1. CMOS Analog Design Using All-Region MOSFET Modeling 1 Chapter 9 Fundamentals of integrated continuous-time filters

2. CMOS Analog Design Using All-Region MOSFET Modeling 2 Types of CT-filters Active-RC MOSFET-C OTA-C Current mode Active RLC Filter coefficients are sensitive to process and temperature variations, and aging. Tuning of components that determine the frequency response is required.

3. CMOS Analog Design Using All-Region MOSFET Modeling 3 Applications of CT-filters - Anti-aliasing & reconstruction filters, - Read channel of disk drives, - Data communication circuits, - Sigma-delta ADCs - Sensors applications - ……………………

4. CMOS Analog Design Using All-Region MOSFET Modeling 4 +vi-+vi- -+-+ R2R2 R1R1 +vo-+vo- Active RC filters (d) C +vo-+vo- -+-+ R +vi-+vi-

5. CMOS Analog Design Using All-Region MOSFET Modeling 5 MOSFET-C filters - 1 (a) VGVG V S =V Q V D =V Q +V in IDID V D (V) 0123 4 5 0 VQVQ V in I D (  A) -25 25 (b) V G =4.5 V 3 V IFIF (a) MOSFET symbol and applied voltages (b) MOSFET output characteristics for V G =4.5 V, 3 V and V Q = 1 V. In the triode region the MOSFET is a NON-LINEAR voltage controlled resistor, controlled either by the gate voltage or the source voltage.

6. CMOS Analog Design Using All-Region MOSFET Modeling 6 MOSFET-C filters - 2 Specific current generator VQVQ V Q +V in -+-+ +vo-+vo- V DD For the topology shown

7. CMOS Analog Design Using All-Region MOSFET Modeling 7 MOSFET-C filters - 3 For balanced input signal, matched transistors, and common dc voltage, even-order harmonics are cancelled out. VGVG VQVQ V D1 =V Q +V in ID2ID2 ID1ID1 VQVQ VGVG V D2 =V Q -V in M1M1 M2M2 A fully-differential MOSFET transconductor

8. CMOS Analog Design Using All-Region MOSFET Modeling 8 MOSFET-C integrator - 1 V CM +v o1 V CM +v i -+-+ +-+- C C VGVG VGVG V CM -v i V SS ID1ID1 ID2ID2 M2M2 M1M1 V CM -v o2 V CM +v y The time constant of the integrator can be tuned by either V G or V CM

9. CMOS Analog Design Using All-Region MOSFET Modeling 9 MOSFET-C integrator - 2 Non-ideal effects: Unbalanced inputs; Offset voltage; Non-linear MOSFET Distributed MOSFET channel; Op amp finite gain; Op amp non-zero output admittance C v in +Vx-+Vx- GmvxGmvx GoGo CoCo vovo 1/g ms Integrator quality factor

10. CMOS Analog Design Using All-Region MOSFET Modeling 10 MOSFET-C integrator - 3 Tow-Thomas biquad

11. CMOS Analog Design Using All-Region MOSFET Modeling 11 Basics of OTA-C filters +vi_+vi_ (c) _+_+ GmGm i +vi_+vi_ (d) +_+_ GmGm ioio vovo C (a) +vi_+vi_ GmviGmvi +_+_ GmGm i o =G m v i +vi_+vi_ (b) (a) Small-signal equivalent circuit of the ideal transconductor, (b) its symbol, (c) the use of a transconductor as a resistor (i i /v i =G m ), and (d) the G m -C integrator.

12. CMOS Analog Design Using All-Region MOSFET Modeling 12 Transconductors - 1 (a) Simple MOSFET and (b) simple differential transconductors. iOiO M1M1 M2M2 + v in /2 - V DD M3M3 M4M4 1:1 ITIT (b) + -v in /2 - V DD (a) M1M1 IBIB iOiO IDID + v in -

13. CMOS Analog Design Using All-Region MOSFET Modeling 13 Transconductors - 2 M5M5 M1M1 M2M2 M4M4 2I B M3M3 V DD M6M6 -i O IBIB IBIB +i O + v in /2 - + -v in /2 - Fully-differential (CMFB circuit not shown) transconductor

14. CMOS Analog Design Using All-Region MOSFET Modeling 14 Transconductors - 3 I OUT V DD M 3B M 4B M 1A M 1B + V IN - IBIB M 3A M 4A V SS M 2A M 2B M 5B M 5A I OUT M 3C M 4C M 1C M 5C M 5D Fully-balanced transconductor with source degeneration

15. CMOS Analog Design Using All-Region MOSFET Modeling 15 G m -C integrator +_+_ G m (s) vivi vovo C CPCP GoGo Gm-C integrator and parasitic elements

16. CMOS Analog Design Using All-Region MOSFET Modeling 16 W/L= 120/4  m/  m, n=1.2,  t = 25 mV,  = 400 cm 2 /V-s, I SH = 100 nA, and V E =5 V/  m. (a) Calculate  u of the ideal integrator; (b) Calculate  relative to the ideal integrator due to both the distributed effect of the MOSFET and the finite gain of the transconductor; (c) What would be  u for C P =0.25·C L and what would be the value of I B required to restore the nominal value of  u ? Problem: V DD vivi M1M1 I B =300  A vovo C L =10 pF (a)  u =1.8/10 mA/V/pF = 180 Mrad/s (b) g m =1.25·g m | if=100 50% increase in power consumption I B =(151/100)·300 = 450  A (c)

17. CMOS Analog Design Using All-Region MOSFET Modeling 17 Signal-to-noise ratio and power consumption - 1 +V DD vovo vivi +-+- M1M1 M2M2 ioio -V DD I D2 I D1 “Idealized” class-B transconductor gmvigmvi vivi + vgvg gogo C vovo channel noise  (log) uu bb 0 -20 dB/dec AV= gm/goAV= gm/go VBVB VPVP vivi I D2 I D1 i o = I D2 + I D1

18. CMOS Analog Design Using All-Region MOSFET Modeling 18 Signal-to-noise ratio and power consumption - 2 Output noise voltage Output signal voltage Power delivered by the supplies is (i) (ii) (iii) From (i) – (iii): with When V P =V B /2, we can write +V DD vovo vivi +-+- M1M1 M2M2 ioio -V DD I D2 I D1

19. CMOS Analog Design Using All-Region MOSFET Modeling 19 Implementation of gyrators with transconductors Implementation of a gyrator with transconductors; (b) realization of a grounded inductor; (c) realization of a floating inductor

20. CMOS Analog Design Using All-Region MOSFET Modeling 20 Digitally programmable CT filters MOCD Digitally programmable V-I converter for application in MOSFET-C filters

21. CMOS Analog Design Using All-Region MOSFET Modeling 21 Tuning schemes - 1 On-chip direct tuning schemes (a) Interrupted filtering (b) Uninterrupted filtering

22. CMOS Analog Design Using All-Region MOSFET Modeling 22 Tuning schemes - 2 Reference frequency in Slave filter Master filter or VCO Signal in Signal out Phase detector Amplifier & low-pass filter Control voltage Tuning system VCVC Filter/VCO output On-chip indirect tuning scheme with either a voltage-controlled filter or a voltage-controlled oscillator as the master. The dotted line indicates a connection for the case of the master filter only but not for the case of the master VCO