Chuong 4_Ma Tran Tan Xa_SV

7/31/2019 Chuong 4_Ma Tran Tan Xa_SV

1/18

Chng4. Mng mt v nhiu ca

Nguyn Trng Hi Trang 55

CHNG 4.MNG MT V NHIU CA

I. KHI NIM

K hiu, quy c chiu ca in p v dng in trong mng mt ca v nhiu ca

1. Ma trn tr khng Z

1 11 12 1 1

2 21 22 2 2

1 2

. . .

. . .

. . . . . .

. . . . . .

. . . . . .

. . .

N

N

N N N NN N

v Z Z Z i

v Z Z Z i

v Z Z Z i

hay

IZV

in p ti ca n vi n=1Nc cho nh sau

NNiZiZiZv 12121111 ...

NNiZiZiZv 22221212 ...

NNNNNN iZiZiZv ...2211

Mi phn t tr khng trong ma trn c th c xc nh nh sau

mkforim

n

nm ki

vZ 0

l t s in p o c ti cng n v dng in vo cng m trong iu kin hmch cc cng khc (ik= 0; k m )

MngMt ca

i1

v1

MngHai ca

i1

v1

i2

v2

Ca 1 Ca 2

Mng

N ca

i1

v1

i2

v2Ca 1 Ca 2

i3

v1Ca 3 v4 Ca 4

vN Ca N

i4

iNiN-1

vN-1Ca N-1


2/18



2. Ma trn Y dn np

NNNN

N

N

N

Nv

v

v

YY

YY

Y

Y

YYY

i

i

i

.

.

.

...

...

...

...

...

.

.

.

...

.

.

.

2

1

2

222

1

21

11211

2

1

hay

VYI tng t

mkforvm

n

nm k

v

iY

0

so snh vi ma trn Z tr khng

1 YZ

V d,

Cho mng sau, tm ma trn tr khng v dn np cho mng sau

p s

Vy, ma trn Z tr khng nh sau

BACCA

CACBA

CBAZZZZZ

ZZZZZ

ZZZZ

1

Tng t cho ma trn Y dn np

CBB

BBA

CBB

BBA

YYY

YYY

ZZZ

ZZZY

111

111

111 ,,

CCBBAAZYandZYZY

V d trn ch ra rng ma trn Y v Z l i xng, ngha l

mnnm ZZ

ZA ZC

ZB

i1

v1 v2

i2

Ca 1 Ca 2


3/18



3. Ma trn h (hybrid)

2

1

2221

1211

2

1

v

i

hh

hh

i

v

vi

0

2

112 1

iv

vh

V d, thit lp ma trn h m t BJT sau

p s

BCBE

BEBC

v

B

BE

rr

rr

i

vh

CE 011

(tr khng vo)

BCBE

BE

i

CE

BE

rr

r

v

vh

B

012(t s hi tip in p)

BCBE

BEBC

v

B

C

rr

rr

i

ih

CE

021

(h s khuch i dng tn hiu nh)

BCBECE

i

CE

C

rrrv

ih

B

11022

(dn np ng ra)

V rBC ln hn nhiu rBE, ma trn h gn ng ca BJT nh sau

BEv

B

BE r

i

vh

CE 011

0012 BiCE

BE

v

vh

021 CEvB

C

i

ih

BCCE

i

CE

C

rrv

ih

B

1022

Ma trn rt thng dng v thng c cho trong datasheet cc BJT

iB

iCiB iCrBC

rBE rCEBi

i'B


4/18



V d,

Datasheet ca 2N3904, c cc thng s sau: 5ieh K ,42 10reh x

, 250feh ;

20oeh S , xc nh , ,BE BC CEr r r

p s,

Ma trn tng ng h ca BJT nh sau

BCBE

BEBC

ierr

rrh

BCBE

BE

rerr

rh

BCBE

BEBC

ferr

rrh

BCBECE

oerrr

h

11

Gii h phng trnh trn

MhhrreieBC

71/

KhhrreieBE

51/

02.3001/ refere hhh

Khhhhhh

hr

rerefereieoe

ieCE 35.632 2

4. Ma trn ABCD

2

2

1

1

i

v

DC

BA

i

v

V d,

Tnh ton ma trn ABCD cho mng 2 ca sau

i1

v1

i2

v2

Ca 1 Ca 2

Z


5/18


6/18



5. Kt ni cc ma trn

Khi cc mng hai ca kt ni ni tip vi nhau, c th tm ton b cc thng s zbng cch cng cc thng s z thnh phn li.

V d

Kt ni ni tip dng thng s z v ng dng

aa

aa

zz

zz

2221

1211

bb

bb

zz

zz

2221

1211

ai1

bv2

bi1

av1

+

_

2i

av2

+

_

+

__

+bv1

bi1

2v1v

bi1

1i

+

_

2v

2i

1i

+

_

1v

Ma trn z tng ng

2

1

22222121

12121111

22

11

2

1

i

i

zzzz

zzzz

vv

vv

v

v

baba

baba

ba

ba

Khi mng hai ca c mc song song, c th tm ton b thng s y bng cchcng cc thng s y thnh phn.

V d,

Kt ni song song dng thng s y v ng dng

aa

aa

YY

YY

2221

1211

a

i1

bi1

+

_

2i

+

bi2

2v1v

b

i21i

bb

bb

YY

YY

2221

1211

a

N

bN

+

_2v

2i1i

+_1v

a

N

bN

R


7/18



Ma trn y tng ng

2

1

22222121

12121111

22

11

2

1

v

v

yyyy

yyyy

ii

ii

i

i

baba

baba

ba

ba

Khi mng hai ca mc theo kiu cascade (mt xch), ma trn ABCD c dng sdng

V d,

Kt ni cascade dng thng s ABCD v ng dng.

v v2a

=v1b

v -i2a

= i1b

. Ma trn ABCD y l tch cc ma trn thnh phn.

b

b

bb

bb

aa

aa

a

a

aa

aa

a

a

i

v

DC

BA

DC

BA

i

v

DC

BA

i

v

i

v

2

2

2

2

1

1

1

1

a a

a a

A B

C D

b b

b b

A B

C D


8/18



6. Bin i qua li gia cc ma trn

Z Y h ABCD

Z 22211211

ZZ

ZZ

Z

Z

Z

ZZ

Z

Z

Z

1121

1222

2222

21

22

12

22

1

ZZ

Z

Z

Z

Z

Z

21

22

21

2121

11

1

Z

Z

Z

Z

Z

Z

Z

Y

Z

Y

Z

YZ

Y

Z

Y

1121

1222

2221

1211

YY

YY

1111

21

11

12

11

1

Y

Y

Y

Y

Y

Y

Y

21

11

21

2121

22 1

Y

Y

Y

Y

YY

Y

h

2222

21

22

12

22

1

hh

h

h

h

h

h

1111

21

11

12

11

1

h

h

h

h

h

h

h

2221

1211

hh

hh

2121

22

21

11

21

1

hh

h

h

h

h

h

ABCD

C

D

C

C

ABCD

C

A

1

B

A

B

B

ABCD

B

D

1

D

C

D

D

ABCD

D

B

1

DC

BA

7. Ma trn tn x S

Vi mch in hot ng tn s thp (kch thc ca mch in rt nh so vibc sng lan truyn), c th o c cc gi tr in p v dng in ti mt imbt k

Vi cc mch in hot ng tn s siu cao (kch thc ca mch c th so snhc vi bc sng), phi m hnh ha mch in tn s siu cao bng cc phnt tng ng c cc thng s phn b, biu din di dng ma trn tn x S(Scatering Matrix) mt hoc nhiu ca.

Cng sut chun ha sng ti ti cng n

nnn

IZV

Z

a 002

1

Cng sut chun ha sng phn x ti cng n

nnn

IZVZ

b 002

1

T 2 phng trnh trn suy ra

nnn baZV 0

nnn

ba

Z

I 0

1


9/18



Vy

222

1Re

2

1nnnnn baIVP

Tch ri thnh phn sng ti v sng phn x ca cng sut,

n

n

nIZ

Z

Va 0

0

n

n

nIZ

Z

Vb 0

0

tng t vi biu thc in p v dng in

nnnnn

IZIZVVV 00

vy, ma trn tn x S cho mt mng 2 ca nh sau

2

1

2221

1211

2

1

a

a

SS

SS

b

b

vi

2

111 0

1

a

bS

a (t s cng sut phn x ti ca 1 v cng sut ti ti ca 1)

2

221 0

1

a

bS

a (t s cng sut truyn n ti ca 2 v cng sut ti ti ca 1)

1

222 0

2

a

bS

a (t s cng sut phn x ti ca 2 v cng sut ti ti ca 2)

1

112 0

2

a

bS

a (t s cng sut truyn n ti ca 1 v cng sut ti ti ca 2)

iu kin a2 = 0 v a1 = 0 ngha l khng c cng sut sng phn x li mng ticc ca 2 v 1, iu ny ch xy ra khi cc cng c phi hp tr khng ng.

V cc thng s S da trn cc quan h v cng sut. Cng sut trung bnh ti cng1 c cho bi

2110

2

12

0

2

1

1 12

11

2

1S

Z

V

Z

VP in

vi

110

1

1

1

1

2S

a

b

V

Vain


10/18



T , h s sng ng VSWR ti cng 1

11

11

1

1

S

SVSWR

Cng sut ti cng 1

22

12

1

2

11 122

1inrefinc

abaPPP

nu h s phn x S11 = 0;

Cng sut sng ti (incident power) biu din theo a1 l cc i

22

12

0

2

1 i

inc

aP

Z

V

Tng t cho cng 2

22

22

2

2

22 122

1out

abaP

Ma trn tn x ca mt s linh kin tch cc

M t.

2SC3355 l transistor loai Silicon, s dng chocc b khuch i nhiu thp ti di tn VHF,UHF v CATV

Chc nng

Low noise and high gain

NF = 1.1 dB TYP., Ga = 8.0 dB TYP. @VCE = 10 V, IC = 7 mA, f = 1 GHz

NF = 1.8 dB TYP., Ga = 9.0 dB TYP. @

VCE = 10 V, IC = 40 mA, f = 1 GHz

High power gain : MAG = 11 dB TYP. @

VCE = 10 V, IC = 20 mA, f = 1 GHz


11/18



{2SC3355 NEC NPN, f=1.0GHZ ; Vce=10V, Ic=40mA}

f s11 s21 s12 s22

0,2 0.011 -60.1 13.76 105.4 0.040 -73.3 0.421 -17.5

0,4 0.028 -42.9 7.338 82.9 0.069 66.7 0.416 -22.80,6 0.027 25.1 4.996 72.7 0.114 69.4 0.414 -28.7

0,8 0.043 65.7 3.801 61.9 0.144 67.8 0.406 -35.7

1,0 0.074 75.1 3.134 57.6 0.183 63.4 0.386 -41.8

1,2 0.098 75.6 2.759 52.4 0.221 62.1 0.373 -49.8

1,4 0.120 74.1 2.351 44.4 0.247 55.7 0.356 -56.3

1,6 0.146 75.8 2.203 36.0 0.291 49.6 0.347 -66.6

1,8 0.171 77.2 1.910 29.9 0.299 46.0 0.342 -78.8

2,0 0.205 78.0 1.825 21.3 0.344 39.4 0.355 -89.6

8. Ma trn thng s chuyn i T

Thng s mt xch, cn gi l thng s chuyn i phn b hay thng s T, c sdng ghp tng cc mch.

2

2

2221

1211

1

1

a

b

TT

TT

b

a

Quan h gia S v T nh sau

21

221112

21

11

21

22

21

2221

1211

1

S

SSS

S

S

S

S

S

TT

TT

v

21 21 1222

11 12 11 11

21 22 12

11 11

1

T T TT

S S T T S S T

T T

Thng s T thng dng trong phn tch mng hai ca mc cascade.

Mng hai ca mc cascade

aa

aa

TT

TT

2221

1211

bb

bb

TT

TT

2221

12111a '1a

'

1b

2b

2a'

2a

'

2b

1b


12/18



Ma trn T c vit thnh nhm ma trn phn b mt xch thnh phn

2

2

2221

1211

1

1

a

b

TT

TT

b

aaa

aa

,

2

,

2

2221

1211

,

1

,

1

a

b

TT

TTba

bb

bb

v

,

2

,

2

2221

1211

2221

1211

1

1

a

b

TT

TT

TT

TT

b

abb

bb

aa

aa

Biu thc trn thng dng trong phn tch v thit k nhng b khuch i cao tndng k thut thit k vi s tr gip ca my tnh.

9. Bin i gia thng s Z v S

Ta c

aSb

nhn hai v vi 0Z

0 0Z b V Z S a S V

Cng 2 v vi 0V Z a

V S V V S E V

(*) vi [E] l ma trn n v

So snh vi ma trn Z: V Z I v bii din V theo I bng cch

Tr 2 v ca 0V Z a vi VS

IZbaZVSV 00 t suy ra

ISEZV 10

Thay vo phng trnh (*)

ISEESZVESV 10

hay

1

0Z Z S E E S

cui cng

11 12

21 22

Z Z

Z Z

111 12 11 12

021 22 21 22

1 1

1 1

S S S SZ

S S S S


13/18



11 120

22 1221 22

21 1111 22 21 12

1

11

11 1

S SZ

S SS S

S SS S S S

II. NG DNG MA TRN TN X

1. Mch khuch i siu cao tn

Cc phng trnh li cng sut

Sb 2b

1a

1b 2a

S L11S 22S

12S

21S

AVSP INP AVNP LP

*SIN

INAVS PP

*OUTL

LAVS PP

Hnh trn minh ha th dng tn hiu mch khuch i cao tn v nhng cngsut khc nhau s dng trong cc phng trnh li cng sut: li cng sutbin i (Transducer power Gain)GT, li cng sut ng (Operating PowerGain) GP, v li cng sut hu ch (Available Power Gain) GAc nh nghanh sau:

AVS

L

TP

PG Cng sut truyn n ti/Cng sut c ch t ngun.

IN

L

PP

PG Cng sut truyn n ti/Cng sut cung cp cho mch K.

*

L OUT

AVNA T

AVS

PG G

P Cng sut c ch t mch/Cng sut c ch t ngun.

Nhn thy rng biu thc2

1

2

1 baPIN v cng sut c ch t mch PAVN l

cng sut c truyn t mch n ti phi hp lin hp.

11 12

21 22

S S

S S

b2

b1

a1

a2

ZS

VS

ZLPLPinc

S L

OUTIN


14/18



Cc phng trnh li cng sut:

2 2

2

212 2

22

1 1

1 1

S L

T

IN S L

G SS

(GT tnh theo IN )

2 2

2

212 2

11

1 1

1 1

S L

T

S OUT L

G SS

(GT tnh theo OUT )

*

22

212 211

1 1

1 1L OUT

SA T

S OUT

G G SS

2 221

2 222

1

1 1

LL L A A

P TIN A IN IN IN L

SP P P P

G GP P P P S

L

L

INS

SSS

22

211211

1

S

S

OUTS

SSS

11

211222

1

V d,

Mt mch khuch i RF c cc thng s sau

0

11 0,3 70S ;0

21 3,5 85S ;0

12 0,2 10S ;0

22 0, 4 45S

Ng vo ca mch khuch i c k ni vi mt ngun 5 0osV v 40sZ

Ng ra l anten c tr khng 73antenZ ; gi s cc thng s S c o vi tr

khng c tnh 0 50Z .

Xc nh

(a). GT, GA, GP

(b). Cng sut truyn n ti PL, cng sut c ch PA v cng sut sng ti Pinc.

Phi hp tr khng cho mch khuch iS mch khuch i c phi hp tr khng

S00SV0Z

S IN OUT L

0Z

MachPHTK vao

MachPHTK ra


15/18



Mc ch ca vic phi hp tr khng truyn cng sut cc i t ngun n ti.

C nhiu cch phi hp tr khng:

Dy chm ( stub ).

Mch thun hoc ngc.

Balun

ng truyn vi di.

li cng sut t cc i khi transistor c phi hp tr khng ng, ta c:

1212

21 KKS

SGP

Vi :

2 2 2

11 2212 21

1

2

S S

K S S

v 21122211 SSSS

2112

2

22

2

11

2

2

1

SS

SSG

T

S n nh ca mch khuch i

Trong b khuch i l tng S12= 0 do mch khuch i n nh v iu kin.Nu S12 0, cc h s phn x vo, ra vi ZL, ZS bt k nh sau:

S

S

S

S

OUT

L

L

L

L

IN

S

S

S

SSS

S

S

S

SSS

11

22

11

211222

22

11

22

211211

11

11

mch n nh v iu kin cc bt ng thc sau y tha mn ng thi:

1in v 1out

Do

12

1

2112

2

22

2

11

2

SS

SSK

Khi K > 1 th linh kin c th lm vic vi bt c ngun no v ti th ng no mkhng s b dao ng.

Khi K < 1 phi tm hai vng trn kho st s n nh ti v ngun cho BJT/FET.

Vng trn n nh i vi ngun :


16/18



Tm22

11

2

1122

2

11

2211 )(

S

SS

S

SSCS

Bn knh22

11

2112

S

SSRS

Vng trn n nh i vi ti :

Tm22

22

2

2211

2

22

1122 )(

S

SS

S

SSCL

Bn knh22

22

2112

S

SSRS

Trn th Smith, ta xc nh cc vng trn trn tm phn n nh cho mch.H s nhiu

nh gi ch tiu k thut v nhiu ca phn t khuch i, nh ngha h snhiu F l t s gia tn hiu trn nhiu ng vo vi t s tn hiu trn nhiu ng ra.

Xt trng hp 2 tng khuch i:

1

21

1

G

FFF

Nhn thy rng h s nhiu tng cng F l do h s nhiu F1 ca tng u quyt

nh, do khi thit k mch khuch i nhiu tng, cn phi quan tm n nhiuca tng u tin sao cho mch c h s nhiu b nht.

i vi mt tng khuch i, cng thc tnh h s nhiu theo h s phn x:

2

2 201 1

n S LMIN

S

RF F

trong 0Z

ZR n

n v Z0 = 50.

Cc thng s Fmin, Rn, 0 do nh sn xut cho bit.

Mch khuch i nhiu thp LNA (Low Noise Amplifier)

Ti u vo ca cc thit b thu, tn hiu t anten xung s c khuch i nhkhi LNA, cht lng ca khi LNA s nh hng rt ln n cht lng ca tnhiu cn thu. Nhim v ca khi LNA l khuch i tn hiu ln a n bMixer, ng thi hn ch mc nhiu sao cho thp nht.

Cc ch tiu k thut ca khi LNA :

Tng nhy.

H s tp m thp ( t s S/N cao ).

H s nhiu : 1,5 4dB.


17/18



m bo bng thng mong mun( chn lc cao).

Phng php

a) Chn mch khuch i dng FET hoc BJT c dng phn cc ICQ v VCE nh(phn cc lp A).

b) Thit k mch phi hp u vo v ra c h s phm cht Q cao ( chn lccao- khuch i cng hng.

c) Chn h s phn x u vo (IN) nm trong vng c F fmin.

d) Chn h s phn x u ra (OUT) sao cho cng sut truyn n ti l ln nht.

M hnh cho mch khuch i nhiu thp

S00

SV0Z

S IN OUT L

0Z

Mach

PHTK vao

Mach

PHTK ra

minS F F

(Cho h s nhiu thp)

OUTLOUTS

SSS

011

0211222

1

Mch khuch i cng sut cc i (max gain)

Ti u ra ca my pht, tn hiu trc khi pht i s qua b khuch i cng sut.Mc ch ca b khuch i ny l khuch i tn hiu ln mc cng sut cn thit pht i.

Qu trnh thit k mch khuch i Max gain :

a. Chn BJT (FET) c mc cng sut max ln hn mc cng sut ra cn thit k.

b. T BJT (FET) chn, da vo thng s ma trn [S] ca BJT (FET) tnh toncc h s phn x vo v ra nh sau:

21122211 SSSS

22

22

2

111 1 SSB

*

22111 SSC

22

11

2

222 1 SSB

*

11222 SSC

c. H s phn x vo v ra tng ng:

1

2

12

11

2

4

C

CBBS

2

2

2

2

22

2

4

C

CBBL


18/18



Lun c 2 nghim cho S (vo) v L (ra)

ChnS v L sao cho 1S v 1L

C c h s phn x ta tnh c tng dn chun ha:

S

SS

Y

11

L

LL

Y

11

T tnh ton phi hp theo th Smith hay dng gii thut a vo Matlab tnh phi hp.

M hnh mch khuch i Max gain:

S00SV0Z

S IN OUT L

0Z

MachPHTK vao

MachPHTK ra

*

1

2

1

2

11

2

4INS

C

CBB

*

2

2

2

2

22

2

4OUTL

C

CBB

V d,

Thit k mch khuch i cao tn s dng GaAs FET hat ng tn s f = 6Ghz

vi li cng sut chuyn i ln nht. Cc thng s S ca transistor c o im phn cc tuyn tnh VDS=4V, vIDS=0.5IDSS.0

11 3.171641.0 S 0

12 3.16057.0 S

0

21 5.28058.2 S 0

22 7.95572.0 S

00V50

176.0

169.0

615.050

185.0

Hnh 3.7.2 S oac cua mach khuech ai cao tan GaAsFET. Tatcacac ng dai hep cotrkhang ac tnh 50

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