a multistage amplifier, it consists of basic building blocks as shown in Figure 1.

 

Figure 1: Block diagram of a typical op-amp

 

The block diagram of op-amp consists of four stages in cascade. The first stage is a dual-input balanced output (double-ended) differential amplifier. It provides a high voltage gain so that any loss in the consequent stages can be easily compensated. This stage also decides the input resistance of the op-amp. An op-amp, in general, has a high input resistance. The output of this stage drives the second stage called the intermediate stage which is also a differential amplifier and is a dual input unbalanced (single-ended) output. The dc voltage present at the output of this stage is well above the ground potential and acts as an error voltage in the desired output signal. Such error voltage will result in a shift in the operating point of the following stages and distort the output signal. Therefore, it is essential to use a level shifting stage at the output of intermediate stage to shift the dc level at the output of intermediate stage down to zero volts with respect to ground. The final stage is a push-pull complementary amplifier output stage. The purpose of this stage is to increase the output voltage swing and the current supplying capability of the amplifier. It also determines the low output resistance which is one of the characteristics of an ideal op-amp.

 

Schematic symbol of an op-amp

 

The schematic symbol of an op-amp is shown in figure 2. The circuit has two differential inputs – v1, the non-inverting input and v2, the inverting input, represented by the symbols (+) and (−) respectively and one output.

Figure 2: Schematic symbol of an op-amp

   A signal applied to the non-inverting input terminal results in an amplified output in the same phase whereas, a signal applied to the inverting terminal results in an amplified output voltage which is 180° out of phase with the input. If A is the voltage gain of the op-amp, then, the differential input voltage, is given by

 

?? = ??? = ?1 − ?2                        (1)

 

Output voltage,

 

?? = ??? = ?(?1 − ?2)                 (2)

i.e output voltage is directly proportional to the differential input voltage. The voltages v1, v2 and vo are measured with respect to ground.

 

An op-amp requires bipolar (equal and opposite) voltages for its operation. IC 741 is the general purpose op-amp IC which can be used for a variety of applications such as summing amplifier, integrator, differentiator etc. The pin out diagram of 741 IC is shown in Fig. 3. It is available in 8-pin metal can DIP package.

 

Figure 3: Pin-out diagram of IC 741

 

For 741 op-amp IC, The supply voltages should not exceed ±18 V. The output voltage is limited by the supply voltages. On an average, the maximum output voltage is 2 to 3 volts less than the supply voltage.

 

Equivalent circuit of an op-amp

 

The equivalent circuit of op-amp is useful in analyzing the basic operating principles of op-amps and in observing the effects of feedback arrangements. In the equivalent circuit of an op-amp, Avid is the equivalent thevenin voltage source, RO is the thevenin equivalent resistance looking back into the terminals of op-amp. If A is the large signal voltage gain, then the output voltage vO is given by

 

?? = ???? = ?(?1 − ?2)                       (3)

 

Thus, op-amp amplifies the difference in the voltages applied at the two inputs and not the voltages themselves. Polarity of the output voltage depends on the polarity of the differential input voltage.

Ideal voltage transfer curve

 

Voltage transfer curve is a curve between the output voltage vo plotted against the differential input voltage vid, keeping gain A constant. Thus, it is a graphical representation of equation (3). It is known as ideal as here, the output offset voltage is assumed to be zero. For practical op-amps, the output voltage is nearly zero.

Figure 3: Ideal voltage transfer curve

 

The curve in figure 3 reveals that the output voltage increases linearly with the differential input voltage only until it attains the saturation value after which it becomes constant. Positive and negative saturation voltages are specified by an output voltage swing rating of the op-amp for given values of supply voltages. This curve is not drawn to scale as if it were drawn to scale, the curve would be almost vertical because of very large voltage gain A.

 

An op-amp has the two configurations namely open-loop and closed-loop configurations. In open-loop configuration, op-amp functions as a high-gain amplifier in three configurations – Differential amplifier, Inverting amplifier and non-inverting amplifier. In all the three open-loop configurations, any differential input signal (slightly greater than zero) drives the output into saturation because of the high voltage gain of op-amp (nearly infinite). Thus, when an op-amp is operated in the open-loop configuration, the output either goes to positive saturation or negative saturation or switches between the two saturation levels. This limits the use of open-loop configuration for linear applications. However, they can be used in non-linear applications such as square wave generators etc. The gain of an op-amp can be controlled by introducing a modification in the circuit which involves the use of feedback, that is the output signal is fed back to the input either directly via another network. This is known as closed-loop configuration. For most practical applications, op-amp is operated in closed-loop configuration.

 

Closed-loop op-amp configurations

 

An op-amp that uses a feedback is called feedback amplifier or closed-loop amplifier. The name ‘closed-loop’ is derived from the fact that the feedback forms a closed loop between the input and output. The feedback may be positive or negative. If the signal fed back is of opposite polarity (i.e. 180° out of phase) with respect to the input signal, the feedback is called negative feedback. It is also called as degenerative feedback voltage is in phase with the input signal, the feedback is called positive feedback or regenerative feedback. Here, the feedback signal increases the input signal. Positive feedback is necessary in oscillator circuits.

 

Negative feedback is used in amplifiers, as it stabilizes the gain, increases the bandwidth, increases the input resistance and decreases the output resistance. Negative feedback also reduces the variation in output of an op- amp due to variations in temperature and supply voltages. Thus, we will be studying about op-amp in negative feedback configuration.

 

Negative feedback is of four types – voltage-series feedback, voltage-shunt feedback, current-series feedback and current-shunt feedback. Voltage-series feedback and voltage-shunt feedback are the most important and widely used in amplifiers whereas, current-series feedback and current-shunt feedback are seldom used. Voltage-series feedback and voltage-shunt feedback are known as non-inverting and inverting amplifiers respectively and are discussed in detail as follows.

 

Non-Inverting amplifier

 

In this configuration, the feedback circuit is composed of two resistors R1 and RF. The inverting input terminal is grounded through R1 and output is fed back to the inverting input terminal through the feedback circuit. The circuit is known as non-inverting amplifier because the input signal is applied to the non-inverting terminal of the op-amp.

 

Figure 4: Non-inverting amplifier with feedback

 

The closed-loop gain of the non-inverting amplifier can be determined as follows:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Thus, equation (5) shows that the output voltage is in phase with the input signal (since the input is applied to the non-inverting terminal). The magnitude of output voltage (closed-loop gain) can be varied by adjusting the values of the two resistors R1 and Rf or particularly, it can be inferred that it’s the ratio of the two resistors Rf and R1 which determines the gain instead of their absolute values. For eg: For designing a non-inverting amplifier of gain 11, we can choose R1 = 1 KΩ and Rf = 10 KΩ or alternately, R1 = 100 Ω and Rf = 1 KΩ.

 

Closed-loop gain is also related to the gain of the feedback circuit (B) as:

 

 

 

 

 

 

 

 

 

 

 

 

This is the expression for the gain of an amplifier with negative feedback.

 

Voltage follower

 

It can be observed from equation (5) that the lowest closed loop gain that can be obtained from a non-inverting amplifier is 1.When the non-inverting amplifier is adjusted for unity gain, it leads to an interesting application of op-amp called as voltage follower. The name is derived from the fact that the output voltage is equal in magnitude and is in phase with the input signal i.e. output signal tracks or follows the input signal in magnitude and phase. In order to obtain the voltage follower circuit for unity gain, we can see from eqn. (5) that Rf should be set to zero (short-ckt.) and R1 should be infinite (open-ckt) as shown in the circuit in figure 5. From the circuit, 2 = and 1 = , so

 

Thus, = in a voltage follower and hence the name. Along with the unity gain, the circuit provides a high input resistance (few MΩ) and a low output resistance (~mΩ) which makes it ideal for impedance matching. Thus, voltage follower circuit is widely used as buffer between the two networks and is used to prevent the loading on the preceding stage.

Figure 5: Voltage follower using op-amp

 

Inverting amplifier

 

Inverting amplifier is also known as voltage shunt feedback amplifier. Figure 6 shows the circuit of an inverting amplifier using an op-amp. In this circuit, the input is applied to the inverting terminal of the op-amp through resistor R1, output is fed back to the inverting terminal though a feedback resistor Rf and the non-inverting terminal is grounded.

Figure 6: Inverting amplifier with feedback

 

Before finding out the closed loop gain of the inverting amplifier, it is essential to introduce the concept of virtual ground. We know that VO = AVid. Since A is of the order of 105 and the output voltage VO is less than the supply voltage (let us say, 15 V in this case), then input voltage,

 

 

 

 

Thus, the value of Vid is very small and can be assumed to be zero. Voltage at the inverting input terminal (v2) is equal to the voltage at the non-inverting terminal (v1). Since, v1 is at ground potential, so v2 is also equal to zero. This implies that there exists a virtual ground at the inputs of op-amp due to vid = 0 i.e. there is no current through the amplifier input to ground although the input voltage is nearly zero. This concept is useful in the analysis of amplifier circuits using op-amp.

 

Closed-loop gain

 

Applying Kirchoff’s current law at node v2, we have Iin = If + IB. The concept of virtual ground implies that IB = 0, which means that Iin = If

 

 

 

 

 

 

The negative sign clearly shows that the output voltage is 180° out of phase with the input signal as the input signal is applied to the inverting input terminal of op-amp. It is thus, called an inverting amplifier. As, open-loop gain (A) is very large (≈ 105), in the denominator, 1 ≫ 1+   i.e. 1+   + 1 ≅

 

 

 

 

As for the non-inverting amplifier, closed-loop voltage gain or output voltage of an inverting amplifier depends on the values of R1 and Rf or more specifically on the ratio of Rf and R1. Since, the gain of an inverting amplifier can be adjusted to any value, therefore, it is one of the highly versatile circuits and is used for performing a number of applications.

 

Some interesting facts:

 

Today the application of negative feedback is so common that it is often taken for granted. But this wasn’t always the case. Working as a young Western Electric Company engineer on telephone channel amplifiers, Harold S. Black first developed feedback amplifier principles. Note that this was far from a brief inspirational effort, or narrow in scope. In fact, it took some nine years after the broadly written 1928 patent application, until the 1937 issuance. Additionally, Black outlined the concepts in a Bell System Technical Journal article and much later, in a 50th anniversary piece where he described the overall timeline of these efforts.

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References:

  • Op-Amps and Linear Integrated Circuit, R. A. Gayakwad, 4th edition, 2000, Prentice Hall. Operational Amplifiers, 5th Edition by George Clayton, Steve Winder, Elsevier India, 2012,
  • Operational Amplifiers & Linear ICs, David A. Bell, Oxford University press, 3rd Edition, (2011).
  • Operational Amplifiers and Linear Integrated Circuits, Robert F. Coughlin, Frederick F. Driscoll, 6th Edition, Pearson.