UNIT 2
A: The Operational Amplifier
One problem with electronic devices corresponding to the generalized amplifiers is that the gains, Au or A~, depend upon internal properties of the two-port system (p, fl, R~, Ro, etc.)?~ This makes design difficult since these parameters usually vary from device to device, as well as with temperature. The operational amplifier, or Op-Amp, is designed to minimize this dependence and to maximize the ease of design. An Op-Amp is an integrated circuit that has many component part such as resistors and transistors built into the device. At this point we will make no attempt to describe these inner workings.
A totally general analysis of the Op-Amp is beyond the scope of some texts. We will instead study one example in detail, then present the two Op-Amp laws and show how they can be used for analysis in many practical circuit applications. These two principles allow one to design many circuits without a detailed understanding of the device physics. Hence, Op-Amps are quite useful for researchers in a variety of technical fields who need to build simple amplifiers but do not want to design at the transistor level. In the texts of electrical circuits and electronics they will also show how to build simple filter circuits using Op-Amps. The transistor amplifiers, which are the building blocks from which Op-Amp integrated circuits are constructed, will be discussed. The symbol used for an ideal Op-Amp is shown in Fig. 1-2A-1. Only three connections are shown: the positive and negative inputs, and the output. Not shown are other connections necessary to run the Op-Amp such as its attachments to power supplies and to ground potential. The latter connections are necessary to use the Op-Amp in a practical circuit but are not necessary when considering the ideal 0p-Amp applications we study in this chapter. The voltages
at the two inputs and the output will be
represented by the symbols U+, U-, and Uo. Each is measured with respect t~ ground potential. Operational amplifiers are differential devices. By this we mean that the output voltage with respect to ground is given by the expression
Uo =A(U+ -U-) (1-2A-l)
where A is the gain of the Op-Amp and U+ and U - the voltages at inputs. In other words, the output voltage is A times the difference in potential between the two inputs.
Integrated circuit technology allows construction of many amplifier circuits on a single composite \the \number A in Eq. (1-2A-1) can be on the order of 100,000 or more. (For example, cascading of five transistor amplifiers, each with a gain of 10, would yield this value for A.) A second important factor is that these circuits can be built in such a way that the current flow into each of the inputs is very small. A third important design feature is that the output resistance of the operational amplifier (Ro) is very small. This in turn means that the output of the device acts like an ideal voltage source.
We now can analyze the particular amplifier circuit given in Fig. 1-2A-2 using these characteristics. First, we note that the voltage at the positive input, U +, is equal to the source voltage, U + = Us. Various currents are defined in part b of the figure. Applying KVL around the outer loop in Fig. 1-2A-2b and remembering that the output voltage, Uo, is measured with respect to ground, we have
-I1R1-I2R2+U0=0 (1-2A-2)
Since the Op-Amp is constructed in such a way that no current flows into
-either the positive or negative input, I =0. KCL at the negative input terminal then yields
I1 = I2
Using Eq. (1-2A-2) and setting I1 =I2 =I,
U0=(R1+R2)I (1-2A-3) We may use Ohm's law to find the voltage at the negative input, U-, noting the assumed current direction and the fact that ground potential is zero volts:
(U-0)/ R1=I
-So, U=IR1
-
and from Eq. (1-2A-3), U=[R1/(R1+R2)] U0
Since we now have expressions for U+ and U-, Eq. (1-2A-l) may be used to calculate the output voltage,
-
U0 = A（U+-U-）=A[US-R1U0/(R1+R2)]
Gathering terms,
U0 =[1+AR1/(R1+R2)]= AUS (1-2A-4) and finally,
AU = U0/US= A(R1+R2)/( R1+R2+AR1) (1-2A-5a) This is the gain factor for the circuit. If A is a very large number, large enough that AR~ >> (R1+R2),the denominator of this fraction is dominated by the AR~ term. The factor A, which is in both the numerator and denominator, then cancels out and the gain is given by the expression AU =(R1+R2)/ R1 (1-2A-5b)
This shows that if A is very large, then the gain of the circuit is independent of the exact value of A and can be controlled by the choice of R1and R2. This is one of the key features of Op-Amp design the action of the circuit on signals depends only upon the external elements which can be easily varied by the designer and which do not depend upon the detailed character of the Op-Amp itself. Note that if A=100 000 and (R1 +R2)/R1=10, the price we have paid for this advantage is that we have used a device with a voltage gain of 100 000 to produce an amplifier with a gain of 10. In some sense, by using an Op-Amp we trade off \
A similar mathematical analysis can be made on any Op-Amp circuit, but this is
cumbersome and there are some very useful shortcuts that involve application of the two laws of Op-Amps which we now present.
1) The first law states that in normal Op-Amp circuits we may assume that the voltage difference between the input terminals is zero, that is,
U=U
2) The second law states that in normal Op-Amp circuits both of the input currents may be assumed to be zero:
I=I=0
The first law is due to the large value of the intrinsic gain A. For example, if the output of an Op- Amp is IV and A= 100 000, then ( U+ - U- )= 10-SV. This is such a small number that it can often be ignored, and we set U+ = U-. The second law comes from the construction of the circuitry inside the Op-Amp which is such that almost no current flows into either of the two inputs.
B: Transistors
Put very simply a semiconductor material is one which can be 'doped' to produce a predominance of electrons or mobile negative charges (N-type); or 'holes' or positive charges (P- type). A single crystal of germanium or silicon treated with both N-type dope and P-type dope forms a semiconductor diode, with the working characteristics described. Transistors are formed in a similar way but like two diodes back-to-back with a common middle layer doped in the opposite way to the two end layers, thus the middle layer is much thinner than the two end layers or zones.
Two configurations are obviously possible, PNP or NPN (Fig. 1-2B-l). These descriptions are used to describe the two basic types of transistors. Because a transistor contains elements with two different polarities (i.e., 'P' and 'N' zones), it is referred to as a bipolar device, or bipolar transistor.
A transistor thus has three elements with three leads connecting to these elements. To operate in a working circuit it is connected with two external voltage or polarities. One external voltage is working effectively as a diode. A transistor will, in fact, work as a diode by using just this connection and forgetting about the top half. An example is the substitution of a transistor for a diode as the detector in a simple radio. It will work just as well as a diode as it is working as a diode in this case.
The diode circuit can be given forward or reverse bias. Connected with forward bias, as in Fig.l-2B-2, drawn for a PNP transistor, current will flow from P to the bottom N. If a second voltage is applied to the top and bottom sections of the transistor, with the same polarity applied to the bottom, the electrons already flowing through the bottom N section will promote
+
-
+
-
a
flow of current through the transistor bottom-to-top.
By controlling the degree of doping in the different layers of the transistor during manufacture, this ability to conduct current through the second circuit through a resistor can be very marked. Effectively, when the bottom half is forward biased, the bottom section acts as a generous source of free electrons (and because it emits electrons it is called the emitter). These are collected readily by the top half, which is consequently called the collector, but the actual amount of current which flows through this particular circuit is controlled by the bias applied at the center layer, which is called the base.
Effectively, therefore, there are two separate 'working' circuits when a transistor is working with correctly connected polarities (Fig. 1-2B-3). One is the loop formed by the bias voltage supply encompassing the emitter and base. This is called the base circuit or input circuit. The second is the circuit formed by the collector voltage supply and all three elements of the transistor. This is called the collector circuit or output circuit. (Note: this description applies only when the emitter connection is common to both circuits ~ known as common emitter configuration.) This is the most widely used way of connecting transistors, but there are, of course, two other alternative configurations -- common base and common emitter. But, the same principles apply in the working of the transistor in each case.
The particular advantage offered by this circuit is that a relatively small base current can control and instigate a very much larger collector current (or, more correctly, a small input power is capable of producing a much larger output power). In other words, the transistor works as an amplifier.
With this mode of working the base-emitter circuit is the input side; and the emitter through base to collector circuit the output side. Although these have a common path through base and emitter, the two circuits are effectively separated by the fact that as far as polarity of the base circuit is concerned, the base and upper half of the transistor are connected as a reverse biased diode. Hence there is no current flow from the base circuit into the collector circuit.
For the circuit to work, of course, polarities of both the base and collector circuits have to be correct (forward bias applied to the base circuit, and the collector supply connected so that the polarity of the common element (the emitter) is the same from both voltage sources). This also means that the polarity of the voltages must be correct for the type of transistor. In the case of a PNP transistor as described, the emitter voltage must be positive. It follows that both the base and collector are negatively connected with respect to the emitter. The symbol for a PNP transistor has an arrow on the emitter indicating the direction of current flow, always towards the base. ('P' for positive, with a PNP transistor).
In the case of an NPN transistor, exactly the same working principles apply but the polarities of both supplies are reversed (Fig. 1-2B-4). That is to say, the emitter is always made negative
relative to base and collector ('N' for negative in the case of an NPN transistor). This is also inferred by the reverse direction of the arrow on the emitter in
the symbol for an NPN transistor, i.e., current flow away from the base. While transistors are made in thousands of different types, the number of shapes in which they are produced is more limited and more or less standardized in a simple code -- TO (Transistor Outline) followed by a number.
TO1 is the original transistor shape a cylindrical 'can' with the three leads emerging in triangular pattern from the bottom. Looking at the base, the upper lead in the 'triangle' is the base, the one to the fight (marked by a color spot) the collector and the one to the left the emitter.[2] The collector lead may also be more widely spaced from the base lead than the emitter lead.
In other TO shapes the three leads may emerge in similar triangular pattern (but not necessarily with the same positions for base, collector and emitter), or in-line. Just to confuse the issue there are also sub-types of the same TO number shape with different lead designations. The TO92, for example, has three leads emerging in line parallel to a flat side on an otherwise circular 'can' reading 1,2,3 from top to bottom with the flat side to the right looking at the base.
With TO92 sub-type a (TO92a): 1=emitter 2=collector 3=base With TO92 sub-type b (TO92b): 1=emitter 2=base 3=collector
To complicate things further, some transistors may have only two emerging leads (the third being connected to the case internally); and some transistor outline shapes are found with more than three leads emerging from the base. These, in fact, are integrated circuits (ICs), packaged in the same outline shape as a transistor. More complex ICs are packaged in quite different form, e.g., flat packages.
Power transistors are easily identified by shape~ They are metal cased with an elongated bottom with two mounting holes. There will only be two leads (the emitter and base) and these will normally be marked. The collector is connected internally to the can, and so connection to the collector is via one of the mounting bolts or bottom of the can.
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