Amplification We have seen in earlier notes that a carbon composition resistor continuously dissipates heat to the environment. Most circuit elements do likewise to some degree, including the capacitor and inductor, because they possess some amount of resistance. For this reason most circuit designs require some amplification or boosting of voltage, current or power to offset the losses of electrical energy to heat. In this note we describe what is meant by amplification. We survey how a transistor and an operational amplifier work, and cover the issues of gain, frequency response and input and output impedances. What is an Amplifier? The idea of an amplifier is sketched in Figure 9-1. A signal of amplitude is applied to a system and has its amplitude increased to a value. This process takes energy. The energy is drawn from a source like a battery or a power supply. In its simplest terms, amplification is a process in which a smaller signal controls a larger signal. It is not like an image being magnified by a glass lens. The amp in the figure represented by the triangle can be transistor, operational amplifier or a number of stages of amplication. Vin nergy from supply amp Vout Figure 9-1. The idea of amplification. An amplifier is best understood in general terms as a four terminal network (Figure 9-2). It has an input and an output. One of the input and output lines are often tied together and to ground. The amplifier in the figure is shown to have input and output impedances Z in and Z out whose absolute values have the unit ohms (Ω). Z in G( jω) = AH( jω) Z out Figure 9-2. An amplifier as a four terminal network. Amplifiers are described as to type, gain, frequency response, input impedance and output impedance among others. Some of these attributes are mutually related. There are four types: voltage, current, power, and impedance. We shall describe each in a separate section. Gain The gain of an amplifier is expressed, in general, as the complex number G(jω): G( jω) = AH( jω). [9-1] Here A is a real number called the amplification factor and H(jω) is the transfer function describing the amplifier s filter characteristic. H(jω) has the meaning we gave it in Note 05 for passive filters. The absolute value of G is the absolute value of the output quantity divided by the absolute value of the input quantity. As we shall see in a moment G(jω) can be expressed as a voltage gain, a current gain, a power gain or an impedance gain. G(jω) contains within it the frequency response of the amplifier and the phase angle φ(ω) that the output leads or lags the input. In essence, then, eq[9-1] differs from eq[5-7] only in the real number A. An amplifier can therefore function as an active low-pass, high-pass, band-pass or band-reject filter. 1 Input and Output Impedances An amplifier, like any electrical device, has an input and an output impedance. These values are important when the amplifier forms one link in a chain of devices. If the amplifier in Figure 9-2 drives a speaker as a load then the output impedance Z out should be matched as closely as possible to the input impedance of the load so as to transfer maximum power. The input and output impedances are characteristic of the amplifier type. Amplifier Types Voltage A voltage amplifier is often the first stage of amplification in a system. In a radio receiver a voltage amplifier is used at the antenna input to amplify the minute voltage signals that are received on the antenna into signals large enough to be detected. The 1 If an amplifier has an A of 1 then it is electrically indistinguishable from a passive filter. N9-1
gain of this kind of amplifier needs to be quite large, in the range 10 3 to 10 6. In many respects this kind of amplifier is the easiest to understand. urrent A current amplifier is in many respects like a power amplifier. The most fundamental form of a current amplifier is a transistor. Power A power amplifier is often the last stage of amplification in a system before a signal is sent to a target device or load requiring power for its operation. An example is the final audio amplifier in a domestic stereo system with a speaker as load. A speaker produces sound in air by moving a cone back and forth against the air. This requires power. The matching of impedances in this case is important. Traditionally, speakers are manufactured to have nominal impedances across the audio range of 4 Ω, 8 Ω or 16 Ω. The output impedance of an audio power amplifier must be relatively low but not zero. Impedance An impedance amplifier is usually a stage of gain unity whose purpose is to match one stage with another. We shall point out one example when we get to the subject of operational amplifiers. Measuring Amplifier Properties xperimentally Gain and Phase Difference To give an example of how amplifier gain and phase difference might be measured, Figure 9-3 shows the input and output signals for a typical amplifier displayed on the screen of an oscilloscope. The input signal is shown at the top (on H1), the output at the bottom (on H2). The absolute value of the gain G is 10 since the ratio of the peak-to-peak values of H2 to H1 (here 5.04V/504mV) is 10. The phase difference is 180 degrees since the output is inverted with respect to the input. 2 Input Impedance The input impedance of an amplifier can be measured with the circuit in Figure 9-4. is the impedance to be measured (appearing in effect between input and ground) and R s is an external resistance that is added to make the measurement. For this procedure to work the amplifier must be operating linearly so that G is independent of the voltage input to the amplifier itself. The procedure consists of applying a signal of the same amplitude V to points A and (in which case the voltages applied to the amplifier itself are V i and V i '). Suppose the corresponding output voltages are V 0 and V 0 '. A input R s amplifier gain G output Figure 9-4. A circuit to measure an amplifier s input impedance. When the voltage is applied to point A the same voltage is input to the amplifier itself so V i = V and V 0 = GV i = GV. [9-2] ut when the voltage is applied to point the voltage input to the amplifier itself is determined by the voltage divider: V i ' = R 0 V so that V 0 ' = GV i ' = G R s V. [9-3] Figure 9-3. The input signal (top) and output signal (bottom) of a typical amplifier. N9-2 2 We write G = G(jω) for convenience.
Dividing eq[9-2] by eq[9-3] we get so that = V 0 V 0 ' = R s, V 0 ' V 0 V 0 ' R s. With V 0, V 0 and R s known, can be calculated. [9-4] Output Impedance An amplifier s output impedance can be found using the same procedure as for the Thévenin equivalent of a D black box. The open circuit output voltage is first measured (that is, with no load connected to the amplifier). Then a variable resistance R load is connected to the output and varied until the voltage drops to 1/2 the open circuit output voltage. The output impedance then equals the value of R load. Amplifiers to be Described Two of the most popular discrete amplifier devices in use today are the bipolar junction transistor (abbreviated JT) and the field effect transistor (abbreviated FT). The integrated circuit (I) type of amplifier called the operational amplifier (or opamp for short) is even more important in a practical sense because of its easy and widespread use. We shall therefore discuss in the next section the JT only briefly in anticipation of spending most of our time on the opamp. We leave the FT to a course in electronics. The Transistor Amplifier The two most important transistor types are the JT and the FT. The latter was the first to be invented but the former was the first to be widely adopted by the industry. xcept for special applications today, Is have largely replaced discrete transistors. The preferred discrete transistor type is the FT. Therefore, we begin our discussion of transistors with the JT, not because it is state-of-the-art, but because in many respects it is a natural evolution of the PN junction technology we have surveyed in Note 07. The ipolar Junction Transistor We discuss here the bipolar junction transistor (for convenience we shall just use the word transistor). A transistor can be used to amplify an A signal as well as a D signal, but before it will work at all, it must be prepared with certain D voltages set up between its terminals or D currents made to flow through its body. We begin, therefore, with the issue of D preparation or bias and defer until later a discussion of the response of the transistor to an A signal. lasses There are two classes of transistor: the NPN and the PNP. oth are made from materials like germanium, silicon and exotics like gallium arsenide. oth consist of three sections of doped semiconductor arranged in a kind of sandwich (Figure 9-5). The layers of the sandwich are called the collector, the base and the emitter, and are each provided with an electrical connection. You should be able to recognize the origin of the nomenclature NPN and PNP from the order of the sections in the figure. collector base emitter N P N I I (a) collector base emitter P N P Figure 9-5. omposition and circuit symbol of bipolar junction transistors: NPN class (a) and PNP class (b). To make our task easier we shall think of both classes as having the same geometry. The base is the center material, the collector and emitter are the outer materials. The base is lightly doped, the emitter and collector are more heavily doped. (For a description of doping see Note 07.) And the emitter is more heavily doped than the collector. The classes differ in the direction of current flow into the base terminal of the NPN and out of the base terminal of the PNP (indicated by an arrow on the transistor symbol). urrent flows from collector to emitter through the NPN and in the reverse direction through the PNP. We shall focus on the NPN class in our discussion here, though the PNP class is used just as often in circuit design. lectrical haracteristics of the NPN Transistor To make a transistor work, two external D voltages must be applied to it (Figure 9-6). These may be derived from two separate power sources, as is implied in the figure, or from a single source. There are two loop currents: a base current I induced by the voltage V applied between the base and emitter and I I (b) N9-3
a collector current I induced by the voltage V applied between collector and emitter. I is typically two orders of magnitude larger than I and V is much larger than V. I and I add together in the base material to form the emitter current I. I V N P N I V Figure 9-6. iasing of an NPN transistor. Recalling our description of the PN junction diode in Note 07 you should recognize (Figure 9-7) that the base emitter junction functions much like a PN diode. The purpose of the base-emitter voltage V is to turn on the base-emitter junction (to reduce its resistance to a low value) thereby allowing a collector current I to flow. If V were not applied, the resistance of the base-emitter junction would remain high enough to reduce the flow of I to a point where the transistor could not function as intended. NPN transistor is normally operated with the baseemitter junction forward biased (0.3 volts for germanium and 0.7 V for silicon) and the base-collector junction reverse biased by a few volts. Transistor haracteristics Much of the electrical behavior of a transistor is summarized in its families of characteristic curves. One family is the collector characteristics (Figure 9-8). The curves show how the collector current depends on the collector-emitter voltage when the base current is held constant at various values. To function as a linear amplifier, a transistor must be operated in a state representing a point on the graph where the variables depend linearly on one other. This range, called the plateau region, is where the collector current is directly proportional to the base current and is relatively independent of small changes in the collector-emitter voltage. In this region the transistor can be modelled as a current source in series with a diode (Figure 9-9). I Plateau region V Figure 9-8. The family of I vs V curves of a typical JT. I 3 I 2 I 1 I V I N P N I I = β I I I = h F I I V Figure 9-7. An attempt to illustrate how a small base-emitter current in a transistor (bottom loop) controls a much larger collector-emitter current (top loop). The base-emitter junction works as a kind of valve (like a tap to turn on water in a sink). Small variations in V (and therefore in I ) produce small changes in the base-emitter resistance, which in turn cause large variations in I. Small variations in I causing large variations in I is amplification in action. Thus an V PN Figure 9-9. Model of a typical NPN JT. The three currents in a transistor, I, I and I are related to one another: I = αi, = βi = h F I, [9-5] N9-4
where α and β, which are approximately constant, are called the alpha- and beta-parameters. h F, also a constant, is a basic parameter specified by transistor manufacturers. α and β are themselves related by β = α 1 α. [9-6] Typically β is about 99 and α about 0.99. These numbers indicate that the ratio I /I is large, meaning that a transistor can be used to amplify current. Since V /V is also large (at least for some configurations as we shall show in the next section), a transistor can be used to amplify voltage. Transistor onfigurations Since a transistor has three electrical terminals, a signal can be applied between any pair of its terminals three different ways. This leads to three configurations (Figure 9-10). The two terminals on the left in each figure represent the input, the two terminals on the right the output. One terminal is common to both input and output. The configurations are therefore dubbed the common emitter (), the common base () and the common collector () configurations. in out ommon emitter, (a) in in out (c) ommon base, out ommon collector, (b) Figure 9-10. The configurations of an NPN transistor: common emitter (), common collector (), and common base (). For simplicity, we have omitted the important external components from the diagrams. ach configuration has its own advantages and disadvantages. They can be summarized in the following points. The amplifier has both current and voltage gain. It is used as a general purpose amplifier. The amplifier has current gain but a voltage gain of only unity (V ~ 0.6 V so V /V ~ 1). It is used as a coupling stage when high input impedance and low output impedance are required. The amplifier has voltage gain but a current gain of only unity (I /I ~ 1). It is used in high frequency circuits since the capacitance linking output to input is small. In order to design a working amplifier based on one of these configurations the transistor must be properly biased, as we have already stated. This means it must be operated in an electrical state with values I, I and V defining a point in the plateau region of the collector curves (Figure 9-8). Only in this region does the amplifier function in a linear fashion with the collector current being directly proportional to the base current and more-or-less independent of the collector-emitter voltage. A point in this region is also far removed from a state in which maximum current flows through the transistor, the state called saturated (corresponding to V = 0) or a state in which no current flows through the transistor at all, the state called cut off (corresponding to I = 0). This point is called an operating or quiescent point. To achieve this, we must add external resistors, capacitors, etc., to the transistor to effect the necessary current limiting. Working JT ircuits In a course of this nature it is not practical to attempt a detailed analysis of a transistor amplifier circuit. That is best left to a course in electronics. However, it is important for you to know what a real amplifier circuit looks like and to be able to recognize its various components and the reason for their presence in the circuit. A typical general-purpose single-stage JT amplifier circuit is drawn in Figure 9-11. In fact, this is the circuit you will study in xperiment 4, Amplifiers. You should be able to identify the input, the output and the symbol for the NPN transistor used. Recall that the arrow on the symbol indicates the direction of current flow through the transistor. In this case the transistor has the part number 2N3904. 3 Recall from the previous sections that a transistor must be prepared or biased with steady D currents flowing through it before an A signal can be applied. 3 All semiconductor devices are sold under a part number. This transistor is in use in many other schools. You can obtain more information on it from the internet by googling. N9-5
That is the reason for the resistors. The capacitors 1 and 2 are present to prevent D currents from flowing out of the circuit into the previous stage (not shown to the left) or out into the following stage (not shown to the right). apacitor 3 is present for a technical reason you will learn about in the experiment. An external 12V source must be connected between point P and ground. = 470kΩ input R 2 = 4.7kΩ P 12V R 3 = 10kΩ 1 2 2N3904 R 4 = 270Ω 3 R 5 = 270Ω output bypass Figure 9-11. A working amplifier circuit employing a 2N3904 NPN JT. Analysis shows that the voltage gain of this amplifier (without emitter bypass capacitor) is given by G = R R, [9-7] where R is the resistance in the collector circuit and R the resistance in the emitter circuit. Thus in this example G comes to about 20. The minus sign means that the output signal is 180 out of phase with the input. This is the midband voltage gain at a frequency where the amplifier s filter characteristics are negligible. 4 The Operational Amplifier The operational amplifier, or opamp for short, is a much easier device to use in a circuit of one s own design than is a discrete transistor. For one thing, an opamp, unlike a transistor, needs no bias. An opamp is fabricated as a single I and is intended to be used like a black box, that is, with no need to be concerned with its internal structure. One need only connect it to a energy source, provide the appropriate feedback element (resistor, capacitor, whatever) and then ensure that the signal applied is of an amplitude small enough not to induce distortion in the output. Here we describe the properties of the opamp and how to construct useful devices with it. The Need to Know The opamp is in many respects the goal of our review of amplifier devices. Thousands of signal conditioning circuits that are used with sensors employ opamps as straight signal amplifiers, as filters or for other purposes. It is useful to have a working knowledge of opamps so as to better understand how sensor devices do their job. It is instructive for the user, whether student or professional engineer, to regard an opamp as an ideal element first, then later as the real device that it is. We begin therefore by explaining what is meant by an ideal opamp and then consider the ideal opamp in a number of what are called linear applications, where the output is directly proportional to the input. The Ideal OpAmp A view of the bare bones of an opamp is given in Figure 9-12. Shown is the opamp I itself (the triangle), the two signal inputs ( and ), the output, the power supply lines V and V and the ground line. (The power lines, most often ±15 volts usually derived from the same power supply, are nearly always omitted from circuit diagrams, and we shall omit them from now on.) reference voltage V I V I sample voltage A(jω) V ( 15 V) V ( 15 V) = A (V V ) 4 For details see L. R. Fortney, Principles of lectronics Analog & Digital (Harcourt race Jovanovich, 1987). N9-6 Figure 9-12. Schematic of an opamp. The reference and sample voltages can be applied to either input.
The equivalent circuit of the ideal opamp I itself is drawn in Figure 9-13. The opamp has two inputs, labelled and, and one output. A ground line is common to them all. One or the other of the inputs is often connected to ground. If the input is grounded and a signal is applied between the input and ground, then the output signal is inverted (or phase shifted by 180 ) with respect to the input. If the input is grounded and a signal is applied between the input and ground, then the output signal is not inverted. For these reasons the and inputs are called, respectively, the inverting and non-inverting inputs. You should not confuse the - and as indicating electrical polarity, as in the case of a battery. Rule 2: The voltages V and V are equal (a consequence of being very small). These rules make up what is called the ideal amplifier approximation. We shall see in what follows that these rules are, indeed, approximations, and are not strictly true. ut by making them we can calculate many useful properties of opamp circuits. Thus before we look at the opamp from the point of view of being a real device we study it in a number of circuits we can analyze using the ideal amplifier approximation. Gain d 100 open loop V I 40 closed loop R o I A (V V ) log f V Figure 9-14. Gain curves of a typical opamp with and without feedback. Figure 9-13. The equivalent circuit of an opamp I. The input resistance is very large, at least 1 MΩ, and the output resistance R o is very small, of the order of ohms. haracteristics An opamp has the important characteristic that its output voltage is proportional to the difference between its input voltages (V V ). For this reason it is said to have a differential input. Another characteristic is a very large gain when no feedback element is in place (Figure 9-14). (A feedback element resistor, capacitor, whatever is nearly always connected between the output and one of the inputs.) The gain without feedback is called the open loop gain. As we have stated, over frequencies of interest, an opamp behaves almost like an ideal device. y this we mean it has an input resistance so high it can be regarded as effectively infinite, and an output resistance so low it can be regarded as zero (Figure 9-13). This means that an opamp can be described to a good approximation by the following rules: Rule 1: The input currents I and I are zero (a consequence of ). The OpAmp With Feedback One of the simplest opamp circuits for the beginner to study is one that has a single input resistor and a single feedback resistor (Figure 9-15a). The noninverting input is tied to ground and the input signal is applied between the inverting input and ground. The equivalent circuit of this amplifier is drawn in Figure 9-15b. You should be able to see that this circuit is just the circuit of Figure 9-13 with and added. Since the inverting input is used here we can write = AV i. [9-8] where A denotes the very large open-loop gain factor and the sign indicates phase inversion. Summing the currents flowing into node S we have V i V i I = 0. [9-9] Assuming I = 0 (Rule 1) and substituting eq[9-9] into eq[9-8] and expanding, we have N9-7
I 1 S V i S V i I R o I o A V i (a) (b) Figure 9-15. An opamp with feedback (a) and its equivalent circuit (b). 1 1 1 =. A A ( R out = R F ) R AR o << R o. [9-12] 1 The conclusion we draw is that the opamp with feedback in the above configuration has a large input impedance (equal to ) and a low output impedance (much less than the output impedance of the opamp itself). These are desireable characteristics. q[9-11] is the D closed-loop gain. The closed loop gain curve is drawn in Figure 9-14 over a wide frequency range along with the open loop gain. The D closed loop gain is arbitrarily shown as 100 or 40 d (representative of the Motorola 741, a common opamp in many signal conditioning circuits). The closed loop gain curve is flat out to a frequency at which it meets the open loop gain curve. learly, feedback enhances the amplifier s frequency response or bandwidth and reduces its low frequency gain. Noninverting Unity Gain Amplifier One of the odder opamp circuits is one that has no external components as such: the output is tied directly to the inverting input (Figure 9-16). Since A>>1 the second and third terms in parentheses are negligible and can be dropped. Thus we are left with, so that G = =. [9-10] Figure 9-16. Noninverting unity-gain amplifier. This is the amplifier s midband closed-loop gain. It is the midband gain in the sense of being the gain when the frequency is neither very low nor very high or when the effects of the amplifier s filter characteristics are negligible. Since V i = V V 0 the summing node S is at zero potential or virtual ground. We can calculate the input and output impedances of the amplifier as a whole. Note that Detailed analysis would show that n = I 1. [9-11] is applied to the non-inverting input. Applying Rule 2 we have: = V = V =! [9-13] Thus the gain is 1, and the output and input signals are in phase. The circuit is technically known as a voltage follower. The impedance between the noninverting input and ground is very high. This circuit is typically used to match a device whose output impedance is high to a device whose input impedance is low. Impedance matching is important in electronics. It is often (though not always) desired that maximum power be transferred from one stage to another, and this can only be achieved if the impedances are matched in this way. N9-8
Noninverting Amplifier with Gain If we add two resistors to the previous circuit we get the circuit in Figure 9-17. I R 2 G = R 2 A I = 0 R 2 I GAIN R 2 bw R IN 10 1 kω 9 kω 100 khz 400 MΩ 100 100 Ω 9.9 kω 10 khz 280 MΩ 1000 100 Ω 99.9 kω 1 khz 80 MΩ Figure 9-17. A noninverting amplifier with gain. Shown below the figure are typical specifications for a Motorola 741. According to Rule 1, I = 0. The voltage at the inverting input is given by the voltage divider equation =, V = R 2 GAIN R 2 bw R IN 1 10 kω 10 kω 1 MHz 10 kω 10 1 kω 10 kω 100 khz 1 kω 100 1 kω 100 kω 10 khz 1 kω 1000 100 Ω 100 kω 1 khz 100 Ω Figure 9-18. Inverting amplifier with gain. Shown below the figure are typical specifications for a Motorola 741. urrent to Voltage onverter The current to voltage amplifier (Figure 9-19) is a variation of the inverting amplifier. Summing the currents flowing into node A we have so that I 0 R I = R, = 0, applying Rule 2. Thus the closed-loop gain is G = = R 2. [9-14] Thus the amplifier has gain but does not invert. The input impedance is very high, as it was in the previous example. This circuit is typically used as a general-purpose amplifier. I A R I = RI Inverting Amplifier With Gain We briefly return to the inverting amplifier with gain (reproduced in Figure 9-18). Typical values of external components are tabled below the figure. Here G = R 2. [9-15] The amplifier has gain but inverts. The input impedance is essentially. Figure 9-19. urrent to voltage converter. and = IR. [9-16] The output voltage is proportional to the input current. This function might look a little unusual, but the circuit, called a current to voltage converter, is often employed as a first stage in matching a sensor to conditioning electronics. Sensors often have to be placed some distance from the controlling electronics and the connecting cables can be quite long. To sidestep the voltage drop that would otherwise occur in a long N9-9
connecting cable the sensor is designed as a current source. This means that at the controlling end the current must be converted to a voltage. Sum Amplifier With the circuit shown in Figure 9-20, analog signals can be effectively added together. We can show that the output voltage is proportional to the algebraic sum of the input currents. V 1 R 2 V x A V V A V 2 R 3 = A V x = A(V V ) Figure 9-21. A difference amplifier. R1 S also = A( V V ). [9-20] V1 N9-10 V2 R2 Figure 9-20. A summer amplifier. This circuit is shown with two inputs, but in principle could have any number of inputs. Summing the currents flowing into node S we have: V 1 V 2 R 2 = 0. In the event that = = R 2 we have the simple result: ( V 1 V 2 ). [9-17] The output equals the sum of the inputs (with inversion). Difference Amplifier The circuit of Figure 9-21 gives an output proportional to the difference between the two inputs. Assuming an ideal opamp we neglect the currents entering the inverting and non-inverting inputs. Thus we can add the currents flowing into nodes A and, V 1 V V = 0, [9-18] V 2 V R 2 0 V R 3 = 0. [9-19] If we take for simplicity = R 2 = = R 3 (different values lead to a weighting of the inputs), we can eliminate V and V from eqs[9-18], [9-19] and [9-20] to give V out 1 2 A = V V 2 1. For A>>1, = V 2 V 1. Thus the circuit can be used to subtract signals. Real OpAmps We hope that with the examples we have chosen you can appreciate the usefulness of the ideal amplifier approximation. Though not quite true and leading to expressions of gain that are not quite correct the approximations are nevertheless good enough to provide the functionality we need most of the time. However, there are times when we need to take account of how real opamps differ from the ideal. The following list of parameters points out characteristics and limitations of the typical opamp you should be aware of: A o (open loop voltage gain) Typically 100,000 or 100 d Z in (input impedance) Typically 1 MΩ for JTs, 1 MMΩ for FTs. The larger this number is the better. Z out (output impedance) Typically a few hundred ohms I (input bias current) Typically a fraction of a µa for JTs and a few picoa for FTs. The smaller this number is the better. V (supply voltage range)
Typical limits are ± 3 volts to ± 15 volts V I (max) (input voltage range) Typically 2 volts less than V 50 khz output waveform V IO (input-offset voltage) Typically a few mv f T (Transition Frequency) The transition frequency is the frequency at which the open loop gain curve falls to unity (or the frequency at which Log(gain) = 0). For the 741 f T = 1 MHz. f T can also be used as a gain-bandwidth product, i.e., f T = G x bandwidth. Opamps with much larger f T s than the 741 have been on the market for some years. 1 KHz output waveform Figure 9-23. The slew rate is given by y/x, where x is in µs and y is in volts. The higher the frequency the greater the slew rate limiting becomes apparent. y x Gain At this stage you should be able to test your understanding of opamps. Here is an example. 1000 10 1 3 5 6 log f xample Problem 9-1 Properties of an OpAmp The opamp shown in Figure 9-24 may be considered to be ideal. What is the gain to be expected of this circuit? If the opamp s f T is 1 x 10 6 Hz, what is the bandwidth to be expected? Gain bandwidth ft 1 1 x 10 6 10 6 10 1 x 10 5 10 6 1000 1 x 10 3 10 6 Figure 9-22. The gain-bandwidth product of an opamp is a constant. The data below the figure are for a typical Motorola 741. 100 kω 200 kω Slew Rate An opamp is expected to faithfully reproduce the swing or skew in the signal applied to it. ut if the frequency and amplitude of the input signal are large enough then the output signal may not be able to accurately follow the slew in the input (Figure 9-23). This inertia or lag is quantified by engineers with a parameter called the slew rate, expressed in volts per second. Typical values are in the range 1 V/µs to 10 V/µs. One effect of slew rate limiting is that the bandwidth of the amplifier is greater for small input signals than it is for large input signals. Figure 9-24. An op amp amplifier. Solution: The gain of the amplifier is given by eq[9-14] where and R 2 are 200 kω and 100 kω, respectively. Thus G = (200 kω 100 kω)/200kω = 1.5. The gain-bandwidth product, f T, is given as 1 x 10 6 Hz. Therefore the bandwidth to be expected is: bw = f T /G = 1 x 10 6 /1.5 = 6.67 x 10 5 Hz. This bandwidth is quite large, meaning that the circuit could be used through the audio range of frequencies N9-11
and well beyond. Practice Problems N9-12