Let us now consider the effect of connecting a load resistor RI. across the output of the CE amplifier. Figure 5-17 shows the circuit we studied earl.er, modified to include a capacitor-coupled load resistor of 6 kfl. It is important to realize that as far as lie performance is concerned, R/. is ill parallel with Re. A de source is {/ short circuit /0 ae sign aIs, so the 3·kfl resistor in Figure 5-17 is effec i -ely grounded through (he 18-V source, and the ac voltage at the collector “sees” 3 kfl in parallel with 6 k!!. Another way of viewing this is from the standpoint of analysis by superposition: If we are interested in the output voltage due only to the ac source, V.I, \” C replace all other voltage sources by short circuits.
In our exarnple, “L = (3 kO) I! (6 kfl) = 2 kO. The de load resistance is, of course, still equal to’}’ kfl,because the coupling capacitor blocks the flow of de current into the 6-kD. resistor
he existence of an ac load that differs from the dc load means that the output volt age i~ no longer determined by variations along a load line based Oil R, = 3 kfl. Instead, the output is determined by variations along an ae load line, based on r, =- 2 k!l. The load line based only on the value of R, will hereafter be called the de load line. Since the ac load line represents all possible combinations of collector voltage and current. it must include the point where the ac input goes through O. That point is, of course, the Q-point on the de load line, so we conclude that the
It is an exercise at the end of this chapter to show that equations 5-17 and 5-18 also apply to the de load line when Rc is substituted for rc (i.e., for the case RL = 1).
It must be emphasized again that the ac load line represents all possible comb inations \)~:::>lector-emitter voltage and collector current, and that the dc load line no longer applies. It is a common mistake to believe that the dc load line governs the voltage across Rc while the ac load line governs the voltage across RL• Remember
that the current through and voltage across RL are pure ac waveforms that go both positive and negative, since the capacitor blocks the de component of the collector waveform, The only difference between VI. and the collector voltage is the de component in the lauer..
The practical implication of the ac load line is that it makes the magnitude of the ac output voltage smaller than it would be if the output variations were determined by the de load line. This fact is illustrated in Figure 5-19, where the output voltages determined by both de and ac load lines are plotted. The same base current variation is assumed for both, and it can be seen that the steeper ‘Slope of the ac load line results in a smaller output. The connection of a load across the output of an amplifier always reduces the amplitude of its ac output.
If the base resistance Ru is changed, the Q-point will shift to a new location on the de load line. Since the ac load line passes through the Q-point, it too will shift. As illustrated in Figure 5-20, ac load lines corresponding to different Qpoints are parallel to each other, since all have the same slope,
AMPLIFIER ANALYSIS USING SMALL-SIGNAL MODELS
Small-Signal Parameters
Since transistor circuits are usually analyzed using algebraic rather than graphical methods, it is convenient to have an equivalent circuit that can be substituted for the transistor wherever it appears. Many different kinds of equivalent circuits have been developed for transistors, each of which has special features that make it more useful or- more accurate than others for a particular kind of analysis. The form that an equivalent circuit takes depends on the transistor part/meters that are chosen as the basis for the circuit. A transistor parameter is simply a transistor characteristic or property that can be given a numerical value. For example, a and f3 are transistor .pararneters. The latter are examples of derived parameters: they are computed from a numerical relationship between two quantities (the ratio of two currents, in this case). Transistor parameters can also specify inherent physical characteristics, such as the resistance of the base region, orthe width of the collector-base depletion region.
Small-signal parameters are parameters whose values are determined under small-signal (ac) operating conditions. For example, the small-signal value of f3 is defined to be
Equation 5-19 states that small-signal f3 is the ratio of ac collector current to ac base current at a specified (fixed) value ,of Vn,’o Small-signal f3 can be determined from a set of collector characteristics by constructing a vertical line (a line of constant Yn:) and finding AI cl A//J along that line. (As an exercise, use Figure 5-13 , tofind the small-signal f3 at Vc/i = 10,V when III varies from 20 /LA to 40 /LA.) Up ” jo now, we have computed the (approximate) value of f3 by taking the ratio of two .dc, currents: f3 “‘” lei In- To distinguish this value from the small-signal value, many authors use the notation f3lJc (“dc beta”) when referring ‘to the ratio of de currents. , In most practical applications, the small-signal and dc values of f3 are close en ugh to be assumed ‘equal, and we will hereafter use the notation f3DC only when it is ecessary to emphasize that we ‘are referring strictly to the devalue. Like smallsignal f3, small-signal a is defined in terms of ac currents:
important physical parameter of a transistor is its small-signal resistance from emitter to base.called the emitter resistance and designated r., This resistance is the same as the small-signal input resistance of the transistor in its common-base configuration, It is defined as
The small-signal collector resistance r, is the ac resistance from collector to base. It is the same as the output resistance of a transistor in its common-base configuration and typically has a value of several megohms, because it is across a reverse-biased junction.
