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Engineering Class Home Pages UUNIVERSITY OF SSOUTHERN CCALIFORNIA SCHOOL OF ENGINEERING DEPARTMENT OF ELECTRICAL ENGINEERING EE 348: Lecture Supplement #3 Fall, 1998 Canonic Bipolar Junction Transistor Cells Choma & Trujillo 11.2.2.1. INTRODUCTION The circuit configurations of linear signal processors realized in bipolar technology are as diverse as are the system operating requirements that these circuits are designed to satisfy. Despite topological diversity, most practical open loop linear bipolar circuits derive from interconnections of surprisingly few basic subcircuits. These subcircuits include the diode- connected bipolar junction transistor (BJT), the common emitter amplifier, the common base amplifier, the common emitter-common base cascode, the emitter follower, the Darlington connection, and the balanced differential pair. Because these open loop subcircuits underpin linear bipolar circuit technology, they are rightfully termed the canonic cells of linear bipolar circuit design. By examining the low frequency performance characteristics of the canonic cells of linear bipolar technology, this section achieves two objectives. First, the forward gain, the driving point input resistance, and the driving point output resistance are catalogued for each canonic circuit. This information produces Thévenin and Norton I/O port equivalent circuits that expedite the analysis and design of multistage electronics. Second, the forthcoming work establishes a basis for prudent circuit design in that all analytical results are studied by highlighting the attributes and uncovering the limitations of each cell. The understanding that resultantly accrues paves the way toward systematic design procedures that yield optimal circuit architectures capable of circumventing observed subcircuit shortcomings. 11.2.2.2. SMALL SIGNAL MODEL The fundamental tool exploited in the analyses that follow is the low frequency, small signal equivalent circuit of a bipolar junction transistor shown in Fig. (11.1a). This equivalent circuit, which applies to NPN and PNP discrete component and monolithic transistors, derives from the low frequency, large signal, NPN BJT model offered in Fig. (11.1b)[1]-[2]. As is depicted in Fig. (11.1c), the PNP large signal transistor model is topologically identical to its NPN counterpart. The only difference between the two models is a reversal in the direction of all controlled current sources and branch currents and a reversal in polarity of all assigned branch and port voltages. EE 348 University of Southern California J. Choma, Jr. r r b c base collector c i r b i r p o c r e (a). emitter r r b i c i c collector baseb collecto v 12c i 1 1 c1 i 1 1 base b v I v I v e BE x CC ce 1 2 2 v v v ce be be c 2 2 c r emitter e 2 2 c (b). emitter r r b i c i c collector base b collecto v 2 c 1 i 2 2 c2 i 2 2 base b v I v I e BE x CC v 2 ec 1 1 v v v eb eb c ec 1 1 c r emitter e 1 1 c (c). emitter FIGURE (11.1). (a) Low Frequency, Small Signal Model Of A Bipolar Junction Transistor. (b) Low Frequency, Large Signal Model Of An NPN Bipolar Junction Tran- sistor. (c) Low Frequency, Large Signal Model Of A PNP Bipolar Junction Transistor. Lecture Supplement #3 147 Fall Semester, 1998 EE 348 University of Southern California J. Choma, Jr. The large signal models in Figs. (11.1b) and (11.1c) are simplified to reflect transistor biasing that assures nominally linear device operation for all values of applied input signal voltages. A necessary condition for linear operation is that the internal emitter-base junction voltage, ve, be at least as large as the threshold voltage, say vγ , of the junction for all time; that is v(t)> v , for all e g (11-1) For silicon transistors, vγ is typically in the neighborhood of 700 mV to 750 mV. A second condition underlying transistor operation in its linear regime is that the internal base-collector junction voltage, vc, is never positive; that is v(t)< 0 , for all c (11-2) In the models of Figs. (11.1b) and (11.1c), rb represents the effective base resistance of a BJT, rc is its net internal collector resistance, and re is the net internal emitter resistance. All three resistances, and particularly rb, decrease monotonically with increasing quiescent base and [3]-[4] collector currents, IBQ and ICQ, respectively . The collector resistance also decreases with increases in the intrinsic collector-emitter voltage, vx. Large base, collector, and emitter resistances conduce reduced circuit gain, diminished gain-bandwidth product, and increased electrical noise. In view of these observations and in the interest of formulating a mathematically tractable analysis that produces conservative estimates of bipolar circuit performance, these resistances are usually interpreted as constants equal to their respective low current, low voltage values. In a monolithic fabrication process, unacceptably large internal device resistances can be reduced by exploiting the fact that rb, rc, and re are inversely proportional to emitter-base junction injection area. This area is a designable parameter chosen to ensure that the transistor in question conducts the proper density of collector current. Unfortunately, the engineering price potentially paid for a reduction of device resistances through increases in junction area is circuit response speed, since the capacitances associated with transistor junctions are directly proportional to device injection area. The current, IBE, in Figs. (11.1b) and (11.1c) is given approximately by A J E S v /n V I 5 ee f T (11-3) BE b F where AE is the aforementioned emitter-base junction injection area, JS, is the density of transistor β saturation current, and F is the forward, short circuit current transfer ratio. Moreover, nf is the injection coefficient of the emitter-base junction, ve is the internal junction voltage serving to forward bias the emitter-base junction, and kT j VT 5 (11-4) q Lecture Supplement #3 148 Fall Semester, 1998 EE 348 University of Southern California J. Choma, Jr. is the Boltzman voltage. In the latter expression, k is Boltzman's constant [1.38(10-23) joules -per- Kelvin degree], Tj is the absolute temperature of the emitter-base junction, and q is the magnitude of electron charge [1.6(10-19) coulombs]. [5] The current, ICC, derives from I v ve /n f VT CC x I 5 A J e 12 11 (11-5) CC E S I V KF AF [6] where IKF, which is proportional to AE, is the forward knee current of the transistor , and VAF, [7] which is independent of AE, is the forward Early voltage . Note that the base current, ib, is the current IBE, while the collector current, ic, is ICC. Thus, the static common emitter current gain (often referred to as the "DC beta"), hFE, of a bipolar junction transistor is i I i v c CC c x h 5 5 5 b 12 11 (11-6) FE i I F I V b BE KF AF which is functionally dependent on both the collector current and the intrinsic collector-emitter volt- age. Unlike the base, collector, and emitter resistances, the resistance, rπ, in the small sig- nal model of Fig. (11.1a) is not an ohmic branch element. It is a mathematical resistance that arises from the Taylor series expansion of the current, IBE, about the quiescent operating point, or Q-point, of the transistor. In particular, rπ, which is known as the emitter-base junction diffusion resistance, derives from 1 ] I BE 5 (11-7) r ] v p e |Q where it is understood that the indicated derivative is evaluated at the Q-point of the device. This Q-point is unambiguously defined by the zero signal, or static, values of the base current, IBQ, the collector current, ICQ, and the internal collector-emitter voltage, VXQ. Using (11-3), (11-6), and the + fact that ib IBE, h n V FE f T r 5 (11-8) p I CQ The inverse dependence of rπ on quiescent collector current renders rπ large at low collector current biases. Similarly, ro, the forward Early resistance, derives from Lecture Supplement #3 149 Fall Semester, 1998 EE 348 University of Southern California J. Choma, Jr. ] I 1 CC 5 (11-9) r ] v o x |Q It can be shown that V 1 V XQ AF r 5 (11-10) o I CQ I 12 CQ I KF Like rπ, ro is also large for low level biasing. Finally, the parameter β, which is the low frequency, small signal, common emitter, short current gain (often more simply referred to as the "AC beta") of the transistor, is b 5 g r m p (11-11) where gm, the forward transconductance of a BJT is ]ICC g 5 (11-12) m ] v e |Q From (11-5), (11-6), (11-8), and (11-11), I CQ b 5 h 12 (11-13) FE I KF << β To the extent that ICQ IKF, is nominally independent of both Q-point collector current and emit- ter-base junction injection area. 11.2.2.3. SINGLE INPUT-SINGLE OUTPUT CANONIC CELLS DIODE-CONNECTED TRANSISTOR The simplest of the single input-single output, or single ended, canonic cells for linear bipolar circuits is the diode-connected transistor offered in Fig. (11.2a). This transistor connection emulates the volt-ampere characteristics of a conventional PN junction diode. It can therefore be used in rectifier, voltage regulator, DC level shifting, and other applications that exploit Lecture Supplement #3 150 Fall Semester, 1998 EE 348 University of Southern California J. Choma, Jr. conventional diodes.
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