Low-voltage Cmos Syllabic-companding Log Domain Filter

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Low-Voltage CMOS Syllabic-Companding Log Domain Filter Ippei AKITA, Kazuyuki WADA, and Yoshiaki TADOKORO Graduate School of Engineering, Toyohashi University of Technology, Toyohashi, 441–8580, Japan Email: [email protected] Vin Abstract— This paper presents a low-voltage CMOS syllabiccompanding log domain filter with wide dynamic range. The proposed filter is synthesized based on the idea of varying a voltage which is fixed on a dynamically adjustable biasing (DAB) filter. A low-voltage envelope detector necessary for a DAB filter is also designed including quantization mechanism. Simulation results show the proposed filter is effective in widening dynamic range. I BIAS Iin Vin Ms Vout Min Mout Log Domain Filter Core 0 II. T HE L OW VOLTAGE S YLLABIC -C OMPANDING L OG D OMAIN F ILTER A schema of a filter based on the DAB technique is shown Fig. 1. In this circuit it is assumed that all MOSFETs are in weak inversion region where a drain current Id of an arbitrary MOSFET exponentially depends on its gate-to-source voltage Vgs as Id = IS exp(Vgs /nUT ). IS is a current dependent on a fabrication process and proportional to an aspect ratio, and n and UT are a slope factor and a thermal voltage, respectively. The diode-connected MOSFET Min logarithmically converts an input current Iin into a voltage Vin with an amplitude moderate enough to expand signal-to-noise ratio (SNR) of an output Iout without distortion. Mout expands a log domain voltage Vout to provide an output current Iout which is linear with Iin . The appropriate adjustment of the log-compressing 0-7803-9390-2/06/$20.00 ©2006 IEEE Vb M0 I. I NTRODUCTION Low-voltage CMOS analog circuits are in great demand for portable devices. Dynamic range of a non-carefully designed analog circuit with a supply voltage decreased becomes narrower than that with a higher voltage because of small voltage swing. A dynamically adjustable biasing (DAB) [1] [2], which has syllabic companding effects, is an attractive technique to realize wide dynamic range signal processing. Since the DAB technique changes bias voltages of internal nodes, there has been a problem that its implementation under a low supply voltage still becomes difficult. In this paper, a solution of the above problem is proposed by appropriately changing a nodal voltage which has been fixed in the conventional DAB based filter. The proposed filter includes a low-voltage quantized envelope detector which outputs three value currents. Simulation results show that the proposed filter has the effectiveness of wide dynamic range for low-voltage operation compared with a conventional filter using only the DAB technique. VDD Iout envelope of Iin :I g Fig. 1. Example circuitry of dynamically adjustable biasing(DAB) log domain filters(one half only). ratio, which is calculated as a differential coefficient of a logarithmic function, for wide dynamic range of AC components can be realized by adaptively changing input bias current Ig . Ig can be an arbitrary signal for a linear signal processing but is often an envelope of Iin to obtain a large swing of Vin . An effect due to adding Ig to an input signal can be avoided by additional use of a circuit shown in Fig. 1 with an input replaced by −Iin and subtracting its output current from an output responding to Iin [1] [2]. In addition MS , M0 and a current source IBIAS compose a level shifter with a low output impedance at the source node of MS due to negative feedback. In a filter based on the DAB technique an AC component of Vin does not vary much and the dynamic range can be widen. Nevertheless, it is difficult to apply the DAB-based schema shown in Fig. 1 to a low-voltage filter because the bias voltage of Vin changes when Ig does. The smaller the magnitude of Iin is, the lower the bias voltage of Vin becomes, and a large magnitude of Iin causes the bias voltage to be too high. For avoiding the problem of the change of Vin corresponding to Ig control of a source voltage of MS is considered here. Figure 2(a) shows an overall schema of the proposed syllabiccompanding log domain filter which is a pseudo differential version of Fig. 1 except for a different current of MS , that is Ig underlined. The log-compressing function Vinp of Iinp realized by Minp and the exponentially-expanding function Ioutp of Voutp by Moutp are given by
 Iinp (1) Vinp = nUT ln 1 + + Vb Ig
and 3337 Ioutp = Ig exp Voutp − Vb nUT  , (2) ISCAS 2006 Iinp Envelope Detection Ig I BIAS Iinp Ig Ig Ig Minp Iinm Minm Vb Vinp Voutp Vinm Voutm M0 (a) Mp2 2 Vinp M2 Mf SVC current : Ioutm Mp4 SVC current : I2 nUTC2 M6 C1 M5 I g’ Ig Voutp M7 M4 4 Pseudo Differential Log-Domain Filter Core M3 M1 4 Moutp Mp3 I g’ nUTC1 Ig I1 Iout Ioutp Moutm Ms VDD Mp1 VDD State Variable Correction (SVC) C2 M8 (b) Fig. 2. The overall syllabic-companding log domain filter. (a) The proposed syllabic-companding log domain filter circuitry, (b) Second-order low-pass log domain filter core (one half only) [5] with the additional current sources for state variable correction (SVC). respectively. Since the first term in the right-hand side of Eq. (1) becomes 0 for Iinp = 0, the term does not contain a DC component of Vinp . This fact implies that the bias voltage of Vinp is kept constant Vb in spite of adding Ig to Iinp at the input terminal. It is also proven from the only AC component in the equation that this circuit takes over a feature of a constant swing of Vinp even with an amplitude of Iinp varied because of Ig tracking the amplitude as an envelope of Iinp . The output voltages Voutp and Voutm of pseudo differential log domain filter cores explained below are expanded by Moutp and Moutm in accordance with Eq. (2), and Ioutm is subtracted from Ioutp by using a pMOSFET current mirror to delete an output disturbance which appears in an expression of Ioutp without Voutp as an unnecessary additional term due to injection of Ig into an input signal. Figure 2(b) shows a schema of the second-order low-pass log domain filter core presented in [5]. MOSFETs M1 to M4 , Mp1 and Mp2 , and a capacitor C1 consist the first integrator, and the other MOSFETs and C2 do the second integrator. Mf is used for negative feedback. The additional current sources, nUT C1 Ig
/Ig and nUT C2 Ig
/Ig connected in shunt with the capacitor nodes, are required for realizing externally-linear operation. These current sources are called as state variable correction (SVC) circuits and can be considered to compensate for nonlinearities. The necessary compensation signals are obtained by solving differential equations of Iinp and Ioutp including a log domain filter core [3] [4]. Applying this log domain filter core to the proposed syllabic-companding filter shown in Fig. 2(a), Ioutp and Ioutm have linear relations with Iinp and Iinm , respectively, and thus written as Ioutp (s) = H(s)(Iinp (s)+ Ig (s)) and Ioutm (s) = H(s)(Iinm (s)+ Ig (s)) where H(s) = s2 2Ω1 Ω2 . + (Ω1 + Ω2 )s + 2Ω1 Ω2 (3) In addition Ω1 and Ω2 are unity gain angular frequencies of the first and the second integrators, respectively, which are determined as Ω1 = I1 /(nUT C1 ) and Ω2 = I2 /(nUT C2 ). Letting Iinp and Iinm relate to Iin as Iinp − Iinm = 2Iin and an output current Iout be Ioutp − Ioutm obtained by use of a pMOSFET current mirror, the total transfer function becomes Iout (s)/Iin (s) = 2H(s). Therefore, Ig is eliminated and the filter has linear relation between Iin and Iout . III. T HE L OW VOLTAGE P EAK D ETECTOR AND S TATE VARIABLE C ORRECTION C IRCUIT The DAB technique requires a control signal Ig and it should be an envelope of Iin for wide dynamic range. Since realization of a perfect envelope detector under a low voltage is difficult, not a perfect envelope but a quantized one is used as Ig . This choice does not inherently cause any distortion because any signal is available to Ig to obtain a linear filter. Figure 3(a) shows a three-value quantized envelope detector and a circuit generating a current nUT CIg
/Ig (C = C1 or C2 ) for SVC. In Fig. 3(a), the comparator A1 , diode D1 , and a holding capacitor CH compose a voltage peak detector of V1 which is converted from Iinp by the diode-connected MOSFET Ma . The output of A1 becomes high only when V1 is greater than a held voltage V2 , and then the CH is charged by a current flowing through the diode D1 to make V2 hold a peak value of V1 . In order to discharge for CH , an inverter, a switch, and Md are added. Md produces a discharge current Idis which decides discharge speed of CH . Two comparators A2 and A3 compare the peak voltage V2 with two reference voltages, which are determined by reference currents Iref 1 and Iref 2 through diode-connected MOSFET Mb and Mc . Then, two 1-bit signals of comparison results are fed to a decoder for switching reference current sources through D Flip-Flops (DFF’s). Although outputs of A2 and A3 probably 3338 I ref2 Iinp I ref1 V1 DFF I dis A2 Q V2 D Md Discharge current Decoder D1 Ma Mc gain [dB] Mb A1 A3 CH Q 10k Ig=5.6uA 100k 1M (a) 10M 10k 100k 1M (b) 10M freq. [Hz] Fig. 4. Frequency Responses in cases the each Ig , (a) The DAB filter, (b) The proposed filter. D I dis Ig=900nA Ig=100nA 20 10 0 -10 -20 -30 -40 -50 -60 -70 1.5 bit structure is employed. Furthermore the diode D1 in Fig. 3(a) is realized by the equivalent circuit drawn in Fig. 3(c) which is used as a log domain integrator core in Ref. [3]. The fact that an output current Ido equals IB exp{(Vi − Vo )/nUT } implies that this circuit is an equivalent diode except for a current of a terminal where Vi is applied. Because an input impedance of this circuit is very high, the comparator A1 does not need to drive D1 with a large output current. Use of this equivalent circuit is suitable for low-voltage realization of A1 . VDD CL Mp6 Mp5 Mp7 RL IB Ig X Mn2 Mn1 nUTC Ig IB C I ref1 I ref2 I ref3 (a) I g’ Ig SVC Circuit VDD IV. S IMULATION R ESULTS OUT The proposed syllabic-companding log domain filter is simulated together with a conventional filter based on the DAB technique, which is called as a DAB filter hereafter. In a DAB filter a potential of a common-source node of compressing and expanding parts and a log domain filter is fixed as shown in Fig. 1 and an envelope detector is the circuit illustrated in Fig. 3. All aspect ratio (width/length) of Minp , Minm , and MS are set as 20µm/1µm and those of Moutp and Moutm are as 80µm/1µm. These filters are designed using a 0.35-µm CMOS process and a 0.8-V supply voltage VDD . Obtaining the second-order low-pass Butterworth frequency response with a 100-kHz cut-off frequency fc , 1.0 µA is 2 chosen as bias √ currents I1 and I2 , and 2Ω1 Ω2 = (2πfc ) and Ω1 +Ω2 = 2(2πfc ) from Eq. (3) are solved for capacitances. As a result of calculation both C1 and C2 are set as 80 pF. In the three-value quantized envelope detector reference currents are chosen as Iref 1 = 100 nA, Iref 2 = 900 nA, and Iref 3 = 5.6 µA. Therefore it is determined that 5.6 µA is also set to IBIAS of the DAB filter for making the maximum input range of two filters almost equal. The proposed filter has more current consumption as about 20 µA than the DAB one due to extra SVC circuit and some current mirrors. Frequency Response: Figure 4 shows AC responses of Iout in cases that Ig is fixed at some different DC values, These filters have about 17-dB passband gain because of a gain of 2 derived from the pseudo differential schema and a ratio 4 of sizes of Moutp and Moutm to those of Minp and Minm . Cut-off frequencies of the proposed filter are kept at around 100 kHz, while that of the DAB filter decreases as Ig becomes small. This is because a low Vinp decreases drainsource voltage of M4 , and then a MOSFET as a current source I1 cannot be in saturation region. OUT (b) VDD IB I do Vo Vi Md1 I do Vi Vo Md2 Md3 (c) Fig. 3. Building blocks. (a) Three-value quantized envelope detector and the SVC circuit, (b) Comparator circuit A1 , A2 and A3 , (c) Equivalent diode circuit with a high-input impedance. very often flop due to ripple of V2 , frequent switching is undesirable. For relaxing this problem, DFF’s load outputs of the comparators only when the output of A1 is high, i.e. in charge phase for CH . Any of the decoded three signals is high and a corresponding current, Iref 1 , Iref 2 , or Iref 3 , is selected as a quantized envelope signal of Iinp . This current flows in Mp5 and Mp6 mirrors it. A resistor RL and a capacitor CL are employed as a simple low-pass filter for avoiding too large an output current due to differential operation of SVC circuit itself. A schema of comparators A1 , A2 , and A3 used here is shown in Fig. 3(b) where a positive feedback (regenerative) 3339 6u 100u Iout@Prop. Iout@DAB Noise@Prop. 100n THD@Prop. 10n 1n Noise@DAB 100p 10p 100n input curret [A] (a) 1u 10u 300u 400u (a) 500u 600u 700u time [sec] 500m Prop. 30 Vinp [V] SNDR [dB] Iin 200u 550m 50 DAB 20 450m 400m Vinp@Prop. 350m Vinp@DAB 300m 10 0 0 100u 60 40 2u -2u THD@DAB 10n Ig 4u 1u Iin & Ig [A] current [A] 10u 250m 10n 100n input curret [A] (b) 1u 100u 200u 300u 400u (b) 500u 600u 700u time [sec] 100u 200u 300u 400u (c) 500u 600u 700u time [sec] 10u 15u 10u Iout [mA] Fig. 5. Dynamic Range characteristics at a 100-kHz sinusoidal input current. (a) The fundamental of Iout , total harmonic distortion (THD) components, and output current noises in r.m.s. versus input current Iin , (b) Signal to noise plus distortion ratio(SNDR) versus Iin . 5u 0 -5u -10u Signal to Noise plus Distortion Ratio(SNDR): Figure 5(a) shows the magnitudes of the fundamental components, the total harmonic distortions (THDs) of output currents, and the output noises in r.m.s. versus the amplitude of a 100-kHz sinusoidal input current Iin on the horizontal axis. The plots of the fundamental magnitude are simply denoted as “Iout ” and the THD is defined as the summation of the 2nd to the 9th harmonic components in the sense of r.m.s. In addition an RMS noise is calculated as an r.m.s. value of an output noise current during one period. In Fig. 5(a), the fundamental of a conventional DAB filter begins to decrease when Iin is nearly equal to 900 nA. This is consistent with results shown in Fig. 4 where cut-off frequencies of the DAB filter are degraded when Ig = 900 nA and Ig = 100 nA. The SNDR of the proposed filter in Fig. 5(b), which can be obtained from results of Fig. 5(a), is high in a wider range than that of the DAB filter because the fundamental keeps following the input level even for a relatively small input. Therefore, it is confirmed that dynamic range of proposed filter is greater than that of the DAB filter in Fig. 5(b) when the input range of triple or more decades is needed. Transient Response: Figure 6(a) shows a 100-kHz sinusoidal input signal with an envelope changed as well as Ig which is an output of a quantized envelope detector in Fig. 3(a). In Fig. 6(b) waveforms of the log-compressed voltages Vinp ’s of the DAB filter and the proposed one are depicted. It is verified that the bias voltage of Vinp of the proposed filter keeps almost constant value, while that of the DAB filter changes as Ig does. Figure 6(c) shows the output current Iout of the proposed filter. When it is about 200 µsec., for example, the magnitude of the envelope of Iout is equal to 4.6 µA and the gain is 4.6 µA/1.0 µA = 13 dB. It is seen that the transient results accord with the frequency response in Fig. 4. -15u Fig. 6. Transient responses. (a) Iin and Ig , (b) Log-compressed voltage Vinp of the proposed and the DAB filters, (c) Output current Iout of the proposed filter. V. C ONCLUSION A low-voltage syllabic-companding log domain filter with a floating common nodal voltage adaptively changed has been proposed. An envelope detector is also designed for lowvoltage realization by quantizing its output. Simulation results show the proposed filter has a wider dynamic range than the conventional syllabic-companding log domain filters under low voltage. Future works are fabrication, measurement, etc. ACKNOWLEDGMENT This study was supported by the 21st Century COE Program “Intelligent Human Sensing” from the ministry of Education, Culture, Sports Science and Technology of Japan and VLSI Design and Education Center (VDEC), the University of Tokyo in collaboration with Cadence Design Systems, Inc. R EFERENCES [1] N.Krishnapura and Y.Tsividis and D.R.Frey, “Simplified technique for syllabic companding in log-domain filters, ” Electron. Lett., vol.36, pp.1257-1259, July 2000. [2] N.Krishnapura and Y.Tsividis, “Noise and power reduction in filters through the use of adjustable biasing, ” IEEE J. Solid-State Circuits, vol.36, pp.1912-1920, Dec. 2001. [3] Y.Tsividis, “Externally linear time-invariant systems and their applications to companding signal processors, ” IEEE Trans. Circuits and Systems II, vol.44, pp.65-85, Feb. 1997. [4] G.Palaskas and Y.Tsividis, “Design considerations and experimental evaluation of a syllabic companding audio frequency filter, ” in Proc. 2002 Int. Symp. Circuits and Systems, vol.3, pp.305-308, 2002. [5] D.Python and C.C.Enz, “A micropower class-AB log-domain filter for DECT applications, ” IEEE J. Solid-State Circuits, vol.36, pp.1067-1075, Dec. 2001. 3340