Mixed signal design I. Introduction II. Analog VLSI filters III. RF CMOS basics

1. Mixed signal design I. Introduction II. Analog VLSI filtersIII. RF CMOS basics P.V. Ananda Mohan Fellow IEEE CDAC, Bangalore. 15 June 2017.

2. A typical DSP based System Band Limiting Filter Smoothing filter A/D DSP A/D Analog I/F

3. A modern CMOS RF receiver (IEEE Solid-State Circuits Magazine Spring 2015)

4. Anti-Aliasing or band limiting filter for telephony • Example: PCM filter for telephony 3.4KHz 4.6KHz odB -32dB 300Hz 4KHz 50Hz and harmonics rejection needed in telephony, Biomedical applications

5. Row frequencies 697 770 825 941 1209 1336 1477 Column Frequencies DTMF Receivers • Any Button pressed generates one column and one row frequency

6. Bandpass Filter+FWR+LPF L O G I C Low Group Filter AGC Input Dialled digit High-Group Filter

7. GSM transmitter D/A +Filter GMSK Modulator Output stage Speech encoder 90 PA A/D LO D/A +Filter High Frequency operation needed

8. Signal conditioning –what it means • Amplification • Attenuation • Filtering • Isolation • Excitation • Linearization • Sampling • Multiplexing • Coding (A/D conversion)

9. - + - + S1 S2 CH Open-loop type Sample and Hold • Zero-order hold H(s) = (1-e-sT)/s , H(j ω )= Sin (ωT/2)/(ωT/2) Ts Sampling frequency = 1/Ts

10. Smoothing filter 2.6dB Smoothed output Stair case type output of D/A Effect of Sample and hold is droop in frequency response Sinx/x . Correction needed for Sinx/x in smoothing filter .

11. Filter Design Choices • Active RC • Switched-Capacitor • OTA-C • Current –mode • Digital

12. Design Requirements • Power Consumption • Supply Voltage • Requirement for clock (in case of SC filters) • Dynamic Range (noise floor/distortion) • Frequency of operation • Area -Total capacitance, Resistance, opamps • Sensitivity (Process , Voltage and temperature (PVT) variation) • Tuning to achieve required specifications • Spread of capacitors/ resistors/ transconductance values • Ease of Design (without needing experts) • Programmability

13. Options for structures • Cascade design • Ladder Filters • Component simulation based or operational simulation based

14. Cascade Design of Filters • Useful for realizing complex high-order responses by cascading several second-order and first-order filters output 1 2 n input

15. C R C R First-order Filters Vi V0 V0 Vi

16. R R R - + R C C R R - + C R All-pass filters Vi V0 -Vi Vi V0 Needs one inverting amplifier, Floating capacitor V0 Needs Grounded capacitor Vi Needs Floating capacitor

17. Transistor based designs for low power and minimum area • First-order All-pass delay cell (2013 IEEE Trans. CAS II Garakoui et al.)

18. First-order All-pass filter • Low pass type response, delay is 2τ

19. C - + - + R R - + C Differentiators and Integrators Lossless and Lossy Vi Vi V0 V0 R2 R C C2 - + Vi R1 C1 Vi V0 V0

20. - + - + Negative resistance Circuits R1 R R Vi -R1 R Vi R1 R -R1

21. R R - + R R C R - + R C - + R Non-inverting integrators Negative resistance Deboo Integrator Uses Negative resistance Grounded capacitor Needs one opamp only Vi V0 Vi Needs Two Opamps V0

22. R V1 C Differential Integrator Needs Matching of two time constants Vo= (V2-V1)/sCR V2 V0 R C C R V0 Vi Differential Integrator Needs Matching, balanced Differential output also. Vo=Vi/sCR -Vi R -V0 C - + - +

23. Fully Differential opamp • Does not give balanced outputs (Vout+ may not exactly equal Vout-)

24. Banu, Khoury, and Tsividis, IEEE JSSC, Dec 1988

25. Second-order filters • Second-order transfer function also is expressed in standard form as • Qz , z are zero-Q , zero frequency • Qp , p are pole-Q and pole frequency • p/Qp is the bandwidth • K is gain

26. Second-Order Transfer Functions Various types of second-order transfer functions Low-pass n2=0,n1=0 High-pass n1=0,n0=0 Band-pass n2=0, n0=0 Symmetric Notch or Null n1 = 0, n0 = n2 Low-pass Notch n1=0, (n0/n2)>(d0/d2) ωz > ωp High-pass notch n1=0, (n0/n2)<(d0/d2) ωz < ωp All-pass (n1/n2) = (-d1/d2), (n0/n2) = (d0/d2), ωz = ωp, Qz = -Qp

27. s-domain Marginally stable Imaginary Unstable Region Stable Region Real

30. K gain of the amplifier Vy= Vo/k Vo R1 Vi R2 C2 C1 Sallen-Key Filter (1955) x y • Write two KCL equations at x and y nodes Vx

31. Sallen-Key Filter • Funda: Sensitivity to passive components always shall be on actual expressions and not on simplified version to get correct picture

32. Sensitivity • SQK = (Q/Q)/(K/K) • % change in Q for a percentage change in K • Also defined as (dQ/dK).(K/Q) • Defined for o also. • e.g. o = 1/(C1C2R1R2)1/2 • S oC1 = -½.

33. Frequency scaling • Filter design tables give in terms of normalized frequency of 1rad/sec (you can deal with small numbers). At the end, scaling can be done • Butterworth second-order example

34. Non-ideal Opamp • Finite Bandwidth • Single-pole model Va Vb - + Vo Vo=(Vb-Va).B/(s+a) B unity Gain Bandwidth a is the first pole

35. Second Differential Gain stage and Frequency compensation First Differential gain stage/Front-end Level Shifter / third gain stage Three pole model of the Opamp

36. Effect of Non-ideal OA • Parasitic poles as many as the number of OAs are introduced • Q-enhancement and Pole-Frequency reduction are the result.

37. R R - + - + • What are the bandwidths? Gain = 1 Gain = -1

38. R - + C Effect of Opamp Bandwidth on Differentiator • A second-order band-pass filter and not a first-order high-pass filter !!!!!! Vi Vo -Vos/B

39. Analysis of effects of OA pole Substitute 1/ ωoQ (1/(ωoQ)) is same. Hence (ΔQ/Q)= -(Δωo/ ωo) Result is decrease of o and increase of Q. Approximation valid for High-Qs (Akerberg-Mossberg Approximation) Sometimes system may oscillate.

40. R2 - + Vi R1 C1 Vo Active-Gm-RC • Also known as Partially Active R (K.R.Rao et al, Ananda Mohan, D’Amico et al) • Internal Dynamics of Opamp is used (i.e. finite Bandwidth) • Tuning needed • Performance depends on Power supply, tolerances, Bandwidth of Gm block

41. R’ R’ C C R VZ Vi Vx R R1 Vy V3 R2 - + - + - + Kerwin, Huelsman and Newcomb (KHN) Biquad • Also called State-Variable Biquad

42. - + - + - + - + Tow-Thomas Biquad (Two-Integrator Loop) R’ C R’ R C BP QR’ Vi R’ LP R Rc Rb Rf Ra Biquadratic Transfer Function

43. Programmable integrator resistor

44. Filter design Flow Chart Specification Synthesis of Transfer Function Use filter design programs,Tables Choice of implementation Cascade, ladder etc, number of Opamps, area etc Choice of component values Scaling For optimal dynamic range. Ordering, Pole-zero pairing

45. Butterworth Filters

46. Chebychev Filters

47. Comparison of Responses of various types

48. Group delay versus frequency • Delays of Fourth order filters

49. 7th order low-pass elliptic filter

50. en2= 4KTRB R Noise in Filters • Dynamic range depends on Noise Floor • Noise is due to resistors and active devices such as OAs, OTAS. • Resistors have Johnson noise • Noise expressed as noise spectral density • Resistor R has noise spectral density en2= 4kTRB where k is Boltzmann’s constant, B is the bandwidth of measurement, T is the absolute Temperature In practice B is the effective bandwidth decided by the circuit around the resistor