bipolar junction transistor

Bipolar JunctionTransistor

Electronic CircuitsElectronic Circuits

CHO, Yong HeuiCHO, Yong Heui


EM Wave EM Wave LabLab

2

1. Physical operation

Device structure



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Mode EBJ CBJ

Cutoff Reverse Reverse

Active Forward Reverse

Rev. Act. Reverse Forward

Saturation Forward Forward


Device structure



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Operation in active mode



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Operation in forward active mode



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Minority carrier profile



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Collector current



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For short Emitter

LP

IB2 = Qn/τb

1

1 1

Qn = AE·q·1/2·np(0)·W = (AE·q·W·ni2/2NA)evBE/VT

IB = IB1 + IB2 = IC/βDp

Dn

NA

ND

WB

Lp

W2

2Dnτbβ = +[ ]

-1: common emitter current gain


Base current



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: common base current gain

α = αF, β = βF : at forward active


Emitter current



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Equivalent model



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Ebers-Moll model



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Ebers-Moll Model at saturation Mode


Ebers-Moll model



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Saturation Mode


Saturation mode



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PNP transistor



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2. I-V

Example



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2. I-V

Common-base



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iC = ISeVBE/VT·(1+vCE/VA)

∂iC

∂vCE

ro ≡vBE=constant

-1

2. I-V

Common-emitter



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βdc = ICQ/IBQ

βac = ΔiC/ΔiB : vCE=constant

2. I-V

Current gain



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βforced = ICsat/IB

βforced < βF

2. I-V

Saturation voltage



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∂vCE

∂iCRCEsat ≡ iB=IB

iC=ICsat

2. I-V

Saturation resistance



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∂vCE

∂iCRCEsat ≡ iB=IB

iC=ICsat

2. I-V

Saturation resistance



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vO = vCE = VCC - RCiC

vO = VCC - RC·ISevI/VT : at active

ICsat = (VCC – VCEsat)/RC

0 < vI < 0.5 : Cutoff (switch off)

: at saturation

Av ≡dvo

dvi vI=VBE

= -(1/VT)·ISeVBE/VT·RC

= -ICRC/VT = -VRC/VT

VRC = VCC - VCE

For max gain and swing

3. Amplifier

Large signal



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vCE = VCC-RCiC

iC = VCC/RC – vCE/RC

vBE = VBB-RBiB

iB = VBB/RB – vBE/RB

3. Amplifier

Graphical analysis



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3. Amplifier

Graphical analysis



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IB(EOS)

3. Amplifier

Bias point

Operation as switch



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4. BJT circuits

Example



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-

4. BJT circuits

Example



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≡

4. BJT circuits

Example



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4. BJT circuits

Example



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RE : negative feedback

5. Bias

Discrete-circuit biasing



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Biasing using a collector-to-base feedback resistor

VCB = IBRB = IERB/(β+1)

Small RB small swing

5. Bias

Discrete-circuit biasing



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I = IREF = (VCC + VEE – VBE)/R

Large RB 사용가능

5. Bias

Current source biasing



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6. Small-signal operation

Bias point



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Transconductance



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Small signal Emitter resistance : re

Voltage Gain

vc = -icRC = gmvbeRC = (-gmvbe)RC Av = vc/vbe = -gmRC = -ICRC/VT


Input resistance



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Hybrid model



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T model



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Example



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Example



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Av = vc/vbe = -gm(RC//rO)


Output resistance



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Bypass Capacitor : CE

Coupling Capacitor : CC1, CC2

At DC analysis

7. BJT amplifier

Common-emitter amplifier



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Rib = rπ Rin = vi/ii = RB//Rib ≒ rπ vsigvi =Rin

Rin+Rsig

vsig= rπ

rπ+Rsig

vi = vπvO = -gmvπ(RC∥RL∥rO)

Av = -gm(RC∥RL∥rO) Avo = -gm(RC∥rO) ≒ -gmRC (rO≫RC)

Rin

Rin+Rsig

AvGv =

rπ

rπ+Rsig

≒ - gm(Rc∥RL∥rO) ≒ Av (rπ≫Rsig)

Rout = RC∥rO ≒ RC

Ais = ios/ii = -gmRin ≒ -gmrπ= -β

7. BJT amplifier

Small signal circuit



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vi

re+Re

vo = -ic(RC∥RL) = -αie(RC∥RL) = -α(RC∥RL)

Rin = RB//Rib Rib = vi/ib = (β+1)(re+Re) ≒ rπ(1+gmRe)

rO = ∞

Av ≒ -(RC∥RL)/(re+Re)

Avo = -αRC/(re+Re) ≒ -gmRC/(1+gmRe) Rout = RC∥rO ≒ RC

Ais = ios/ii = -αie/(vi/Rin) = -αRinie/vi = -α(RB∥Rib)/(re+Re) = -α(β+1)(re+Re)/(re+Re) = -β

ie = vi/(re+Re)

7. BJT amplifier

Emitter resistance



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Rin

Rin+Rsig

AvGv =

Rin

Rin+Rsig

= -α(RC∥RL)

re+Re ≒ -

β(RC∥RL)

Rsig+(β+1)(re+Re)

: less sensitive to β

vπ = vi re

re+Re

11+gmRe

≒ vi

Rib is increaed by the factor (1+gmRe)

The voltage gain is reduced by the factor (1+gmRe)

For the same nonlinear distortion, vi can be increased by the factor (1+gmRe)

Overall voltage gain is less sensitive to β

High frequency response is improved.

Effects of negative feedback through Re

7. BJT amplifier

Emitter resistance



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vi

re+Re

vo = -αie(RC∥RL) = α(RC∥RL) ie = -vi/reRin = re

Av = gm(RC∥RL) Avo = gmRC Rout = RC

Ais = ios/ii = -αie/(-ie) = αvi

vsig

Rin

Rin+Rsig

re

re+Rsig

==

re

re+Rsig

AvGv = = gm(RC∥RL)

re

re+Rsig

α(RC∥RL)

re+Rsig

=

7. BJT amplifier

Common base amplifier



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Rib = vb/ib = (β+1)[re+(ro∥RL)]

Rin = RB∥Rib

7. BJT amplifier

Emitter follower



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vo/vsig ≒RL

[Rsig/(β+1)] +re+RL

RB≫Rsig, ro≫RL

Rout = ro∥Rsig∥RB

re + β+1[ ] Rsig∥RB

re + β+1≒

Gvo =ro

[(Rsig∥RB)/(β+1)] +re+roRsig+R

B

RB

7. BJT amplifier

Emitter follower



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8. BJT capacitance

Internal capacitance



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hfe : CE short-circuit current gain

Ib = Vπ· (1/rπ//sCπ//sCμ) Ic = Vπ· (gm - sCμ)

hfe ≡ Ic/Ib = 1/rπ+ sCπ+ sCμ

gm - sCμ

1 + s(Cπ+Cμ)rπ

gmrπ≒1 + s/ωβ

β0=: STC LPF

(Cπ+Cμ)rπ

1ωβ = ωT = β0·ωβ =

Cπ+Cμ

gm fT = 2π(Cπ+Cμ)

gm

8. BJT capacitance

High frequency model



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High level Injection

8. BJT capacitance

Collector current



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RB//rπ

RB//rπ+Rsig

AM = - gm(Rc∥RL∥rO)

9. Frequency response

Frequency bands



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High frequency model



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Iμ = sCμ(Vπ-Vo)

= sCμ(Vπ+ gmRL’Vπ)

= sCμ(1 + gmRL’)Vπ

= sCeqVπ

Ceq = sCμ(1 + gmRL’)

1 + s/ω0

1V’sigVπ =

ω0 = 1/CinRsig’


High frequency response



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1 + s/ω0

1Vo

Vsig

RB

RB + Rsig

AM =1 + s/ω0

1= -

rπ+rx+(RB∥Rsig)

rπ·gmRL’


High frequency response



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ωP1

ss+ ωP2

ss+ ωP3

ss+

Vo

Vsig

= - AM

High Freq. gain X 3 poles


Low frequency response



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(RB//rπ)+Rsig+ sCC1

1

RB//rπVsigVπ =Vo = - gmVπ(Rc∥RL)

(RB//rπ)+Rsig

RB//rπ gm(Rc∥RL)

CC1[(RB//rπ)+Rsig]1

s +

s ωP1

ss+

Vo

Vsig

= - AM= -


Capacitance effect



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(RB//Rsig)+(β+1)(re sCE

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VsigIb =Vo = - βIb(Rc∥RL)

Vo

VsigωP2

ss+

= - AM= -

)

RB

RB + Rsig

CE[re+

1s +

s

RB//Rsig

β+1 ]

RB

RB + Rsig

β(Rc∥RL)

(RB//Rsig)+(β+1)re


Capacitance effect



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(RB//rπ)+Rsig

RB//rπVsigVπ = Vo = - gmVπ

sCC2

1RC

++R

L

RL

RC

(RB//rπ)+Rsig

RB//rπ gm(Rc∥RL)

CC2(RC+RL)1

s +

s ωP3

ss+

Vo

Vsig

= - AM= -


Capacitance effect

bipolar junction transistor

Technology

v r c r

v r c r

c r c r

r c r o r c r

r r sig

e r c r

r c r e

r e r e