CNU EE 8.1-1

Microelectronic Circuits II

Ch 8 : Frequency Response

8.2 High-Frequency Model of the MOSFET and the BJT8.3 High-Frequency Response of CS & CE Amplifier

CNU EE 8.1-2

Internal Capacitive Effects and High-Frequency Model of MOSFET

§ Internal capacitances in the MOSFET- Assumption: steady-state charges on the gate-to-channel capacitance are acquired

instantaneously : constant amplifier gains independent of frequencyà finite time is required to charge & discharge the various internal capacitances

Gate capacitive effect:- parallel-plate capacitor with gate electrode (polysilicon) & the channel, - the oxide layer as the capacitor dielectric à gate capacitance CoxSource-body and drain-body depletion-layer capacitances:- the capacitances of the reverse-biased pn junctions formed by- n+ source region (source diffusion) and the p-type substrate, - n+ drain region (drain diffusion) and the substrate.Five capacitances : Cgs , Cgd , Cgb , Csb and Cdb

The gain of MOSFET amplifiers falls off at some high frequency

- Gain fall-off at the low-frequency end : coupling & bypass capacitors - Gain falloff at high frequency : capacitive effects internal to the transistors- Capacitive effects & device small-signal taken these effects into accounted

CNU EE 8.1-3

MOSFET Internal Capacitances

oxovov

oxgbgdgs

gdoxgs

oxgdgs

CWLC

WLCCCC

CWLCC

WLCCC

=

===

==

==

;0

0;32

21

00

00

/ 1

/ 1

SBsb sb

DBdb db

VC CV

VC CV

= +

= +

§ Gate capacitive effect:Cgs, Cgd & Cgb

- Cox : oxide capacitance (=eox/tox)

§ Junction capacitances:two reverse biased pn junctions

(1) When vDS << 1 in “TRIODE region”

(2) In “SATURATION”

(3) In “CUT-OFF”

(4) Overlap capacitance

where V0 : junction built-in voltage (0.6~0.8 V)VSB, VDB : reverse bias voltage

where Lov = 0.05~0.1 LWLCox : gate-channel capacitance

CNU EE 8.1-4

High-Frequency MOSFET Model

§ small-signal model of the MOSFET including Cgs , Cgd , Csb and Cdb§ predicts high-frequency response of MOSFET amplifier§ is limited to computer simulation, SPICE

CNU EE 8.1-5

§ When the source is connected to the body§ Cgd plays a significant role in the high frequency response

§ When Cdb is neglected.

High-Frequency MOSFET Model

CNU EE 8.1-6

MOSFET Unity-Gain Frequency (fT)

( ) ( )gdgs

m

i

ogdgsigs

gsmgsgdgsmo

CCsg

IICCsIV

VgVsCVgI

+=®+=

»-=

/

§ MOSFET Unity-gain frequency (fT):the frequency at which the short-circuit current-gain of the common-source configurationbecomes unity : transition frequency

0

Cgd <<1 at the frequencies of interest

CNU EE 8.1-7

MOSFET Unity-Gain Frequency (fT)

( ) ( )

( ) ( )gdgs

mT

gdgs

mT

gdgs

m

i

o

gdgs

m

i

o

CCgf

CCg

jsforCC

gII

CCsg

II

+=®

+=\

==+

=®+

=®

pw

ww

2

1

The magnitude of the current gain becomes unity at

§ Since fT is proportional to gm and inversely proportional to the FET internal capacitances, the higher the value of fT, the more effective the FET becomes as an amplifier.

§ fT : 100 MHz at 5mm CMOS process or many GHz at 0.13mm process

CNU EE 8.1-8

MOSFET High-Frequency Model Summary

CNU EE 8.1-9

The BJT internal Capacitances and High-Frequency model

nFCFC

nn D

WwhereiiD

WQ22

22

=== tt

§ Transistor model including capacitors or inductors- time or frequency dependence- charge–storage phenomena that limit speed of frequency response- add capacitances to the hybrid-p model

§ The Base-Charging or Diffusion Capacitance Cde- Qn : minority-carrier charge stored in the base region operating in the

active mode

T

CFmF

BE

CF

BE

nde V

Igdvdi

dvdQC ttt ===º

- tF : forward base-transit time : average time a charge carrier (electron)spends in crossing the base (10 ps ~ 100 ps)

- Since iC ~ exponentially vBE & Qn ~ vBE à nonlinear capacitive effect- small-signal diffusion capacitance Cde :

CNU EE 8.1-10

BJT Internal Capacitances

00

021 je

m

e

BEjeje C

VVCC »÷÷

ø

öççè

æ-=

-

§ Base-Emitter Junction capacitance Cje- depletion-layer capacitance at the base-emitter junction

§ BJT internal capacitances- emitter-base capacitance Cp = Cde + Cje (a few pF ~ a few tens of pF) - collector-base capacitance Cm ( a fraction of pF ~ a few pF)

when EBJ is forward biased in the active mode

§ Collector-Base Junction capacitance Cm- depletion capacitance when CBJ is reverse biased in active-mode operation

m

c

BC

VV

CC-

÷÷ø

öççè

æ+=

00

1mm

where Cm0 : Cm at zero voltage, V0c : CBJ built-in voltage (~ 0.75V), m : 02~0.5

where Cje0 : Cje at zero voltage, V0e : EBJ built-in voltage (~ 0.9V), m : 0.5

CNU EE 8.1-11

High-Frequency Hybrid-p Model

§ BJT internal capacitances- emitter-base capacitance Cp = Cde + Cje (a few pF ~ a few tens of pF) - collector-base capacitance Cm ( a fraction of pF ~ a few pF)

§ Added Resistor rx- resistance of the silicon material of the base region between the base terminal B

and a fictitious internal base terminal B’- a few tens of ohms, rx << rp- dominant effect at high frequency

CNU EE 8.1-12

Cutoff Frequency

where b0 : low-frequencyvalue of b

( ) ( )

( )

( ) ( ) mpmppmp

p

mpp

m

mppmppppm

wb CgwhenrCCsrCCs

rgCCsr

sCgIIh

sCsCrICCrIVVsCgI

mm

m

b

cfe

bbmc

>>++

=++

»

++-

=º

++==-=

11

/1

1////

0

§ hfe , CE short-circuit current gain to determine Cp & Cm

- hfe : single-pole (STC) response with a 3-dB frequency at w=wb

( ) pmpbw

rCC +=

1

CNU EE 8.1-13

Cutoff Frequency

( )mp

mpb

b

p

wbw

w

b

CCgf

CCg

shSince

mT

mT

ofe

+=

+==

+=

2

1

0

§ Unity-gain bandwidth wT- the frequency at which |hfe|=1

§ Variation of fT with IC- fT : 100MHz ~ tens of GHz- the high-frequency hybrid-p model iseffective up to a frequency of about 0.2fT

CNU EE 8.1-14

BJT High-Frequency Model Summary

CNU EE 8.1-15

High-Frequency response of CS Amplifiers§ Objective : Identify the mechanism that limits the high-frequency performance of

the CS amplifiers - fH at which the gain falls by 3dB below its value at midband frequencies |AM|- simple approach to find fH for discrete-circuit, capacitively coupled amplifiers and

IC amplifiers- At the high-frequency band, all coupling and bypass capacitors behave as perfect short

circuits

Frequency response of a direct-coupled (dc) amplifier. The gain does not fall off at low frequency, and the midband gain AM extends down to zero frequency

CNU EE 8.1-16

-

Common-Source Amplifier§ frequency independent analysis

- CC1, CC2,CS (mF): short circuit- Cgs, Cgd (pF range): open circuit- |AM| = constant in the midband

)||||( LDomsigG

G

sig

oM RRrg

RRR

VVA

+=º

§ CS amplifier high-frequency equivalent circuit model

- Eliminating DC sources- RD : a passive resistance or the output

resistance of a current-source load- Simplified by Thevenin theorem at the

input and the output à input :Vsig’ & Rsig’ , three parallel

resistance RL’ : RL’ = ro//RD//RL- Midband gain AM by Cgs=Cgd=0

( )/Lm

sigG

G

sig

oM Rg

RRR

VVA

+-==

CNU EE 8.1-17

High-frequency response of CS amplifier

- Cgd à much larger Ceq (multiplication effect) because Cgd is connected between nodes G and D, whose voltages are related by a large negative gain (-gmRL

/). - Multiplication effect à Miller effect, (1+gmRL

/ ) à Miller multiplier

- bridging capacitor Cgd thatconnects the output node &the input node

- load current (gmVgs – Igd) :à gmVgs = output current

of transistor à Igd = current supplied

through Cgd

gsLmgd

gsLmgsgd

ogsgdgd

gsLmLgsmO

VRgsC

VRgVsC

VVsCIVRgRVgV

)1(

)]([

)()(

/

/

//

+=

--=

-=

-=-» - at XX/,the existence of Cgd is known only through Igdà replace Cgd by an equivalent capacitance Ceq between

gate & ground as long as Ceq draws a same Igd

)1(

)1(/

/

Lmgdeq

gsLmgdgseq

RgCC

VRgsCVsC

+=

+=

>

- At frequency in the vicinity of fH, igd << gmVgs at the frequency à Vo is approximated by

CNU EE 8.1-18

High-frequency response of CS amplifier§ with Cgd replaced with Ceq- STC circuit of low-pass type

/

/

/

/

/

/

21

2

1

1

1

1)(

||

)1(

1

1

1

sigin

HH

siginoH

H

M

o

LmsigG

G

sig

o

Gsigsig

Lmgdgs

eqgsin

sigino

o

sigsigG

Ggs

RCf

RCsA

sRg

RRR

VV

RRR

RgCC

CCCRC

sV

RRR

V

ppw

ww

w

w

w

w

==

==+

=

+÷÷ø

öççè

æ

+-=

=

++=

+=

=

+÷÷ø

öççè

æ

+=

- high-frequency response plot = low-pass STC network with a 3-dBfrequency fH determined by the time constant CinRsig

/

CNU EE 8.1-19

High-frequency response of CS amplifier

§ low-pass STC network with a upper 3-dB frequency fH by time constant CinRsig/

§ 3-dB frequency by Rsig/=Rsig || RG & Cin=Cgs+Cgd(1+gmRL

/)- Rsig

/ ~ Rsig since RG >> 1 - larger Rsig à lower fH

§ Cin is dominated by Ceq, which is made larger by the multiplication effect of Cgd§ Multiplication factor (1+gmRL

/) is approximately equal to the midband gain of theamplifier

§ Miller effect causes the CS amplifier to have a large total input capacitance Cin and hence a low fH

§ Multiplication effect of Cgd because it is connected between two nodes whose voltages are related by a larger negative gain (-gmRL

/ )à Miller effect & (1+gmRL

/ ) : Miller multiplier§ To extend the high-frequency response, Miller effect must be absent or at least reduced§ STC model is based on neglecting Igd relative to gmVgs

CNU EE 8.1-20

Common-Emitter amplifier§ frequency independent analysis

- CC1, CC2,CE (mF): short circuit- Cp , Cm (pF range): open circuit- |AM| = constant in the midband

§ three frequency bands- midband : useful band of amplifier- low-frequency band : CC1, CC2,CE- high-frequency band : Cp , Cm

)||||()||(

)||(LCom

sigB

B

sig

oM RRrg

RrRrR

VVA

+-=º

p

p

§ bandwidth or 3-dB bandwidthBW = fH – fL

~ fH when fL << fH§ gain-bandwidth product

GB = |AM|BW: trade-off gain for bandwidth

CNU EE 8.1-21

High-frequency response of CE amplifier

CE amplifier equivalent circuit

Simplified circuit at the input & output

§ Thevenin theorem twice atthe input side:Vsig’ & Rsig’

§ three parallel resistance RL’RL’ = ro//RC//RL

§ bridging capacitor Cmload current = gmVp – Im

§ Since Im << gmVp around fH

pm

ppm

pmm

pp

VRgsC

VRgVsC

VVsCIVRgRVgV

Lm

Lm

o

LmLmO

)1(

)]([

)()(

/

/

//

+=

--=

-=-=-»

§ replace Cm by Ceq between B/

& ground w/ same Im drawn

)1(

)1(/

/

Lmeq

Lmeq

RgCC

VRgsCIVsC

+=

+==

m

pmmp

>

CNU EE 8.1-22

High-frequency response of CE amplifier§ STC circuit by using Ceq

/0

/

0

/

/

/

/

/

/

21

2

1

1

1

1)||(

)1(

11

1

siginH

sigino

M

o

Bsigx

Lm

sigB

B

sig

sig

sig

o

sig

o

Lm

eqin

sigino

osig

RCf

RCsA

sRRrrRgr

RRR

VV

VV

VV

VV

RgCC

CCCRC

sVV

ppw

w

w

w

w

w

p

p

p

p

mp

p

p

==

=+

=

+÷÷ø

öççè

æ

++×

+-=

=

++=

+=

=

+=

CNU EE 8.1-23

High-frequency response of CE amplifier

§ low-pass STC network with a upper 3-dB frequency fH by time constant CinRsig

/

§ 3-dB frequency fH- Rsig

/ ~ Rsig||rp if RB >> Rsig & rx <<Rsigà Rsig

/ ~ rp if Rsig>>rpà if Rsig ~ rp , Rsig influences on fH

§ Cin is dominated by Ceq, which is made larger by the multiplication effect of Cm

§ multiplication effect of Cm because it is connected between two nodes whosevoltages are related by a larger negative gain (-gmRL

/ )à Miller effect & (1+gmRL

/ ) : Miller multiplierà increased Cin by Miller effect in CE amplifier à lower fH

§ Miller effect must be reduced for the improved high-frequency response§ STC model is based on neglecting Im relative to gmVp