EE 105 --- Spring 2005 --- Discussion Notes (written by Amin) Monday, May 2, 2005 EE 105 Discussion Section 101 Announcements The Importance of BJTs There are two major types of transistors: (i) MOSFETs, and (ii) BJTs. While MOSFETs are currently the prevalent technology due to their superior digital performance, BJTs play important roles in certain analog applications. To name a few examples, BJTs are preferred choice for power amplifiers (i.e. amplifiers that are designed to deliver a large amount of power to a load). Also, BJTs provide more gm as compared to their MOSFET counterparts for the same bias current. Hence, one can obtain larger gain for less power using BJT transistors. Lastly, the transit frequency (i.e. Tω) of BJTs has historically been larger than MOSFETs for any given technology node. This translates into better frequency response for the BJT transistor. It should be noted, however, that recent lithographic and manufacturing advancements have narrowed the gap between the Tω of the BJT and MOSFET transistor. The focus in EE105 is to have enough understanding of BJT operation such that one can analyze and design BJT amplifier circuits. To this end, we will follow the same outline as that for the MOSFET. More specifically, 1. Develop a model based upon device physics that relates the DC currents set up in response to DC voltages applied at the terminals of the device. This essentially encapsulates the development of the BJT large signal equations, thereby allowing one to analyze biasing issues in BJT circuits. 2. Construct the equivalent small-signal model for the BJT based upon the derived large signal equations. 3. Use the small-signal model to analyze and design circuits that process small changes in current and/or voltage (i.e. small signals). BJT Structure and Regions of Operation The bipolar junction transistor is nothing more than two pn junctions in series to one another, back to back. This is pictorially depicted in Figure 1. As was the case for MOSFETs, BJTs come in two different flavors. While the transistor structure appears to be symmetrical based upon Figure 1, it is not in practice. More specifically, the doping in the emitter and collector regions are quite different from one another. 1EE 105 --- Spring 2005 --- Discussion Notes (written by Amin) B EC C B EeffEW, effBW,CB E CB E Figure 1a. NPN BJT Figure 1b. PNP BJT Legend n-type Si p-type Si The effective base width (see Figure 1), , is an important device parameter for the BJT. Analogous to the length of a MOSFET, one strives to have as small of a as possible for performance. Also, the dashed regions in Figure 1 are indicating the depletion regions present in the BJT structure. effBW,effBW, Considering that the BJT consists of two diodes, it takes on 3 regions of operation: 1. Cutoff: Both pn junctions are reverse-biased, with very little current (ideally zero) flowing through the resultant device, 2. Saturation: Both pn junctions are forward-biased, and 3. Active: One pn junction is forward-biased, while the other is reverse-biased. Note: The saturation region of operation should be avoided for amplifier design, as was the case for the triode region for MOSFETs. The region resembling the MOSFET saturation region in BJTs is the active region of operation. Note: Here, the forward active region of operation shall be the focus. This region of operation is marked by the BE junction being forward-biased and the CB junction reverse-biased. The reverse active region of operation is when the BE junction is 2EE 105 --- Spring 2005 --- Discussion Notes (written by Amin) reverse-biased and the CB junction forward-biased. These two regions are different from one another because the emitter and collector dopings of the device are different from one another in practice. Large Signal Model for the PNP Transistor in Forward Active In order to derive equations for the DC currents set up in a BJT in response to DC voltages applied at the terminals, one needs to focus on the minority carrier concentrations within the device. The reason for this is discussed in EE130. As such, let’s first focus on the minority carrier concentrations present within the PNP structure at thermal equilibrium. Using relationships discussed in the early part of the semester, the minority carrier concentrations are as follows: emitterAiemitterNnn,2= (1) baseDibaseNnp,2= (2) collectorAicollectorNnn,2= (3) Note: In practice, . collectorAbaseDemitterANNN,,,>>>> Figure 2 depicts a PNP transistor biased in the forward active region of operation through the application of a couple of DC bias voltage sources. As will be discussed in EE130, BICIEI BCVEBV C BE 13426 5 Figure 2. PNP in Forward Active RegionpdiffusionI,ndiffusionI, 3EE 105 --- Spring 2005 --- Discussion Notes (written by Amin) the minority carrier concentrations at the depletion edges of a pn junction are ⎟⎟⎠⎞⎜⎜⎝⎛′thVVexp times their corresponding thermal equilibrium values, where handat diode particular by the undergone voltagebias forwardin change theand temp,roomat 26=′≈=VmVqkTVth Using this relationship then yields the following expressions: ⎟⎟⎠⎞⎜⎜⎝⎛+⋅=thEBemitterAiVVNnn exp,21 (4) ⎟⎟⎠⎞⎜⎜⎝⎛+⋅=thEBbaseDiVVNnp exp,22 (5) 0exp,23≈⎟⎟⎠⎞⎜⎜⎝⎛−⋅=thBCbaseDiVVNnp (6) 0exp,24≈⎟⎟⎠⎞⎜⎜⎝⎛−⋅=thBCcollectorAiVVNnn (7) Note: The expressions in (6) and (7) are approximately zero because the exponential term ends up being a very small number in practice (e.g. typical values for are 1-2V). BCV In areas far away from the depletion regions, the minority carrier concentrations are approximately those at thermal equilibrium. Hence, emitterAiNnn,25= (8) collectorAiNnn,26= (9) In order to then approximate the minority carrier concentrations in the regions in between, a linear concentration gradient is assumed between the aforementioned end points. Note: This simplification is only valid if one neglects recombination of minority carriers. It will suffice, however, for our purposes here in EE105. Note: Concentration gradients are developed in the base and emitter regions. As a result, diffusion currents are set up across the BE junction considering that it is forward-biased. Although a concentration gradient is also set up in the collector, it 4EE 105 --- Spring 2005 --- Discussion Notes (written by
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