1. Linearized MOSFET Resistors
Dr. Paul Hasler

2. Review of Gm-C Filters
Gm-C filters: voltage mode/current mode/log-domain
Use amplifier dynamics as filtering elements:
If making 10kHz filter, why make amplifiers run at 10MHz?
Good properties
Highest bandwidth / power consumed
Smallest number of elements / area consumed
Lowest noise levels / power consumed (thermal)
Utilizes capacitor matching (ie. C4)
Electronically tunable

3. Issues for Gm-C Filters
Improvement by
Floating-Gate Techniques
Tuning
Need control schemes (direct or indirect) – adds significant amount of control overhead
Mostly compensates: slight adjustments due to transistor aging / T changes, etc.
Matching
Huge issue for current-mode techniques
Design to eliminate these issues
Distortion
Techniques to improve linear range, but at a cost of lower gm/I (lower speed, higher noise, higher power)
More techniques to improve linear range
Most Gm-C techniques are fairly recent (80’s-90’s),
and Floating-Gate techniques are even more recent (90’s - ).

4. Other Filter Techniques
Utilizing higher frequency elements / additional elements,
to improve distortion (as well as 1/f noise, etc.).
Two techniques:
Amplifiers: (Op-amps), that run at much faster frequencies than filter cutoff.
Can use feedback to widen the linear range. Significant power increase.
Oversampling: Using a wider bandwidth than necessary to lower
noise per unit bandwith (and more power) and distortion.
Nonlinear systems can utilize noise shaping (Sigma-Delta Modulators)
Common in sampled data systems.
Switched Capacitor Blocks
Blocks based upon traditional, discrete RC active fitlers.

5. How to Build Resistances?
Resistors in a CMOS process
- Sometimes High resistance poly layer in a given process
- Poly, diffusions, or Well, but larger area consumed
Fairly linear, can be large for frequencies under 1MHz.
Not tunable: therefore RC > 20% mismatch, so we have a problem for
precission filters…so either laser trimming,
EEPROM trimming, (could tune cap, but…)
or imprecise filters, like anti-alaiasing filter.
MOSFET as a Resistor

6. MOSFET as a Resistor
Ohmic Region: how linear will that be, well only over a small region.
We have a gate voltage, so it is tunable, but of course,
we still need a method of tuning.
MOSFET has an ohmic region both in subthreshold
and above threshold operation.
Resistance is not exactly a constant,
except for a fixed source voltage….
resistance changes with source / drain voltage.
Could imagine an nFET and a pFET in parallel,
but still not a precission element.

7. MOSFET as a Resistor Two things to improve the situation.
1. Typically built around an amplifier to fix one of the terminals
(mostly op-amps, but could also be a Norton or
transisresistance approach as well)
The amplifier must keep terminals nearly fixed to
eliminate distrotion; therefore, in general the amplifier
must run a lot faster than expected by a simple GmC stage.
2. Can use a combination of MOSFETs to linearize the behavior.

8. Linearized MOSFET resistors
Simple Structure
Balanced Differential Element Vc + Va + Vc + - Va + Vi + Vi
Iout +
Iout +
Iout - Vi
Iout - Vi - Va - Vc - Va -

9. Linearized MOSFET resistors
In practice, one might use even
lower input impedance elements Vc + - Vi +
Iout +
Iout - Vi -
Iout - Va +
Iout + Va -
GND
GND
GND
GND

10. Basic Resistive FeedbackVc + Vi +
GND
Vout
Vout +
Vin Vc - Vc - R1
Vout - Vi - Vb + - R2 Vc +

11. Basic Integrator StructureVc + Vi +
Vout +
GND
Vout
Vin Vc - Vc -
Vout - R1 Vi - C Vc + C Vb - Vb - Vb + Vb + Vb + Vb -
Ideal Integrator if =

12. Tow-Thomas SOS (Lowpass)C1 R3 C2 R R1 R4 R2
Vin R
GND V1
Vout
GND V2
GND
R4 needed for stability
Tuning can be interesting (tuning pots)
All amps must be sufficiently fast

13. Tow-Thomas SOS (Lowpass)C R C R R R4 R
Vin R
GND
Vout
GND
GND
t = RC
Q = R4 / R