A VHF OTA-C Topology Having Low Phase Error WithGm Tuning

Kshitij Yadav and Pradip MandalElectronics & Electrical Communication Engineering Department,

Indian Institute of Technology,Kharagpur, India

Kshitij.YadavWiitkgp.ac.in and pradipWece.iitkgp.ernet.in

Abstract- In sub-micron process, while speed of device issuitable for VHF applications, phase variation at unity gainfrequency of OTA-C cell with frequency tuning is high. This ismainly because of high value of channel length modulationparameter of the devices. A technique which makes the phaseresponse robust to frequency tuning is proposed here. Basedon this technique a VHF CMOS OTA-C cell is designed in a.18u CMOS process. The phase error of the cell is within .3 ,

over a range of unity-gain frequency from 300MHz to 1.2GHz.The small phase error over a wide range of frequency impliesthe use of just one Q-tuning loop for all the integrators havingunity-gain frequency within this range. Also this makes thiscircuit suitable for application in programmable transferfunction filters.

I. INTRODUCTION

OTA-C filters find extensive use in hard disk drivers filters,sigma-delta ADC and IF transreceivers. Phase equalization,anti-aliasing and polyphase filtering being the respectiveapplications.

Integrators are the basic building blocks of thesefilters. Key parameters of an integrator are its unity gainfrequency (fug) and quality factor. The unity gain frequencyof an OTA-C cell is given by is Gm / 2 TCintg, where Gm istransconductance of the OTA-C cell and Cintg. is theintegrating capacitor. Quality factor of an integrator isdefined as the reciprocal of phase error at unity gainfrequency [1]. OTA-C cells are often accompanied by f-tuning and Q-tuning circuits to take into account thevariation of these parameters with process and temperature.

Over a particular application, the transconductanceof the integrators used may differ appreciably. Generally,widely varying Gm of the integrators makes the use ofseparate Q-tuning loops for each integrator necessary.However, making the Q factor independent of Gm will notonly result in use of one Q-tuning loop, but will alsofacilitate the implementation of programmable transfer

functions [2]. [3] proposes an enlightening way of makingthe phase error independent of the Gm-tuning.

In this paper, we show that in sub-micron process,due to high value of channel length modulation parameterphase response is highly dependent on d.c. operating point.Hence, the phase at fug changes with Gm tuning. Based onthis observation a VHF topology is adopted where the phasevariation with frequency-tuning is reduced.

II. PROPOSED TOPOLOGY & PHASE ROBUSTNESS WITHFREQUENCY -TUNING

For VHF applications choice of OTA-C topologies isrestricted to ones which lack internal nodes [1] ,[4]-[5]. Thetopology proposed in [4] is among the most promising.Apart from good high frequency response some of theadvantages of this topology are: First, Output commonmode level is stabilized by diode connected PMOStransistors, which eliminates the need of expensive CMFBand CMFF circuits. Second, use of cross-coupleddifferential pairs results in high linearity. Also, constant tailcurrent ensures that for long-channel devices the phase erroris small even as the transconductance is varied. However,this topology does not ensures a small phase error for short-channel devices.For this OTA, the transconductance is given by:

Gm=2KVB (1)

Where VB which is the difference between gateoverdrive voltages of the two differential pairs, is used totune the Gm.. The circuit presented in this paper is derivedfrom this topology. Instead of the VB we propose to use thedifference between their tail currents to tune the Gm. of theOTA cell. The proposed OTA cell is shown in Fig. 1. Thetail current difference is in turn controlled by VWne. At thesource end of M13-M14 a non-ideal current source is usedto achieve robustness of phase with Gm. The non-idealcurrent source is represented by a Norton equivalent model.

0-7803-9584-0/06/$20.00(2006 IEEE. 2327

NRLII dd

VCQ

Fig. 1. Proposed OTA with a non-ideal current source for robust phase response.

Vdd

tune CO

The phase error at fug is given by:

AO = 1wugrCintg

r=2(RNI rd,5,71 IrdS6,8), RN being the negative NRL resistance.

(IW tune co

Fig. 2 Current-mode biasing for f-tuning voltage and VCQ.

Biasing and tuning in current-mode (Fig.2) ensures goodPSRR.

The topology offers a large dc gain, as the resistanceseen looking into the drain of differential pairs M5-M8 iscompensated by negative resistance of the cross coupledPMOS transistors M1-M4.

1 1 1

RN rds5,7 rds6,8(gm6 -g )

(3)

Let us say, initially the NRL resistance fully compensates

the NMOS resistance, we calculate deviations (A) fromthis ideal case as Vt.1e is varied.

RN-gm2 + + gm, (4)

RN rdSI rdS2Assuming M5=M7, M6=M8, and applying approximation

1 +x =1+x/2 change in NRL is given by:

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(2)

A( 1 2A(d5 +Ad6) _K(K VK)[AJd5 +Jd6] (5)RN 1+AVds12 2(Id5 + Id6)

Since, initially we assumed NRL to be compensatingrds5,7 rds6,8 completely, order of (,rK K2)1 2(Id5 + Id6 )

is same as that ofA, while AId5 and AId6 vary withopposite signs. Thus NRL resistance is practically constantas Vlune is varied. Resistance seen looking into the drain ofthe diff. pairs changes with f-tuning, according to theequation:

A( 1 LAJd5 + AJd( (6)rds5,7 rds6,8 1+ Vds5,7 1+ Vds6,8

Since variation in RN is small, for a robust phase we requirethe positive resistance variation, shown in (6), to be ideallyzero even as V1une is varied. Assuming M9=MIO,Ml1=M12, M13=M14 (6) implies the following conditionon changes in drain currents ofM13 and M14.

Al,13 (1+ AVd-s5,7) (1+A' 10sl ) (I+A' Vds

ad 14 (1±+ ds6J8) (1+A'Vds9) (1+A&Vdsl2)

AId,=> dl_- -VB )(7)

'.is the channel length modulation parameter for M9 -M14. Since bandwidth of OTA is determined by high speedoperation of M5-M8, minimum L (for a given technology)for these transistors implies A > A' . We ignore the effectof i' and higher order A terms. VB is the difference in theoverdrive voltages of the two differential pairs and,

Adsl3, AIdsl4 in (7) are the changes in drain currents ofM13 and M14 as V1une is varied (f-tuning), neglectingchannel-length modulation.

For purpose of simplicity we consider two extremes of acurrent source:

a.) Current source is idealFor modem day transistors, with larger value ofA an idealcurrent source does not satisfy the condition (7). Thus, useof an ideal current source can not ensure small phase erroras the frequency is tuned.

b.) A small-valued resistance

Assuming the square I-V law to be valid for transistors and

assuming AVy <<AVue and K13 KI4, we have:

AIdsl3 -(VY- VcQ -VTH) AVy

Adsl4 (VY -FV/une- VTH) AV1uneand

AVy = -RAI

(8)

(9)

Vy is the voltage at the source end ofM13-M14.Where I is the current through the resistor R. Combining (8)and (9) and assuming that

- Mdsl4We have

AIdsl3 _-2RK13(VY -VCQ -VTH) (10)

Combining this with (7) the condition for zero phase erroris:

2RK13 (VY VCQ VTH) = (1-AAVB) (1 1)

As the frequency is tuned by changing V,ne, both VBand Vy vary, but in opposite sense, so (11) remains validover a wide range of Vw,1, values. Since for a small resistor

value the change in Vy is small compared to change in VB,a necessary condition for phase robustnessis2RK13 >> i. This equation puts a limit on theminimum possible value of R we can use, for a givenprocess.

Condition in (11), must be satisfied for phase error to besmall. Any mismatch between the two sides of (11) can beadjusted by varying the value of R, hence R is used for Q-tuning. For transistors with appreciable channel-lengthmodulation, a carefully chosen value of R results in smallphase error over a larger range of transconductane valuesthan an ideal current source. Note that in the proposedcircuit none of the internal nodes carry a high frequencysignal.

III. SIMULATION RESULTSVerification of this theory was done in .1 8u CMOS process.The circuit in Fig. 1 was designed for a nominal unity gainfrequency of 750MHOz. with an integrating capacitor of lpF.Unity gain frequency was then varied from 250MHz to1.2GHz by changing Vw,ne (280mV to 600mV),VcQ=700m.In the design the total tail current (M9 and M1O) is 1.8mAat the nominal point. Values of IC=0 and R=200 Q give a

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-+ 1 /(rds57lIIrds668)-t 1/IRNI-I- conductance across Cintg.+.48mS

X1 ZIt

-_ -_ t

~~-n~~X-----

800Unity gain frequency (MHz)

1200 1400

Fig. 3. Variation ofNRL conductance (magnitude), conductance looking into the drain of differential pairs and net conductance across integratingcapacitor (actual value +.48mS).

desirable phase response in this process. The simulatedphase response is shown in Fig. 4. The phase error is within+ 3 ° over this frequency range. It is well compensatedwith a convex profile. This is because of a similar variationin 1/(rdS5,7 rds6,8) while RN is relatively constant (Fig. 3) withf-tuning as suggested by equation (3).To measure process sensitivity of the circuit it is

simulated at slow and fast process corners also. It is

fl,z

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062

0D.,

d 0

N.

4~~~~~~

s \~~~~~~

I I

, 4;1-1EtSw - e

@: ~ ~ ~~~~I--, . ,*~A.Ea

nily gain teqlency (MHil

observed that to attain low phase error around the nominalfrequency the resistor R need to be adjusted to 110 Q and350 Q for slow and fast process corner respectively. Phaseerror at slow corner is from - 30 to +. 3 5 ° with over

400MHz to 770MHz. fug range. For fast process corner thephase error is within _3° with a fug range of 550MHz to1.1GHz.

For performance comparison the topology in [4] is

OTAP papsd 141efpicl corner

FPpUs,e TA

;-¢ypical C rmer

. st corner

10[3 1200 *1400

Fig. 4. Comparison of phase error between proposed OTA (slow, fast and typical corners) and OTA in [4].

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4.85~

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4.75 -

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4004 hS

IU.A

4--

I

I

FV

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-0.3 :

r _.r- _ _ r _ r r A I __g, _ U rm.. ... ........ ,,,,,. E .. ._.m. S. g lI_ a - W 4 .......... ----- - I |ra a r-raFig. 5. Gain and phase plots for proposed OTA with unity gain frequencies

tuned from 300M to 1.2GHz.

simulated in the same process with similar bias conditionand with same nominal fg. The corresponding phaseperformance at typical process corner is shown in Fig. 4.For a phase error of +. 3 0 the fug range is from 600MHz to850MHz. To conclude the comparison, for the sameallowable phase error, the frequency range of the proposedOTA is almost four times of that of OTA in [4]. Note thatfor stand-alone integrators RHP may cause instability, butintegrator applications usually involve feedback which leadsto stabilization. So in our analysis we have consideredpositive phase error also as a possible region of operation.

tuning, while for sub-micron devices the trend shiftstowards the use of a small valued resistor. Inverted parabolanature of the phase error curve (Fig. 4) is exploited toimprove the frequency range. An implementation in a .1 8uprocess, the range of fug for acceptable phase error isimproved from 250 MHz (OTA in [4]) to 950 GHz.An optimum design will be one in which the non-monotonicportion of the phase error curve is within the frequencyrange of interest. This type of phase response not onlymeans that just one Q-loop can be used for integrators withwidely different unity gain frequencies, but also facilitatesthe implementation ofprogrammable transfer functions.

An interesting research will be compensating thedifferential mode impedance variation with change in Gm ofthe OTA (with f-tuning) in order to keep phase error smallfor still larger ranges of fg. Future work will involveimplementing the circuit on silicon.

ACKNOWLEDGMENT

The authors would like to acknowledge the technicalassistance from the Advanced VLSI Design Laboratory, IITKharagpur.

REFERENCES[1] H. Khorrambadi and P. R. Gray, "High-frequency continuous-time

filters," IEEE J. Solid-State Circuits, vol. 19, pp. 939-948, Dec. 1984.[2] R. L. Geiger and E. Sinchez-Sinencio, "Active filter design using

operational transconductance amplifiers: A tutorial," IEEE CircuitsDevices Mag., vol. 1, pp. 20-32, Mar. 1985.

[3] E. J. van der Zwan, E. A. M. Klumperink, and E. Seevinck, "ACMOS OTA for HF filters with programmable transfer function",IEEE Journal of Solid-State Circuits, vol. 26, No. 11, pp. 1720-1724,November 1991.

[4] S. Szczepa'nski, J. Jakusz, and R. Schaumann, "A linear fullybalanced CMOS OTA for VHF filtering applications," IEEE Trans.Circuits and Systems, II, vol. 44, pp. 174-187, Mar. 1997.

[5] B. Nauta, "A CMOS transconductance-C filter technique for veryhigh frequencies," IEEE J. Solid-State Circuits, vol. 27, pp. 142-153,Feb. 1992.

IV. DISCUSSION & CONCLUSIONAn OTA-C topology with robust phase response isproposed. Operation of the OTA is based on the use of anon-ideal current source. It is analyzed that for long-channeldevices, an ideal current source makes the phase robust to f-

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