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**Linearized MOSFET Resistors**

Dr. Paul Hasler

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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

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**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 - ).

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**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.

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**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

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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.

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**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.

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**Linearized MOSFET resistors**

Simple Structure Balanced Differential Element Vc + Va + Vc + - Va + Vi + Vi Iout + Iout + Iout - Vi Iout - Vi - Va - Vc - Va -

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**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

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**Basic Resistive Feedback**

Vc + Vi + GND Vout Vout + Vin Vc - Vc - R1 Vout - Vi - Vb + - R2 Vc +

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**Basic Integrator Structure**

Vc + Vi + Vout + GND Vout Vin Vc - Vc - Vout - R1 Vi - C Vc + C Vb - Vb - Vb + Vb + Vb + Vb - Ideal Integrator if =

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**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

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**Tow-Thomas SOS (Lowpass)**

C R C R R R4 R Vin R GND Vout GND GND t = RC Q = R4 / R

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