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1. Lecture #19 ANNOUNCEMENT вАҐ Quiz #4 (Thursday 4/3) to cover Chapters 10 & 11 OUTLINE вАҐ BJT transient response вАҐ BJT small-signal model, fT Reading: Chapter 12 Spring 2003 EE130 Lecture 19, Slide 1 BJT Switching - Qualitative Spring 2003 EE130 Lecture 19, Slide 2 1

2. Turn-on transient вАҐ We know: dQB = I BB вИТ QB where IBB=VS/RS dt ѕДB вАҐ The general solution is: QB (t ) = I BBѕД B + Ae вИТ t / ѕД B вАҐ Initial condition: QB(0)=0. since transistor is in cutoff п£Ђ п£ґ п£ђ п£Ј QB (t ) = I BBѕД B (1 вИТ e вИТ t / ѕД B ) t r = ѕД B lnп£ђ 1 п£Ј п£ђ VCC / RL п£Ј п£± QB (t ) I BBѕД B + Ae вИТ t / ѕД B п£ђ1вИТ I ѕД п£Ј п£≠ п£Є п£іп£і ѕД = ѕДt L0 вЙ§ t вЙ§ tr BB B iC (t ) = п£≤ t п£і VCC Lt вЙ• t r п£іп£≥ RL Spring 2003 EE130 Lecture 19, Slide 3 Turn-off transient вАҐ We know: dQB = вИТќЊI BB вИТ QB dt ѕДB вАҐ The general solution is: QB (t ) = вИТќЊI BBѕД B + Ae вИТ t / ѕД B вАҐ Initial condition: QB(0)=IBBѕДB [ QB (t ) = I BBѕД B (1 + ќЊ )e вИТ t / ѕД B вИТ ќЊ ] п£Ђ п£ґ п£ђ п£Ј п£ђ 1+ ќЊ п£Ј п£± I CC L0 вЙ§ t вЙ§ t sd t sd вЙЕ ѕД B ln п£і п£ђ I CCѕД t п£Ј iC (t ) = п£≤ QB (t ) I BBѕД B [(1+ќЊ )e вИТt / ѕД B вИТќЊ ] п£ђ I ѕД +ќЊ п£Ј п£≠ п£Є п£і ѕД = Lt вЙ•t BB B п£≥ t ѕДt sd Spring 2003 EE130 Lecture 19, Slide 4 2

3. Small-Signal Model B C Forward-active mode, Common-emitter configuration: + CѕА vbe rѕА gm vbe I C = ќ± F I F e qVBE / kT вИТ E E transconductance: dI C d gm вЙ° = (ќ± F I F e qVBE / kT ) At 300 K, for example, dVBE dVBE gm=IC /26mV. q = ќ± F I F e qVBE / kT = I C /(kT / q ) kT g m = I C /(kT / q ) Spring 2003 EE130 Lecture 19, Slide 5 Small-Signal Model (cont.) 1 dI B 1 dI C g = = = m rѕА dVBE ќ≤ dc dVBE ќ≤ dc ќ≤ dc ќ≤ dc rѕА = rѕА = gm gm dQF d (ѕД F I C ) CѕА = = = ѕД F gm dVBE dVBE This is the minority-carrier charge-storage capacitance, better known as the diffusion capacitance. Add the depletion-layer capacitance, CJBE : CѕА = ѕД F g m + CdBE Spring 2003 EE130 Lecture 19, Slide 6 3

4. Forward Transit Time ѕДF QF ѕД F = ѕД E + ѕД BE + ѕД t + ѕД BC = IC where ѕД E = emitter delay time ѕД BE = emitter-base depletion region transit time ѕД t = base transit time ѕД BC = base-collector depletion-region transit time вАҐ To reduce the forward transit time, the emitter as well as the depletion layers must be kept thin. Spring 2003 EE130 Lecture 19, Slide 7 Example: Small-Signal Model Parameters A BJT is biased at IC = 1 mA and VCE = 3 V. ќ≤dc=90, ѕДF=5 ps, and T = 300 K. Find (a) gm , (b) rѕА , (c) CѕА . Solution: 1 mA mA (a) g m = I C /(kT / q) = = 39 = 39 mS (milli siemens) 26 mV V (b) rѕА = ќ≤dc / gm = 90/0.039 = 2.3 kвД¶ c) CѕА = ѕД F g m = 5 √Ч10 вИТ12 √Ч 0.039 вЙИ 1.9 √Ч10 вИТ14 F = 19 fF(femto farad) Spring 2003 EE130 Lecture 19, Slide 8 4

5. Application of Small-Signal Model Once the model parameters have been determined, one can analyze circuits with arbitrary source and load impedance. B C The parameters are routinely + Signal C vbe rѕА gm vbe Load determined through comprehensive source ѕА - measurement of the BJT AC E E and DC characteristics. rb C¬µ rc B C + CѕА rѕА C dBC Full BJT equivalent circuit: vbe gm vbe ro вИТ re E Spring 2003 EE130 Lecture 19, Slide 9 Cutoff Frequency fT B C + Signal Load 1 C source ѕА vbe rѕА gm vbe ќ≤ ac = 1 at fT = - 2ѕА (ѕД F + C JBE kT / qI C ) E E The load is a short circuit, and the signal source is a current source, ib , at frequency, f. At what frequency does the a.c. current gain fall to unity? ib ib vbe = = input admittance 1 / rѕА + jѕЙCѕА ic = g m vbe ic gm 1 ќ≤ (ѕЙ ) = = = ib 1 / rѕА + jѕЙCѕА 1 / ќ≤ F + jѕЙѕД F + jѕЙCdBE kT / qI C Spring 2003 EE130 Lecture 19, Slide 10 5

6.For the full BJT 1 fT = equivalent circuit: 2ѕА (ѕД F + (CdBE + CdBC )kT / (qI C ) + CdBC (re + rc )) SiGe HBT by IBM fT is commonly used as a metric for the speed of a transistor. Spring 2003 EE130 Lecture 19, Slide 11 Cutoff Frequency fT 1 fT = 2ѕА (ѕД F + (CdBE + CdBC )kT / (qI C ) + CdBC (re + rc )) вАҐ To maximize ft: вАУ Increase IC вАУ Minimize CdBE, CdBC вАУ Minimize re, rc вАУ Minimize ѕДF Spring 2003 EE130 Lecture 19, Slide 12 6

7.Base Widening at High IC: the Kirk Effect вАҐ At very high current densities (> 0.5 mA/¬µm2), base widening occurs*, so QB increases. вЖТ tt and ѕДBC increase, so ѕДF increases and fT decreases. *For an NPN BJT, the electron Top to bottom : density in the collector (n = NC) VCE = 0.5V, 0.8V, becomes insufficient to support 1.5V, 3V. the collector current even if the electrons move at the saturation velocity. I C = qAnvsat IC ѕБ dep ,C = qN C вИТ qn = qN C вИТ Avsat Eventually, ѕБ changes sign as IC increases (for fixed VBC), and the base width is effectively widened. Spring 2003 EE130 Lecture 19, Slide 13 BJT Structure for High Speed B E C P+polySi N+ polySi P+polySi p+ P base p+ Shallow N+ N collector trench Deep Deep trench N+ subcollector trench вАҐ Narrow base PвИТ substrate вАҐ n+ poly-Si emitter вАҐ Self-aligned p+ poly-Si base contacts вАҐ Lightly-doped collector вАҐ Heavily-doped epitaxial subcollector вАҐ Shallow trenches and deep trenches filled with SiO2 for electrical isolation Spring 2003 EE130 Lecture 19, Slide 14 7

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