6. BJT Transistors & Circuits - Arraytool · PDF file4/6/2016 · 6. BJT Transistors & Circuits ... One can implement digital and analog functions utilizing MOSFETs almost exclusively

Physical Operation IV Characteristics BJT as an Amplifier Biasing Small Signal Model BJT Amplifiers Frequency Response Summary

6. BJT Transistors & Circuits

S. S. Dan and S. R. Zinka

Department of Electrical & Electronics EngineeringBITS Pilani, Hyderbad Campus

April 11, 2016

6. BJT Transistors & Circuits ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus


Outline

1 Physical Operation

2 IV Characteristics

3 BJT as an Amplifier

4 Biasing

5 Small Signal Model

6 BJT Amplifiers

7 Frequency Response

8 Summary



Outline




4 Biasing


6 BJT Amplifiers


8 Summary



MOSFET vs BJT

MOSFETs are more popular and widely used because:

• MOSFET has become by far the most widely used electronic device, especially inthe design of integrated circuits

• Compared to BJTs, MOSFETs can be made quite small and their manufacturingprocess is relatively simple

• Operating MOSFETs requires comparatively little power compared to BJTs• One can implement digital and analog functions utilizing MOSFETs almost

exclusively (i.e., with very few or no resistors)

However,

• BJT can switch faster than MOSFET due to the less capacitance (so BJTs arepreferred over MOSFETs in RF applications)

• BJTs have high voltage gain• the reliability of BJT circuits under severe environmental conditions (e.g.,

automotive applications)• BJTs are Cheaper and they do not get damaged by static robust



MOSFET vs BJT






However,






MOSFET vs BJT






However,






MOSFET vs BJT






However,






MOSFET vs BJT




• Operating MOSFETs requires comparatively little power compared to BJTs

• One can implement digital and analog functions utilizing MOSFETs almostexclusively (i.e., with very few or no resistors)

However,






MOSFET vs BJT






However,






MOSFET vs BJT






However,






MOSFET vs BJT






However,






MOSFET vs BJT






However,


• BJTs have high voltage gain

• the reliability of BJT circuits under severe environmental conditions (e.g.,automotive applications)

• BJTs are Cheaper and they do not get damaged by static robust



MOSFET vs BJT






However,



automotive applications)

• BJTs are Cheaper and they do not get damaged by static robust



MOSFET vs BJT






However,






BiCMOS

Bipolar transistors can be combined with MOSFETs to create innovative circuits thattake advantage of the high-input-impedance and low-power operation of MOSFETs

and the very-high-frequency operation and high-current-driving capability of bipolartransistors.

The resulting technology is known as BiCMOS, and it is finding increasingly largerareas of application.



BiCMOS






BiCMOS






Device Structure of npn BJT

n-type n-type

Emitterregion

Emitter–basejunction(EBJ)

Collector–basejunction(CBJ)

Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)



Device Structure of npn BJT

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)



Actual Structure of npn BJT

E B C

n

np

The collector virtually surrounds the emitter region, thus making it difficult for theelectrons injected into the thin base to escape being collected. In this way, the resulting

α is close to unity and β is large.

Also, observe that the device is not symmetrical, and thus the emitter and collectorcannot be interchanged.




E B C

n

np







E B C

n

np







E B C

n

np






Operation of BJT



Operation of BJT

B

C

iEiE

iCiE

E

Forward-biased

n p n

VBE

iB



Operation of BJT (EBJ Forward & Collector Open)

B

C

iEiE

iCiE

E

Forward-biased

n p n

VBE

Injectedelectrons

Diffusingelectrons

iB



Operation of BJT (EBJ Forward & Collector Open)

B

C

iEiE

iCiE Injected holes

E

Forward-biased

n p n

VBE

Injectedelectrons

Diffusingelectrons

iB



Operation of BJT (EBJ Forward & CBJ Short)

B

C

iEiE iC iC

i

iB

iB2iCiE

Recombinedelectrons (iB2)

Injected holes (iB1

E

Forward-biased

iE

iC

n p n

VBE

(

Injectedelectrons

Diffusingelectrons

Collectedelectrons



Operation of BJT (EBJ Forward & CBJ Short)

B

C

iEiE iC iC

i

iB

iB2iCiE


Injected holes (iB1

E

Forward-biased

iE

iC

n p n

Accelerated through the depletion region

VBE

(

Injectedelectrons

Diffusingelectrons

Collectedelectrons



Operation of BJT (EBJ Forward & CBJ Reverse)

B

C

iEiE iC iC

i

iB

iB2iCiE


Injected holes (iB1

E

Forward-biased

iE

iC

n p n


VBE

(

Injectedelectrons

Diffusingelectrons

Collectedelectrons

VCB



Operation of BJT (EBJ Forward & CBJ More Reverse)

B

C

iEiE iC iC

i

iB

iB2iCiE


Injected holes (iB1

E

Forward-biased

iE

iC

n p n


VBE

(

Injectedelectrons

Diffusingelectrons

Collectedelectrons

VCB



Operation of BJT (EBJ Forward & CBJ Forward)

B

C

iEiE iC iC

i

iB

iB2iCiE


Injected holes (iB1

E

Forward-biased

iE

iC

n p n


VBE

(

Injectedelectrons

Diffusingelectrons

Collectedelectrons

VCB



Operation of BJT (EBJ Forward & CBJ More Forward)

B

C

iEiE iC iC

i

iB

iB2iCiE


Injected holes (iB1

E

Forward-biased

iE

iC

n p n

No depletion region & electrons are repelled by VCB

VBE

(

Injectedelectrons

Diffusingelectrons

VCB



BJT – Modes of Operation

Mode EBJ CBJ

Cutoff Reverse ReverseActive Forward Reverse∗

Saturation Forward Forward∗

Reverse Active Reverse Forward



BJT – Modes of Operation

Mode EBJ CBJ

Cutoff Reverse ReverseActive Forward Reverse∗

Saturation Forward Forward∗

Reverse Active Reverse Forward



iC vs vCB

vCB

Saturationmode

Active mode

α IE iE= IE

- 0.4 V

iC

0�� Where is cut-off region located in the above graph?



iC vs vCB

vCB

Saturationmode

Active mode

α IE iE= IE

- 0.4 V

iC

0

�� Where is cut-off region located in the above graph?



iC vs vCB

vCB

Saturationmode

Active mode

α IE iE= IE

- 0.4 V

iC




iC vs vCE

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC

0

�� Where is cut-off region located in the above graph?



iC vs vCE

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC




Since BJT can be visualized as a combination of two pn junction diodes, let’srecap the theory of pn junction diode ...



Since BJT can be visualized as a combination of two pn junction diodes, let’srecap the theory of pn junction diode ...



Minority Carrier Injection & Recombination




0

n regionp region

x




0

n regionp region

pn, np

x




0

Depletionregion

n regionp region

pn, np

-xp xn x




0

Depletionregion

n region

Thermal equilibriumvalue

p region

pn0

pn, np

np0

-xp xn x




0

Depletionregion

n region

Excessconcentration


p regionpn

pn0

(xn)

pn(x)

pn, np

np0

-xp xn x




0

Depletionregion

n region

Excessconcentration


p regionpn

pn0

(xn)

pn(x)

pn, np

np

np0

( p)

-xp xn x

np(x)

-x




0

Depletionregion

n region

Excessconcentration


p regionpn

pn0

(xn)

pn(x)

pn, np

np

np0

( p)

-xp xn x

np(x)

-x

pn (xn) = pn0eV/VT

pn (x) = pn0 + pn0

(eV/VT − 1

)e−(x−xn)/Lp

Jp (xn) = −qDpdpn (x)

dx

∣∣∣∣x=xn

=qDppn0

Lp

(eV/VT − 1

)




0

Depletionregion

n region

Excessconcentration


p regionpn

pn0

(xn)

pn(x)

pn, np

np

np0

( p)

-xp xn x

np(x)

-x

pn (xn) = pn0eV/VT

pn (x) = pn0 + pn0

(eV/VT − 1

)e−(x−xn)/Lp


dx

∣∣∣∣x=xn

=qDppn0

Lp

(eV/VT − 1

)




0

Depletionregion

n region

Excessconcentration


p regionpn

pn0

(xn)

pn(x)

pn, np

np

np0

( p)

-xp xn x

np(x)

-x

pn (xn) = pn0eV/VT

pn (x) = pn0 + pn0

(eV/VT − 1

)e−(x−xn)/Lp


dx

∣∣∣∣x=xn

=qDppn0

Lp

(eV/VT − 1

)




0

Depletionregion

n region

Excessconcentration


p regionpn

pn0

(xn)

pn(x)

pn, np

np

np0

( p)

-xp xn x

np(x)

-x

pn (xn) = pn0eV/VT

pn (x) = pn0 + pn0

(eV/VT − 1

)e−(x−xn)/Lp


dx

∣∣∣∣x=xn

=qDppn0

Lp

(eV/VT − 1

)




0

Depletionregion

n region

Excessconcentration


p regionpn

pn0

(xn)

pn(x)

pn, np

np

np0

( p)

-xp xn x

np(x)

-x

pn (xn) = pn0eV/VT

pn (x) = pn0 + pn0

(eV/VT − 1

)e−(x−xn)/Lp


dx

∣∣∣∣x=xn

=qDppn0

Lp

(eV/VT − 1

)



In this chapter, we are more interested in active mode because of it’samplification property ... So, let’s derive the expressions for various currents

in active mode ...



In this chapter, we are more interested in active mode because of it’samplification property ... So, let’s derive the expressions for various currents

in active mode ...



Minority Carrier Concentrations (Active Mode)

Emitter(n)

EBJdepletion

region

Base(p)

CBJdepletion

region

Collector(n)

Car

rier

con

cent

rati

on

Holeconcentration

Effective basewidth W

Distance (x)

np (0)

Electronconcentrationnp (ideal)

np (withrecombination)

pn (0)pn0

np (0) = np0evBE/VT (1)



Minority Carrier Concentrations (Active Mode)

Emitter(n)

EBJdepletion

region

Base(p)

CBJdepletion

region

Collector(n)

Car

rier

con

cent

rati

on

Holeconcentration


Distance (x)

np (0)



pn (0)pn0

np (0) = np0evBE/VT (1)



Electron Diffusion Current in the Base Region

Electron diffusion current In in the base region is directly proportional to the slope ofthe straight-line concentration profile and is given by

Jn = qDndnp (x)

dx

⇒ In = AEqDndnp (x)

dx

= AEqDn

(−

np (0)W

)= −

AEqDnnp0

WevBE/VT , (2)

where AE is the cross-sectional area of the base–emitter junction, q is the magnitudeof the electron charge, Dn is the electron diffusivity in the base, and W is the effectivewidth of the base.�

�We have neglected the recombination current in the base region, and the current due to

holes injected from the base region into the emitter region. Why?





Jn = qDndnp (x)

dx


dx

= AEqDn

(−

np (0)W

)= −

AEqDnnp0

WevBE/VT , (2)








Jn = qDndnp (x)

dx


dx

= AEqDn

(−

np (0)W

)= −

AEqDnnp0

WevBE/VT , (2)








Jn = qDndnp (x)

dx


dx

= AEqDn

(−

np (0)W

)= −

AEqDnnp0

WevBE/VT , (2)








Jn = qDndnp (x)

dx


dx

= AEqDn

(−

np (0)W

)=

−AEqDnnp0

WevBE/VT , (2)








Jn = qDndnp (x)

dx


dx

= AEqDn

(−

np (0)W

)= −

AEqDnnp0

WevBE/VT , (2)








Jn = qDndnp (x)

dx


dx

= AEqDn

(−

np (0)W

)= −

AEqDnnp0

WevBE/VT , (2)

where AE is the cross-sectional area of the base–emitter junction, q is the magnitudeof the electron charge, Dn is the electron diffusivity in the base, and W is the effectivewidth of the base.

�







Jn = qDndnp (x)

dx


dx

= AEqDn

(−

np (0)W

)= −

AEqDnnp0

WevBE/VT , (2)






The Collector Current

When collector-base junction is reversed biased ( to be precise not forward biased ),most of the electrons will be swept across the CBJ depletion region into the collector.So,

iC = −In =

(AEqDnnp0

W

)evBE/VT = IS evBE/VT . (3)

�

�Since IS is directly proportional to the junction area (i.e., the device size), it will also be

referred to as the scale current.�

�An important observation to make here is that the magnitude of iC is independent of

vCB. Does it remind you of anything?





iC = −In =

(AEqDnnp0

W


�









iC = −In =

(AEqDnnp0

W


�


referred to as the scale current.

�







iC = −In =

(AEqDnnp0

W


�







The Base Current

For deriving the approximate expression for collector current, we have neglected therecombination current in the base region, and the current due to holes injected fromthe base region into the emitter region. Though small, like collector current, these twocurrent components also are proportional to evBE/VT . So, iB can be written as a fractionof collector current as given below:

iB =iCβ

=ISevBE/VT

β(4)

where β is a transistor parameter, usually called the common-emitter current gain (forreasons that will become clear later).



The Base Current

For deriving the approximate expression for collector current, we have neglected therecombination current in the base region, and the current due to holes injected fromthe base region into the emitter region.

Though small, like collector current, these twocurrent components also are proportional to evBE/VT . So, iB can be written as a fractionof collector current as given below:

iB =iCβ

=ISevBE/VT

β(4)




The Base Current

For deriving the approximate expression for collector current, we have neglected therecombination current in the base region, and the current due to holes injected fromthe base region into the emitter region. Though small, like collector current, these twocurrent components also are proportional to evBE/VT .

So, iB can be written as a fractionof collector current as given below:

iB =iCβ

=ISevBE/VT

β(4)




The Base Current


iB =iCβ

=ISevBE/VT

β(4)




The Base Current


iB =iCβ

=ISevBE/VT

β(4)




The Emitter Current

Since the current that enters a transistor must leave it (according to KCL), the emittercurrent

iE is equal to the sum of the collector current iC and the base current iB ;

that is,

iE = iC + iB =

(β + 1

β

)iC =

iCα

=ISevBE/VT

α≈ iC (5)

where α = ββ+1 . For reasons that will become apparent later, α is called the common-

base current gain.



The Emitter Current

Since the current that enters a transistor must leave it (according to KCL), the emittercurrent iE is equal to the sum of the collector current iC and the base current iB ;

that is,

iE = iC + iB =

(β + 1

β

)iC =

iCα

=ISevBE/VT

α≈ iC (5)


base current gain.



The Emitter Current

Since the current that enters a transistor must leave it (according to KCL), the emittercurrent iE is equal to the sum of the collector current iC and the base current iB ; that is,

iE = iC + iB =

(β + 1

β

)iC =

iCα

=ISevBE/VT

α≈ iC (5)


base current gain.



Large Signal Equivalent Models (Active Mode)




(ISE= IS α)

C

E

B

iB

iE

vBE DE

iC

ISevBE VT

+




C

E

B

(ISE= IS α)

C

E

B

iB

iE

vBE DE

iC

iB

iC

DEiE

vBE

iE

iE

ISevBE VT

+

(ISE= IS α)+

α




C

E

B

(ISE= IS α)

C

E

B

iB

iE

vBE DE

iC

iB

iC

DEiE

vBE

iE

iE

E

B C

iB

DB

iC

iE

vBE

ISevBE VT

+

(ISE= IS α)+

α

+ISe

vBE VT

(ISB= IS )β




C

E

B

(ISE= IS α)

C

E

B

iB

iE

vBE DE

iC

iB

iC

DEiE

vBE

iE

iE

E

B C

iB

DB

iC

iE

vBE

E

BiB

β iB

iEvBE

C

iCiB

DB

ISevBE VT

+

(ISE= IS α)+

α

+ (ISB= IS )β

+ISe

vBE VT

(ISB= IS )β



Active or Saturation Mode?

We can determine whether the BJT is in the saturation mode by either of the followingtwo tests:

1 Is the CBJ forward biased by more than 0.4 V?

2 Is the ratio iC/iB lower than β ?





















VCEsat

We know thatVCE = VC −VE = VCB −VEB = VBE −VBC. (6)

In saturation mode, both VBE and VBC are positive and VBC will be usually smaller thanVBE (because CBJ has a much larger area than the EBJ). Thus, in saturation mode,

VCEsat ≈ 0.1 to 0.3 V. (7)



VCEsat



VCEsat ≈ 0.1 to 0.3 V. (7)



VCEsat


In saturation mode, both VBE and VBC are positive and VBC will be usually smaller thanVBE (because CBJ has a much larger area than the EBJ).

Thus, in saturation mode,

VCEsat ≈ 0.1 to 0.3 V. (7)



VCEsat



VCEsat ≈ 0.1 to 0.3 V. (7)



βforced

Because iC/iB of a saturated transistor can be set to any desired value lower than β byadjusting vBC, this ratio is known as forced β and denoted βforced,

βforced =iCiB

∣∣∣∣saturation

≤ β. (8)



βforced

Because iC/iB of a saturated transistor can be set to any desired value lower than β byadjusting vBC, this ratio is known as forced β and denoted βforced,

βforced =iCiB

∣∣∣∣saturation

≤ β. (8)



MOSFET vs BJT



MOSFET vs BJT

n+

L

Metal

Channelregion

Oxide (SiO2)(thickness = tox)

p-type substrate(Body)

n+

Source (S) Gate (G) Drain (D)

Bod y (B)

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)



MOSFET vs BJT

n+

L

Metal

Channelregion



n+


Bod y (B)

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

iD

vDS sat =

vGS = +Vt

0

Triode Saturation

vOV

Current saturates because thechannel is pinched off at thedrain end, and vDS no longeraffects the channel.

vDSvOV



MOSFET vs BJT

n+

L

Metal

Channelregion



n+


Bod y (B)

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC

0

iD

vDS sat =

vGS = +Vt

0

Triode Saturation

vOV


vDSvOV



MOSFET vs BJT

n+

L

Metal

Channelregion



n+


Bod y (B)

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC

0

iD

vDS sat =

vGS = +Vt

0

Triode Saturation

vOV


vDSvOV



MOSFET vs BJT

n+

L

Metal

Channelregion



n+


Bod y (B)

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC

0

iD

vDS sat =

vGS = +Vt

0

Triode Saturation

vOV


vDSvOV



MOSFET vs BJT

n+

L

Metal

Channelregion



n+


Bod y (B)

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC

0

iD

vDS sat =

vGS = +Vt

0

Triode Saturation

vOV


vDSvOV



MOSFET vs BJT

n+

L

Metal

Channelregion



n+


Bod y (B)

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC

0

iD

vDS sat =

vGS = +Vt

0

Triode Saturation

vOV


vDSvOV



MOSFET vs BJT

n+

L

Metal

Channelregion



n+


Bod y (B)

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC

0

iD

vDS sat =

vGS = +Vt

0

Triode Saturation

vOV


vDSvOV



MOSFET vs BJT

n+

L

Metal

Channelregion



n+


Bod y (B)

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC

0

iD

vDS sat =

vGS = +Vt

0

Triode Saturation

vOV


vDSvOV



MOSFET vs BJT

n+

L

Metal

Channelregion



n+


Bod y (B)

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC

0

iD

vDS sat =

vGS = +Vt

0

Triode Saturation

vOV


vDSvOV



MOSFET vs BJT

n+

L

Metal

Channelregion



n+


Bod y (B)

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC

0

iD

vDS sat =

vGS = +Vt

0

Triode Saturation

vOV


vDSvOV



pnp BJT

VEB VBC

B

C

vBCvEBiEiE

iE

iCiC

iB

iB

iB1

iB2

iC

Recombinedholes

Injectedelectrons

E

Forward-biased

iE

iC

p n p

Reverse-biased

++ ––

Injected holes Diffusing holes Collected holes



pnp BJT

VEB VBC

B

C

vBCvEBiEiE

iE

iCiC

iB

iB

iB1

iB2

iC

Recombinedholes

Injectedelectrons

E

Forward-biased

iE

iC

p n p

Reverse-biased

++ ––

Injected holes Diffusing holes Collected holes



Large-signal Model of pnp BJT

(IS α)

C

E

B

iB

iE

vEB DE

iC

ISevEB VT

+

E

B C

iB

DB

iC

iE

vEB+

ISevEB VT

(IS )β



Large-signal Model of pnp BJT

(IS α)

C

E

B

iB

iE

vEB DE

iC

ISevEB VT

+

E

B C

iB

DB

iC

iE

vEB+

ISevEB VT

(IS )β



Outline




4 Biasing


6 BJT Amplifiers


8 Summary



Circuit Symbols and Conventions

B

C

E

B

C

E

iC

iE

iB

iC

iEiB



Circuit Symbols and Conventions

B

C

E

B

C

E

iC

iE

iB

iC

iEiB



iC vs vCB

vCB

iC

Saturationmode

Active mode

α IE iE= IE

Expandedscale

0.4 V 0



iC vs vCB

vCB

iC

Saturationmode

Active mode

α IE iE= IE

Expandedscale

0.4 V 0



iC vs vBE (Active Mode)

vCB

vBE

iC

0

- 0.4 V

(V)0.5 0.7

vCB

vBE

iC

0

- 0.4 V

(V)

T1 T2 T3

T1 T2 T3

iC =

(AEqDnnp0

W

)evBE/VT = IS evBE/VT .




vCB

vBE

iC

0

- 0.4 V

(V)0.5 0.7

vCB

vBE

iC

0

- 0.4 V

(V)

T1 T2 T3

T1 T2 T3

iC =

(AEqDnnp0

W





vCB

vBE

iC

0

- 0.4 V

(V)0.5 0.7

vCB

vBE

iC

0

- 0.4 V

(V)

T1 T2 T3

T1 T2 T3

iC =

(AEqDnnp0

W




Base-width Modulation Effect

Emitter(n)

EBJdepletion

region

Base(p)

CBJdepletion

region

Collector(n)

Car

rier

con

cent

rati

on

Holeconcentration


Distance (x)

np (0)



pn (0)pn0

iC =

(AEqDnnp0

W

)evBE/VT = ISevBE/VT




Emitter(n)

EBJdepletion

region

Base(p)

CBJdepletion

region

Collector(n)

Car

rier

con

cent

rati

on

Holeconcentration


Distance (x)

np (0)



pn (0)pn0

iC =

(AEqDnnp0

W





Emitter(n)

EBJdepletion

region

Base(p)

CBJdepletion

region

Collector(n)

Car

rier

con

cent

rati

on

Holeconcentration


Distance (x)

np (0)



pn (0)pn0

iC =

(AEqDnnp0

W




Early Effect

vCE

iC

0

Saturationregion

Activeregion

-VA

iC = IS

(1 +

vCE

VA

)evBE/VT (9)



Early Effect

vCE

iC

0

Saturationregion

Activeregion

-VA

iC = IS

(1 +

vCE

VA

)evBE/VT (9)



Large-signal Models of npn (Including Early Effect)

E

B C

iB

DB

iC

iE

vBE+

(ISB= IS )β

E

B C

iB

DB

iC

iE

vBE+

(ISB= IS )β

ISevBE VT

β iB



Large-signal Models of npn (Including Early Effect)

E

B C

iB

DB

iC

iE

vBE+

(ISB= IS )β

E

B C

iB

DB

iC

iE

vBE+

(ISB= IS )β

ISevBE VT

β iB



Outline




4 Biasing


6 BJT Amplifiers


8 Summary



Stripped Down Version of CE Amplifier & its VTC




vBEvO= vCE

RC

VCC

iC

+-

+

vCE = VCC−iCRC




vBEvO= vCE

RC

VCC

0 0.5 V vBE

X Y

Z

iC

0.3 V

Edgeof Saturation

Cut off SaturationActivemode

+-

+

vCE

vCE = VCC−iCRC



Biasing the BJT to Obtain Linear Amplification

VCC

vCE

0 VBE vBE

X Y

VCE

Z

Q

VBEVCE

RC

VCC

IC

+

At point Q (bias / operating / quiescent point),

VCE = VCC − ICRC = VCC − RCISeVBE/VT . (10)




VCC

vCE

0 VBE vBE

X Y

VCE

Z

Q

VBEVCE

RC

VCC

IC

+






VCC

vCE

0 VBE vBE

X Y

VCE

Z

Q

VBEVCE

RC

VCC

IC

+





Biasing the BJT ... Cont’d

vBE

vce

Q

Z

XSlope= Av

Time

Time

0

vCE

VCC

VCE

vbe

Cutoff SaturationActivemode

0.5

Y

VBE

RC

VCC

vBEvbe

VBE

vCE

iC

+-

+

+



Biasing the BJT ... Cont’d

vBE

vce

Q

Z

XSlope= Av

Time

Time

0

vCE

VCC

VCE

vbe

Cutoff SaturationActivemode

0.5

Y

VBE

RC

VCC

vBEvbe

VBE

vCE

iC

+-

+

+



The Small-signal Voltage Gain

Since in active region,

vCE = VCC − iCRC = VCC − RCISevBE/VT ,

small-signal voltage gain (i.e., the slope of the tangent to the VTC at Q) is given by

Av =∂vCE

∂vBE

∣∣∣∣vBE=VBE

= −RCISeVBE/VT × 1VT

= − IC

VTRC. (11)

Therefore,

|Av|max ≈VCC

VT. (12)







Av =∂vCE

∂vBE

∣∣∣∣vBE=VBE


= − IC

VTRC. (11)

Therefore,

|Av|max ≈VCC

VT. (12)







Av =∂vCE

∂vBE

∣∣∣∣vBE=VBE


= − IC

VTRC. (11)

Therefore,

|Av|max ≈VCC

VT. (12)







Av =∂vCE

∂vBE

∣∣∣∣vBE=VBE


= − IC

VTRC. (11)

Therefore,

|Av|max ≈VCC

VT. (12)



Locating the Bias Point Q using VTC



Locating the Bias Point Q using VTC

VCC

vCE

0 VBE vBE

VCE Q



Locating the Bias Point Q using VTC ... Cont’d

VCC

vCE

0 VBE vBE

VCE Q



Locating the Bias Point Q using VTC ... Cont’d

VCC

vCE

0 vBE

As RC valueincreases

0.5 V

0.3 V



The Concept of Load Line

= . . .

iC

IC

V

Z

Y

CE VCC vCE

Load line

Slope =1RC

Q

0

vBE

= . . .vBE

= . . .vBE

vBE



Locating Q using the Load Line

iC

vCE

Load-line A

QB

QA

VCEQB

VCE VCC

Load-line B

QA

= . . .vBE

= . . .vBE

=vBE VBE



Outline




4 Biasing


6 BJT Amplifiers


8 Summary



Biasing & Bias Stabilization

We need biasing for choosing an appropriate operating point.

Bias stabilization is necessary to obtain same gain irrespective of variation inparameters such as β, T, etc.

Bias stabilization can be achieved by maintaining constant IC, similar to thecase of MOSFET where we tried to maintain constant ID.





















1. Biasing by Fixing VBE (Bad)

RB2

RB1

VBE

RC

VCC

IC

IBVCE

RB RC

VCC

IC

IB

VCE

VBE

+ +




RB2

RB1

VBE

RC

VCC

IC

IBVCE

RB RC

VCC

IC

IB

VCE

VBE

+ +




iC

vBEVBE

IC1

0

IC2

Device 2

Device 1




iC

vBEVBE

IC1

0

IC2

Device 2

Device 1



2. The Classical Discrete-Circuit Bias Arrangement

R1

RER2

VCC

RC

VBB VCCR1 R2

R2

RB R1 R2

IB

IE

IC

=

RC

RE

VCC

=

+

VBB = IBRB + VBE + IERE

⇒ IE =VBB −VBE

RE + RB1+β

.

So, to make IE insensitive to temperatureand β variation,

VBB � VBE

RE � RB

β + 1




R1

RER2

VCC

RC

VBB VCCR1 R2

R2

RB R1 R2

IB

IE

IC

=

RC

RE

VCC

=

+


⇒ IE =VBB −VBE

RE + RB1+β

.


VBB � VBE

RE � RB

β + 1




R1

RER2

VCC

RC

VBB VCCR1 R2

R2

RB R1 R2

IB

IE

IC

=

RC

RE

VCC

=

+


⇒ IE =VBB −VBE

RE + RB1+β

.


VBB � VBE

RE � RB

β + 1




R1

RER2

VCC

RC

VBB VCCR1 R2

R2

RB R1 R2

IB

IE

IC

=

RC

RE

VCC

=

+


⇒ IE =VBB −VBE

RE + RB1+β

.


VBB � VBE

RE � RB

β + 1




R1

RER2

VCC

RC

VBB VCCR1 R2

R2

RB R1 R2

IB

IE

IC

=

RC

RE

VCC

=

+


⇒ IE =VBB −VBE

RE + RB1+β

.


VBB � VBE

RE � RB

β + 1




R1

RER2

VCC

RC

VBB VCCR1 R2

R2

RB R1 R2

IB

IE

IC

=

RC

RE

VCC

=

+


⇒ IE =VBB −VBE

RE + RB1+β

.


VBB � VBE

RE � RB

β + 1




R1

RER2

VCC

RC

VBB VCCR1 R2

R2

RB R1 R2

IB

IE

IC

=

RC

RE

VCC

=

+


⇒ IE =VBB −VBE

RE + RB1+β

.


VBB � VBE

RE � RB

β + 1



2. A Two-Power-Supply Version of the Classical BiasArrangement

RE

RB

+VCC

RC

-VEE

IB

IE




RE

RB

+VCC

RC

-VEE

IB

IE



3. Biasing Using a Collector-to-Base Feedback Resistor

IB

IE

IC

RC

VCC

RB

IE

VCC = IBRB + VBE + IERC

⇒ IE =VCC −VBE

RC + RB1+β


VBB � VBE

RE � RB

β + 1




IB

IE

IC

RC

VCC

RB

IE


⇒ IE =VCC −VBE

RC + RB1+β


VBB � VBE

RE � RB

β + 1




IB

IE

IC

RC

VCC

RB

IE


⇒ IE =VCC −VBE

RC + RB1+β


VBB � VBE

RE � RB

β + 1




IB

IE

IC

RC

VCC

RB

IE


⇒ IE =VCC −VBE

RC + RB1+β


VBB � VBE

RE � RB

β + 1




IB

IE

IC

RC

VCC

RB

IE


⇒ IE =VCC −VBE

RC + RB1+β


VBB � VBE

RE � RB

β + 1




IB

IE

IC

RC

VCC

RB

IE


⇒ IE =VCC −VBE

RC + RB1+β


VBB � VBE

RE � RB

β + 1




IB

IE

IC

RC

VCC

RB

IE


⇒ IE =VCC −VBE

RC + RB1+β


VBB � VBE

RE � RB

β + 1



4. Biasing Using a Constant-Current Source






Outline




4 Biasing


6 BJT Amplifiers


8 Summary



The Input Resistance at the Base (rπ)

vberπ =

ib

ib

+

vbe

Since iB = ISβ evBE/VT ,

rπ =∂vBE

∂iB

∣∣∣∣vBE=VBE

=

[1

VT

IS

βeVBE/VT

]−1

=VT

IB. (13)

.




vberπ =

ib

ib

+

vbe


rπ =∂vBE

∂iB

∣∣∣∣vBE=VBE

=

[1

VT

IS

βeVBE/VT

]−1

=VT

IB. (13)

.




vberπ =

ib

ib

+

vbe


rπ =∂vBE

∂iB

∣∣∣∣vBE=VBE

=

[1

VT

IS

βeVBE/VT

]−1

=VT

IB. (13)

.



Transconductance (gm)

ic

+

vbe

vBE

iC

0

vCB - 0.4 V

(V)0.5 0.7

Q

Slope = gm

Since iC = ISevBE/VT ,

gm =∂iC

∂vBE

∣∣∣∣vBE=VBE

=1

VTISeVBE/VT =

IC

VT. (14)




ic

+

vbe

vBE

iC

0

vCB - 0.4 V

(V)0.5 0.7

Q

Slope = gm


gm =∂iC

∂vBE

∣∣∣∣vBE=VBE

=1

VTISeVBE/VT =

IC

VT. (14)




ic

+

vbe

vBE

iC

0

vCB - 0.4 V

(V)0.5 0.7

Q

Slope = gm


gm =∂iC

∂vBE

∣∣∣∣vBE=VBE

=1

VTISeVBE/VT =

IC

VT. (14)



Small Signal (π) Model of BJT

E

B C+

–

ib ic

ie

vbegmvbe

rπ

E

B C+

–

ib ic

ie

vbe rπ β iB

E

B C+

–

ib ic

ie

vbe rπ αiE

gmvbe =IC

VT× ibrπ =

IC

VT× ib

VT

IB= βib = αie




E

B C+

–

ib ic

ie

vbegmvbe

rπ

E

B C+

–

ib ic

ie

vbe rπ β iB

E

B C+

–

ib ic

ie

vbe rπ αiE

gmvbe =IC

VT× ibrπ =

IC

VT× ib

VT

IB= βib = αie




E

B C+

–

ib ic

ie

vbegmvbe

rπ

E

B C+

–

ib ic

ie

vbe rπ β iB

E

B C+

–

ib ic

ie

vbe rπ αiE

gmvbe =

IC

VT× ibrπ =

IC

VT× ib

VT

IB= βib = αie




E

B C+

–

ib ic

ie

vbegmvbe

rπ

E

B C+

–

ib ic

ie

vbe rπ β iB

E

B C+

–

ib ic

ie

vbe rπ αiE

gmvbe =IC

VT× ibrπ

=IC

VT× ib

VT

IB= βib = αie




E

B C+

–

ib ic

ie

vbegmvbe

rπ

E

B C+

–

ib ic

ie

vbe rπ β iB

E

B C+

–

ib ic

ie

vbe rπ αiE

gmvbe =IC

VT× ibrπ =

IC

VT× ib

VT

IB

= βib = αie




E

B C+

–

ib ic

ie

vbegmvbe

rπ

E

B C+

–

ib ic

ie

vbe rπ β iB

E

B C+

–

ib ic

ie

vbe rπ αiE

gmvbe =IC

VT× ibrπ =

IC

VT× ib

VT

IB= βib

= αie




E

B C+

–

ib ic

ie

vbegmvbe

rπ

E

B C+

–

ib ic

ie

vbe rπ β iB

E

B C+

–

ib ic

ie

vbe rπ αiE

gmvbe =IC

VT× ibrπ =

IC

VT× ib

VT

IB= βib = αie



Small Signal (T) Model of BJT

E

B C+

–

ib ic

ie

vbegmvbe

rπ

C

B

E

ic

ib

re

ie

gmvbe

+

–

vbe

�� If both the above circuits are equivalent, then what should be the value of re?




E

B C+

–

ib ic

ie

vbegmvbe

rπ

C

B

E

ic

ib

re

ie

gmvbe

+

–

vbe





E

B C+

–

ib ic

ie

vbegmvbe

rπ

C

B

E

ic

ib

re

ie

gmvbe

+

–

vbe




Small Signal T Model of BJT ... Cont’d

E

B C+

–

ib ic

ie

vbegmvbe

rπ

C

B

E

ic

ib

re

ie

gmvbe

+

–

vbe

Voltage drop across rπ and re is same and equal to vbe. Therefore,

reie = rπ ib ⇒ re = rπibie

=rπ

1 + β. (15)




E

B C+

–

ib ic

ie

vbegmvbe

rπ

C

B

E

ic

ib

re

ie

gmvbe

+

–

vbe



=rπ

1 + β. (15)




E

B C+

–

ib ic

ie

vbegmvbe

rπ

C

B

E

ic

ib

re

ie

gmvbe

+

–

vbe

Voltage drop across rπ and re is same and equal to vbe.

Therefore,


=rπ

1 + β. (15)




E

B C+

–

ib ic

ie

vbegmvbe

rπ

C

B

E

ic

ib

re

ie

gmvbe

+

–

vbe



=rπ

1 + β. (15)



Small Signal Model (Including Early Effect)

vCE

iC

0

Saturationregion

Activeregion

-VA

iC = IS

(1 +

vCE

VA

)evBE/VT (16)




vCE

iC

0

Saturationregion

Activeregion

-VA

iC = IS

(1 +

vCE

VA

)evBE/VT (16)




vCE

iC

0

Saturationregion

Activeregion

-VA

iC = IS

(1 +

vCE

VA

)evBE/VT (16)



Small Signal Model (Including Early Effect) ... Cont’d

gm = IC /VTrπ = IBVT/

E

B C+

–

ib ic

ie

vbegmvbe

rπ ro

E

B C+

–

ib ic

ie

vbe rπ roβ iB

From (16),

ro =

(∂iC

∂vCE

∣∣∣∣vBE=constant

)−1

=

(IS

VAeVBE/VT

)−1

=VA

ISeVBE/VT=

VA

I′C, (17)

where I′C is the value of the collector current with the Early effect neglected.





E

B C+

–

ib ic

ie

vbegmvbe

rπ ro

E

B C+

–

ib ic

ie

vbe rπ roβ iB

From (16),

ro =

(∂iC

∂vCE


)−1

=

(IS

VAeVBE/VT

)−1

=VA

ISeVBE/VT=

VA

I′C, (17)






E

B C+

–

ib ic

ie

vbegmvbe

rπ ro

E

B C+

–

ib ic

ie

vbe rπ roβ iB

From (16),

ro =

(∂iC

∂vCE


)−1

=

(IS

VAeVBE/VT

)−1

=VA

ISeVBE/VT=

VA

I′C, (17)




Outline




4 Biasing


6 BJT Amplifiers


8 Summary



BJT is Basically a Current Amplifier!


E

B C+

–

ib ic

ie

vbegmvbe

rπ ro

E

B C+

–

ib ic

ie

vbe rπ roβ iB

rπ ≈ 0 and ro → ∞





E

B C+

–

ib ic

ie

vbegmvbe

rπ ro

E

B C+

–

ib ic

ie

vbe rπ roβ iB






E

B C+

–

ib ic

ie

vbegmvbe

rπ ro

E

B C+

–

ib ic

ie

vbe rπ roβ iB




Basic Configurations (Stripped Down Versions)

vi

RL

(c) Common-Collector (CC)or Emitter Follower

vo

_+

vi

RC

(a) Common-Emitter (CE)

vo

_+ vi

RC

(b) Common-Base (CB)

vo

_+




vi

RL


vo

_+

vi

RC


vo

_+ vi

RC


vo

_+



Various Definitions of Gain – Recap

+vi

+

vo

+

R0

RiAvovi+vs RL

RSii io

Avo =vo

vI

∣∣∣∣RL→∞

Av = AvoRL

RL + Ro

Gv =vo

vs= Avo

(Ri

Ri + RS

)(RL

RL + Ro

)



Various Definitions of Gain – Recap

+vi

+

vo

+

R0

RiAvovi+vs RL

RSii io

Avo =vo

vI

∣∣∣∣RL→∞

Av = AvoRL

RL + Ro

Gv =vo

vs= Avo

(Ri

Ri + RS

)(RL

RL + Ro

)



First Let’s Analyze Simple CS Amplifier ...



1. CE Amplifier



1. CE Amplifier

vi

Rin Ro

voRC

vsig

Rsig

_+



1. CE Amplifier

vi

Rin Ro

voRC

vsig

Rsig

v = vi

Rin=

vsig

Rsig

vo

Ro= RC||ro

gmvbeRCro

_+

_+ rπ

rπ

Avo = −gm (ro ‖ RC) Av = −gm (ro ‖ RC ‖ RL) Gv = Av × rπRsig+rπ



1. CE Amplifier

vi

Rin Ro

voRC

vsig

Rsig

v = vi

Rin=

vsig

Rsig

vo

Ro= RC||ro

gmvbeRCro

_+

_+ rπ

rπ

Avo = −gm (ro ‖ RC)

Av = −gm (ro ‖ RC ‖ RL) Gv = Av × rπRsig+rπ



1. CE Amplifier

vi

Rin Ro

voRC

vsig

Rsig

v = vi

Rin=

vsig

Rsig

vo

Ro= RC||ro

gmvbeRCro

_+

_+ rπ

rπ

Avo = −gm (ro ‖ RC)

Av = −gm (ro ‖ RC ‖ RL) Gv = Av × rπRsig+rπ



1. CE Amplifier

vi

Rin Ro

voRC

vsig

Rsig

v = vi

Rin=

vsig

Rsig

vo

Ro= RC||ro

gmvbeRCro

_+

_+ rπ

rπ

Avo = −gm (ro ‖ RC) Av = −gm (ro ‖ RC ‖ RL)

Gv = Av × rπRsig+rπ



1. CE Amplifier

vi

Rin Ro

voRC

vsig

Rsig

v = vi

Rin=

vsig

Rsig

vo

Ro= RC||ro

gmvbeRCro

_+

_+ rπ

rπ




2. CB Amplifier



2. CB Amplifier

vi

vo

Ro

vsig

Rsig

Rin

RC

_+




2. CB Amplifier

vi

vo

Ro= RC

Rin= re

vsig

Rsig

RC

ie

ie

re

vi

vo

Ro

vsig

Rsig

Rin

RC

_+_+

Avo = +gmRC Av = +gm (RC ‖ RL) Gv = Av × reRsig+re



2. CB Amplifier

vi

vo

Ro= RC

Rin= re

vsig

Rsig

RC

ie

ie

re

vi

vo

Ro

vsig

Rsig

Rin

RC

_+_+

Avo = +gmRC

Av = +gm (RC ‖ RL) Gv = Av × reRsig+re



2. CB Amplifier

vi

vo

Ro= RC

Rin= re

vsig

Rsig

RC

ie

ie

re

vi

vo

Ro

vsig

Rsig

Rin

RC

_+_+

Avo = +gmRC Av = +gm (RC ‖ RL)

Gv = Av × reRsig+re



2. CB Amplifier

vi

vo

Ro= RC

Rin= re

vsig

Rsig

RC

ie

ie

re

vi

vo

Ro

vsig

Rsig

Rin

RC

_+_+




3. CC Amplifier / Emitter Follower




vsig

Rsig

RL

RoRin

vovi_+ vsig

Rsig

re

RLvo

vi

ie

Ro= re_+

αie

?

?

Avo = 1 Av = RLre+RL

Gv = Av × RinRsig+Rin




vsig

Rsig

RL

RoRin

vovi_+ vsig

Rsig

re

RLvo

vi

ie

Ro= re_+

αie






vsig

Rsig

RL

RoRin

vovi_+ vsig

Rsig

re

RLvo

vi

ie

Ro= re_+

αie

Avo = 1

Av = RLre+RL





vsig

Rsig

RL

RoRin

vovi_+ vsig

Rsig

re

RLvo

vi

ie

Ro= re_+

αie






vsig

Rsig

RL

RoRin

vovi_+ vsig

Rsig

re

RLvo

vi

ie

Ro= re_+

αie





4. CE Amplifier with Emitter Resistance

vi

vo

Rin Ro

vsig

Rsig

Re

RC

vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_+

_

+

_

+



4. CE Amplifier with Emitter Resistance

vi

vo

Rin Ro

vsig

Rsig

Re

RC

vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_+

_

+

_

+



4. CE Amplifier with Emitter Resistance ... Rin

vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_

+

ib = ie − αie = (1− α) ie

ie =vi

re + Re

Rin =viib

=vi

(1− α) ie=

vi (re + Re)

(1− α) vi= (1 + β) (re + Re)




vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_

+


ie =vi

re + Re

Rin =viib

=vi

(1− α) ie=

vi (re + Re)

(1− α) vi= (1 + β) (re + Re)




vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_

+


ie =vi

re + Re

Rin =viib

=vi

(1− α) ie=

vi (re + Re)

(1− α) vi= (1 + β) (re + Re)




vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_

+


ie =vi

re + Re

Rin =viib

=vi

(1− α) ie=

vi (re + Re)

(1− α) vi= (1 + β) (re + Re)



4. CE Amplifier with Emitter Resistance ... Gains

vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_

+

vo = −gmvbeRC

gmvbe = αie = αvi

re + Re

Avo =−αRC

re + ReAv =

−α (RC ‖ RL)

re + ReGv = Av

Rin

Rsig + Rin




vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_

+

vo = −gmvbeRC

gmvbe = αie = αvi

re + Re

Avo =−αRC

re + ReAv =

−α (RC ‖ RL)

re + ReGv = Av

Rin

Rsig + Rin




vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_

+

vo = −gmvbeRC

gmvbe = αie = αvi

re + Re

Avo =−αRC

re + Re

Av =−α (RC ‖ RL)

re + ReGv = Av

Rin

Rsig + Rin




vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_

+

vo = −gmvbeRC

gmvbe = αie = αvi

re + Re

Avo =−αRC

re + ReAv =

−α (RC ‖ RL)

re + Re

Gv = AvRin

Rsig + Rin




vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_

+

vo = −gmvbeRC

gmvbe = αie = αvi

re + Re

Avo =−αRC

re + ReAv =

−α (RC ‖ RL)

re + ReGv = Av

Rin

Rsig + Rin



4. CE Amplifier with Emitter Resistance ***




+

−

vbegmvbe




+

−

vbegmvbe

+

−

vs+

−

vf




+

−

vbegmvbe

+

−

vs+ −vf

Rearranging the figure in the previous slide like the above shown gives you abetter picture of the feedback phenomena.




+

−

vbegmvbe

+

−

vs+ −vf

Rearranging the figure in the previous slide like the above shown gives you abetter picture of the feedback phenomena.




+

−

vsg'mvs

g′m =gm

1 + gm

(REα

)

r′π = rπ ×[

1 + gm

(REα

)]




+

−

vsg'mvs

g′m =gm

1 + gm

(REα

)

r′π = rπ ×[

1 + gm

(REα

)]




+

−

vsg'mvs

g′m =gm

1 + gm

(REα

)

r′π = rπ ×[

1 + gm

(REα

)]




+

−

vsg'mvs

g′m =gm

1 + gm

(REα

)

r′π = rπ ×[

1 + gm

(REα

)]



BJT Amplifiers – Summary

Type Ri Ro Avo Av Gv

CE rπ RC −gm (ro ‖ RC) −gm (ro ‖ RC ‖ RL) AvRin

Rin+Rsig

CB re RC +gm (ro ‖ RC) +gm (ro ‖ RC ‖ RL) AvRin

Rin+Rsig

CC (1 + β) (re + RL)* re 1 RLRL+re

AvRin

Rin+Rsig

CE with Re (1 + β) (re + Re) RC−αRCre+Re

−α(RC‖RL)re+Re

AvRin

Rin+Rsig






Rin+Rsig


Rin+Rsig


AvRin

Rin+Rsig


−α(RC‖RL)re+Re

AvRin

Rin+Rsig



Outline




4 Biasing


6 BJT Amplifiers


8 Summary



BJT Internal Capacitances & High Frequency Model

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

gmro

rx




n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

gmro

rx




n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

gmro

rx



Unity Gain Bandwidth (ωT)

gmro

rx

Vπ =Ib

1rπ

+ s(Cµ + Cπ

)Ie = gmVπ = gm

Ib1

rπ+ s

(Cµ + Cπ

)

Ie

Ib=

gmrπ

1 + srπ

(Cµ + Cπ

) =β0

1 + srπ

(Cµ + Cπ

)ωβ =

1rπ

(Cµ + Cπ

)ωT =

gm

Cµ + Cπ




gmro

rx

Vπ =Ib

1rπ

+ s(Cµ + Cπ

)Ie = gmVπ = gm

Ib1

rπ+ s

(Cµ + Cπ

)

Ie

Ib=

gmrπ

1 + srπ

(Cµ + Cπ

) =β0

1 + srπ

(Cµ + Cπ

)ωβ =

1rπ

(Cµ + Cπ

)ωT =

gm

Cµ + Cπ




gmro

rx

Vπ =Ib

1rπ

+ s(Cµ + Cπ

)Ic = gmVπ = gm

Ib1

rπ+ s

(Cµ + Cπ

)

Ic

Ib=

gmrπ

1 + srπ

(Cµ + Cπ

) =β0

1 + srπ

(Cµ + Cπ

)ωβ =

1rπ

(Cµ + Cπ

)ωT =

gm

Cµ + Cπ




gmro

rx

Vπ =Ib

1rπ

+ s(Cµ + Cπ

)

Ic = gmVπ = gmIb

1rπ

+ s(Cµ + Cπ

)

Ic

Ib=

gmrπ

1 + srπ

(Cµ + Cπ

) =β0

1 + srπ

(Cµ + Cπ

)ωβ =

1rπ

(Cµ + Cπ

)ωT =

gm

Cµ + Cπ




gmro

rx

Vπ =Ib

1rπ

+ s(Cµ + Cπ

)Ic = gmVπ = gm

Ib1

rπ+ s

(Cµ + Cπ

)

Ic

Ib=

gmrπ

1 + srπ

(Cµ + Cπ

) =β0

1 + srπ

(Cµ + Cπ

)ωβ =

1rπ

(Cµ + Cπ

)ωT =

gm

Cµ + Cπ




gmro

rx

Vπ =Ib

1rπ

+ s(Cµ + Cπ

)Ic = gmVπ = gm

Ib1

rπ+ s

(Cµ + Cπ

)

Ic

Ib=

gmrπ

1 + srπ

(Cµ + Cπ

) =β0

1 + srπ

(Cµ + Cπ

)

ωβ =1

rπ

(Cµ + Cπ

)ωT =

gm

Cµ + Cπ




gmro

rx

Vπ =Ib

1rπ

+ s(Cµ + Cπ

)Ic = gmVπ = gm

Ib1

rπ+ s

(Cµ + Cπ

)

Ic

Ib=

gmrπ

1 + srπ

(Cµ + Cπ

) =β0

1 + srπ

(Cµ + Cπ

)ωβ =

1rπ

(Cµ + Cπ

)

ωT =gm

Cµ + Cπ




gmro

rx

Vπ =Ib

1rπ

+ s(Cµ + Cπ

)Ic = gmVπ = gm

Ib1

rπ+ s

(Cµ + Cπ

)

Ic

Ib=

gmrπ

1 + srπ

(Cµ + Cπ

) =β0

1 + srπ

(Cµ + Cπ

)ωβ =

1rπ

(Cµ + Cπ

)ωT =

gm

Cµ + Cπ



Frequency Response of CE Amplifier

VEE

VCC

CC1

CE

Rsig

Vsig

Vo

RL

CC2

I

RB

RC

_+

_




VEE

VCC

CC1

CE

Rsig

Vsig

Vo

RL

CC2

I

RB

RC

_+

_




Vo(dB)

Low-frequencyband

ViMidband

All capacitances can be neglected

High-frequency band

Gain falls offdue to the effectof Ci , CSand Co

3 dB

20 log |AM| (dB)

fL fH f (Hz)

Gain falls offdue to the internalcapacitive effectsof the MOSFET




Vo(dB)

Low-frequencyband

ViMidband

All capacitances can be neglected

High-frequency band

Gain falls offdue to the effectof Ci , CSand Co

3 dB

20 log |AM| (dB)

fL fH f (Hz)

Gain falls offdue to the internalcapacitive effectsof the MOSFET



High Frequency Response of CE Amplifier

RB

Rsig

Vsiggm

Voro RC RL

rx

R 'L

_+_

+

_

+

Applying Miller’s theorem gives time constant,

τ ={[(

Rsig ‖ RB)+ rx

]‖ rπ

} [Cπ + gmR′LCµ

]. (18)

So, for the CE amplifier fH is given as

fH =1

2πτ=

12π{[(

Rsig ‖ RB)+ rx

]‖ rπ

} [Cπ + gmR′LCµ

] . (19)




RB

Rsig

Vsiggm

Voro RC RL

rx

R 'L

_+_

+

_

+


τ ={[(

Rsig ‖ RB)+ rx

]‖ rπ

} [Cπ + gmR′LCµ

]. (18)


fH =1

2πτ=

12π{[(

Rsig ‖ RB)+ rx

]‖ rπ

} [Cπ + gmR′LCµ

] . (19)




RB

Rsig

Vsiggm

Voro RC RL

rx

R 'L

_+_

+

_

+


τ ={[(

Rsig ‖ RB)+ rx

]‖ rπ

} [Cπ + gmR′LCµ

]. (18)


fH =1

2πτ=

12π{[(

Rsig ‖ RB)+ rx

]‖ rπ

} [Cπ + gmR′LCµ

] . (19)




RB

Rsig

Vsiggm

Voro RC RL

rx

R 'L

_+_

+

_

+


τ ={[(

Rsig ‖ RB)+ rx

]‖ rπ

} [Cπ + gmR′LCµ

]. (18)


fH =1

2πτ=

12π{[(

Rsig ‖ RB)+ rx

]‖ rπ

} [Cπ + gmR′LCµ

] . (19)




RB

Rsig

Vsiggm

Voro RC RL

rx

R 'L

_+_

+

_

+

So, the total high frequency response is given as

Vo (s)Vi (s)

= AM1

1 + sτ, (20)

where τ ={[(

Rsig ‖ RB)+ rx

]‖ rπ

} [Cπ + gmR′LCµ

]and AM = −gm (ro ‖ RC ‖ RL).




RB

Rsig

Vsiggm

Voro RC RL

rx

R 'L

_+_

+

_

+


Vo (s)Vi (s)

= AM1

1 + sτ, (20)

where τ ={[(

Rsig ‖ RB)+ rx

]‖ rπ

} [Cπ + gmR′LCµ





RB

Rsig

Vsiggm

Voro RC RL

rx

R 'L

_+_

+

_

+


Vo (s)Vi (s)

= AM1

1 + sτ, (20)

where τ ={[(

Rsig ‖ RB)+ rx

]‖ rπ

} [Cπ + gmR′LCµ




Low Frequency Response of CE Amplifier

−+

gmvbe

vbe rπ




−+

gmvbe

vbe rπ



Low Frequency Response of CE Amplifier – τ1

−+

gmvbe

vbe rπ




−+

gmvbe

vbe rπ




−+

gmvbe

vbe rπ




−+

gmvbe

vbe rπ

So, the total low frequency response is given as

Vo (s)Vi (s)

= AM ×sτ1

1 + sτ1× sτ2

1 + sτ2× sτ3

1 + sτ3, (21)

where AM = −gm (RC ‖ RL).




−+

gmvbe

vbe rπ


Vo (s)Vi (s)

= AM ×sτ1

1 + sτ1× sτ2

1 + sτ2× sτ3

1 + sτ3, (21)





−+

gmvbe

vbe rπ


Vo (s)Vi (s)

= AM ×sτ1

1 + sτ1× sτ2

1 + sτ2× sτ3

1 + sτ3, (21)




Outline




4 Biasing


6 BJT Amplifiers


8 Summary



Operation of BJT in Active Mode

B

C

iEiE iC iC

i

iB

iB2iCiE


Injected holes (iB1

E

Forward-biased

iE

iC

n p n


VBE

(

Injectedelectrons

Diffusingelectrons

Collectedelectrons

VCB



iC vs vCB

vCB

Saturationmode

Active mode

α IE iE= IE

- 0.4 V

iC




iC vs vCE

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC






Jn = qDndnp (x)

dx


dx

= AEqDn

(−

np (0)W

)= −

AEqDnnp0

WevBE/VT ,






Currents in Active Mode

B

C

E

iC

iE

iB

iC = −In =

(AEqDnnp0

W

)evBE/VT = IS evBE/VT

iB =iCβ

=ISevBE/VT

β

iE = iC + iB =

(β + 1

β

)iC =

iCα

=ISevBE/VT

α≈ iC

α =β

1 + β

β =α

1− α



MOSFET vs BJT

n+

L

Metal

Channelregion



n+


Bod y (B)

n-type n-type

Emitterregion



Collector(C)

Emitter(E)

Metalcontact

Collectorregion

p-type

Baseregion

Base(B)

vCE

Saturationmode

Active mode

α IE iE= IE

+ 0.3 V

iC

0

iD

vDS sat =

vGS = +Vt

0

Triode Saturation

vOV


vDSvOV



Early Effect

vCE

iC

0

Saturationregion

Activeregion

-VA

iC = IS

(1 +

vCE

VA

)evBE/VT




RB2

RB1

VBE

RC

VCC

IC

IBVCE

RB RC

VCC

IC

IB

VCE

VBE

+ +




iC

vBEVBE

IC1

0

IC2

Device 2

Device 1




R1

RER2

VCC

RC

VBB VCCR1 R2

R2

RB R1 R2

IB

IE

IC

=

RC

RE

VCC

=

+


⇒ IE =VBB −VBE

RE + RB1+β

.


VBB � VBE

RE � RB

β + 1




RE

RB

+VCC

RC

-VEE

IB

IE




IB

IE

IC

RC

VCC

RB

IE


⇒ IE =VCC −VBE

RC + RB1+β


VBB � VBE

RE � RB

β + 1







E

B C+

–

ib ic

ie

vbegmvbe

rπ

E

B C+

–

ib ic

ie

vbe rπ β iB

E

B C+

–

ib ic

ie

vbe rπ αiE



Small Signal T Model of BJT

E

B C+

–

ib ic

ie

vbegmvbe

rπ

C

B

E

ic

ib

re

ie

gmvbe

+

–

vbe

rπ =VT

IBgm =

IC

VTre =

VT

IE





E

B C+

–

ib ic

ie

vbegmvbe

rπ ro

E

B C+

–

ib ic

ie

vbe rπ roβ iB

ro =VA

I′C,≈ VA

IC





vi

RL


vo

_+

vi

RC


vo

_+ vi

RC


vo

_+



1. CE Amplifier

vi

Rin Ro

voRC

vsig

Rsig

v = vi

Rin=

vsig

Rsig

vo

Ro= RC||ro

gmvbeRCro

_+

_+ rπ

rπ




2. CB Amplifier

vi

vo

Ro= RC

Rin= re

vsig

Rsig

RC

ie

ie

re

vi

vo

Ro

vsig

Rsig

Rin

RC

_+_+





vsig

Rsig

RL

RoRin

vovi_+ vsig

Rsig

re

RLvo

vi

ie

Ro= re_+

αie






vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_

+


ie =vi

re + Re

Rin =viib

=vi

(1− α) ie=

vi (re + Re)

(1− α) vi= (1 + β) (re + Re)




vi

vo

Rin

Ro

ic

ib

ie

vsig

Rsig B

E

C

RC

re

Re

gmvbe

_+

_

+

vo = −gmvbeRC

gmvbe = αie = αvi

re + Re

Avo =−αRC

re + ReAv =

−α (RC ‖ RL)

re + ReGv = Av

Rin

Rsig + Rin




+

−

vbegmvbe

+

−

vs+

−

vf




+

−

vsg'mvs

g′m =gm

1 + gm

(REα

)

r′π = rπ ×[

1 + gm

(REα

)]






Rin+Rsig


Rin+Rsig


AvRin

Rin+Rsig


−α(RC‖RL)re+Re

AvRin

Rin+Rsig




gmro

rx

Vπ =Ib

1rπ

+ s(Cµ + Cπ

)Ic = gmVπ = gm

Ib1

rπ+ s

(Cµ + Cπ

)

Ic

Ib=

gmrπ

1 + srπ

(Cµ + Cπ

) =β0

1 + srπ

(Cµ + Cπ

)ωβ =

1rπ

(Cµ + Cπ

)ωT =

gm

Cµ + Cπ




RB

Rsig

Vsiggm

Voro RC RL

rx

R 'L

_+_

+

_

+


Vo (s)Vi (s)

= AM1

1 + sτ,

where τ ={[(

Rsig ‖ RB)+ rx

]‖ rπ

} [Cπ + gmR′LCµ





−+

gmvbe

vbe rπ




−+

gmvbe

vbe rπ




−+

gmvbe

vbe rπ




−+

gmvbe

vbe rπ


Vo (s)Vi (s)

= AM ×sτ1

1 + sτ1× sτ2

1 + sτ2× sτ3

1 + sτ3,



Documents

6. BJT Transistors & Circuits - Arraytool · PDF file4/6/2016 · 6. BJT Transistors & Circuits ... One can implement digital and analog functions utilizing MOSFETs almost exclusively