Notes on two-port networks

1

Electronic Circuits 1

Two Port Characterizations

Prof. C.K. Tse: 2-port networks

Contents• Input and output resistances• Two port networks• Models

2Prof. C.K. Tse: 2-port networks

Impedances and loading effectsVoltage amplifiers

+– AvvinRin

Rout

RLOAD

+vo–

+vin–

+–vs

Rs

smaller the better(the best is 0)

larger the better(the best is ∞)

3Prof. C.K. Tse: 2-port networks

Impedances and loading effectsCurrent amplifiers

AiiinRin Rout

larger the better(the best is ∞)

smaller the better(the best is 0)

RLOADioutRsis

iin

4Prof. C.K. Tse: 2-port networks

Impedances and loading effectsTransconductance amplifiers

Gmvin

Rin Rout

larger the better(the best is ∞)

larger the better(the best is ∞)

RLOADiout+–vs

Rs

+vin–

5Prof. C.K. Tse: 2-port networks

Impedances and loading effectsTransresistance amplifiers

Rin

smaller the better(the best is 0)

smaller the better(the best is 0)

RLOAD+– Rmiin

Rout

+vo–

Rsis

iin

6Prof. C.K. Tse: 2-port networks

Finding impedancesInput impedance

Inject a current to the input, find the voltage. The ratio ofthe voltage to current gives the input resistance.

+vx–

ix

Rin

WITH Outputopen-circuit if it issupposed to be a voltageoutput (e.g., voltageamplifiers andtransresistance amplifiers)

short-circuit if it issupposed to be a currentoutput (current amplifiersand transconductanceamplifiers)

7Prof. C.K. Tse: 2-port networks

Finding impedancesOutput impedance

Inject a current at output, find the voltage. The ratio ofthe voltage to current gives the output resistance.

+vx–

ix

Rout

WITH inputshort-circuit if it issupposed to be a voltageinput (e.g., voltageamplifiers andtransconductanceamplifiers)

open-circuit if it issupposed to be a currentinput (current amplifiersand transresistanceamplifiers)

8Prof. C.K. Tse: 2-port networks

Example: CE amplifier with ED

B C

E E

gmvBE~

rπ ro

RE

RB1 || RB2

+vo–

rin

vin

iB

rvi

v vi

vi

vi

rvi

rv

ir R

inin

B

BE E

B

BE

B

E

B

E

B

E

E

E

= =+

= +

= +

= ++

= + +

π

π

π

β

β

/( )

( )

1

1

Input resistance is

9Prof. C.K. Tse: 2-port networks

Example: EF amplifier

B C

E E

gmvBE~

rπ ro

RE

rout

Output resistance is

rvi

vi

vi i g v

v

ivr

g vR r

g

Rg

gR

g

Rg

outm

m

BE

m

BE

E B m BE

E

EE

m EE

m

E

mm

Em

Em

= =−

=−

− −

=

+ +

=

+ +

=

+ +

≈

+

=

π π

β

11 1

11

11

1||

+–

vm

im

10Prof. C.K. Tse: 2-port networks

Quick rule 1

RE

r REπ β+ +( )1

11Prof. C.K. Tse: 2-port networks

Example

RE1r R r RE Eπ πβ β+ + + +( )[ || ( ( ) )]1 11 2

RE2

12Prof. C.K. Tse: 2-port networks

Quick rule 2

11gR

m

B++ β

RB

11gR

Rm

BE+

+

β

RB

RE

13Prof. C.K. Tse: 2-port networks

Example

11g

R RR

m

L BE+

+

+

β

RE

RL

RB

14Prof. C.K. Tse: 2-port networks

General two port characterizations

+v1–

i1

+v2–

i2

1 2

15Prof. C.K. Tse: 2-port networks

Types of characterizations

Immittance parameters- z-parameters- y-parameters

Hybrid parameters- h-parameters- g-parameters

16Prof. C.K. Tse: 2-port networks

z-parameters

vv

z zz z

ii

zvi

zvi

zvi

zvi

i

i

i

i

1

2

11 12

21 22

1

2

111

1 0

121

2 0

212

1 0

222

2 0

2

1

1

2

=

=

=

=

=

=

=

=

=

(open-circuit port 2)

(open-circuit port 1)

(open-circuit port 2)

(open-circuit port 2)

+v1–

i1+v2–

i21 2

17Prof. C.K. Tse: 2-port networks

y-parameters

ii

y yy y

vv

yiv

yiv

yiv

yiv

v

v

v

v

1

2

11 12

21 22

1

2

111

1 0

121

2 0

212

1 0

222

2 0

2

1

1

2

=

=

=

=

=

=

=

=

=

(short-circuit port 2)

(short-circuit port 1)

(short-circuit port 2)

(short-circuit port 2)

+v1–

i1+v2–

i21 2

18Prof. C.K. Tse: 2-port networks

h-parameters

vi

h hh h

iv

hvi

hvv

hii

hiv

v

i

v

i

1

2

11 12

21 22

1

2

111

1 0

121

2 0

212

1 0

222

2 0

2

1

2

1

=

=

=

=

=

=

=

=

=

(short-circuit port 2)

(open-circuit port 1)

(short-circuit port 2)

(open-circuit port 1)

+v1–

i1+v2–

i21 2

h11 = rπ input resistanceh21 = hfe = βh22 = 1/ro Early resistance

BJT model in some books:

19Prof. C.K. Tse: 2-port networks

g-parameters

iv

g gg g

vi

giv

gii

gvv

gvi

i

v

i

v

1

2

11 12

21 22

1

2

111

1 0

121

2 0

212

1 0

222

2 0

2

1

2

1

=

=

=

=

=

=

=

=

=

(open-circuit port 2)

(short-circuit port 1)

(open-circuit port 2)

(short-circuit port 1)

+v1–

i1+v2–

i21 2

20Prof. C.K. Tse: 2-port networks

Example

+v1–

i1+v2–

i2R1

R2

hvi

R RR R

R R

hvv

RR R

hii

RR R

hiv R R

v

i

v

i

111

1 01 2

1 2

1 2

121

2 0

2

1 2

212

1 0

2

1 2

222

2 0 1 2

2

1

2

1

1

= = =+

= =+

= =−

+

= =+

=

=

=

=

||

21Prof. C.K. Tse: 2-port networks

Connecting two-ports — series-series

Z+v1–

i1

+v2–

i2

Z’+v3–

i3

+v4–

i4

Total [Z]T = [Z]+[Z’]

22Prof. C.K. Tse: 2-port networks

Connecting two-ports — shunt-shunt

Y+v1–

i1

+v2–

i2

Y’+v3–

i3

+v4–

i4

Total [Y]T = [Y] + [Y’]

23Prof. C.K. Tse: 2-port networks

Connecting two-ports — shunt-series

G+v1–

i1

+v2–

i2

G’+v3–

i3

+v4–

i4

Total [G]T = [G] + [G’]

24Prof. C.K. Tse: 2-port networks

Connecting two-ports — series-shunt

H+v1–

i1

+v2–

i2

H’+v3–

i3

+v4–

i4

Total [H]T = [H] + [H’]

25Prof. C.K. Tse: 2-port networks

Circuit modelsWe can develop circuit model for each type of two-port descriptions.

Example: h-parameter

vi

h hh h

iv

v h i h vi h i h v

1

2

11 12

21 22

1

2

1 11 1 12 2

2 21 1 22 2

=

⇒= +

= +

+–

h11

h12v2

1/h22

h21i1

i2i1

+v1–

+v2–

26Prof. C.K. Tse: 2-port networks

Example: BJT modelWe can model the BJT as a h-parameter model:

h11 = rπ input resistanceh12 ≈ 0h21 = hfe = βh22 = 1/ro Early resistance

rπro

βi1= gmv1

i2i1

+v1–

+v2–