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 BJT Small-Signal Equivalent Circuit Models Our next objective is to develop small-signal circuit models for the BJT. We’ll focus on the npn variant in this lecture. Recall that we did this for the diode back in In order to develop theseBJT_Small-signal models, there are two small-signal resistances that we must first determine. These are: 1. r p: the small-signal, active mode input resistance between the base and emitter, as “seen looking into the base.” 2. re: the small-signal, active mode output resistance between the base and emitter, as “seen looking into the emitter.” These resistances are NOT the same. Why? Because the transistor is not a reciprocal device. Like a diode, the behavior of the BJT in the circuit changes if we interchange the terminals. Determine r p Assuming the transistor in this circuit is operating in the active mode, then The AC small-signal equivalent circuit from Notice the “AC ground” in the circuit. This is an extremely important concept. Since the voltage at this terminal is held constant at VCC, there is no time variation of the voltage. Consequently, we can set this terminal to be an “AC ground” in the small-signal circuit. For AC grounds, we “kill” the DC sources at that terminal: short circuit voltage sources and open circuit current sources. So, from the small-signal equivalent circuit above: we see that Hence, using (2) in (3) This r p is the BJT active mode small-signal input resistance of the BJT between the base and the emitter as seen looking into the base terminal. (Similar to a Thévenin resistance, this statement means we are fictitiously separating the source from the base of the BJT and observing the input resistance, as indicated by the dashed line in Fig. 2.) Determine re We’ll determine re following a similar procedure as for r p, but beginning with The AC component of iE in (5) is or with IE =I c|c , As indicated in Fig. 1 above, re is theBJT_Small-signal resistance between the emitter and base seen looking into the emitter: Mathematically, this is stated as Assuming an ideal signal voltage source, then e be ve=-vbe and Using (7) in this equation we find But from (5.87) Therefore, using this last result in (10) gives This is the BJT active mode small-signal resistance between the base and emitter seen looking into the emitter. It can be shown that Rz=(b+1)re[ed] It is quite apparent from this equation that e r r p . . This result is not unexpected because the active mode BJT is a non-reciprocal device, as mentioned on page 1 of these notes. BJT Small-Signal Equivalent Circuits We are now in a position to construct the equivalent active mode, small-signal circuit models for the BJT. There are two families of such circuits: 1. Hybrid- p model 2. T model. Both are equally valid models, but choosing one over the other sometimes leads to simpler analysis of certain circuits. Hybrid- p Model Version A. Let’s verify that this circuit incorporates all of the necessarysmall-signal characteristics of the BJT: ib= vbe |rp as required by (3). ic= gm vbe as required by (5.86), which we saw in the last lecture. ib+ ic= ie as required by KCL. We can also show from these relationships that ie= vbe| re. Version B. We can construct a second equivalent circuit by using Hence, using this result the second hybrid- p model is T Model The hybrid- p model is definitely the most popular small-signal model for the BJT. The alternative is the T model, which is useful in certain situations. The T model also has two versions: Version A. Version B. The small-signal models for pnp BJTs are identically the same as those shown here for the npn transistors. It is important to note that there is no change in any polarities (voltage or current) for the pnp models relative to the npn models. Again, these small-signal models are identically the same.