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

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.

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 - ……………………

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-

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) VQVQ V in I D (  A) (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.

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

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

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

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

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

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.

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 -

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 / v in /2 - Fully-differential (CMFB circuit not shown) transconductor

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

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

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)

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 dB/dec AV= gm/goAV= gm/go VBVB VPVP vivi I D2 I D1 i o = I D2 + I D1

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

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

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

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

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