We assume that base current remains relatively the same as for the active mode

# We assume that base current remains relatively the

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the transistor given this collector current. We assume that base current remains relatively the same as for the active mode: We call this gain , and it is strictly lower than the gain of the transistor would be if it were in active mode: . This represents the idea that the transistor is trying to pull its collector as close in potential to the emitter as possible (to draw more collector current, as determined by its ‘goal’ of ). However, it is limited by this lower limit of . We define a new factor based on this adjusted gain: We now have a choice. Our first option is to model the C E circuit with something like the piecewise linear model for the diode. In this case, we define , which is a series resistance: This model will work in most cases, but we do not know without further information, much like with the diode. Some common values are known for all transistors, though. For example, with an overdrive factor of 2 (i.e., ), most transistors will have . This process suffers from the same problem that we were trying to solve, though, so it is rarely used. Mostly, we go directly to the complete formula for , which is much like the exponential model for the diode: | | [ ] This will give a direct relation for in saturation mode to any value of and incoming base current (through calculating ). In general, though, the additional accuracy of this method (and the previous PWL option) is rarely needed, unless extremely high currents are in use.

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227 BJT Switch Example Consider the following circuit, where an NPN BJT is used to switch an load on and off. Estimate the efficiency of the switch and the power dissipated by the BJT from C E when the BJT is conducting, given . Assume that . Compare this to a similar type of MOSFET which has . Solution Since we are told the circuit is switching a load on and off, and we are analyzing a case where current is conducted through the load, when guessing the transistor mode we can try one of the two conducting modes first. In particular, since the transistor is used as a switch, then it is a good idea to guess saturation mode. In this case, is fixed at the given : (1) We can calculate the current through the load (and collector) directly by assuming that from there is a constant drop of : (2) 𝑅 𝐿
228 This gives us the final power dissipation, as we know and . Efficiency can be found by also calculating the useful power delivered to the load. (3) To compare this figure with the MOSFET, we assume triode mode and replace the MOSFET with : (4) We can see that the MOSFET is more efficient, but only slightly. For most low to medium-current applications, the BJT and MOSFET are relatively comparable. Here, we only have a load current of a few amps in both cases. However, the MOSFET quickly supersedes the BJT in efficiency at high currents (i.e., greater than 10A).

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