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OPERATIONAL AMPLIFIER PRINCIPLES.

A 1. INTRODUCTION

An amplifier is a device which increases the power contained within a signal. It is important to appreciate the difference between an amplifier, which provides a true power gain, and a device such as a transformer, which increases the voltage in a signal but gives no power gain.

One way of visualising a power gain is to think of it in terms of input and output impedances. If the power in a signal is to be stepped up then the amplifier must be capable of supplying the signal at an increased current. Thus, an amplifier must have a high input impedance, so that it only draws a little current, and a low output impedance, so that it can supply a larger current. In circuit analysis we often use a so-called "ideal amplifier", which is said to have an infinite input impedance and a zero output impedance.

The "ideal amplifier" is also assumed to have infinite gain, since this greatly simplifies the analysis of circuits containing these amplifiers. If the open-loop gain is greater than about 1000, the gain of a closed loop circuit containing an amplifier will be almost independent of the open-loop gain (see Ref 1. for details).

Real operational amplifiers (op-amps) approach these ideals with varying degrees of success How close they get usually depends on how much money you are willing to spend.

A2. OPERATIONAL AMPLIFIER CIRCUIT BASICS:

The output voltage range of the amplifier is limited by the supply voltage. Generally a dual voltage power supply is used, and ± 1 5V is common which allows an output swing of about 28 or 29V. However it is often convenient to run an op amp circuit from a single voltage supply of twice the voltage. For example +30V might be used instead of ± 1 5V. An amplifier which is usually supplied by a dual voltage power supply can be operated from a single voltage supply if an external voltage divider is used to set up the input midway between the two voltage extremes. Figure A2 shows a 741 amplifier (normally operated from ±15V) being operated from a 30V supply. Note that the input and output signals are capacitively coupled to the circuit.

The + and - symbols on Figure Al indicate the non-inverting (or adding) and inverting (or subtracting) inputs to the amplifier. When the noninverting (+) input is made more positive than the inverting (-) input the output becomes positive, and vice versa. The + and - symbols do not imply that one input must be kept more positive than the other, but tell you what phase the output will have with respect to the input. For example, if a sinusoidal signal is connected to the inverting input of an op-amp, the output will be out of phase by 180š (¼ radians) with respect to the input.

The package and its connections are shown in Figure A4. The 741 is popular because it is simple to use, usually tolerates maltreatment without permanent damage, performs well and is cheap to obtain. However, it is worth remembering that much better op-amps can be obtained when necessary.

A3. ANALYSING OPERATIONAL AMPLIFIER CIRCUITS:

The behaviour of almost all op-amp circuits with external feedback can be understood by applying a pair of simple rules. These are:

I. The current drawn by the inputs is so small that for most purposes we may assume that THE INPUTS DRAW NO CURRENT.

II. Since the open-loop gain is so high, a tiny differential voltage is sufficient to swing the output over its full range. Thus, it is reasonable to assume that THE INPUTS ARE AT THE SAME VOLTAGE.

Rule II needs some further explanation. It does not mean that an op-amp actually changes the voltage at one input in response to a change at the other. (if it did it would break rule II). What it does mean is that the device adjusts its output so that the external feedback network brings the differential input voltage to zero (if possible). To illustrate the use of these rules, consider the inverting amplifier circuit shown in Figure A5.

In an inverting amplifier the input signal is applied to the inverting (-) input as shown in Figure A5, and the output is out of phase by 180š (¼ radians) with respect to the input.

A4 THE GAIN-BANDWIDTH PRODUCT:

The gain-bandwidth product of an op-amp is the product of the DC gain and the frequency at which the gain is reduced by 3dB, as shown in Fig. A6. The rate at which gain decreases as the frequency increases is known as the roll-off. For op-amps the roll-off is almost invariably 6dB/octave.

A diagram such as Figure A6 in which the open-loop gain is plotted logarithmically against frequency is known as a gain-bandwidth diagram. An open-loop gain-bandwidth diagram can be used to calculate the bandwidth of a closed-loop circuit, since if the roll-off is 6dB/octave the gain-bandwidth product is a constant (Ref. 2). Adding negative feedback to an amplifier reduces its gain, and since the gain-bandwidth product is constant the bandwidth (the frequency range over which the gain is constant) must increase as the gain is reduced. Thus, the gain-bandwidth diagram for an op-amp is essential information for the circuit designer, since it allows him to predict the frequency at which the gain of his circuit will begin to reduce.

A5. THE OP-AMP'S DEPARTURES FROM IDEAL BEHAVIOUR

As mentioned in the introduction to this datasheet, op-amps approach the characteristics of the ideal amplifier (infinite gain, infinite input impedance, zero output impedance) with varying degrees of success. The purpose of this section is to outline some of the ways in which op-amps can misbehave. This misbehaviour largely arises because op-amp circuits are designed assuming ideal behaviour; when the op-amp refuses to oblige and obstinately persists in displaying "real" characteristics the designer can be caught out! The following are descriptions of the ways in which this non-ideal behaviour is measured and quantified, together with some indications of ways around the problems.

Common Mode Gain (CMG): An ideal op-amp amplifies only differential signals, and has a gain of zero for common-mode signals (exactly identical signals which are applied to both inputs). Real amplifiers have non-zero values of CMG. The size of the CMG is a function of the magnitudes of the common and the differential input signals. A typical CMG value for a 741 op-amp with open-loop differential gain of 105 is about 3.

Common Mode Rejection Ratio (CMRR): CMRR is defined as the absolute value of the ratio of differential gain to common-mode gain, i.e.

Voltage Supply Rejection Ratio (VSRR): The characteristics of an op-amp are quoted for a standard supply voltage. If this voltage changes, in general the output of the amplifier will change. The size of this output variation is expressed in terms of the equivalent differential input voltage arising from a 1V change in supply. In other words, the input to the amplifier which would produce the same output change as that caused by a 1V supply change is quoted as a measure of the device's sensitivity to supply variations. The VSRR for a 741 amplifier is around 20 µV/V or 94dB.

Input Offset Voltage (IOV): For an ideal op-amp V_out is zero when V_in is zero. Because components in symmetrical positions inside the amplifier are impossible to match precisely this rarely occurs in practice. A pair of terminals are provided as shown in Figure A7 for balancing out the unwanted input offset. It should be borne in mind however that IOV is temperature sensitive, and balancing must therefore be carried out at the circuit's operating temperature.

Input Bias Current: It is necessary to supply small currents to both terminals of an op-amp to correctly bias the transistors within the amplifier. As can be seen from Figure A8 earthing the unused input leads to an imbalance in these currents, and this results in an offset voltage appearing at the output of the device. To avoid this effect the unused terminal should be earthed through a resistor equal in value to the parallel combination of the input and feedback resistors. Figure A9 shows an inverting example. Biasing resistors are usually omitted from op-amp circuit diagrams, but this does not mean they are unnecessary!

Figure A8

Slew Rate: The slew rate of an op-amp is the maximum rate of change of output voltage with time. Suppose the output is a sine wave:

A typical slew rate is 0.5V/µsec (for a 741), but with special op-amps such as the NE5539 it can be as high as 800V/µsec.

Care should be taken in applying the above analysis to non-sinusoidal periodic signals. To take a common example, suppose an op-amp is used to amplify a square wave of period T. It can be shown by Fourier analysis that a square wave consists of a sum of sinusoidal components at frequencies 1/T, 3/T, 5/T, ... n/T, where the amplitude of each component is proportional to l/n. Thus a 1kHz square wave contains sinusoidal components at frequencies of 1Khz, 3kHz, 5kHz etc. The spectral content of a signal must therefore be considered before determining the slew rate required by a particular circuit.

NOTE: Whilst every effort has been made to ensure that the information given is correct and up-to-date, SEED, the publishers and authors cannot be held responsible for any errors or omissions that might occur in this Guide. Use of the methods or data on projects for application outside the educational environment should be justified and validated during the course of the designer's normal professional duties. Copyright© SEED 1991