Bipolar transistors Two port representation of the bipolar ... › skaidres › Devices › Transistors › Transistors 3.pdfThe T-type model of a BJT in its CB configuration A BJT

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1

Bipolar transistors

• Two port representation of the bipolar transistor

• Models of bipolar transistors

Objectives:

Systems of r, g and h parameters of BJTs

Meanings of r, g and h parameters

Finding (calculation) of h and other parameters

Methodology of composing of the T-type equivalent circuit for a BJT in its CB

configuration

Calculation of parameters of thr equivalent circuit and application of the circuit

ELEKTRONIKOS ĮTAISAI 2009

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2

Two port representation of a BJT

1. I-U characteristics of BJTs are not linear. The powerfull tools of

linear circuit analysis cannot be used.

2. When transistor is used for processing of small signals, only small

parts of non-linear characteristics are used. Then the linear

approximations of the characteristics at the quiescent operating

points are possible.

3. At processing of small signals, the linear models of BJTs can

be used.

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3

Sets of equations, describing BJTs

2121111 IZIZU +=

2221212 IZIZU +=

2121111 IrIrU +=

2221212 IrIrU +=

2121111 UYUYI +=

2221212 UYUYI +=

2121111 UgUgI +=

2221212 UgUgI +=

2121111 UHIHU += 2121111 UhIhU +=

2221212 UHIHI += 2221212 UhIhI +=

Z – impedance;

r – resistance

Y – admittance;

g – conductance

H, h – hybrid

parameters

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r parameters

2121111 IrIrU +=

2221212 IrIrU +=

021

111 ==

II

Ur

012

112 ==

II

Ur

021

221 ==

II

Ur

012

222 ==

II

Ur

– the input resistance when output is open

– the reverse transfer resistance when the input is open

– the forward transfer resistance when the output is open

– the output resistance when the input is open

1. The open circuit conditions (for alternating current) must be arranged.

2. Difficulties arise when resistances r11 and r21 are measured.

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g parameters

– the input conductance when the output is shortened

– the reverse transfer conductance when the input is shortened

– the forward transfer conductance when the output is shortened

– the output conductance when the input is shortened

1. The short circuit regimes (for alternating voltage) must be arranged.

2. Difficulties arise when conductances g12 and g22 are measured.

021

111 ==

UU

Ig

012

112 ==

UU

Ig

021

221 ==

UU

Ig

012

222 ==

UU

Ig

2121111 UgUgI +=

2221212 UgUgI +=

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h parameters

– input resistance with shortened output

– open circuit reverse voltage gain

– short circuit forward current gain

– output conductance with input open

1. There are no difficulties to arrange output shortened and input open

conditions and measure h parameters.

2. The set of h parameters includes information about current gain:

h21B= –α, h21E = β

2121111 UhIhU +=

2221212 UhIhI +=

021

111 ==

UI

Uh

012

112 ==

IU

Uh

021

221 ==

UI

Ih

012

222 ==

IU

Ih

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Parameters of BJTs

2221

1211

gg

gg

2221

1211

rr

rr

2221

1211

hh

hh

A BJT as a linear network can be represented by three sets of

parameters:

h parameters of a BJT are known. Derive formulas for calculation of

its r parameters.

ELEKTRONIKOS ĮTAISAI 2009

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2121111 UhIhU +=

2221212 UhIhI +=

2121111 IrIrU +=

2221212 IrIrU +=

Parameters of BJTs

222

122

212

1I

hI

h

hU +−=

222

121

22

2112111 )( I

h

hI

h

hhhU +−=

.1

,

,,

2212

22

2121

22

1212

22

21121111

hr

h

hr

h

hr

h

hhhr

=−=

=−=

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Evaluation of h parameters

QCECEB

BE

21

1E11 const∆

∆

0 UUI

U

UI

Uh

===

==

BQB1CE3CE

BE

BCE

BE

12

1E12

∆

const∆

∆

0 IIUU

U

IU

U

IU

Uh

=−=

==

==

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h parametrų skaičiavimas

QCEC1B3B

1C3C

CEB

C

21

2E21

const∆

∆

0 UUII

II

UI

I

UI

Ih

E =−

−=

==

==

Q12

222 const∆

∆

0 BBCE

CE IIU

I

IU

Ih

===

==

Evaluation of h parameters

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h parametrų skaičiavimasTransistor models

Equivalent circuits of a pnp transistor corresponding to

the Ebers-Moll equations

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h parametrų skaičiavimasThe T-type model of a BJT in its CB configuration

2121111 UhIhU +=

2221212 UhIhI +=

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2B221B212

2B121B111

UhIhI

UhIhU

+=

+=

CB22

EB22

B212

CB22

B12E

B22

B21B12B111

1I

hI

h

hU

Ih

hI

h

hhhU

+−=

+

−=

( )( )( )ECCC

CCEB2

CEBEE1

IαIrU

UIIrU

IIrIrU

+=

++=

++=

( )( ) ( )CBCBKE2

CBEEB1

rrIIrαrU

IrIrrU

+++=

++=

( )B22KB

EBB11

EB

B22B12B

1

1

...

hrr

rαrh

rr

hhr

=+

+−=

=+

=

( )B22C

EB11B

EQQE

1

025,0qk

hr

rhβr

II

T/r

E

≅

−≅

≅≅

The T-type model of a BJT in its CB configuration

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h parametrų skaičiavimash parametrų skaičiavimash parametrų skaičiavimasThe T-type model of a BJT in its CB configuration

CQCQE

025,01

q

k

II

Tr ≅≅

Tπ2

1

f=ατ CB τττ α −≅ EBE / rC τ=CBC Cr=τ

( )EB11B rhr −≅ β CEB22C /1 rhr β≅≅

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The T-type model of a BJT in its CB configuration

A BJT is in its CB configuration. According to I-U characteristics h

parameters were found at the given Q point (emitter current – 15 mA,

collector-base voltage – 5 V): input resistance 4 Ω, emitter current gain –

0,99, output conductance – 50 µS. Sketch the T-type model of the

transistor and find parameters of equivalent circuit elements.

ELEKTRONIKOS ĮTAISAI 2009

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The T-type model of a BJT in its CB configuration

CQCQE

025,01

q

k

II

Tr ≅≅

Tπ2

1

f=ατ KB τττ α −≅ EBE / rC τ=KBK Cr=τ

( )EB11B rhβr −≅ CEB22C /1 rβhr ≅≅

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The T-type model of a BJT in its CE configuration

( )EKKK IIrU α−=

( )α−= 1KKE rr

( )

( )BKKE

BKKK

11

IIr

IIrU

βαα

α

−=

=

−

−−=

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The T-type model of a BJT in its CE configuration

2E221E212

2E121E111

UhIhI

UhIhU

+=

+=

CE22

BE22

E212

CE22

E12B

E22

E21E12E111

1I

hI

h

hU

Ih

hI

h

hhhU

+−=

+

−=

( )( )( )BCCE

CCBE2

CBEBB1

IIrU

UIIrU

IIrIrU

C β−=

++=

++=

( )( ) ( )CEECBCEE2

CEBEB1

rrIIrrU

IrIrrU

++−=

++=

β

( )

E22E

E22CE

EE11B

EQE22

E12E

11

1

q/k...

hr

hr

rβhr

I

T

h

hr

≅−=

+−=

≅==

I1 = IB

rB

βΙΒ I2 = IC

U1 U2 rE rCE

IE

C B

E

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The T-type model of a BJT in its CE configuration

CQCQE

025,01

q

k

II

Tr ≅≅

βωω

βββ

/j1

0

+=⇒ 0T / βff β ≅

)(, CEE KCC

)1(EE11B βrhr +−= E22CE /1 hr ≅

CCE CβC ≅

B

rB

βΙΒ

CE rE

rCE

C

E

CCE

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Composing and application of the T-type equivalent

circuit of a BJT in its CE configuration

A BJT is in its CE configuration. At the given Q-point (base current 0.1 mA,

CE voltage 5 V) the input resistance is 300 Ω, the base current gain is 100, and

the output conductance is 200 µS.

Sketch the equivalent circuit of the BJT.

Find the parameters of the circuit.

Find the voltage gain at input voltage of 10 mV and load resistance of 300 Ω.

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21

Composing and application of the T-type equivalent

circuit of a BJT in its CE configuration

CQCQE

025,0

q

k

II

1Tr ≅≅ EB11B )1( rhr +−≅ β CEB22C β/1 rhr ≅≅

I1 = IB

rB

βΙΒ I2 = IC

U1 U2 rE rCE

IE

C B

E