08-1 BJT Models - brd4.braude.ac.il
Theory of Analog Electronics BJT Part 1. BJT Models * In this presentation definitions and examples from Wikipedia, HowStaffWorks and some other sources were used ORT Braude Engineering College. Course: Theory of Analog Electronics 31401. Lecturer: Dr. Samuel Kosolapov [email protected] Quiz 08. 1 (before the start): Do You need this lecture ? 2 Items to be defined/refreshed/discussed • BJT appearance • Ebers-Moll Model • BJT Characteristics 3 BJT BJT – Bipolar Junction Transistor Transistor – TRANsformer of reSISTance P-N-P BJT Transistor N-P-N BJT Transistor 4 BJT: 4 Operation Modes Operating Modes in the BJT (2 Junctions 4 combinations are possible) Mode Forward-active Cutoff Saturation Reverse-active Emitter-Base Junction State Forward biased (open) R F R Collector-Base Junction State Reverse biased (closed) R F F For Analog Electronics: only Forward-Active Mode (Region) is relevant Other modes are used in Digital Electronics 5 BJT: Modes for Digital Electronics Cut-Off state: (VCE>0, VBE<0.7V all currents are very small) Both diodes are Reverse-Biased ; transistor equivalent is “OPEN SWITCH”: Saturation State: (Left non-linear part of IC - F(VCE, IB) curves. IB > ICsat/HFE ) Both diodes are Reverse-Biased; transistor equivalent is “CLOSED SWITCH”: More info (and info about Reverse-Active mode) sees in Digital Electronics books (Mauro, and Millman course). Used in 74** TTL gates. 6 BJT: Idea Device Nobel Prize Hard Work Non-Linear Model (DC & AC) Linear Small-signal AC model Ebers-Moll Model of BJT NPN Transistor (By P.Lynch. Worked Examples in Physical Electronics, 1972 (absent in ORT Library) See also Millman-Hakias. Integrated Electronics, pp. 147-148 Millman-Grabel. Microelectronics. 621.381 MIL pp. 87-89 7 BJT: Ebers-Moll Model 8 BJT: Ebers-Moll Model Input Characteristics IB=F1( VBE, VCE ) ~ Simple Diode. Nearly no influence of Vce: (0.3V and 10 V) 9 BJT: Ebers-Moll Model Input Characteristics IB=F1( VBE, VCE ) in 3D Taylor Approximation will be good here !!! Attention: For Vce < ~0.2 V more complex graph 10 BJT: Ebers-Moll Model Output Characteristics IC=F2( Vce, IB ) {MAPLE: Symbolic formula is ~ 6 pages} 11 BJT: Ebers-Moll Model Output Characteristics IC=F2( Vce, IB ) in 3D 12 BJT: Ebers-Moll Model H-Parameters Feedback: ~ 0 Good H12=HFE = b ~ 100: Current Gain H22=HOE : Exaggeration H11=HIE = 1kW: 13 BJT: Ebers-Moll Model Large Signal Model #1 14 BJT: Ebers-Moll Model Large Signal Model #2 15 BJT: Ebers-Moll Model Large Signal Model #3 Rebf 16 BJT: Example: Common Base Amplifier Results of Simulation: Mode test: Inspecting E-B-C Voltages: VEB < 0 VBE>0 BE diode is Forward-Biased VCB > 0 CB diode is Reverse-Biased Forward-Active Mode Voltage Gain: (10.06-10.55) /( (-2.8) – (-2.7 ) = +4.9 17 BJT: Example: Common Base Amplifier Manual Solution with simplest model No sub-division for DC and AC !!!!! SUPPOSE (and this MUST be CHECKED at the end, (otherwise we CAN NOT use this model), that transistor is in Forward-Active state. First step: REPLACE transistor to its model (Model 2 here): 18 BJT: Example: Common Base Amplifier Manual Solution with simplest model Calculate Voltages and Currents IE V signal V0 Rsignal F VC F I E RC VCC ; b ; 1 F F Vsignal V0 RC b RC Vsignal V0 VCC VC VCC Rsignal b 1 Rsignal 1 VC RC 1 F I E VCC RC 19 BJT: Example: Common Base Amplifier Manual Solution with simplest model Get Numerical Results b = 100 – parameter of the transistor. VC1 = (100/(1+100))*(5/1)*(2.7-0.7)= 9.900990100 V VC2 = (100/(1+100))*(5/1)*(2.8-0.7) = 10.39603961 V “Voltage Gain” = 4.96 DC Test: For Vsignal used, VBE >0 ( VEB<0) , VBC<0 (VCB>0) Forward-Active Region, By the way, Vc ~ Vcc/2 RESULT: DC state wasestimated. Voltage/Current Gain was estimated. 20 BJT: More Models More BJT Models: Reminder: Original Ebers-Moll Model: Active Region: Dbe if Forward Biased (open) Battery 0.7 V + resistor Dbc is Reverse Biased (closed) No connection Icr = 0 Ar*Icr = 0 Ebers-Moll for Active Region is 21 BJT: Model and Relevant Equations I C F I E ; I E I B I C I B F I E ; IB F IB IE ; I C F I E ; I C H FE I B ; 1F 1F F H FE {b } ; {H FE H 21 } {FE : Forward Emitter} 1F Example : F 0.99 H FE 99 ~ 100 I E I B I C I B H FE I B 1 H FE I B 22 BJT: Alternative Drawing I EF I E ; F IB F I EF F I E I C H FE I B b I B 1F b ~ 100 23 BJT: Addition to Ebers-Mall Model Model for AC Generally, “BASE” is “inside” the transistor, so RBB must be added (“bad wire” from the B pin to Base junction). (X point is “real “BASE” ) RBE is practically very small (dynamic resistance of the diode ~ 5 W ) RBB ~ 100W.. 1 kW For AC Analysis Vbeo must be shorten, RBE is practically very small ( ~ 5 W ), so AC model from here is: ( X E ) ~H parameters 24 BJT: From H to Y parameters Problem with nodes analysis: Current IB in current controlled voltage source must be replaced to some voltage. Ib = Vbe / H11 ; IC = HFE*IB = (HFE/H11)* (VB - VE) ~ Y parameters Gm ? + Rce Q. What is the difference from FET AC model ??? A. Value of “Input resistance” 25 BJT Model: Practical Remarks Basically Ebers-Moll original model may be (and was) used for calculations of ALL states of the BJT. Practically, in Analog Electronics “DC” and “small-signal AC” analyses are used for Active Region only. Parameters of full Ebers-Moll Model are parameters evaluated from physical and geometry properties of the specific BJT. Parameters of “small-signal AC model” depends on chosen Q-point DC parameters != AC parameters HFE for DC != Hfe for AC To distinguish: hFE - means DC parameters hfe – means AC small-signal parameters BUT in most “electronics books” “good value” ~ 100 is used as b as for AC as for DC. 26 Control Questions • • • • • What have I learned Questions Why did I learn it How can I apply this (We’ll use this for…) Challenge 27 Literature to read 1. TBD 2. Mauro 3. (See Roland E. Thomas. The Analysis and Design of Linear Circuits 621.319.2 THO) 4. http://users.ece.gatech.edu/~alan/ECE3040/Lectures/Lectur e19-BJT%20Ebers-MollModel.pdf 28
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