more continuous time filters

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More Continuous Time Filters

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Motivation

SWC filters have a few drawbacks:• They are sampled. Noise is aliased. Antialiasing and smoothing filters are required.• They are slow. They require a fairly large ratio between clock frequency and processed signals.

Standard active RC filters have other issues:• Resistors are bulky.• Time constant and transfer function are loosely controlled.

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Motivation

There is a strong motivation to replace the bulky resistor witha more compact device.

In parallel, a better control of the time constant is also desirable.

The integrator, being the primary block of integrated filters, isagain the target module.

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MOSFET - C ?

CVc

Resistor built with MOSFET

Small!Non linear!Loosely controlled performances!

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Vs Vd

Vg

Vt

(Long Channel)

MOSFET in the ‘triode’ region

The MOSFET is highly non linear.

sdds

tgds VV2

VVVVbI

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MOSFET in the ‘triode’ region is fairly quadratic.

More accurate modeling shows that other non linearities are pretty small (60dB lower)!

If we can cancel the 2nd term, we may therefore pretend to obtain fairly good performances.


22sdsdds VVVVI

2nd order non linearity Linear resistance

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Many methods have been proposed.

We will review 4 of them here.

How to obtain a good linearity?

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4 ways to linearity (a)

sdds

tgds VV2

VVVVbIMOSFET

tcx VVbRwith

R

VI

/1

2

Vc

-Vx

Vx

I

Even non-linearitiesare cancelled.

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Still..


tcx VVbRwith

R

VI

/1

2

The resistance of the linearised MOSFET is depending on

• the gate control voltage Vc• the threshold voltage Vt• the mobility of the carriers in the channel• the gate oxide thickness• the geometrical parameters (W, L)• the parameters not included in the simplistic model

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Solution (a)

Vc

-Vx

Vx

I

Fairly limited..

Examples:

NO

NO

NO

NO

NO

NO

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4 ways to linearity (b)

tcx VVbRwith

R

VII

/1

2'''

VyVx

Vc

Vc

Vy-Vx

I’’

I’ Even non-linearitiesare cancelled

sdds

tgds VV2

VVVVbIMOSFET

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Solution (b)

Interesting.Could we do better?

An example:

VyVx

Vc

Vc

Vy-Vx

I’’

I’NO

NO

OK for integrator!

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4 ways to linearity (c)

tcyx VVbRwith

R

VVII

/1

2'''

VyVx

Vc

Vc

-Vy-Vx

I’’

I’ Even non-linearitiesare cancelled

sdds

tgds VV2

VVVVbIMOSFET

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Solution (c)

GOOD!Still third order non linearities are not cancelled.

Examples:

VyVx

Vc

Vc

-Vy-Vx

I’’

I’

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Solutions a, b and c achieve regularly

SDR 60 dB

For an input dynamic range of 1V and a power supply of 5V.

This is a remarkable performance. This is due to the small high order non linearities of the long channel MOSFET.

Still, 60dB is not too much.


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4 ways to linearity (d)

21/1

2'''

cc

x

VVbRwithR

VII

Vx

Vc1

Vc2

I’Vy

-Vx

Vc2

Vc1

I’’Vy

Even and Oddnon-linearitiesare cancelled

Double balancing sd

dstgds VV

2

VVVVbIMOSFET

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That’s it!

• theoretically very linear• does not depend on Vt• does not depend on the body effect• does not depend on the substrate voltage• realizes high resistance when (Vc1-Vc2) is small• allows high value of Vc1 and Vc2 without modifying the resistance• compatible with balanced architecture

Vx

Vc1

Vc2

I’

Vy

-Vx

Vc2

Vc1I’’

Vy

Solution (d)

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Still..


The resistance of this linearised MOSFET is depending on

• the matching of the devices• the difference between gate control voltages Vc1, Vc2• the absolute values of the MOSFET

Vx

Vc1

Vc2

I’

Vy

-Vx

Vc2

Vc1I’’

Vy

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Matching ?

The cancellation of the distortion inbalanced structures is sensitive to the matching of the elements.

Matching devices is severely impactedby additional structural limitations:

• mobility non constancy• thermal feedback


Vx

Vc1

Vc2

I’

Vy

-Vx

Vc2

Vc1I’’

Vy

SDR 70 dB max

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MOSFET in the ‘saturation’ region

Vs Vd

Vg

Vt

(Long Channel)

The MOSFET is again highly non linear.

2tsgds VVVkI

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MOSFET in the ‘saturation’ region

cthc VVVVkI 2

2tsgds VVVkIMOSFET

Vc

V

I

Just an example.

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Tuning requested!

The mobility and the threshold voltage depend on theprocess and on the temperature.

The gate control voltage is probably depending on the process, the matching, the temperature and the power supply.

Trimming is necessary but is not sufficient!

On fly calibration is requested!

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MOSFET as a linear capacitor

The MOSFET is a pretty effective capacitor as soon as itsoperates in full inversion. Unhappily the operation is asymmetrical and the capacitor must be biased.

Vp

Vm

Vm

Vp

Vp > ( Vm + |Vt| )

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MOSFET as a linear capacitor

MOS Capacitors must be grounded. To reach a minimumof accuracy, all related capacitors of a filter must be grounded.

This is a severe constraint.

Grounded capacitors are less affected by parasitics as thecapacitor from the bottom plate to the substrate is shorted out.

Still, the use of grounded only capacitors require additionalactive devices, increasing power consumption, area, noiseand distortion.

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MOSFET - C Integrator

We will use the MOSFET in its ‘triode’ region to build the resistorsof a RC integrator. We will refrain to use the MOSFET capacitor.

For the best performances, we will choose a fully balancedarchitecture (i.e. symmetrical and differential).

We will have to tune the RC to obtain a reasonable precision.

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MOSFET - C Integrator

CVV c2c1

Vin

Vc1

Vc2

Vc2

Vc1

C

C

Vout

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MOSFET - C Lossy Integrator

An example ofa more sophisticatedmodule

Vc1

Vc2

Vc2

Vc1

C

C

Vc1

Vc2

Vc2

Vc1

Vin Vout

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Tuning a MOSFET - C module

There are plenty of techniques to tune a MOSFET-C module.

Many of them are using a replica module.

Some performance of the replica is controlled by a tuningvoltage. This performance is continuously measured andtuning voltage is adjusted accordingly.

Frequency control and Q control of the transfer functionshould be considered in a MOSFET-C filter.

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Tuning. A simple example.

refsSWC C

CF )( tuningCMOS VfunctionC

Cref C

V Vout

1

2 1

2

RW/L

Sampling: Fs

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CMOSSWC

feedback

V

Vout

Negative R

Positive R

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tuning voltage

C

MOS-C Filter

LPF

Replica

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Tuning a MOSFET - C module

In practice, the tuning circuitry could be much more sophisticated.

Effective tuning implies measuring the filter performances, comparing with a reference, computing the error andapplying a correction to the system.

There is a common consensus that the frequency of systemclock is the most practical and the best reference.

Methods to apply this concept largely differ and are verycircuit specific.

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The MOSFET building resistors could have a pretty long channel.

This is introducing a distributed RC line in place of the resistor.

In some cases, the expected transfer function is not obtained.

Vb

Vs Vd

Vg

Transfer Function

Vs

Vg

Vd

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Vs Vd

Vg

Vb

Although first order approximations with lumped elements areoften appropriate, it is recommended to get distributed MOSFETmodels.

Distributed RC in the channel of the long channel MOSFET affects the filter response. It is quite easy to modify the filtersparameters to get back to the specified transfer function.

MOSFET - C Performances

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MOSFET - C Performances

Noise is easily evaluated.

As each transistor operates in the triode region, its internal noiseis the same as the noise of a linear resistor, whose value equalsthe transistor small-signal channel resistance. Pretty neat! Distortion is the major issue.

As the dynamic range of the signals is limited, design marginwill be narrow. Extensive simulations must be run to verify thedistortion performances and to guarantee a reasonable yield.

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MOSFET - C

They are reasonably fast.

They are reasonably accurate.

The power consumption is fairly good.

They are not sampled.

Their usage is limited by the signal to distortion ratio.

The dynamic range is limited.

The tuning module could be a true overhead!

more continuous time filters

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