【正文】 r 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 (12A5b) 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 OpAmp 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 OpAmp 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 OpAmp we trade off power for control. A similar mathematical analysis can be made on any OpAmp circuit, but this is cumbersome and there are some very useful shortcuts that involve application of the two laws of OpAmps which we now present. 1) The first law states that in normal OpAmp 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 OpAmp 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 )= 10SV. This is such a small number that it can often be ignored, and we set U+ = U. The second law es from the construction of the circuitry inside the OpAmp 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 39。doped39。 or positive charges (P type). A single crystal of germanium or silicon treated with both Ntype dope and Ptype dope forms a semiconductor diode, with the working characteristics described. Transistors are formed in a similar way but like two diodes backtoback with a mon 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. 12Bl). These descriptions are used to describe the two basic types of transistors. Because a transistor contains elements with two different polarities (., 39。 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 fetting 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 , 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 bottomtotop. By controlling the degree of doping in the different layers of the transistor during manufacture, this ability to conduct current through the second c