In general though we would never give something this difficult on a test or

# In general though we would never give something this

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force this to converge after just 3 or 4 iterations. In general, though, we would never give something this difficult on a test or exam. However, to build useful circuits in real life, you will often need to be able to at least perform basic analysis of such complex circuits.

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241 This last lecture will cover the small signal model for the BJT. As we will see, it shares many similarities with that of the MOSFET, so many of our old techniques still apply. Current Topics: BJT SS Examples The basic process for solving BJT small signal circuits is the same as what we studied for MOSFETs. To begin, we must solve the BJT circuit at DC. Next, we replace capacitors and DC voltage sources with a short circuit, and DC current sources with an open circuit. These steps are part of the general small-signal analysis process, and are identical for the MOSFET and BJT. The last step is to replace the BJT with an equivalent small-signal model. BJT Small Signal Models The basic small-signal model for the BJT is called the hybrid-pi model. Like the default model for the MOSFET, this is the general-purpose replacement for the BJT in SS analysis. You will find it tends to work best for finding open-circuit voltage gain (all cases), and input/output resistance when there is no emitter resistor or common-base connection. The primary difference from the MOSFET model is the addition of the resistor from base to emitter, , and the different formula for . Like the MOSFET, both of these small-signal parameters are determined by the particular bias point (DC current solution) of the circuit: As with the NMOS and PMOS, the above model is valid for the NPN transistor. For the PNP model, it is very important to note that the model is identically the same as to the NPN. There are no changes in any voltage or current polarities. Be careful of this small detail. The governing equations for the parameters of the above model are as follows: Transconductance Base-Emitter Resistance Early Effect | | | | | | As with the MOSFET, the BJT may be modeled with an added parallel resistance caused by what is called the Early effect. Note that the formula for for the BJT actually depends on (while Class Notes BJT Small Signal Analysis
242 channel-length modulation for the MOSFET did not depend on ). Usually this effect is small compared to the magnitude of , hence the approximation. As with the MOSFET, the values of , , and come from our DC solution of the circuit. The value of would be given if needed. Lastly, the value of is the same thermal voltage from the diode exponential model; at standard temperature. Note that the Early effect is less significant for the BJT at DC, and is commonly ignored. It, however, often has a larger effect than the MOSFET in small signal domain. Lastly, like the MOSFET, the BJT has an alternate model, also called the T-model.

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