전자파 연구실

10. Noise and active RF components10. Noise and active RF components

1

전자파 연구실

10.1 Noise in microwave circuit10.1 Noise in microwave circuit

Lattice scattering

전자

원자핵

2

전자파 연구실

kTBRe

BRhfV

kThfn 41

4)/(

fkTRe

fRhfV

fkTRR

VRI

e

fhfP

kThfn

nkThfn

41

441

)/(2

2

22

)/(

Spectrum analyzer

Noise power :

Noise voltage :

Measurement setup:

k: Boltzmann constant (1.38e-23 J/K)B : bandwidth in HzT : Absolute temperature in KelvinR : resistance in Ω.

kTBPn Planck 법칙에 의한 radiation

Noise power, noise voltageNoise power, noise voltage

Planck 법칙에 의한 복사 전력

3

전자파 연구실

Figure 10-4 (p. 490)The equivalent noise temperature, Te, of an arbitrary white noise source.

Equivalent noise temperature: Equivalent noise temperature: TTee

kB

NT o

e

Equivalent noise power

on NP

4

전자파 연구실

Figure 10-5 (p. 491)Defining the equivalent noise temperature of a noisy amplifier. (a) Noisy amplifier. (b) Noiseless amplifier.

Equivalent noise temperature of an amplifierEquivalent noise temperature of an amplifier 5

전자파 연구실

Figure 10-6 (p. 492)The Y-factor method for measuring the equivalent noise temperature of an amplifier.

BGkTBGkTN

BGkTBGkTN

e

e

22

11

e

e

TT

TT

N

NY

2

1

2

1

121

Y

YTTTe

Noise temperatureNoise temperature 6

전자파 연구실

Dynamic range of an amplifierDynamic range of an amplifier

Power output threshold

입력신호와 상관없이 회로 자체에서 생기는 noise 로 인한

출력

7

전자파 연구실

Noise figureNoise figure

1/

/

oo

ii

NS

NSFNoise figure :

회로 자체에서 생기는 noise 로 인해 SNR 이 얼마나

나빠졌는가의 척도

11])(/[

)/(

/

/

00

0

T

T

BTTGkGS

BkTS

NS

NSF e

ei

i

oo

ii

oe TFT )1(

8

전자파 연구실

Noise figure ofNoise figure of a lossy networka lossy network

LN

L

SNS

NS

NSF

ii

ii

oo

ii /

/

/

/

Lossy network 의 noise figure 는 loss 와 같다 .Noise 는 loss 에 의해 감쇄되지 않고 온도와 관련됨 .

9

전자파 연구실

Noise figure ofNoise figure of a cascaded systema cascaded system

BkTGBkTGN e11011

1

21021

221021

2212

)(

G

TTTkBGG

BkTGTTkBGG

BkTGNGN

ee

ee

eo

)( 021 caso TTkBGGN

1

21 G

TTT e

ecas

1

21

1

G

FFFcas

21

3

1

21

11

GG

F

G

FFFcas

10

전자파 연구실

11

BkTGBkTGN e11011

1

21021

221021

2212

)(

G

TTTkBGG

BkTGTTkBGG

BkTGNGN

ee

ee

eo

1

21

1

21

10

2

0

1

21

0

21

11111

/

/

/

/

/

G

FF

G

FF

GT

T

T

T

GG

NN

NSGG

NS

NS

NSF

ee

i

oi

ii

oo

ii

BkTN i 0

10

2

0

121

1

210

0

21 1/GT

T

T

TGG

G

TTT

BkT

kBGGNN eee

eio

oeoe TFTTFT )1(,)1( 2211

전자파 연구실

Example 10.2 Noise analysis of a wireless receiverExample 10.2 Noise analysis of a wireless receiver

BkTN Ai

dB55.28.1)79.0)(10(

151.2

10

126.158.1

11

fa

m

a

fa GG

F

G

FFF

51.2dB4,26.1dB1,58.1dB2

5.0dB3,79.0dB1,10dB10

mfa

mfa

FFF

GGG

KTFTe 232)290)(18.1()1( 0

dBm8.96W1008.2

)95.3)(1010)(232150)(1038.1()(13

623

BGTTkN eAo

dBm8.82W1027.595.3

1008.2100 12

13

G

N

N

S

G

SS o

o

ooi

KTA 150

아래 블록 다이어그램은 무선 단말기의 수신 부이다 . Feeding antenna 의 noise temperature 가 150K 일 때 출력 신호의noise 전력을 구하라 . 또한 출력 신호를 구분 가능한 최소의 SNR 이 20dB 라고 할 때 입력신호의 최소 전압도구하라 .

μV(rms)2.16V1062.1 50

ii SZV

12

전자파 연구실

1310.2 Dynamic range and inter-modulation distortion10.2 Dynamic range and inter-modulation distortion

33

2210 iiio aaaa

0

2

2

2

0

1

0 )0(

i

i

i

o

i

o

o

d

da

d

da

a

DC output

Linear output

Squared output

Dynamic range

전자파 연구실

14

Vout

DCDC1

DCVARVAR1Vin=1.0

EqnVar

AmplifierVCAMP1

Rout=50 OhmGain=(30-1*_v1*_v1)

V_DCSRC1Vdc=Vin V

RR1R=50 Ohm

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80.0 2.0

5

10

15

0

20

Vin

Vou

t

f

전자파 연구실

15Gain compressionGain compression

tVa

tVatVaVaVaa

tVatVatVaa

aaaa iiio

03

03

02

0203

03012

020

3003

20020010

33

2210

3cos2

1

2cos2

1cos

4

3

2

1

)cos()cos(cos

tVi 00 cos

2031

0

30301

)(

)(

4

343

0

0

VaaV

VaVaG

i

o

a3 의 부호는 a1 과 반대가 되는 경우가 많아서 입력

전압이 커질수록 gain 이줄어든다 .

전자파 연구실

16Inter-modulation distortionInter-modulation distortion

전자파 연구실

17

tttVa

tttVa

ttVattVa

tVatVa

tVatVattVaa

ttVattVattVaa

aaaa iiio

)2cos(4

3)2cos(

4

3cos

2

3

)2cos(4

3)2cos(

4

3cos

2

3

3cos4

1cos

4

33cos

4

1cos

4

3

)cos()cos(

2cos12

12cos1

2

1)cos(cos

)cos(cos)cos(cos)cos(cos

121213

03

212123

03

223

03113

03

212

02212

02

22

0212

0221010

321

303

221

20221010

33

2210

)cos(cos 210 ttVi

Output signal from a non-ideal amplifierOutput signal from a non-ideal amplifier

입력 신호

출력 신호

Filter 로 제거 가능Filter 로 제거 가능

Filter 로 제거 불가능

전자파 연구실

18Third-Order intercept pointThird-Order intercept point

0

20

21

2

11 Z

VaP

0

60

23

23

030

2 32

9

4

3

2

121 Z

VaVa

ZP

623

221 32

9

2

1IPIP VaVa

03

31

33

1 1

3

2,

3

4

Za

aP

a

aV OIPIP

주파수 ω1 성분의power

주파수 2ω1 - ω2 성분의 power

출력 주파수 ω1 , 2ω1 - ω2 두 성분의 power 가 같아질 때 입력

전력 .

19

23

3

23

3

0

20

21

20

23

61

30

60

61

0

60

23

23

030

2 )(

)(

)(

21

19481

32

9

4

3

2

11

21

OIPOIP P

P

P

ZVa

Zaa

ZVa

Z

VaVa

ZP

전자파 연구실

20

Figure 10-17 (p. 506)Illustrating linear dynamic range and spurious free dynamic range.

Dynamic rangeDynamic range

Linear dynamic range : P1dB /N0

Spurious free dynamic range : Pω1/P2ω1-ω2 (P2ω1-ω2 = N0)

전자파 연구실

21Intercept point of a cascaded systemIntercept point of a cascaded system

23

3

2 )(

)(1

21

OIPP

PP

03

332

03

2332

23

03

2

3

03

2

2

)(11

)(11

,)()(

1

1

11

11

21

ZPPPG

ZPGPPG

PGPP

ZPG

P

ZPGV

OIPOIP

OIPOIP

OIPOIP

1

3323

11

OIPOIP

totalIP PPG

P

11 2 PGP

3

2

3322 )(

11121 P

PPGP

OIPOIP

1

332

3

2

332

3

22

3

3

11

)(11

)()(

1

1

21

1

OIPOIP

OIPOIP

totalOIP

PPG

PPPG

P

P

PP

전자파 연구실

22Example 10.5Example 10.5

25.06

57

15822

2

3

3

dBG

mWdBmP

mWdBmP

OIP

OIP For amplifierFor mixerFor mixer

dBmmWPPG

POIPOIP

OIP 4.64.411

1

3323

전자파 연구실

2310.3 RF diode characteristics10.3 RF diode characteristics

1. Diode 의 비선형 효과를 이용하여 signal detection,

demodulation, switching, frequency multiplication, oscillation 회로를 만든다 .

Figure 10-20 (p. 510)Basic frequency conversion operations of rectification, detection, and mixing. (a) Diode rectifier. (b) Diode detector. (c) Mixer.

전자파 연구실

24

(1) pn-junction diode (2) Schottky diode

• high frequency 에서 동작을 위해 pn-junction diode 보다 Schottky barrier diode 를 사용한다 .

• pn-junction 은 reverse recovery time 으로 ~100ns 이상의 switching time 이 필요하나 Schottky diode 는 ~100ps 도 가능 .

Turn on voltage : 0.7V

Turn on voltage : 0.25V

Diode Diode 종류종류

전자파 연구실

25

Ele

ctri

c fi

eld

0

Unbiased PN junction Unbiased PN junction ID : Diffusion current.

IS : Drift current

SD II

hI

eI

전자파 연구실

26

Minority-carrier distribution in a forward-biased pn junction. It is assumed that the p region is more heavily doped than the n region; NA @ ND.

전자파 연구실

27

(3) p-i-n diode

RF switch

pn-junction 사이에 intrinsic (doping 이 안된 상태 ) 반도체가 있어 역방향일 때 C (capacitance)를 더욱 줄여주고 , 순방향일 때 직렬 저항을 조절 가능하게 함 .

등가 회로

전자파 연구실

28Diode packageDiode package

전자파 연구실

29

)10~~10(

),1()(

615

s

vs

I

nkT

qeIvI

n=1.2 for Schottky barrier diode, n=2 for point contact silicon diode

RF diode i~v characteristicsRF diode i~v characteristics

Large signal model

Small signal model approximation

0Vv

22

2

0

002

1)(

VV dv

Id

dv

dIIvI

DC bias current

jds

Vs

V RGIIeI

dv

dI 1)( 0

0

0

ddsV

s

V

GGIIeIdv

Id )( 022

2

20

0

200 2

1)( dd GGIiIvI

전자파 연구실

30

Figure 10-22 (p. 511)Equivalent AC circuit model for a Schottky diode.

lead inductance

Shunt capacitanceContact, current-spreading resistance

Junction capacitance, junction resistance

전자파 연구실

31Diode rectifiersDiode rectifiers

tVV 000 cos

tGtGGI

tGtGII

ddd

dd

0

20

00

20

0

02

20

000

2cos4

cos4

cos2

cos

Bias currentDC rectified current

전자파 연구실

32Diode detectorsDiode detectors

)(,cos)cos1()( 000 mm ttmt

tm

tm

tm

tmtm

ttm

tmm

G

tm

tm

tG

ttmGttmGti

mm

mm

mm

d

mmd

mdmd

)(2cos4

)(2cos4

2cos2

)2cos()2cos(

2cos2cos2

cos22

1

2

)cos(2

)cos(2

cos

cos)cos1(2

cos)cos1()(

0

2

0

2

0

2

00

0

22

20

0000

022

20

00

m : modulation index, 0<m<1

입력 power 에 비례한 출력이므로 square law

detector

전자파 연구실

33

Figure 10-24 (p. 513)Square-law region for a typical diode detector.

Diode detector outputDiode detector output

전자파 연구실

34PinPin diodes and control circuitsdiodes and control circuits

Microwave switch

1.mechanical type: high power, slow switching speed2.electronic type : PIN diode, FET. High speed operation (~10ns)

전자파 연구실

35

Figure 10-25 (p. 515)Equivalent circuits for the ON and OFF states of a PIN diode. (a) Reverse bias (OFF) state. (b) Forward bias (ON) state.

Equivalent circuitEquivalent circuit

pFC j 1

nHLi 1.0

5 1

: typical values

전자파 연구실

36

Figure 10-26 (p. 515)Single-pole PIN diode switches. (a) Series configuration. (b) Shunt configuration.

Single-pole PIN diode switchesSingle-pole PIN diode switches

전자파 연구실

37

Figure 10-27 (p. 516)Simplified equivalent circuits for the series and shunt single-pole PIN diode switches. (a) Series switch. (b) Shunt switch.

Switch equivalent circuitsSwitch equivalent circuits

1

210log20

V

VIL

dZZ

ZIL

0

010 2

2log20

010 2

2log20

ZZ

ZIL

d

d

전자파 연구실

38Microwave network analysisMicrowave network analysis

a

1-port network

2-port network

전자파 연구실

39

Impedance and Admittance Matrix

- Generalize Z concept to N-port - Arbitrary N-port Network

t1

t2

t3

t4tN

V1+, I1

+

t1V1-, I1

-

VN+,IN

+ VN-, IN

-

• Impedance matrix

IZV

I

I

I

ZZ

ZZZ

V

V

V

NNNN

N

N

2

1

1

11211

2

1

• Admittance matrix

1

ZY

VYI

Device characterizationDevice characterization

전자파 연구실

40Measurement of impedance parameterMeasurement of impedance parameter

2

1

2221

1211

2

1

I

I

zz

zz

V

V

11z

212Iz

1I

+

-

1V22z

121Iz

2I

+

-

2V

+- +-

Two port network

01

111

2

I

I

Vz

01

221

2

I

I

Vz

• 주파수가 높은 경우 open-circuit 만들기 어려움 . (parasitic capacitance 때문 )

• Admittance parameter 인 경우는 short circuit만들기 어려움 . (parasitic inductance 때문 )

전자파 연구실

41

- in accord with direct measurement- incident, reflected & transmitted wave- easy to adeve impedance matching at high frequency

VSV

S

S S

2

1

1

11211

2

1

NNNN

N

N V

V

V

S

S

V

V

V

jkfor 0 |

kVj

iij

V

VS

Sii reflection coefficient

Sji transmission coefficient

All other part j≠k matched → no reflection Vk→ 0

Scattering MatrixScattering Matrix

전자파 연구실

42

Port 1 Port 2

Transfer switch

Source

B

R

A

S-Parameter Test Set

DUTFwd Rev

1101

111

VVZI

VVV

Measurement of S-parametersMeasurement of S-parameters

][2

1

][2

1

0111

0111

ZIVV

ZIVV

][2

1

][2

1

0222

0222

ZIVV

ZIVV

jkVj

iij

k

V

VS

for0

NNNN

N

N V

V

V

SS

S

SSS

V

V

V

2

1

1

21

11211

2

1Impedance matching 된 상태

전자파 연구실

43

2

1

2221

1211

2

1

V

V

SS

SS

V

V

500Z

500Z

500Z

RR4R=50 OhmVtPulse

SRC2

t

RR3R=50 Ohm

BJT_NPNBJT1

50inZ50inZ

1V

전자파 연구실

44Example 4.4 S-parameter Example 4.4 S-parameter 계산계산

56.8 56.8

8.141Port 1

Port 2

ⅰ) 2port on 0

)1(0

)1(

0

)1(

0 1

111

0

2

2

| Zin

inV

VZZ

ZZ

V

VS

505056.88.141

)5056.8(*8.14156.8)1(

inZ

Thereby S11=0Symmetry of circuit S22=0

0 1

221

2|

VV

VS

ⅱ) since S11=S22=0 & part 2 is terminated with 50ohm

2211 , VVVV

RR9R=50 Ohm

RR10R=50 Ohm

VtPulseSRC4

t

VtPulseSRC3

t

RR7R=141.8 Ohm

RR5R=8.56 Ohm

RR8R=8.56 Ohm

1V

2V

전자파 연구실

45PinPin diode phase shiftersdiode phase shifters

A switched line phase shifter

)( 12 ll

전자파 연구실

46

jbT

jb

jb

jb

jb

2

21

2)1(1

)1(1

2tan 1 b

Loaded line phase shiftersLoaded line phase shifters

Basic circuit

전자파 연구실

47

002

0

00

0

0

)/1(

1

01

0/

0

1

01

BZZBZj

jZBZ

jBZj

jZ

jBDC

BA

eee

eee

Zj

jZ

DC

BA

cos/sin

sincos

2

00

0

1sin/

cos

b

ZZZ

bBZ

ee

e

)2/1(2

0 bZZ

b

e

e

Practical loaded-line phase shifter

전자파 연구실

48

20

20

200

20

200

20

0002

0000

0002

000011

)1(1

)(

)(22

)(

)(22

)(

)/1(/

)/1(/

jBZ

BZ

BZBZj

BZ

BZjjBZ

BZj

BZZZBZjZjZBZ

BZZZBZjZjZBZS

20

200

200

0002

000021

)1(1

2

)(22

2

)(22

2

)/1(/

2

jBZ

j

BZBZj

j

BZjjBZ

BZZZBZjZjZBZS

전자파 연구실

49

A reflection phase shifter using a quadrature hybrid

)(

)(

j

OFF

jON

e

e

전자파 연구실

507.5 Quadrature hybrid coupler7.5 Quadrature hybrid coupler

0V 9020V

18020V

0

전자파 연구실

5110.4 RF transistor characteristics10.4 RF transistor characteristics

Device Si BJT Si CMOS

SiGe HBT

GaAs MESFET

GaAs HEMT

GaAs HBT

Frequency range (GHz)

10 20 30 40 100 60

Typical gain (dB) 10-15 10-20 10-15 5-20 10-20 10-20

Noise Figure (dB) 2.0 (2GHz)

1.0 (4GHz)

0.6(8GHz)

1.0 (10GHz)

0.5(12GHz)

4.0(12GHz)

Power capacity High Low Medium Medium Medium High

Cost Low Low Medium Medium High High

Single polarity power supply

Yes Yes Yes No No Yes

Table 10.2 Performance characteristics of microwave transistors

전자파 연구실

5252

Figure 10-33 (p. 523)(a) Cross section of a GaAs MESFET; (b) top view, showing drain, gate, and source contacts.

FETsFETs

전자파 연구실

mSg

pFC

pFC

pFC

R

R

m

gd

ds

gs

ds

i

40)ctancetranscondu(

01.0)ecapacitancdrain togate(

12.0)ecapacitanc sourcetodrain(

3.0)ecapacitanc sourcetogate(

0)resistance base(

7)resistance gate Series(

Equivalent circuit for a microwave FETEquivalent circuit for a microwave FET

Common-source configuration

1gs

m

g

Cm

g

dsci C

g

I

Vg

I

IG

Unity gain frequency

gs

mT C

gf

2

(Short circuit current gain)

전자파 연구실

54

Figure 10-35 (p. 524)(a) DC characteristics of a GaAs FET; (b) biasing and decoupling circuit for a GaAs FET.

DC bias circuitDC bias circuit

전자파 연구실

55BJTsBJTs

Figure 10-36 (p. 525)(a) Cross section of a microwave silicon bipolar transistor; (b) top view, showing base and emitter contacts.

전자파 연구실

56

mSg

pFC

pFC

R

R

m

C

b

900)ctancetranscondu(

18)ecapacitanccollector (

18)ecapacitanc equivalent(

110)resistance equivalent(

7)resistance base(

Unity gain frequency

C

gf m

T 2

Equivalent circuit for a microwave BJTEquivalent circuit for a microwave BJT

Common-emitter configuration

전자파 연구실

57

Figure 10-38 (p. 526)(a) DC characteristics of a silicon bipolar transistor; (b) biasing and decoupling circuit for a bipolar transistor.

DC bias circuitDC bias circuit

• Zero 가 되어 high frequency 에서oscillation 가능성 있음 .

• 저항 때문에 noise figure 증가함 .• Emitter 는 GND 에 연결되어 있는

형태가 많이 쓰임 .

전자파 연구실

58DC bias network - BJTDC bias network - BJT

),,( BEFECBOC VhIfI

Collector current changes due to temperature variation

Ic doubles every 10℃ rise.

)/%5.0(~ CThFE Ic when IE=0.

)( CBOBFEC IIhI

전자파 연구실

59ExampleExample

C

CC

FE

BC

FE

BECCC

BEBBCECC

R

V

hR

Rh

VVI

VRIRIV

11

T

h

h

I

T

V

V

I

dT

dI FE

FE

CBE

BE

CC

01

)1(

11

)1(

))((

11

1

2

2

T

V

R

T

h

R

V

hT

V

R

T

h

RRh

RRVV

T

V

hR

Rh

BE

C

BE

C

CC

FE

BE

C

BE

BCFE

BCBECCBE

FE

BC

FE

온도가 올라가면 Ic 가 커진다 . 그러나 Rc 가 큰 경우 변화는 미미하다 .

전자파 연구실

60

전자파 연구실

61

전자파 연구실

62

)( CBOBFEC IIhI

ExampleExample

전자파 연구실

63Active bias-BJTActive bias-BJT

전자파 연구실

64

전자파 연구실

65

extCE RR

II||

7.01

1EI

:1:1 CE II

전자파 연구실

66Bias point selection-BJTBias point selection-BJT

전자파 연구실

67DC bias network – GaAs MESFETDC bias network – GaAs MESFET

전자파 연구실

68

전자파 연구실

69Bias point selectionBias point selection

전자파 연구실

70Active bias-GaAsActive bias-GaAs

전자파 연구실

71

Figure 10-39 (p. 528)Layout of a hybrid microwave integrated circuit.

전자파 연구실

72

Figure 10-40 (p. 528)Photograph of one of the 25,344 hybrid integrated T/R modules used in Raytheon’s Ground Based Radar system. This X-band module contains phase shifters, amplifiers, switches, couplers, a ferrite circulator, and associated control and bias circuitry. Courtesy of Raytheon Company, Lexington, MA.

전자파 연구실

73

Figure 10-41 (p. 530)Layout of a monolithic microwave integrated circuit.

전자파 연구실

74

Figure 10-42 (p. 530)Photograph of a monolithic integrated X-band power amplifier. This circuit uses eight heterojunction bipolar transistors with power dividers/combiners at the input and output to produce 5 watts. Courtesy of M. Adlerstein and R. Wohlert, Raytheon Company.