More Continuous Time Filters

1. More Continuous Time Filters ESINSA

2. 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. ESINSA

3. Motivation There is a strong motivation to replace the bulky resistor with a more compact device. In parallel, a better control of the time constant is also desirable. The integrator, being the primary block of integrated filters, is again the target module. ESINSA

4. Vc C MOSFET - C ? Resistor built with MOSFET Small! Non linear! Loosely controlled performances! ESINSA

5. (Long Channel) Vg Vt Vs Vd MOSFET in the ‘triode’ region The MOSFET is highly non linear. ESINSA

6. MOSFET in the ‘triode’ region Linear resistance 2nd order non linearity 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. ESINSA

7. How to obtain a good linearity? Many methods have been proposed. We will review 4 of them here. ESINSA

8. Vx Vc I -Vx 4 ways to linearity (a) Even non-linearitiesare cancelled. ESINSA

9. MOSFET in the ‘triode’ region Still.. • 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 ESINSA

10. Vx Vc I -Vx Solution (a) Examples: NO NO NO NO NO Fairly limited.. NO ESINSA

11. Vc Vx Vy -Vx Vy I’’ I’ Vc 4 ways to linearity (b) Even non-linearitiesare cancelled ESINSA

12. Vc Vx Vy -Vx Vy I’’ I’ Vc Solution (b) An example: NO NO OK for integrator! Interesting. Could we do better? ESINSA

13. Vc Vx Vy -Vx -Vy I’’ I’ Vc 4 ways to linearity (c) Even non-linearitiesare cancelled ESINSA

14. Vc Vx Vy -Vx -Vy I’’ I’ Vc Examples: Solution (c) GOOD! Still third order non linearities are not cancelled. ESINSA

15. MOSFET in the ‘triode’ region 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. ESINSA

16. Vc1 Vx Vy I’ I’’ Vc2 Vc2 Vy -Vx Vc1 4 ways to linearity (d) Even and Odd non-linearitiesare cancelled Double balancing ESINSA

17. Vc1 Vx Vy I’ I’’ Vc2 Vc2 Vy -Vx Vc1 Solution (d) • 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 ESINSA

18. Vc1 Vx Vy I’ I’’ Vc2 Vc2 Vy -Vx Vc1 MOSFET in the ‘triode’ region 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 ESINSA

19. Vc1 Vx Vy I’ I’’ Vc2 Vc2 Vy -Vx Vc1 MOSFET in the ‘triode’ region • Matching ? • The cancellation of the distortion in • balanced structures is sensitive to the matching of the elements. • Matching devices is severely impacted • by additional structural limitations: • mobility non constancy • thermal feedback SDR 70 dB max ESINSA

20. (Long Channel) Vg Vt Vs Vd MOSFET in the ‘saturation’ region The MOSFET is again highly non linear. ESINSA

21. Vc I V MOSFET in the ‘saturation’ region Just an example. ESINSA

22. Tuning requested! The mobility and the threshold voltage depend on the process 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! ESINSA

23. Vp Vm Vp Vm MOSFET as a linear capacitor The MOSFET is a pretty effective capacitor as soon as its operates in full inversion. Unhappily the operation is asymmetrical and the capacitor must be biased. Vp > ( Vm + |Vt| ) ESINSA

24. MOSFET as a linear capacitor MOS Capacitors must be grounded. To reach a minimum of accuracy, all related capacitors of a filter must be grounded. This is a severe constraint. Grounded capacitors are less affected by parasitics as the capacitor from the bottom plate to the substrate is shorted out. Still, the use of grounded only capacitors require additional active devices, increasing power consumption, area, noise and distortion. ESINSA

25. MOSFET - C Integrator We will use the MOSFET in its ‘triode’ region to build the resistors of a RC integrator. We will refrain to use the MOSFET capacitor. For the best performances, we will choose a fully balanced architecture (i.e. symmetrical and differential). We will have to tune the RC to obtain a reasonable precision. ESINSA

26. Vc1 C Vc2 Vout Vc2 C Vc1 MOSFET - C Integrator Vin ESINSA

27. Vc2 Vc1 Vc1 C Vc2 Vout Vin Vc2 C Vc1 Vc1 Vc2 MOSFET - C Lossy Integrator An example of a more sophisticated module ESINSA

28. 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 tuning voltage. This performance is continuously measured and tuning voltage is adjusted accordingly. Frequency control and Q control of the transfer function should be considered in a MOSFET-C filter. ESINSA

29. Sampling: Fs W/L R Cref 1 2 C V Vout 2 1 Tuning. A simple example. ESINSA

30. feedback Positive R Vout Negative R V Tuning. A simple example. ESINSA

31. LPF Replica C MOS-C Filter Tuning. A simple example. tuning voltage ESINSA

32. 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 and applying 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 very circuit specific. ESINSA

33. Vg Vs Vd Vs Vd Vb Vg Transfer Function 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. ESINSA

34. Vg Vs Vd Vb MOSFET - C Performances Although first order approximations with lumped elements are often appropriate, it is recommended to get distributed MOSFET models. Distributed RC in the channel of the long channel MOSFET affects the filter response. It is quite easy to modify the filters parameters to get back to the specified transfer function. ESINSA

35. MOSFET - C Performances Noise is easily evaluated. As each transistor operates in the triode region, its internal noise is the same as the noise of a linear resistor, whose value equals the transistor small-signal channel resistance. Pretty neat! Distortion is the major issue. As the dynamic range of the signals is limited, design margin will be narrow. Extensive simulations must be run to verify the distortion performances and to guarantee a reasonable yield. ESINSA

36. 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! ESINSA