YLD 10/2/99 ESINSA- 1 -

MOSFET in the ‘Triode’ region(revisiting)

YLD 10/2/99 ESINSA- 2 -

MOSFET in the ‘Triode’ region

2323

22

2232

21

2

fbsfbd

bsbd

sdffbbg

ox

VVVV

VVVV

VVVVV

LWCId

FYI, if you want to make precise evaluations, it is necessary touse a more complete formula than the simplistic model:

Still an approximation ….

YLD 10/2/99 ESINSA- 3 -

isidisdsd VVaVVaVVaId ...22

21

Series expansion around 0 for Vs and Vd:

MOSFET in the ‘Triode’ region

YLD 10/2/99 ESINSA- 4 -

232

1

1

233

212

211

22!

52...5311

...

2241

24121

22

ifBi

ioxi

fox

fox

fffbgox

Vi

iLWCa

VbLWCa

VbLWCa

VbVVLWCa

MOSFET in the ‘Triode’ region

small

YLD 10/2/99 ESINSA- 5 -

Transconductor - C

YLD 10/2/99 ESINSA- 6 -

Transconductor - C

gm CVin Vout

Iout

The integrator based on a transconductance:

YLD 10/2/99 ESINSA- 7 -

Transconductor?

Vin

Iout

0

)1(

out

in

inout

Z

RZ

RVI

R

YLD 10/2/99 ESINSA- 8 -

Linear transconductance?

)( q

inout

Ifunction

termsnonlinearVI

Iq+Iout Iq-Iout

2xIq

Vin -Vin

YLD 10/2/99 ESINSA- 9 -

Linear transconductance

2121 2 VVVkII C

I1 I2

I1+I2

V1 V2

Vc Vc

2tsgds VVVkIMOSFET

YLD 10/2/99 ESINSA- 10 -

Linear transconductance

Iq1+Iq2+Iout Iq1+Iq2-Iout

V1 V2

2xIq1 2xIq2 > 2xIq1

YLD 10/2/99 ESINSA- 11 -

Linear transconductance

Iq+Iout

Vin

Iq

Iq-Iout

-Vin

Iq

YLD 10/2/99 ESINSA- 12 -

Linear transconductance

Vin/2

Iq+Iout

Iq

Iq-Iout

-Vin/2

Iq

Vb

Degenerating the sources

YLD 10/2/99 ESINSA- 13 -

Linear transconductance

Vin/2 -Vin/2Vb1

Vb2

YLD 10/2/99 ESINSA- 14 -

Transconductor - C

Vin/2

Iq+Iout

Iq

Iq-Iout

-Vin/2

Iq

Vb

Iout

M1 M2

M3

C

Iout

CMFB

-Vout/2 Vout/2

YLD 10/2/99 ESINSA- 15 -

Transconductor - C

Vin/2

Iq

-Vin/2

Iq

Vb

Iout

M1 M2

M3

CIout

CMFB

-Vout/2 Vout/2

Common ModeFeedback

TransconductanceTuning

YLD 10/2/99 ESINSA- 16 -

Resistor

-gm

R

YLD 10/2/99 ESINSA- 17 -

Balanced Resistor

gmR

YLD 10/2/99 ESINSA- 18 -

Variant Using Gyrators

YLD 10/2/99 ESINSA- 19 -

Gyrator

r

rGwith

VGi

VGi

112

21

V1 V2

i1 i2

YLD 10/2/99 ESINSA- 20 -

Inductance?

r

dt

diCrV

dt

dVCi

rGwith

VGi

VGi

121

22

12

21

1

V1 V2

i1 i2

Inductance!

C

YLD 10/2/99 ESINSA- 21 -

Practical Realization of a Gyrator

gm

gyrator

r

-gmV1 V2

YLD 10/2/99 ESINSA- 22 -

Balanced Gyrator

gm gm

gyrator

r

Minus Sign is here !

V1 V2

YLD 10/2/99 ESINSA- 23 -

A few applications of the Gyrator

r r

L/r 2

L

L

r

L/r 2

Capacitance !!!

YLD 10/2/99 ESINSA- 24 -

r r

L/r 2

L

C

Etc..

C

A few applications of the Gyrator

YLD 10/2/99 ESINSA- 25 -

An Example: RLC Filter

R L2

C1

C2

C3 R

YLD 10/2/99 ESINSA- 26 -

ExampleR L2

C1

C2

C3 R

r r

L2/r 2

Vin/RC3C1

C2

RR

r r

L2/r 2

Vin

C2

C3C1R

R

mapping

YLD 10/2/99 ESINSA- 27 -

Example

-gm

gm gm

-gm

gm

-gm -gmC1 C3

C2

L2/r2

R L2

C1

C2

C3 R

(mapping)

YLD 10/2/99 ESINSA- 28 -

ExampleR L2

C1

C2

C3 R

Balanced version:

r r

L2/r 2

Vin/R

2C2

YLD 10/2/99 ESINSA- 29 -

Example

2C2

R L2

C1

C2

C3 R

C1 C32gm gm 2gm gm gm gm

2C2

2gmL2/r 2

Balanced version:

YLD 10/2/99 ESINSA- 30 -

Tuning the Transconductor - C

Vin/2 -Vin/2

TuningM1

C-Vout/2 Vout/2

YLD 10/2/99 ESINSA- 31 -

Transconductor - C

Same care has to be taken as for other continuous time filters.

Distortion and dynamic range are the major concerns.For high speed modules, bandwidth of the transconductorwill interfere with the transfer function.

Reserve Transconductor-C, like MOSFET-C, to high speedfilters. Do not expect great precision.

It is not yet clear which one will supersede the other, or ifthey will coexist.

YLD 10/2/99 ESINSA- 32 -

Conclusion: Integrated Filters

Very hot topics.

DSP is taking a huge share in the filters. More and more.

Still, analog to digital and digital to analog converters areprocessing samples. Analog filtering cannot be avoided.

Performances demand is increasing every year.There is no reason that this trend will change in the future.