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# 4.4 - 4.4 BJT Dynamic Behavior 4.4.1 Small-Signal...

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ECE3080, Chapter 4.4 1 June 27, 2005 ECE 3080: Chapter 4.4 – BJT O. Brand, 1 of 28 4.4 BJT Dynamic Behavior 4.4.1 Small-Signal Equivalent Circuits – Generalized Two-Port Model – Hybrid-Pi Model 4.4.2 Transient (Switching) Response – Qualitative Observations – Charge Control Relationships – Quantitative Analysis – Practical Considerations Pierret, Chapter 12, page 443-459 June 27, 2005 ECE 3080: Chapter 4.4 – BJT O. Brand, 2 of 28 4.4.1 Small Signal Equivalent Circuit – Two-Port Model – NPN BJT in common emitter configuration as two-port device : DC voltages and currents: I B , I C , V BE , V CE Superimposed AC voltages and currents: i B (V BE + v be ,V CE + v ce ) = I B (V BE ,V CE ) + i b i C (V BE + v be ,V CE + v ce ) = I C (V BE ,V CE ) + i c i b , i c , v be , v ce Pierret, Fig. 12.1

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ECE3080, Chapter 4.4 2 June 27, 2005 ECE 3080: Chapter 4.4 – BJT O. Brand, 3 of 28 Two-Port Model (cont.) Assumption: low frequency , i.e. carrier distributions can follow the frequency (no capacitance effects) Note: this is a strong assumption, which is generally not fulfilled! Comparing with the previous page, we find for i b : i B (V BE + v be ,V CE + v ce ) = I B (V BE + v be ,V CE + v ce ) i C (V BE + v be ,V CE + v ce ) = I C (V BE + v be ,V CE + v ce ) i b = I B (V BE + v be ,V CE + v ce ) Taylor series for small v be , v ce ! " ### \$ ### ! I B (V BE ,V CE ) " # I B (V BE ,V CE ) # V BE V CE v be + # I B (V BE ,V CE ) # V CE V BE v ce June 27, 2005 ECE 3080: Chapter 4.4 – BJT O. Brand, 4 of 28 Two-Port Model (cont.) Analogues, we find for i c : This leads to the following general small signal equivalent circuit : i c ! " I C (V BE ,V CE ) " V BE V CE v be + " I C (V BE ,V CE ) " V CE V BE v ce i b = g 11 v be + g 12 v ce i c = g 21 v be + g 22 v ce Pierret, Fig. 12.1
ECE3080, Chapter 4.4 3 June 27, 2005 ECE 3080: Chapter 4.4 – BJT O. Brand, 5 of 28 Two-Port Model (cont.) So far, the two-port model is purely mathematical; the physics lies in the conductances g ij ! They must be calculated from appropriate models for I C and I B ; in case of npn BJT : I C and I B from e.g. static analysis of Chapter 4.2 + I B in : g 11 ! " I B " V BE V CE g 12 ! " I B " V CE V BE + I C in : g 21 ! " I C " V BE V CE g 22 ! " I C " V CE V BE June 27, 2005 ECE 3080: Chapter 4.4 – BJT O. Brand, 6 of 28 Two-Port Model (cont.) Analogous, we obtain in case of a pnp BJT : + I B out : g 11 ! " I B " V EB V EC g 12 ! " I B " V EC V EB + I C out : g 21 ! " I C " V EB V EC g 22 ! " I C " V EC V EB adapted from Pierret, Fig. 12.1

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ECE3080, Chapter 4.4 4 June 27, 2005 ECE 3080: Chapter 4.4 – BJT O. Brand, 7 of 28 Two-Port Model – Active Mode Assumption : npn transistor in active mode, i.e. V BE > 0 and V BC < 0 From Ebers-Moll model , we find: Using these characteristic equations, the conductances g ij are calculated: I E ! I F0 e qV BE /kT I C ! " F I F0 e qV BE /kT I B = I E # I C ! (1 # " F )I F0 e qV BE /kT June 27, 2005 ECE 3080: Chapter 4.4 – BJT O. Brand, 8 of 28 Two-Port Model – Active Mode (cont.) g 11 ! " I B " V BE V CE = q I B kT = I B I C = # 0 \$ 1 ! g 21 g 12 ! " I B " V CE V BE = 0 g 21 ! " I C " V BE V CE = q I C kT g 22 !
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