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class notes, M. Rodwell, copyrighted 2013 ECE 2C, notes set 7: Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara [email protected] 805-893-3244, 805-893-3262 fax

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Page 1: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

ECE 2C, notes set 7: Basic Transistor Circuits; High-Frequency Response

Mark Rodwell

University of California, Santa Barbara

[email protected] 805-893-3244, 805-893-3262 fax

Page 2: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Goals

gengineerin electrical of partsmost in important :analysis LaPlace

useful. g,interestin real, are they

:exercises good make circuits Transistor

methods. LaPlacein expert Become

analysis.circuit in expert Become

:Goals

reponse.Transient response.Frequency

rolloff.frequency -High rolloff.frequency -Low

).( functionsansfer circuit tr calculate :notes These sH

Page 3: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Field-Effect Transistor High-Frequency Model

given. as model thisesimply tak weece2c,For

classes.later in covered be willescapacitanc theseoforigin Physical

Page 4: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Field-Effect Transistor High-Frequency Model

voltage.bias vary withescapacitanc theseofMany

es.capacitancjunction PNbulk -drain and )(substratebulk -source are and

ct vias.interconne and fields fringing source-gate toduePartly

ecapacitanc channel-gate frompart in arises

ct vias.interconne and fields, fringing source-gate toduePartly

ecapacitanc channel-gate frommostly arises

dbsb

dg

gs

CC

C

C

sbC dbC

Page 5: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Basic Common-Source Amplifier

s.frequenciehigh at gain circuit thereduce will and

s.frequencie lowat gain circuit thereduce will and

gdgs

outin

CC

CC

biasing RC style-s1950' :circuit This

Page 6: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Basic Common-Source Amplifier

s.frequenciehigh at gain circuit thereduce will and

s.frequencie lowat gain circuit thereduce will and

gdgs

outin

CC

CC

:circuit equivalent signal-Small

Page 7: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Basic Common-Source Amplifier

. and neglect ly temporari therefore willWe

s.frequenciehigh at responseconsider first usLet

outin CC

Page 8: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Nodal Analysis: How to solve circuits

equations.t independenlinearly ofset needed thegives Always

voltage. theknownot doyou which nodeeach at 0currents Write

.*tindependenlinearly * bemust equations the

voltagesnodeunknown of # unknowns of # equations of #

:circuit solve To

(red) ltageunknown vo (blue), ageknown volt

?known voltage theis :eachFor nodes.circuit all Label

node

Page 9: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Common-Source Amplifier: Simplifying

:modelNorton a oThevenin t a fromgenerator eConvert th

:formulasresistor parallel use then And

Page 10: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Common-Source: Nodal Analysis

gengengdoutgdgsiin

gengengdoutgdingsiniin

in

GVsCVsCsCGV

GVsCVsCVsCVGV

V

)()(

)(

:zero is at currents of Sum

0)()(

0)()()(

:zero is at currents of Sum

gdLeqoutgdmin

Leqoutgdoutgdinmin

out

sCGVsCgV

GVsCVsCVgV

V

Page 11: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Common-Source: Nodal Analysis

0)()(

)()(

gdLeqoutgdmin

gengengdoutgdgsiin

sCGVsCgV

GVsCVsCsCGV

0

gengen

out

in

gdLeqgdm

gdgdgsi GV

V

V

sCGsCg

sCsCsCG

Page 12: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Common-Source: Nodal Analysis

0

gengen

out

in

gdLeqgdm

gdgdgsi GV

V

V

sCGsCg

sCsCsCG

gen

gen

out

in

gdLeqgdm

gdgdgsiV

G

V

V

sCGsCg

sCsCsCG

0

0

1 gen

genout

in

gdLeqgdm

gdgdgsi G

VV

V

sCGsCg

sCsCsCG

0/

/gen

genout

genin

gdLeqgdm

gdgdgsi G

VV

VV

sCGsCg

sCsCsCG

Page 13: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Common-Source: Nodal Analysis

0)(

and

)(

where

)()(

)()()()(

gdm

gengdgsi

gdLeqgdm

gdgdgsi

gengenout

sCg

GsCsCGsN

sCGsCg

sCsCsCGsD

sVsD

sNsVsHsV

Page 14: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Common-Source: Nodal Analysis

gdmgsgdgdLeqgsLeqgdiLeqi

gdmgdgdLeqgdgsi

gdLeqgdm

gdgdgsi

sCgsCsCsCGsCGsCGGGsD

sCgsCsCGsCsCGsD

sCGsCg

sCsCsCGsD

)(

)(

)(

Page 15: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Common-Source: Nodal Analysis

gdgsgdmgdLeqgsLeqgdiLeqi CCssCgCGCGCGsGGsD

s

2)(

: of powers into organize

Page 16: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Common-Source: Nodal Analysis

gdgsleqigdleqleqmgdigsi

gdgsleqigdleqimgdigsigdleqleqi

gdgsleqigdmgdLeqgsLeqgdileqi

Leqi

CCRRsCRRgCRCRs

CCRRsCRRgCRCRCRsRRsD

CCRRsCgCGCGCGRsR

GGsD

2

2

2

)1(1

1)(

1

/)(

:responsefrequency unitless aby multiplied

units carryingconstant a into Separate

Page 17: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Common-Source: Nodal Analysis

mgdmgengdgenmgen

gdmgen

gdm

gengdgsi

gsCgGsCGgG

sCgGsCg

GsCsCGsN

/1

0)(

:numerator for the rules same theFollow

Page 18: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Common-Source: Nodal Analysis

gdgsleqigdleqleqmgdigsi

mgdmleqigen

gen

out

gdgsleqigdleqleqmgdigsi

mgdmgen

leqi

gdgsleqigdleqleqmgdigsileqi

mgdmgen

CCRRsCRRgCRCRs

gsCgRRGsH

sV

sV

CCRRsCRRgCRCRs

gsCgG

RRsD

sN

CCRRsCRRgCRCRsRRsD

gsCgGsN

2

2

2

)1(1

/1)(

)(

)(

So

)1(1

/1

)(

)(

)1(1)(

/1)(

Page 19: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Common-Source: Nodal Analysis

Ampingen

Ampin

leqm

Ampingengen

Ampingen

leqm

gen

Ampingen

leqm

gen

ileqmmleqigenbandmid

gdgsleqigdleqleqmgdigsi

mgd

normalized

normalizedbandmid

gen

out

RR

RRg

RRR

RRRg

R

RRRg

R

RRggRRGH

CCRRsCRRgCRCRs

gsCsH

sHHsHV

V

,

,

,

,

,

2

)(

||

)1(1

/1)(

)()(

Page 20: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Common-Source Nodal Analysis: the answer

mgd

gdgsleqi

gdleqgdleqimgdigsi

normalized

Ampingen

Ampin

leqmbandmid

normalizedbandmid

gen

out

gCb

CCRRa

CRCRRgCRCRa

sasa

sbsH

RR

RRgH

sHHV

V

/ and

:constant (time)order -Second

:constant order time-First

response.frequency amplifier theis 1

1)(

gain. band-mid theis

where

)(

1

2

2

1

2

21

1

,

,

Page 21: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Comments on the analysis

Page 22: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Finding Poles: Separated Pole Approximation

Page 23: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Finding Poles: Separated Pole Approximation

Page 24: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Amplifier Frequency Response

Page 25: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Example

Page 26: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Frequency Response Example (1): DC

V10/1

V 3.0

mA/V1)2/(

:FET

2

th

ggox

V

LWc

V 3.3

A 50

V 7.0

conditionsDesign

DD

D

DS

V

I

V

V. 52.0

V22.0mA/V1A 50)V 3.0(

)2/()()(

A 50)ignored term())(2/(

:Analysis

2/12

2/12/1

2

gs

gs

ggoxDthgs

thgsggoxD

V

V

LWcIVV

VVLWcI

k 25A 50/)V 7.0V 3.3(

/)(

DDSDDD

DDDDDS

IVVR

RIVV

analysis. signal small

in the term)1( theignorenot Do

.accuratelyfairly yet quickly thiscalculate

to trickssomelearn willECE137A weIn

Hard. formulas. quadratic

solving involves analysis DC thenot, do weIf

error. small some causes thisDoing

analysis. bias

in the term)1( theignoring are we*

DS

DS

V

V

A 1rough current th

k 50 ,k 100

1

g

Lgen

R

RR

,M 782.A 10V)/52.03.3(

,k 520A 1V/52.0

2

1

g

g

R

R

Page 27: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Frequency Response Example (2): Component Values

V 3.3

k 25

k 100

k 520 k 50

M 782.

V 52.0 V 7.0

A 50 A 1

k 200

1S5

V10

A 50

)1(

mS 471.0)V/10V7.01)(V3.0V52.0)(mA/V2(

)1)()(/()1())(2/(

:FET

2

2

D

DS

D

ds

Dds

m

DSthgsggox

gs

DmDSthgsggoxD

IV

I

V

IG

g

VVVLWcV

IgVVVLWcI

S5

mS 47.0

ds

m

G

g

Page 28: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Frequency Response Example (3): Component Values

k5.25

k50||k 25k 100

k438

2.78M|| k 520

mS 47.0mg

00k2

Page 29: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Frequency Response Example (4): Component Values

k82

mS 47.0mg

k6.22

pF 1 pF .250

Page 30: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Frequency Response Example (5): (time)n constants

ns 0.532mS47.0pF/25.0/

ion works.approximat pole separated so, ,/

ns42.1s326.0pF/25.01pFk6.22k82/

s326.0

pF25.0k6.22pF25.0k6.22k82mS47.0pF25.0k821pFk82

. 1

1)(

65.8814.066.10||

||

)(

1

12

122

1

2

21

1

21

21

mgd

gdgsleqi

gdleqgdleqimgdigsi

normalized

gg

gg

leqmbandmid

normalizedbandmid

gen

out

gCb

aaa

aaCCRRa

CRCRRgCRCRa

sasa

sbsH

RR

RRRgH

sHHV

V

Page 31: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Frequency Response Example (6): Transfer Function

ns 0.532 ns,42.1/ s,326.0

))/(1)(1(

165.8

)(

)(

1121

121

1

baaa

saasa

sb

sV

sV

gen

out

plane)-s theof halfright in the (zero MHz 29932ps5

159.0

MHz 112ns42.1

159.0 kHz, 488

s326.0

159.0

)/1)(/1(

/165.8

)2(

)2(

21

21

z

pp

pp

z

gen

out

f

ff

fjffjf

fjf

fjV

fjV

Page 32: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

The Miller Effect

Page 33: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

The Miller Approximation

Page 34: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

The Miller Approximation

Page 35: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

The Miller Approximation

ivgd

iLeqmgd

RAC

RRgC

)1( i.e.

)1( see You will

analysis source-common theback toRefer

Page 36: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Using Miller Approximation to Understand Response

Page 37: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Using Miller Approximation to Understand Response

millergd CC with replace :eApproximat

gdLeqmmiller CRgC )1(

gsCiR

imVgLeqR

outV

Leqmouti RgVV is to fromgain frequency -Low

gdLeqmigsimillergsipole CRgRCRCCRf )1()(2/1

Page 38: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Miller and Exact Solutions

solutionExact

2

1

gdgdleqi

gdleqgdleqimgdigsi

CCRRa

CRCRRgCRCRa

Page 39: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Further Comments Regarding Miller Approximation

Page 40: ECE 2C, notes set 7: Basic Transistor Circuits; High ... · Basic Transistor Circuits; High-Frequency Response Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu

class notes, M. Rodwell, copyrighted 2013

Frequency/Transient Reponse: Real, Important