ece 342 electronic circuits lecture 23 miller effectemlab.illinois.edu/ece342/notes/lec_23.pdf ·...

ECE 442 – Jose Schutt‐Aine 1

Jose E. Schutt-AineElectrical & Computer Engineering

University of [email protected]

ECE 342Electronic Circuits

Lecture 23Miller Effect


22 Dm n ox eff n ox D

eff

W W Ig C V C IL L V

MOSFET High-Frequency Model

2 2mb m mF sb

g g gV

1/ds A DD

r V II

23gs ox ov oxC WLC WL C

gd ov oxC WL C

1

sbosb

SB

o

CCVV

1

dbodb

DB

o

CCVV

2


CS - High-Frequency Response

3


1 2 GR R R


4


'sig sig GR R R

'gd gd gs o gd gs m L gsI sC V V sC V g R V

'1gd gd m L gsI sC g R V


' L ds D LR r R R

5


'1 eq gs gd m L gssC V sC g R V

'1 Miller Capacitance eq gd m LC C g R

g sigin

g sig

R Vv

R R

' o m L gsV g R V

Define Ceq such thatCS – Miller Effect

6


11 /

G siggs

G sig o

R VV

R R jf f

fo is the corner frequency of the STC circuit

'

12

oin sig

fC R

'1 Miller

in gs eq gs gd m LC C C C C g R

CS – Miller Effect

7


' 11 /

o Gm L

sig G sig o

V R g RV R R jf f

1 /

o M

sig H

V AV jf f

'

12

H oin sig

f fC R

CS – Miller Effect

8


Rsig = 100 k, RG=4.7 M, RD =15 k, gm=1mA/V, rds=150 k, RL=10 kCgs=1 pF and Cgd=0.4 pF

' 4.7 1 7.14 74.7 0.1

GM m L

G sig

RA g RR R

': 1eq M m L gdMiller Cap C C g R C

Example

' 150 15 15 7.14 L ds D LR r R R k

0.4 1 7.14 3.26MC pF

9


1

2Hin sig G

fC R R

Upper 3 dB frequency is at:

1.0 3.26 4.26 inC pF

12 6

1 3.822 4.26 10 0.1 4.7 10Hf kHz

3.82Hf kHz

Example (cont’)

10


CE High-Frequency Model

11



1 2BR R R

12


' B

sig sigB sig x sig B

rRV VR R r r R R


13


'L o C LR r R R

'o m LV g v R

'sig x sig BR r r R R


14


The left hand side of the circuit at XX’ knows the existence of C only through the current I replace C with Ceq from base to ground

Bipolar Miller Effect

15


'o m LI sC v v sC v g R v

'1 m LI sC g R v


'1eq m LsC v I sC g R v

'1 , Miller capacitance for BJTeq m LC C g R

16



' 11 /sig

o

v vjf f

'

12o

in sig

fC R

17


'1in eq m Lwhere C C C C C g R

' 1

1 /o m LB

sig B sig ox sig B

V r g RRV R R jf fr r R R

Bipolar Miller Effect (cont’)

11 /

oM

sig o

V AV jf f

'

12H o

in sig

f fC R

18


CS – Miller Effect – Exact Analysis

19


ii

1GR

DD

1GR

gg

1GR

dsds

1gr

'i D m gdo

' ' 2 'i i g gs gd gd D i g gd m D gd gs D

G R g sCvv G G s C C sC R G G sC g R s C C R


'D D ds

D ds

1R R rG g

20


2 ' 'gd gs D gd m D gs ms C C R sC g R or sC g

We neglect the terms in s2 since

'

i D m gdo' '

i i g gs gd m D gd D i g

G R g sCvv G G s C C 1 g R C R G G

ii

1RG

If we multiply through by


21

Miller


'D m gdo

' 'i i g i gs gd m D gd D s g

R g sCvv 1 R G s R C C 1 g R C R 1 R G

i g

H ' 'i gs gd m D gd D i g

1 R Gf

2 R C C 1 g R C R 1 R G

From which we extract the 3-dB frequency point


22


H ' 'i gs gd m D gd D

1f2 R C C 1 g R C R

H 'gd D

1f2 C R

If Gg is negligible

If Ri =0


23


ii

1GR

CC

1GR

1gr

oo

1gr

BJT-CE – Miller Effect – Exact Analysis

'C C o

C o

1R R rG g

24


's C mo

' ' 2 'i i C i m C C

G R g sCvv G g s C C sC R G g sC g R s C C R


25


2 ' 'C m C ms C C R sC g R or sC g

'i C mo

' 'i i m C C i

G R g sCvv G g s C C 1 g R C R G g

'C mo

' 'i i i m D C i

R g sCvv 1 R g s R C C 1 g R C R 1 R g


We neglect the terms in s2 since

If we multiply through by ii

1RG

26

Miller


i

H ' 'i m C C i

1 R gf2 R C C 1 g R C R 1 R g

H 'C

1f2 C R

If Ri = 0


27


Example For the discrete common-source MOSFET amplifier shown, the transistor has VT = 1V, Cox(W/L) = 0.25 mA/V2, = 0, Cgs = 3 pF, Cgd = 2.7 pF and VA = 20 V. Assume that the coupling capacitors are short circuits at midband and high frequencies.

(a) Find the 3dB bandwidth if Ri = 0

(b) Find the 3dB bandwidth if Ri = 10 k

28


If Ri =0, 3 '

12dB

gd D

fC R

20 131.516

Ads

D

Vr k

I

' 13 2 1.736D D dsR R r k

3 12 3

1 33.952 2.7 10 1.736 10dBf MHz

Example – Part (a)

29


If Ri =50 k,

Example Part (b)

'm Dg R 0.870 1.736 1.51

H ' 'i gs gd m D gd D

1f2 R C C 1 g R C R

H1f 32.27 kHz

2 50 3 2.7 1 1.51 2.7 1.736

30

ece 342 electronic circuits lecture 23 miller effectemlab.illinois.edu/ece342/notes/lec_23.pdf ·...

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