generator (M1G-M14G) and the active load (M27-M30) is displayed in Figure 3. CMFB comprises an error amplifier (M15-M18), n- channel (M19-M21) and ...
ON DESIGNING LINEARLY-TUNABLE ULTRA-LOW VOLTAGE CMOS gm-C FILTERS Jader A. De Lima1 & Carlos Dualibe2, 3 1
Electrical Eng. Dept., Universidade Estadual Paulista, Guaratingueta, Brazil Electrical Eng. Dept., Universidad Católica de Córdoba, Córdoba, Argentina 3 DICÉ, FSA, Université Catholique de Louvain, Louvain-la-Neuve, Belgium
2
ABSTRACT - A linearly-tunable ULV transconductor featuring excellent stability of the processed signal common-mode voltage upon tuning, critical for very-low voltage applications, is presented. Its employment to the synthesis of CMOS gm-C highfrequency and voiceband filters is discussed. SPICE data describe the filter characteristics. For a 1.3V-supply, their nominal passband frequencies are 1.0MHz and 3.78KHz, respectively, with tuning rates of 12.52KHz/mV and 0.16KHz/mV, input-referred noise spectral density of 1.3µV/Hz1/2 and 5.0µV/Hz1/2 and standby consumption of 0.87mW and 11.8µW. Large-signal distortion given by THD=1% corresponds to a differential output-swing of 360mVpp and 480mVpp, respectively. Common-mode voltage deviation is less than 4mV over tuning interval. I. INTRODUCTION The remarkable growth in battery-powered systems has demanded continuous efforts on improving ultra-low voltage (ULV) signal processing circuits. The trade-off between dynamic range, bandwidth, power consumption and chip area minimization and, hence, production costs has become a harsh task on designing such circuits. ULV filters can be employed where dynamic range is less strict, such as video and low-quality audio applications. Even though many transconductors reported to date can be reconfigured to meet ULV requirements [1-3], the dependence of the processed signal common-mode voltage on their tuning mechanism, which may severely degrade the filter linearity, hasn’t been thoroughly addressed. This paper introduces a differential-in differential-out ULV transconductor built around a triode-MOSFET whose smallsignal gm is linearly tuned by a dc voltage. Furthermore, an adaptatively-biased CMFB eliminates any meaningful deviation of the common-mode voltage on gm tuning so that signal swing is optimized. In the following sessions, large and small-signal operation of the transconductor are analyzed. Design procedures of tunable gm-C filters in the range of megahertz as well as voiceband filters suitable for micropower hearing aids are discussed. SPICE data are used to demonstrate circuit performance and tunability.
in triode region by means of a differential regulated-cascode loop whose feedback amplifier is made up by M2A-M5A M2B-M5B, M4C and M5C. This amplifier, corresponding to a folded-cascode OTA, is biased by wide-swing current sources IA and IB = kIA (k>1). Upon ideal matching, the tail current IA equally splits into M2A and M3A (M2B and M3B) and imposes identical VGS drops so that VTUNE is replicated to the drain of M1A (M1B). The current through M4A (M4B) corresponds to IB-IA=(k-1)IA. In addition, the loop amplification boosts the transconductor output impedance [4]. An ULV requirement is met since VGS drops are not stacked between the power-supply rails. To understand the replica mechanism, let’s momentarily assume VDS1A < VTUNE. This perturbation increments ID2A, which is compensated by a decrease on ID3A. As IB is constant, M5C current increases and so does the one delivered to the common node of M2A and M4A. Owing to a constant IA, such a current variation impels ID2A to decrease, canceling out the initial disturbance and settling VDS1A=VTUNE. Adopting usual terminology and first-order models [5], the large-signal output current corresponds to Iout =
W1 µnCoxVTUNE [( Vin − VTH1) − (1 + χ)VTUNE / 2] (1) L1
where χ=δVTH/δVBS = γ/[2(2ΦF+VBS)1/2]. Input voltage Vin is the applied signal vin superimposed to a common-mode voltage VCM, usually set to a reference VAGND. The linear dependence of gm on VTUNE is given by
gm = gm 1 A = gm 1 B =
δIout W 1 = µnCoxVTUNE δVin L1
(2)
It’s worthy noticing that the replica circuit works for VTUNE as low as 0V, making the transconductor attractive for lowfrequency applications. The boosted resistance seen through the drain of M6A (M6B) is roughly expressed as
rout ≅
gm 2 gms 6 1 gds 5 gds 6 gds1
(3)
II. TRANSCONDUCTOR DESCRIPTION The transconductor cell schematic is shown in Figure 1. A n-well CMOS process is considered so that sources of p-type FETs are tied to local substrates. Input signal is applied to a differential pair of grounded-source, triode-operated M1A and M1B whereas remaining devices are saturated. Input transistors are kept
The block diagram of a complete transconductor is shown in Figure 2. It features the basic cell with an active load that ensures high-impedance output nodes. A feedback circuit (CMFB) fixes to VAGND the common-mode voltage of Vout+ and Vout-. Moreover, it imposes a load current Io whose value ideally matches the transconductor quiescent current Iout @vin=0. This
structure can be seen as a pair of single-ended circuits whose output is balanced around VAGND. II.1 Adaptative-Bias CMFB Since gm-C filter topologies are mostly based on back-toback connected integrators, it’s essential that the tuning mechanism of internal sections doesn’t tamper with the signal common-mode voltage in order not to degrade linearity. Such a need becomes increasingly worrisome for ULV realizations where signal swing, inherently constrained by a small headroom voltage, would be further limited by common-mode voltage variations. As described by (1), Iout+ and Iout- are VTUNE dependent so that CMFB would not properly fix VCM to VAGND upon gm tuning unless Io exhibits identical dependence. A load current Io whose value is given by making Vin=VAGND in (1) should thus be generated. To accomplish that, a single-input single-ended version of the transconductor cell is used as an adaptative-bias generator. By setting its input to VAGND, a reference Io bearing the desired dependence on VTUNE is obtained. After scaling down, IBIAS = Io/B is mirrored to all stages. The schematic of the CMFB circuit, the adaptative-bias generator (M1G-M14G) and the active load (M27-M30) is displayed in Figure 3. CMFB comprises an error amplifier (M15-M18), nchannel (M19-M21) and p-channel (M23-M26) current mirrors. As discussed, it delivers an adaptative current Io to the load. Wideswing, cascoded current mirrors maximize the signal swing while improving mirroring. VCP and VCN are properly chosen to reduce the voltage compliance to 2VDSAT. The tail current of the error amplifier corresponds to the bias-generator output current Io divided by the factor B. Such a scaling reduces the saturation voltage of current-mirror devices. III. INTEGRATOR DESIGN Based upon the proposed transconductor, an integrator was sized according to a low-voltage, 1.2µm n-Well CMOS fabrication process. Nominal parameters are VTHN = 0.53V, VTHP= -0.57V, γn=0.35V1/2, γp=0.56V1/2, µn=494cm2/Vs, µp=182cm2/Vs and Cox=176nF/cm2. Channel encroachments for width and length are 0.75µm and 0.25µm, respectively. A single 1.3V-power supply gives a 200mV-margin over VTHN + VTHP . A trade-off arises between dynamic range, area minimization and integrator keyparameters such as unity-gain frequency fT =gm/2πC, output resistance and tuning interval. Design procedures for different frequency operations are now described. Unless otherwise stated, voltage-swings are fully-differential. a) High-frequency applications. A high gm leads to relatively large load currents. To maximize the output-swing, current mirrors with very high aspect-ratios are needed to keep VDSAT small. Stray capacitances may critically degrade the integrator excess phase [6] unless short channel-lengths are adopted at the expense of lower output impedance, however. Furthermore, large-sized current mirrors may considerably increase the chip area. Also imposed by the desired input swingrange, tuning interval is limited to the maximum VTUNE that still holds the input transistors on triode region. Nominal and maximum VTUNE values are 85mV and 170mV, respectively. Voltages VAGND and VCM are both set to
vinpeak+VTHN+VTUNEmax = 0.85V to permit a 300mVpp- swing. Transistor drawn dimensions are listed in Table 1 for IA=1µA, IB=1.5µA (k = 1.5) and B=10. Nominal gm and Io are 77.7µA/V and 19.3µA, respectively. For Iomax=54.1µA, the load voltagecompliance, expressed by VDD-VCM-vinpeak=300mV, is ensured by adopting (W/L)27eff =157 and (W/L)29eff=266 which limits VDSAT of M27 and M29 to 0.169V and 0.13V, respectively. Simulation was carried out with PSIPCE and BSim3v2 models. For CLOAD=5pF, dc-gain Adc=41dB and fT=1.16MHz @VTUNE=85mV. Linearity is given by THD=0.62% for Vout=300mVpp. Owing to large stray-capacitances, excess phase prevails over the tuning interval, with a maximum value of 2.87°. The benefits of the adaptatively-biased CMFB upon gm tuning are illustrated in Figure 4. Excellent stability of VCM against VTUNE is represented by a negligible 4mV-variation. Conversely, by making Io independent of VTUNE, VCM departures from VAGND could reach as much as 150mV, compromising up to 50% of the specified output swing. b) Low-frequency applications. Very-low gm values can be achieved by reducing both VTUNE and (W/L)1i. Although its effect is minimized by a balanced structure, random noise added to the tuning voltage may significantly affect the integrator characteristics for very small VTUNE values. A lower limit of 10mV is then imposed to VTUNE. As input-devices must operate in strong inversion, their sizing should comply with Io ≥ 2η(W/L)µCoxUT2 [7]. By setting Iomin = 20nA, (W/L)1i is tailored. To compensate for the gm reduction, rout should be raised to attain high dc gains and, consequently, reduce the phase-error. This is achieved by adopting long-channel load transistors. Moreover, these devices are sized to operate in weak inversion, improving the current mirroring while limiting VDSAT to 100mV, approximately [7]. The channel-length of M5i transistors is also increased to enhance rout. Table 2 shows the transconductor sizing for a low-frequency design. Other parameters are VCM=0.85V, IA=0.1µA, IB=0.15µA and B=1. At a nominal VTUNE=25mV, gm and Io are 0.22µA/V and 58.9nA, respectively. For CLOAD=5pF, fT=3.52KHz, Adc=105.3dB and a 1.4°-excess phase. Linearity is given by THD=0.27% @Vout=300mVpp. VCM deviation is below 1mV for 10mV≤VTUNE ≤ 40mV. IV. ULV FILTER DESIGN The integrators were employed to the synthesis of gm-C filters. Irrelevant VCM departures from VAGND upon tuning were observed in the designed filters a) High-frequency filter. Figure 5 shows the block diagram and specifications of a balanced 3rd-order elliptic low-pass filter with resistive termination using a gyrator-capacitor combination [2]. For a nominal 1MHz-bandwidth @VTUNE=85mV, the corresponding capacitors are C1=12.3pF, C2=1.5pF, C3=12.3pF and C=5.7pF [8]. The CMFB circuit features a 34dB open-loop dc-gain and a 10MHz unity-gain frequency, beyond thus the filter stopband frequency. The simulated transmission shown in Figure 6 gives passband frequency fp=1.01MHz, stopband frequency fs=1.90MHz, passband attenuation Amax=1.01dB and stopband attenuation Amin=36.2dB for a stand-by consumption of 0.87mW. Maximum output swing is 575mVpp. Large-signal distortion is given by THD=1% for Vout=360mVpp @VTUNE=85mV. As shown
in Figure 7, bandwidth is linearly adjusted by VTUNE at a tuning rate of 12.52KHz/mV. b) Low-frequency filter. A voiceband filter suitable for micropower applications was designed. Basic specifications were held by adopting C1=8.2pF, C2=1pF, C3=8.2pF and C=3.8pF. From the simulated frequency response shown in Figure 8 it turns out fp=3.78KHz, fs=7.53KHz, Amax=0.8dB and Amin=35dB @VTUNE=25mV and quiescent consumption of 11.8µW. The filter passband is linearly adjusted at a rate of 0.16KHz/mV. Maximum attainable swing at output is 580mV. A 1%-THD corresponds to Vout=480mVpp @VTUNE=25mV Inherent noise represents a fundamental limitation in ULV applications. Simulated input-referred noise spectral density for the high-frequency integrator and filter are 820nV/Hz1/2 and 1.3µV/Hz1/2, respectively. The corresponding noise figures for the voiceband counterparts are 1.87µV/Hz1/2 and 5.0µV/Hz1/. Statistical analyses on the effect of device mismatching upon VCM regulation were also carried out within the interval 30mV≤VTUNE≤170mV. Tolerances of 7% and 3.5% on (W/L) and VTH, respectively, were imposed to critically-matched M1A, M1B, M1C, M15-18 and M25-26. For a nominal VCM=850mV, a Monte Carlo analysis of high-frequency filter revealed minimum and maximum values of 830mV and 878mV, respectively, a mean of 850.06mV and σ=12.1mV. Worst-case analysis showed a maximum VCM of 880mV and a 4mV-variation with VTUNE. A test vehicle for the designed circuits was implemented and its layout is shown in Figure 9. Including on-chip capacitors, the effective area of the high-frequency filter corresponds to 0.97mm2.
99/04400-4) and continuous support on integrated circuits research and to FNRS (Belgian National Fund for Scientific Research). VII. REFERENCES [1] Pennock, J. - “CMOS Triode Transconductor for ContinuosTime Active Integrated Filters”, Electronic Letters, Vol.21, No.18, August 1985. [2] Krummenacher, F. & Joehl, N. - “A 4-MHz CMOS Continuos-Time Filter with On-Chip Automatic Tuning”, IEEE JSSC, Vol. 23, No. 3, June 1988. [3] Nedungadi, A. & Viswanathan, T. - ”Design of Linear CMOS Transconductor Elements”, IEEE Trans. on Circuits and Systems, Vol. 31, No. 10, Oct. 1984. [4] Bult, K. and Geelen, G.: “A Fast-Settling CMOS Op Amp for SC Circuits with 90-dB DC Gain”, IEEE JSSC, Vol.25, No.6, Dec. 1990. [5] Tsividis, Y. P. - “Operation and Modeling of the MOS Transistor”, McGraw-Hill Inc., 1988. [6] Khorramabadi, H. & Gray, P. - “High-Frequency CMOS Continuos-Time Filters”, IEEE JSSC, vol. 19, No. 6, Dec 1984. [7] Vittoz, E. - “Micropower Techniques”, Design of VLSI Circuits for Telecommunications and Signal Processing, Prentice-Hall, 1994. [8] Van Valkenburg, M. E. - “Analog Filter Design”, Oxford University Press, 1982.
Iout-
I out+ M5C M5A
M5B
1
1
V. CONCLUSION
1
M6A
A linearly-tunable ULV CMOS tranconductor was introduced. By means of an adaptative biasing, a CMFB circuit allows a steady regulation of the signal common-mode voltage VCM against the tuning voltage VTUNE. Trade-off between signal swing, power consumption, bandwidth and area minimization was analyzed. Design procedures for low- and high frequency integrators were discussed and applied to the synthesis of a 3rdorder elliptic low-pass filter. Dc and ac operation of basic circuits was simulated by PSPICE. From a specified 1.3V-supply, integrators parameters were THD=0.62% @fT=1.16MHz and THD=0.27% @fT=3.52KHz for Vout=300mVpp. Departures of VCM from the reference VAGND were as low as 4mV over the tuning interval. Such a VCM regulation is also confirmed by statistical analyses in case of standard device mismatching. For both designed filters, maximum allowed output swing is around 575mV. The high-frequency filter presented a nominal fp of 1MHz, linearly adjusted at 12.52KHz/mV, THD=1% for Vout=360mVpp and input-noise density of 1.3µV/Hz1/2. For a voiceband filter, fp=3.78KHz at a tuning rate of 0.16KHz/mV, THD=1% for Vout=480mVpp and a 5.0µ/Hz1/2 noise figure. Its stand-by consumption of 11.8µW makes it attractive for micropower applications such as hearing aids.
M6B
The authors would like to express their thankfulness to Brazilian Foundation FAPESP for financial assistance (grant
M4C
Vin+
IA
Vin-
M4A
VTUNE
VTUNE M2A
M3A
M3B
M2B
M1A
Vin+
gmcell
M4B
M1B
VTUNE
IA
IB
IA
Vin-
VTUNE
Figure 1. ULV transconductor cell (inset: symbol)
Active Load
I BIAS
Io Vout-
CMFB
I out+
VAGND
IBIAS
Io Vout+ I out-
Vin+ Vin-
Vout+ gm
Vout-
VTUNE
V TUNE
VI. ACKNOWLEDGEMENS
VBIAS
IA
gmcell V in+
V in-
Figure 2. Complete transconductor (inset: symbol)
I out+ I out-
Adaptative-Bias Generator (1X)
CMFB
1
B
M12G
M10G
VCTL
B
B
B
B
M30 M27
M24
Io
M5G
M15 M16
M6G M4G
M7G
M3G
M2G
1
M1G
IA
I o /B
1
1 M13G
I out+
800
I out-
I o /B
1
adaptative Io non-adaptative Io
M21 1
650 30
M22
M20
VTUNE
IA
VCN
M19
1
Vout+
M17 M18
VAGND
I o I BIAS
VTUNE
VCM [mV]
Io
VoutIA
VBIAS
950
M28
M23
M11G
M29
Io '
1
1
M9G
M8G
1
M25
VCP
1
B
Active Load M26
1
M14G
V AGND
100
170
VTUNE [mV]
Figure 3. Adaptative-bias generator, CMFB and active load
Figure 4. Common-mode VCM against VTUNE
C2
20dB
fp = 1 MHz fs = 2 MHz Amax < 1dB Amin > 34dB
R C1
Vin
L2 C3
R
Vout
0dB
2C 2
Vin
gm1
gm2
+
-
2gm
-
+ -
gm
+
gm3
+
C1
+ + 2gm -
-20dB
gm4 + gm
-
gm5
+ -
2C
gm +
gm6 -
-
2gm
+
+
+
gm7 C3
gm +
-
Vout
-40dB
+
VTUNE -60dB 10KHz
2C 2
Figure 5. Balanced 3rd-order gm-C elliptic filter
30KHz
100KHz
300KHz
1MHz
3MHz
Figure 6. High-frequency filter response
20dB
2.09 0dB
F 3dB [MHz]
-20dB
1.214
-40dB
0.337 30
100
170
-60dB 100Hz
VTUNE [mV]
Figure 7. 3dB-cutoff frequency tuning
W(µm) L (µm)
M1i 24 2.4
M2,3i 10 5
M4i 4.8 1.2
300Hz
1KHz
3KHz
10KHz
30KHz
100KHz
Figure 8. Voiceband filter response M5i 16 4
M6i 20 1.2
M9G 150 1.2
M10G 360 1.6
M13G 12 1.2
M14G 24 1.6
Figure 9. Test-vehicle layout M15-18 24 2.4
M23 15 1.2
M25 36 1.6
M27 150 1.2
M29 360 1.6
M23 150 12
M25 360 16
M27 150 12
M29 360 16
Table 1. High-frequency transconductor sizing
W(µm) L (µm)
M1i 5 48
M2,3i 10 5
M4i 4.8 1.2
M5i 16 4
M6i 40 8
M9G 15 12
M10G 36 16
10MHz
M13G 12 1.2
M14G 24 1.6
M15-18 24 2.4
Table 2. Low-frequency transconductor sizing
