Common-Emitter Amplifiers Figure 9-18 how a common-emitter amplifier that is biased using the voltage divider method. Also shown is the small-signal equivalent circuit that resale when the transistor is replaced by its hybrid model. The gain and impedance equations we have already derived are applicable to this circuit, with a few minor modifications. Notice that the load impedance Z is now the parallel combination of R and The principal difference between this equivalent circuit and the general hybrid amplifier we studied earlier (Figure 9-13) is the presence of R = R across the input. This resistance is in parallel with the input impedance of the transistor. so <Putin resistance,.(litany:), is smaller than it would be if R were not present. Using equation 9-21, we have The reduction in amplifier input impedance caused h R reduces the voltage gain. Villus. because of the usual voltage-divider effect at the input Note that Z,. in equations 9-30 and 9-31 is R; II R,.. See. Figure 9-1 S(b). Finally. the pullet impedance of the amplifier is affected by the fact that R, is in parallel with 7…and R is in parallel with r«. Thus. using equation 9-29, we obtain The transistor shown in Figure 9- t 9 has the following h-parameter values: II;. = 1600 h.= 2 x 10= 20 p.S. Find (1) Z(3) A. = v (4) VI (5) A;, and (6) Z..(stage).Use the SPICE models for voltage-controlled voltage sources and current-controlled current sources to verify the values calculated for Au and Vt. lavs in Example 9-7. Solution”. The SPICE circuit corresponding to the hybrid model in Figure 9-1 S(b) is shown in Figure 9-20(a). Note that it is necessary to insert a dummy voltage source, VIB, in series with the base (node 3) to obtain the current that controls the Fl current source. Pay particular attention to the polarities of VIB and Fl. The Fl specification in the data file, Fl 5 0 VIB 80, means that current flowing from node 5 to node 0 equals 80 (h,.) times the current ( ) in VIB. The specification for the voltage-controlled voltage source, E I 4 0 5 0 2 E-4, means that the voltage between nodes 4 and () is 2 x 10 4 (It”.) times the voltage between nodes 5 and O. Since all capacitors are eliminated in the small-signal model a DC analysis can be performed by SPICE as well as an .AC analysis, with the same results. Note that VS is set equal to V so the voltage gain I vs is numerically equal to the output voltage at node 5. The gain A, can be determined by dividing the output voltage the input voltage at the base (node 3). r The results of the analysis are shown in Figure 9-20(b). We see that /US = Y(S) = -64.42 and
CE “‘Parameter Approximations
Certain approximations can be made to obtain simpler equations for amplifier gains and impedance in terms of h parameters. The most common approximation is h = 0, which is equivalent to neglecting the feedback effect of the output voltage Under this assumption, the equations YT have derived are greatly simplified. For example, when h., = 0, the input impedance to the transistor (equation 9-21)
becomes simply Z, =The previous example shows that assumption gives a good approximation since hit = 1600 0 and we calculated 1,= 1572 O. We will derive and present the standard approximations used in h-parameter values, and because the use of approximations is quite valid, considering the wide variation the parameters themselves are likely to have. However it is our view that the main reason for using the hybrid model at all is that it provides an accurate representation of a transistor and is therefore useful in research applications and in the development or new devices. For day-to-day analysis and design activities commercial devices we recommend the techniques and approximate models that were discussed in Chapters 4 and 5. We further note that the advent of computer analysis methods has greatly lessened the need for computational approximations, and has eliminated the need for the analyst to be concerned whether or not the assumptions on which the approximations arc based are valid for a particular situation. Under the assumption II”, “‘” 0, we obtain from equation 9- The quantity is generally much smaller than 1 (notice that it had value 0.036 in Example 9-7), so A. can be further approximated by Using this approximation in Example 9-7 gives A. = -90, compared to the value -88.56 that we calculated using the exact equation. Applying the assumption h 1 to equation 9-18, we obtain Using this approximation in Example 9-7 gives AI = SO,compared to the exact computation of 77.22. As we have already noted. the assumption 0 leads to and arrive at the approximation Z However, this approximation is often invalid, because the quantities.arc usually close in value. Therefore, Z.. is generally much greater than especially when Zs is small. Of course. the approximations given in (9-34) through (9-36) apply to the transistor alone. To determine overall amplifier gains and impedance, the effects of bias resistors must be taken into account in the usual way:WI; should note that all of the and impedance equations for Figure 9-1 B
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