CMOS analog filter design

IDEC 혼성모드시스템설계및실습 CMOS analog filter design Changsik Yoo Department of Electronics and Computer Engineering Hanyang University, Seoul, Korea csyoo@hanyang.ac.kr

Winter Course of IT SoC Center (Dec. 3-7, 004) Introduction

Filters at mixed signal system Pre-Amp Rx-Filter A ADC Analog Media A DAC DSP & MCU Digital Data Driver Tx-Filter AFE Performance Requirements Pre-Amp Rx-Filter AFE AFE < AFE AFE ADC D Analog Media DAC D DSP & MCU Digital Data Driver AFE Tx-Filter 3

Analog filter General digital signal processing system Band limiting Wireless receiver Noise suppression 4

Specification of filter : Magnitude 5

Specification of filter : Phase Phase response is also important. Equal phase for all frequencies is not desired. Equal delay (group delay) for all frequencies is desired. For equal group delay, phase response should be linear function of frequency. For certain type of filters, the variation of group delay may be too large to be tolerated for target application. Group delay equalization is required for some applications such as data communication system. All pass filter with group delay equalization 6

Types of filter Butterworth : Maximally flat gain Chebyshev : Equiripple in passband Inverse Chebyshev : Equiripple in stopband Elliptic (Cauer) : Equiripple in pass/stopband 7 Bessel : Maximally flat group delay

Group delay : Bessel filter 8

Group delay : Chebyshev filter Passband ripple : 0.5dB Passband ripple : db 9

Equalization of group delay with nd order all-pass filter T () s K 0 s s ( ω0 Q) s ω0 ( ω Q) s ω 0 0 0

Classification of analog filters Basic building block of analog filter : integrator Analog filters are classified by the type of basic integrators. Active-RC / MOSFET-C / Gm-C / Gm-Opamp-C / Switched-capacitor Active-RC MOSFET-C Gm-C According to the operating time domain, Continuous-time : Active-RC / MOSFET-C / Gm-C / Gm-Opamp-C Discrete-time : Switched-capacitor / Switched-current

Continuous-time filter Gm-C, active-rc, MOSFET-C filter No pre- and post- processing required Tuning circuits required to have desired frequency characteristics H(s) X(s) Y(s) b a s s M N b a s s M N b a M N s b s a M N H(f) [db] 0-0 -40-60 -80-00 -0 0 0 0 0 4 0 6 0 8 f [Hz] imaginary f [MHz] 5 4 3 0 - - -3-4 -5-0.5 0 0.5 real f [MHz]

Discrete-time filter Switched-capacitor (SC) filter, switched-current (SI) filter Pre- and post- processing required due to its sampling operation Desirably accurate frequency characteristics ( ) H z M M- ( ) bz bz bmz bm ( ) N N- az az amz am N z D z 0 0.8-0 0.6 H(ω) [db] -40-60 imaginary ω 0.4 0. 0-0. -80-0.4-0.6-00 -0.8-0 0 0.π 0.4π 0.6π 0.8π π ω - - -0.5 0 0.5 real ω 3

Comparison of analog filters Active-RC MOSFET-C Gm-C SC Unity-gain freq. of integrator /RC /r on C g m /C (C/C) Linearity High-freq. operation Active circuit Op-amp Op-amp OTA Op-amp Tools for freq. tuning Variable cap. or resistor MOSFET g m Not required Variable voltage gain 4

Implementation of high-order filter () Cascading of Biquad Blocks X(z) H (z)... H i (z)... H N/ (z) Y(z) H(z) H (z)...h i (z)...h N/ (z) N N bz bz b0 i i az az a0 ( ) Hi( z) H z Easy adjustment of frequency characteristics Pole/zero pair matching Biquad permutation issue Gain distribution issue 5

Implementation of high-order filter () X(s) R S I 0 C RLC Prototype L L 4 V V 3 Y(s) I I 4 C 3 R L I V I V I 0 3 4 ( X V ) RS ( I0 I ) sc ( V V3 ) sl ( I I4 ) sc3 ( V3 I4RL ) sl Less sensitive to the variations of component values Easy to obtain Frequency transformation Impedance transformation 6

Analog integrator Most basic building block H(ω) v out ( t) K vin( t) dt VOUT ( ) ( s) H s K V ( s) s IN one one pole pole 0dB -6dB/oct ω unity ω H ( jω) K jω H H ( jω) ( jω) K ω 90 <H(ω) 0 o ω -90 o 7

Analog integrator : active-rc C v in R _ A H( s) v out V V OUT IN ( s) ( s) RC s Linearity guaranteed by negative feedback Large variation of frequency characteristics Resistive loading on op-amp High-performance op-amp is required. 8

Analog integrator : MOSFET-C C v in _ R ON A H( s) v out V V OUT IN ( s) ( s) R C s ON Linearity guaranteed by negative feedback but somewhat degraded due to the non-linear resistance of MOSFET Large variation of frequency characteristics Resistive loading on op-amp High-performance op-amp is required. 9

Analog integrator : Gm-C v IN G m i out G m v in C v out H ( s) V V OUT IN ( s) Gm ( s) C s Low-power and high-frequency operation due to the open-loop architecture Poor linearity Linearized transconductor is required. 0

Analog integrator : SC v in φ C φ - C vout H( z) φ φ V V OUT IN ( z) C z ( z) C z Accurate frequency characteristics Linearity guaranteed by negative feedback Large power dissipation for high frequency operation (f clk >> f signal ) Anti-aliasing and smoothing filter required

IDEC 혼성모드시스템설계및실습 Active-RC / MOSFET-C filter

Active-RC / MOSFET-C filter Active-RC / MOSFET-C integrator With ideal operational amplifier ; C V out Vin scr f unity RC C v in R _ A v out v in R ON _ A v out Unity gain frequency of the integrator is determined by RC time constant. The variation of R and C values does not track with each other and therefore RC time constant can change as much as 50% due to PVT variations. Tuning of frequency characteristics is required. Either automatic or manual 3

Active filter synthesis from passive LC-ladder prototype Doubly terminated LC-ladder filter is most widely used as passive filter prototype. Relatively immune to the variation of component values LC-ladder 4

Synthesis of active filter from passive prototype Element substitution R : R in active-rc filter C : C L : Gyrator Signal flow graph (SFG) Same result as with element substitution Useful for optimization (e.g. dynamic range optimization) Will be explained in next slides. 5

Frequency and impedance scaling Component values of filter design handbook For low-pass filter with cut-off frequency rad/sec and source impedance Ω For cut-off frequency f cut-off [Hz] and source impedance R S [Ω] Component values should be scaled as ; L L IS FS FS π f cut off [Hz] [rad/s] C C FS IS R [ Ω] RS S [ Ω] R R IS 6

7 Frequency translation Low pass High pass ( ω c : cut-off frequency of HP ) Low pass Band pass ( ω 0 : center frequency of BP, B : 3dB bandwidth of BP ) s s c ω ( ) L s L s sl c c ω ω ( ) C s C s sc c ω c ω Bs s s 0 ω ( ) L B s B L s L Bs s sl 0 0 ω ω ( ) C B s B C s C Bs s sc 0 0 ω ω

How to obtain prototype low-pass specification LP prototype 8

9 Element substitution Key component for element substitution ; gyrator g I I V V 0 0 V V g g I I g sc Z in g C L g C L

Signal flow graph (SFG) Graphical representation of KCL and KVL Good design tool for analog filter synthesis Some tips for analog filter synthesis Transfer function does not change as long as the loop gain is conserved. This property will be utilized for dynamic range optimization. Vertex variables (see the example on the next slide) Source voltage Voltage across shunt branches Current through series branches 30

Design example with SFG : 5 th order Chebyshev filter () V S sc GSVS V sc V V ( G V G V I ) S S GSV G S ' ' ' V V3 GS ( V V4 ) V3 slg S sc3 ' ' V3 V G 5 SV4 4 V5 sl4g S sc5 GL ' V ' n I n R S Vertex variables sc G S G K S G S sc3 sl G S sl 4 G S sc G 5 S G L 3

Design example with SFG : 5 th order Chebyshev filter () sc G S G S G S sc3 sl G S sl 4 G S sc G 5 S G L K 3

Design example with SFG : 5 th order Chebyshev filter (3) V ',max V,max V 3,max ' V 4,max Vout, max 0.75 0.65 0.5 α 0.65 0.5.3 β 0.75 0.65. 5 γ 0.75. 33 GS sc G S sl G S G S sc 3 sl 4 G S GS sc G 5 L Voltage scaling for Maximum dynamic range K 33

Operational amplifier (Op-amp) for active-rc filter R C A( s) A s 0 / p V V out in A0 s p ( / p ( A0 ) RC) s RC / p p dm p 0 0 p ndm p ( A ) RC A RC ( A0 ) RC RC p A 0 A 0 Gain /RC should be in this region. Phase -90 o -80 o The phase shift of an ideal integrator is 90 o at the unity-gain frequency which is /RC for active-rc integrator. Required unity-gain BW of opamp in active-rc filter > 0/RC /A 0 RC 0.*p A 0 p A 0 34

Gm-C filter IDEC 혼성모드시스템설계및실습

Gm-C integrator Transconductance (Gm) amplifier vin v in - - G m i out i out G m v in G m ( v v ) in in Gm-C integrator KCL v in v in - - G m i out C v out H(s) v v ( s) ( s) vout ( s) Gm ( s) v ( s) sc out in vin in Low power, high Speed Poor linearity Open-loop characteristics 36

Gm amplifier basics Transconductance (Gm) amplifier vin v in - - G m i out v in v in - G m Single-ended Fully-differential - - i out i out Transconductance amplifier characteristics Linearity I/O impedances i out G v G Operating (dynamic) range Frequency characteristics Electrically programmable Gm value R m in in, m R ( v v ) out in in 37

Gm amplifier : basic differential pair () i i v in M M v - in v x i i i β β out ( v v V ) in ( v v V ) i in i x x TH β v TH in I β SS v in i i ISS I SS I β 4ISS β V G in m Vin 4ISS β Vin II -I G m I SS 0 V in V in -V in - -I SS 0 V in V in -V in - 38

Gm amplifier : basic differential pair () Varying β Varying I SS I I I SS 0 V in 0 V in -I SS i out i i β v in I β SS v in for large I SS, small β & v in i out G m βi SS v βi SS in 39

Gm amplifier : differential pair with degeneration resistance () i v in M M v - in i V C i i i i R R C C I I B B i i ir C i RC I B R C IB M R v in i v out gs i i i RC R C R v C gs { v ( v v )} in v in gs gs for large β and small i - i i v gs out v R gs C v ( VTH i β) ( VTH i β) β( i i ) 0 in When R C Implemented by MOSFET R C β ( V V ) GS THN G M β ( V V ) GS THN 40

Gm amplifier : differential pair with degeneration resistance () Simple output stage Folded-cascode output stage V CMFB V BP V INP M M V GM V INM V BP M GM I B I B V BN V BN 4

Gm amplifier : differential pair w/ degeneration R and feedback V DD I B I B M 5 M 6 I B -i o v in M M - v in V C M9 I B i o i o M 7 M 3 M 4 M 8 I B I B Negative feedback loops (M-M5-M3 & M-M6-M4) forces constant currents I B to flow through M and M v gs v gs V SS Output currents available through current mirrors (M3-M7 & M4-M8) 4

Gm amplifier using MOS in linear Current in linear MOSFET i ds β ( v V ) v v gs TH ds ds Basic principle ( A C ) ( B C ) A B v v in in Example V C _ i i i β ( v V ) _ V C i β inp VC ( v V ) V V inm TH VC TH C C v inp v inm iout i i β inp [( v v ) V ] inm C 43

Gm-Opamp-C integrator Advantages Op-amp input virtually short Ease of designing Gm Small Ro allowed Small parasitic cap. effect Large DC Gain Disadvantages Reduced overall bandwidth Increased power dissipation Good CMFB required Increased noise level G M (s) OPA - V IN V OUT - 44

st order Gm-C filter C X i G m - V in (s) G - m i C A KCL V out (s) ( ) H s V V out in C X ( s) CA CX CA CX ks k ( s) G s ω0 s C s A m C G X m 0 G G m m C X k ω 0 0 k k ( CA CX ) ( C C ) A C A X 45

nd order Gm-C filter : biquad V in (s) KCL G - m4 A C A G m - G - m B G m3 - V out (s) C X G - m5 C B KCL ( ) H s V V out in ( s) ( s) C B CX Gm5 G s s CX CB CX CA Gm3 GmG s s CB CX CA B m ( C C ) ( C C ) m B X G m4 X k s s ks k ω0 s ω Q 0 0 46

High-order Gm-C filter with biquads 6 th order BPF for Japanese PDC x 8th-order BPF Average of f o : 450.5kHz σ of f o : ±.5kHz Tuning range of f o : 40~770kHz 0.35-µm CMOS Power : 4.8mA @.5V Active area :.5mm Fujitsu ( IEEE ISSCC, 999) 47

High-order Gm-C filter from LC ladder () 5 th order Elliptic low-pass filter Differentiator : impossible to implement 48

High-order Gm-C filter from LC ladder () 49

High-order Gm-C filter from LC ladder (3) 50

High-order Gm-C filter from LC ladder (4) 5

Effect of finite output resistance H(0) H(ω) H(s) v v out in Gm R sc R OUT OUT Finite DC gain at BPF and HPF Reduced phase (> -90 o ) φ E arctan G ω0 ω R m OUT 0 <H(ω) 0-90 ω 3dB ω 0 φ E ω ω Q decreases Q Q Q G m R OUT For φ E < o, G m R OUT > 57.3 (35dB) To Resolve, Cascode output stage Compensation technique 5

Effect of parasitic pole of Gm H(0) H(ω) H(s) v v out in G C m s ω p Increased Phase (< -90 o ) Q increases [ ω ] φe arctan ω p 0 <H(ω) 0-90 ω 3dB ω P ω 0 ω ω Q Q Q φ For φ E < o, ω p >57.3 ω o To resolve, Careful design Advanced process Intentional zero added E ω ω 0 p φ E 53

Effect of parasitic zero of Gm H(0) H(ω) H(s) vout vin Gm sc [ s ω ] z Decreased Phase (> -90 o ) [ ω ] φe arctan ω z Q decreases 0 ω Z ω ω 3dB ω 0 <H(ω) 0 ω -90 φ E 54

IDEC 혼성모드시스템설계및실습 Automatic tuning of continuoustime filters

Automatic tuning Frequency characteristics of continuous-time filter such as Gm-C and active-rc can vary as much as /-50% due to process, voltage, and temperature variations. Some kind of automatic tuning scheme is required to get the desired frequency characteristics. Direct tuning Directly measure the frequency characteristics of the filter and tune them till the desired characteristics are obtained. Tuning at power-up or during non-active period Master-slave tuning Measure the frequency characteristics of tuning master which is built with the same building blocks as the filter and tune the master till the desired characteristics are obtained. Then, the slave filter will have the desired characteristics as well if the master and slave filter match well. 56

Direct tuning () Gm-C biquad Frequency and Q-factor are tuned by making 57 ( IEEE Tran. CAS-II, pp. 755-, 003)

Direct tuning () 58 ( IEEE Tran. CAS-II, pp. 755-, 003)

Concept of master-slave tuning Tuning master Voltage controlled oscillator (VCO) or voltage controlled filter (VCF) implemented with the same integrators as in slave filter Frequency tuning loop Cut-off frequency Phase tuning loop Phase shift of integrator 59

VCO based tuning () Oscillation frequency is determined by time constant of the integrators (RC). By tuning the oscillation frequency to f ref, RC time constant can be controlled. Frequency tuning loop PLL 60

VCO based tuning () Phase lead of integrator means the pole is in LHP. Oscillation amplitude decreases exponentially. Phase lag of integrator means the pole is in RHP. Oscillation amplitude increases exponentially. No phase error in integrator Constant oscillation amplitude Phase tuning loop Amplitude locked loop (ALL) 6

VCF based tuning () Second order biquad has low-pass and band-pass outputs. 6

VCF based tuning () Frequency tuning If ω ref ω 0, The phase difference between input and output is 90 o. XOR gate is used to detect the phase difference. Phase tuning After frequency tuning is completed, ω ref ω 0. Phase error appears as the gain error, that is, error in Q value. 63

Single integrator based tuning () Basic element of analog filter is integrator. Why don t we use an integrator as a tuning master? Transfer function of integrator Active-RC filter : Gm-C filter : Frequency tuning Unity gain frequency of the master integrator is controlled, then the integrators in slave filter is also tuned to correct unity gain frequencies. Phase tuning H H ( j ) ( jω) ω jωrc gm jωc Phase shift at the unity gain frequency is tuned to -90 o. 64

Single integrator based tuning () Implementation in Gm-C filter Frequency tuning loop : g m is tuned till the gain at ω ref is. Amplitudes of input and output are detected by the full wave rectifiers RECT and RECT, respectively. 65

Single integrator based tuning (3) Implementation in Gm-C filter Phase tuning loop : Time constant of phase tuning loop is set to be much larger than frequency tuning loop so the frequency tuning completed first. Phase difference between input and output is detected by XOR gate and tuned to be 90 o. 66

How to give tunability to active-rc filter Frequency tunability can be given by Resistor array Capacitor array 3 Resistor and capacitor array 4 MOSFET in series with passive resistor R C 4 Phase tunability Compensation of non-ideal phase shift of op-amp by RHP or LHP zero 67

IDEC 혼성모드시스템설계및실습 Design exercise : Active-RC filter

Lab. : Synthesis of active-rc filter from passive proto R S C L C 3 R L Design target Cut-off frequency.5mhz Draw a block diagram of fully differential active-rc filter Optimize the dynamic range using signal flow graph For SFG, choose V S, V, V R S *I, and V 3 as vertex variables. Set R S 0kΩ. 69

Lab. : Design of fully differential op-amp Design target DC gain > 70dB Phase margin > 45degree with 5pF load capacitance VDD.5V Unity gain frequency > 00MHz CMFB for st and nd stages 70

Lab. 3 : Design of active-rc filter Design a fully differential active-rc filter using the results of lab. and. See if the frequency characteristic is the same as the passive prototype (of course, except for the cut-off frequency). Apply a two-tone sinusoid of MHz and.5mhz and see the output spectrum. By varying the input amplitude, you can find the in-band iip3. Apply a two-tone sinusoid of.5mhz and.5mhz and see the output spectrum. By varying the input amplitude, you can find the out-of-band iip3. 7