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OUTLINE BJT small signal model BJT cutoff frequency BJT transient (switching) response Reading : Finish Chapter 12. Lecture #27. Small-Signal Model. Common-emitter configuration, forward-active mode:. “hybrid-pi” BJT small signal model:. Transconductance:. Small-Signal Model (cont.).

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lecture 27

BJT small signal model

BJT cutoff frequency

BJT transient (switching) response

Reading: Finish Chapter 12

Lecture #27

EE130 Lecture 27, Slide 1

small signal model
Small-Signal Model

Common-emitter configuration,

forward-active mode:


BJT small signal model:


EE130 Lecture 27, Slide 2

small signal model cont
Small-Signal Model (cont.)

where QF is the magnitude of minority-carrier charge stored in the base and emitter regions

forward transit time

EE130 Lecture 27, Slide 3

example small signal model parameters
Example: Small-Signal Model Parameters

A BJT is biased at IC = 1 mA and VCE = 3 V. bdc=90, tF=5 ps, and T = 300 K. Find (a) gm , (b) rp , (c) Cp .Solution: (a)(b) rp = bdc / gm= 90/0.039 = 2.3 kW


EE130 Lecture 27, Slide 4

cutoff frequency f t
Cutoff Frequency, fT

The cutoff frequency is defined to be the frequency (f = w/2p) at which the short-circuit a.c. current gain equals 1:

EE130 Lecture 27, Slide 5


For the full BJT equivalent circuit:

fT is commonly used

as a metric for the

speed of a BJT.


To maximize fT:

  • increase IC
  • minimize CJ,BE, CJ,BC
  • minimize re, rc
  • minimize tF

EE130 Lecture 27, Slide 6

base widening at high i c the kirk effect
Base Widening at High IC: the Kirk Effect
  • At very high current densities (>0.5mA/mm2), base widening occurs, so QB increases.
    • tF increases, fT decreases.

Consider an npn BJT:

At high current levels, the density of electrons (n  IC/qAvsat) in the collector depletion region is significant, resulting in widening of the quasi-neutral base region.

As W increases, the depletion width in the collector also increases, since the charge density decreases:

At very high current densities, the excess hole concentration in the collector is so high that it effectively extends the p-type base.

Top to bottom :

VCE = 0.5V, 0.8V,

1.5V, 3V.

EE130 Lecture 27, Slide 7

summary bjt small signal model
Summary: BJT Small Signal Model

Hybrid-pi model for the common-emitter configuration, forward-active mode:

EE130 Lecture 27, Slide 8

bjt switching qualitative
BJT Switching - Qualitative

EE130 Lecture 27, Slide 9

turn on transient
Turn-on transient

where IBB=VS/RS

  • We know:
  • The general solution is:
  • Initial condition: QB(0)=0. since transistor is in cutoff

EE130 Lecture 27, Slide 10

turn off transient
Turn-off transient
  • We know:
  • The general solution is:
  • Initial condition: QB(0)=IBBtB

EE130 Lecture 27, Slide 11

reducing t b for faster turn off
Reducing tB for Faster Turn-Off
  • The speed at which a BJT is turned off is dependent on the amount of excess minority-carrier charge stored in the base, and also the recombination lifetime tB
    • By reducing tB, the carrier removal rate is increased

Example: Add recombination centers (Au atoms) in the base

EE130 Lecture 27, Slide 12

schottky clamped bjt
Schottky-Clamped BJT
  • When the BJT enters the saturation mode, the Schottky diode begins to conduct and “clamps” the C-B junction voltage at a relatively low positive value.

 reduced stored charge in quasi-neutral base

EE130 Lecture 27, Slide 13