T Kwan Adaptive Analog Continuous Time
- 11,368,176 کتاب کتاب
- 84,837,643 مضامین مضامین
- Z-Library Home
- ہوم پیج
An adaptive analog continuous-time CMOS biquadratic filter
Kwan, T., Martin, K.
ہاں چیک کریں اگر ہاں چیک کریں اگر ہاں چیک کریں اگر ہاں چیک کریں اگر
آپ فائل کو کھولنے کے قابل تھے۔
فائل میں ایک کتاب ہے (مزاحیہ بھی قابل قبول ہیں)
کتاب کا مواد قابل قبول ہے۔
فائل کا عنوان، مصنف اور زبان کتاب کی تفصیل سے ملتی ہے۔ دوسرے شعبوں کو نظر انداز کریں کیونکہ وہ ثانوی ہیں!
نہیں چیک کریں اگر نہیں چیک کریں اگر نہیں چیک کریں اگر نہیں چیک کریں اگر
- فائل کو نقصان پہنچا ہے
- فائل DRM سے محفوظ ہے۔
- فائل ایک کتاب نہیں ہے (مثال کے طور پر قابل عمل، xls, html, xml)
- فائل ایک مضمون ہے۔
- فائل ایک کتاب کا اقتباس ہے۔
- فائل ایک میگزین ہے
- فائل ایک ٹیسٹ صفحہ ہے۔
- فائل ایک سپیم ہے
آپ کو یقین ہے کہ کتاب کا مواد ناقابل قبول ہے اور اسے بلاک کیا جانا چاہیے۔
فائل کا عنوان، مصنف یا زبان کتاب کی تفصیل سے میل نہیں کھاتی۔ دوسرے شعبوں کو نظر انداز کریں۔
This book has a different problem? Report it to us
Change your answer
Thanks for your participation!
Together we will make our library even better
فائل آپ کے ای میل ایڈریس پر بھیجی جائگی۔ اسے موصول ہونے میں 5 منٹ تک کا وقت لگ سکتا ہے۔.
فائل آپ کے Kindle اکاؤنٹ پر بھیجی جائگی۔ اسے موصول ہونے میں 5 منٹ تک کا وقت لگ سکتا ہے۔.
نوٹ کریں : آپ کو ہر کتاب کی تصدیق کرنی ہوگی جسے آپ اپنے Kindle میں بھیجنا چاہیں۔ Amazon Kindle سے تصدیقی ای میل کے لیے اپنا میل باکس چیک کریں۔
IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 26, NO. 6, JUNE 1YY1 859 An Adaptive Analog Continuous-Time CMOS Biquadratic Filter Tom Kwan, Member, IEEE, and Kenneth Martin, Fellow, IEEE Abstract -An adaptive analog continuous-time biquadratic filter is realized in a 2-pm digital CMOS process for operation at 300 kHz. The biquad implements the notch, bandpass, and low-pass transfer functions. The only parameter adapted is the resonant frequency of the biquad, which is identical to the notch frequency and the bandpass center frequency. The update method is based on a least-means-square (LMS) algorithm, which adapts the notch frequency to minimize the power at the notch filter output. The actual update is modified to reduce the circuit complexity to one biquad and one correlator. When the filter is tracking a sinusoid, this update generates a ripple-free gradient that decreases tracking error. Applications include phase-frequency detectors, FM demodulators (linear and FSK), clock extractors, and frequency acquisition aids for PLL's and Costas loops. Measured results from experimental prototypes are presented. Nonidealities of an all-analog implementation are discussed along with suggestions to improve performance. I. INTRODUCTION R ESEARCH on adaptive filtering algorithms has advanced the use of signal processing in such diverse applications as line enhancement, channel equalization, speech coding, and spectral estimation [l].Although most implementations of adaptive algorithms have been digital in nature, all-analog continuous-time realizations can result in smaIler chip area, lower power dissipation, and freedom from clocking and aliasing effects [ 2 ] . Until recently, finite-impulse-response (FIR) adaptive filters have received the most attention. As a result, adaptive FIR filters have matured to the point where they are routinely applied in many commercial systems. However, there is growing interest in infinite-impulse-response (IIR) adaptive filters in some signal processing applications, due to the ; IIR filter's efficiency in meeting difficult frequency response specifications with relatively few multipliers 131. Also, recently, much work has been accomplished in the area of monolithic continuous-time recursive (IIR) filters [4]-[8]. Since these filters are inherently tunable, they are Manuscript received July 30, 1990; revised January 22, 1091. This work was supported in part by the National Science Foundation under Grant MIP-8913164. T. Kwan was with the Integrated Circuits and Systems Laboratory, Department of Electrical Engineering, University of California, Los Angeles, CA 90024. H e is now with Analog Devices. Nowood, MA. K. Martin is with the Integrated Circuits and Systems Laboratory, Department of Electrical Engineering, University of California, Los Angeles, CA 90024. IEEE Log Number 9144582. prime candidates for the analog implementation of adaptive IIR filters. In this paper, we present an analog implementation of an adaptive biquadratic filter designed to track the frequency of a sinusoid. The biquad has a notch, bandpass, and low-pass output and is characterized as constant bandwidth.' The only parameter adapted is the resonant frequency of the biquad, which is identical to the notch frequency and the bandpass center frequency. The update method is based on a least-means-square (LMS) algorithm, which adapts the notch frequency to minimize the power at the notch filter output. The actual update is modified to reduce the circuit complexity to one biquad and one correlator. This modification is referred to as the "one-biquad implementation" in [9]. The modified update is derived from the correlation of the notch and low-pass outputs. When the notch has converged to an input sinusoid, the notch filter will have zero output and hence the update (gradient) will have zero ripple. This lack of ripple translates directly to decreased variance in the demodulated frequency of the input sinusoid. Applications of the adaptive biquad include frequency demodulation (both linear and FSK), frequency acquisition' for PLL and Costas loops, and clock extraction through the tracking bandpass ~ u t p u t . ~ In the following section, we describe an implementation of the constant bandwidth biquad and its update algorithm based on continuous-time transconductance-C filter topology. In Section 111, experimental results of prototypes fabricated using a digital 2-pm n-well CMOS process are presented. Finally, in Section IV, problems with an all-analog implementation are discussed and suggestions to improve performance are given. 11. ADAPTIVE BIQUADA N D UPDATEALGORITHM A block diagram of the biquad and the update algorithm based on fully differential operational transconductance amplifiers (OTAs) is shown in Fig. 1. The notch filter is implemented using an OTA with multiple outputs 'The bandwidth of the filter remains constant when its resonant frequency is changed. 'The VCO should be resonator based and matched to the twointegrator loop of the biquad (see 191). 'This requires a bandpass filter with quality factor of 100 or more. 0018-9200/91/0600-0859$01.OO 01991 IEEE IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 26, NO. 6, JUNE 1991 860 I V' 4 I I 1 Gilbert Cell brrelator 0.5 0.3 i I 1 Fig. 2. Plot of the biquad gradient for a sinusoidal input with amplitude A and normalized frequency CL, and its linear approximation. Fig. 1. Block diagram of the constant bandwidth biquad and update algorithm. to minimize the phase shift around the loop gmq,l / ( s C 2 ) . In an alternate realization using OTA's with single outputs, a transresistance amplifier would be needed to sum the currents between g m i nand gmq, and to convert the result to a voltage for the notch output. Also, an additional OTA would be needed to convert the notch output voltage to a current to be summed with the current output of the cell gmbp,all contributing excess phase shift and impeding high-frequency performance. By using multiple current output OTA's, the notch output becomes current oriented. Moreover, since one input set of the correlator multiplier cell is current driven, this configuration simplifies the correlator circuitry. The biquad structure shown is sufficient in generating the notch current (unOtgmi,,), bandpass output ( c b p ) , and low-pass output ( clp). The notch current, bandpass, and low-pass transfer functions are given by bandpass output, a resonant frequency4 of g,, / C , and a bandwidth of (g,, / g m w ) w O .The resonant frequency of the filter is adapted by tuning g, while g,, remains fixed, thus maintaining constant bandwidth. As shown below, this constant bandwidth property gives a constant "frequency-difference gain" for the gradient which makes the design of the algorithm update simpler. It should be noted that the realization of the bandpass and notch filter functions is not contingent on the matching of the above transconductances and capacitances. A mismatch of the first set (g,,) results only in a nonunity gain for the bandpass output, while the effect on the second and third set (g,,,C) affects only the resonant frequency, which is precisely the parameter being adapted. The adaptation gradient is derived from the correlation between the low-pass and notch outputs of the biquad. For a sinusoidal input and given ( 1 ) and (3), this correlation yields g ( w ) = E [% > t ( t > ~ l l , ( t > ] 1-O2 ( 1- f q 2 + c, . (7) R2 'Zgmbpgmlp where R = w / w 0 and A are the normalized frequency ( 3 ) and the amplitude of the input, respectively. For the above nominal design with g m B / g l n w= 1/2, (7) is plotrespectively, where ted in Fig. 2. gmq gmhpgmlp Algorithm Update: Choosing the update size (or gain in D ( s ) = s - + s+ -. (4) the case of continuous-time systems) in adaptive filters is c 2 CIC2 The peak gain of the bandpass is given by g m i n/ g m q with often an empirical process. The selection process generthe resonant frequency w 0 and half-power bandwidth B ally involves simulating an algorithm's behavior for various step sizes and then selecting the one that will give the given by fastest convergence result while maintaining stability. Fortunately, for this particular adaptive system, one can linearize the gradient about its operating point and apply conventional feedback analysis to ensure stability, analogous to the linearized analysis of phase-locked loops. From the gradient curve of Fig. 2, it can be seen that In a nominal design, g m i nand gmy are matched to gmB, for an input sinusoid of sufficiently small frequency deviagmbp and gmlp are matched to g, and C , and C , are matched to C . This results in a peak gain of one for the 'Identical to the notch and bandpass center frequency. KWAN A N D MARTIN: ADAPTIVE ANALOG CONTINUOUS-TIME CMOS BIQUADRATIC FILTER tion from the resonant frequency w o , the gradient curve is well approximated by a straight line. The slope of this line represents a "frequency-difference gain" and can be found by taking the derivative of the curve with respect to w and inserting w = w o in the final result. This gain is found to be A'C, / g m q . Not only is this linear approximation accurate near the resonant frequency but it also represents an upper bound for the magnitude of the "frequency-difference gain." Thus, an update gain designed to be stable with a sinusoidal input at the resonant frequency will also enjoy global stability. Note that this gain is independent of the resonant frequency of the filter, which makes a linearized feedback analysis of the frequency-tracking loop more accurate. This is not the case with constant Q filters. A. Filter Components 1) Operational Transconductance Amplifier: Unlike an op-amp-based integrator which has a large feedback gain over its operating frequencies to reduce the signal swing at its input, transconductance-C integrators typically operate near their unity-gain frequencies, which imposes a large-signal-linearity requirement for the transconductors. Numerous circuit techniques have been proposed in the implementation of large-signal linear transconductors in CMOS [6], [81, [lo], [13].The one developed here is based on the well-known source-coupled differential pair with source degeneration as shown in Fig. 3(a). Given that the transconductance of the MOSFET's (g,) is much larger than 1 / R , only a small portion of the input voltage lies across the active devices, implying reduced signal swing and distortion. The requirement g, >> 1/ R can usually be satisfied with large transistors and/or bias currents. In many applications, this may not be desirable in terms of area and power consumption. An alternate way is to boost the g, of the p-channel by using a compound device as shown in Fig. 3(b) [15]. This compound configuration is often used in the design of many bipolar output stages instead of a single p-n-p transistor with poor performance. In this case, M 1 acts like a floating voltage source. Its g, is no longer an important factor in the distortion performance of the OTA. However, any threshold voltage shift due to the body effect becomes part of the input signal. For this reason, p-channel input transistors were chosen for the n-well process, in which the body effect can be minimized by connecting the source of each input transistor to its own well. A basic OTA with the compound devices and biasing is shown in Fig. 3(c). The p-channels serve as voltage followers buffering the input voltage across the resistor while the four constant current sources force any change in the resistor current to be directly reflected to the drain currents of M 2 and M2', which is mirrored to the output by M 3 and M3'. Multiple current outputs can be obtained by adding additional transistors to the mirror. a ) Resistor implementation: In a standard CMOS technology, realization of large resistances is impractical 861 Fig. 3. (a) Differential pair with source degeneration. (b) Composite p-channel device. (c) Basic G, cell. because of the low sheet resistance and poor tolerances. By contrast, a MOSFET can exhibit a large linear resistance behavior while operating in the triode region for small drain-to-source bias voltages. A circuit for realizing a floating linear resistor is shown in Fig. 4(a) [141.' A constant floating control voltage (vns) is generated across the gate and source of M 5 and M5' operating in the linear region, which helps to cancel the nonlinear terms in the MOSFET current equation. Linearity of the circuit is dependent on this constant tigs bias, a small body-effect parameter y , and the matching of M 5 and M5'. Further details can be found in [14] and [17].This floating resistor implementation is used to replace the resistor in the basic g, cell of Fig. 3(c). The complete OTA including various enhancements is shown in Fig. 4(b). The addition of M4 keeps the rdSof M 1 constant, which improves its voltage follower action6 and minimizes the effect of Cgd3on the previous stage. M 9 and C, serve to compensate the M I , M 6 , M 2 , M 8 , M4 feedback loop, similar to the compensation of a conventional two-stage CMOS op amp in which a zero at 1.2 times the unity-gain frequency of the loop is added to the loop transfer function for increased stability [19].The compensation capacitor C, is realized between the layers metal, (lower plane) and metal, (upper plane). Since metal, forms a significant parasitic capacitance (shown as dashed lines in Fig. 4(b)) with the substrate (50% of the metal,, metal, capacitance), it is tied to the gate of M 2 to increase the phase margin. Finally, a diode ( M 1 0 ) is used to clamp the maximum gate voltages of M 2 and M 3 to prevent overdriving the load stage in the unlikely event that the common-mode input voltage swings to the negative power rail. This can cause the common-mode output of a two-integrator loop to latch up to the power rail, if the common-mode feedback stage has insufficient current drive. The transconductance of the stage (G,) is determined solely by the resistances of M 5 and M5', which are controlled by their gate-to-source bias voltages. These bias voltages can be varied by changing the bias currents. Given that the current through M11 and M12 is 31, and the current through M 1 is I , an approximate relationship 'Unless otherwise stated, unlabeled transisters in the right half of the circuit are understood to be identical to the left half. 'SPICE simulations show an improvement in gain from 0.93 to 0.90. 862 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 26, N O . 6, JUNE 1991 Vdd Vir M6 VSS (a) (b) Fig. 4. (a) CMOS circuit for realizing a floating linear resistor. (b) Adaptation of a CMOS floating resistor circuit in an OTA. VOH (9) Fig. 5. OTA-based integrator between the G,,, of the OTA and the bias current I is where k , = pC,,(W/L), and V,, is the threshold voltage of M,. The bandwidth of the OTA can be estimated by finding the source of the dominant time constant in the circuit. For the circuit in Fig. 4(b), it can be shown that this time constant comes from the gate node of M 2 where the impedance is highest. The approximate resistance and capacitance seen at this node are the output resistance of M 8 divided by the loop gain and the Miller capacitance due to C,, respectively. 2) Integrator: The signal current from the OTA is mirrored through M 3 of Fig. 4(b) into the cascode load of Fig. 5 to form an integrator. To save area, the integrator capacitor is realized by using a pair of back-to-back PMOS transistors biased in the saturation region [16]. In a standard digital CMOS process, the thin oxide of a MOSFET is the most area-efficient (thinnest) insulator available for realizing capacitors. For the 2-pm process, this translates to a factor of 18 less in area compared to the second most efficient implementation (thick oxide between the two metal layers). 3) Common-Mode Feedback Circuit: The commonmode feedback circuitry for the OTA-based integrator is shown in Fig. 6(b). This circuit is based on the "differential-difference amplifier" concept in [ 111 extended to three (b) Fig. 6 . (a) Differential difference amplifier. (b) Common-mode feedback circuit. sets of inputs from two (see Fig. 6(a)). Both VOH and VOL can swing to Vdd and near 5,. This ensures that the common-mode output voltage stays near V,, (which prevents latch-up problems) regardless of the O T A s common-mode input voltage. The symmetrical bias arrangement (M22 to M 2 6 ) ensures there is no systematic offset in the common-mode output voltage. Compensation of the common-mode feedback loop is provided by the load capacitor. 4) Correlator: As described previously, the gradient signal for the adaptive filter can be generated by correlating the notch and low-pass filter outputs. The first stage of the proposed correlator consists of a Gilbert fourquadrant multiplier which, as mentioned earlier, can accept current as one set of its inputs. Current output from the multiplier is then integrated across a capacitor to form a correlator. This capacitor is made entirely from parasitic capacitances, but its terminals are made accessible off chip so that extra capacitance can be added if needed.' The complete correlator circuit is shown in Fig. 7(a). Defining the quiescent current through M16- M19 to be I D l h ,the transconductance of the differential pair M24, M 2 5 as g m f , and the effective output conductance seen by C, to be go, the output of the correlator can be 'With bonding pads and external wiring, the estimated parasitic capacitance is on the order of 1-2 pF. ~ KWAN AND MARTIN: ADAPTIVE ANALOG CONTINUOUS-TIME CMOS BIQUADRATIC FILTER 863 Off ref ? fback ' I I I 1 L- CURRENT INPUT vss (a) Fig. 8. Linear frequency-signal based model of the biquad tracking loop. (b) Fig. 7. (a) Correlator. (b) Bias circuitry. described by (9) denote time convolution and inwhere " * " and J1 verse Laplace transform, respectively. The current output of the correlator drives a number of bias circuits (shown in Fig. 7(b)), which redistributes the current to the OTA's that control the filter's resonant frequency.* To model the biquad frequency tracking loop as a frequency-signal control system, a frequency-difference gain was derived earlier to approximate the gradient for input sinusoids with small frequency deviations from the resonant frequency. Using the correlator of Fig. 7, an expression for this frequency-difference gain is where E[ .I denotes the expectation operation over time. 5) Output Buffers: The bandpass and low-pass outputs of the biquad have very high output impedance which needs to be buffered for measurement purposes. The OTA cell described earlier is modified to serve as a buffer for the bandpass and low-pass outputs by increasing the size of its output transistors by a factor of 4. The notch output is obtained by wiring a third set of current outputs (not shown in Fig. 1) from the transconductance blocks gmin and gmq in Fig. 1 to the pads. signal whose bandwidth is less than one-tenth of its center frequency, the transient response of the biquad can be ignored relative to the much slower closed-loop response (see [9]). Fig. 8 shows a block diagram of such a linear model of the adaptive filter. The frequency-difference gain K f is in units of microamperes per hertz. The accumulated effect of all dc offsets in the system, including the OTA's and the multiplier, is represented by I,,,. The gain K and the corner frequency w , are given by g,, / g o and g , / C , , respectively, where g m f , g o , and C , are defined as in (9). In nominal operation, the actual current driving the O T A s that control the filter's resonant frequency consists of two components. One component is fixed and gives the filter an initial starting frequency. The second component is derived from the adaptation process and its magnitude defines the tracking range of the biquad. Zref stands for the first component. Finally, K , is the sensitivity of the biquad's resonant frequency with respect to the bias currents in the OTA blocks' g m l p and gmbp in Fig. 1. This sensitivity is simply the derivative of (8) with respect to I normalized by the integration capacitance C. K , is in units of hertz per microampere. The tracking performance can be estimated by simple feedback analysis. Solving for fback in Fig. 8 in terms of f i n , Ioff, and I r e f gives A large K , is essential in minimizing any tracking errors introduced by the offset and reference currents B. Linear Analysis of Tracking Loop With the circuit description of building blocks complete, we can describe a simple linear frequency-signal control system based on circuit parameters to model the tracking behavior of the adaptive filter. For a narrow-band 8The actual frequency control current is routed through an off-chip jumper so that the adaptation loop can be broken to measure the filter response and gradient under a fixed bias. 111. EXPERIMENTAL RESULTS The constant bandwidth biquad was designed to have a resonant frequency of 360 kHz and a bandwidth of 180 kHz. The adaptive biquad was fabricated through MOSIS's 2-pm double-metal single-poly n-well CMOS process. The transistor sizes used in the components of the biquad are listed in Table 1. A chip microphotograph is shown in Fig. 9. There exist significant differences in 864 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 26, NO. 6, JUNE 1991 TABLE I COMPONENT SIZESFOR THE g, CELL(OTA), COMMON-MODE FEEDBACK CIRCUIT (CM), A N D CORRELATOR CIRCUIT (COR) ( W / L I N MICROMETERS) I OTA Mll,M12 M1, M4 M5 M6 M2, M 8 M9 M10 c, c, 48/4 6/2 4/16 4/6 16/4 4/12 4/2 0.15 pF 0.1 pF I CM M1-M4 M5-M8 M9, M 10 Mll-M14 M15,M16 M17-M26 16/4 4/24 4/12 8/4 16/4 8/4 COR M1LM4 M5-M8 M9-M12 M13, M14 M 15 M16-M19 M20-M23 M 24, M 25 M 26, M 27 8/4 12/8 8/4 16/4 2;: 16/4 4/4 32/4 TABLE 11 TYPICAL PERFORMANCE CHARACTERISTICS OF THE TRANSCONDUCTANCE CELLFOR A 10-V SUPPLY VOLTAGE A N D 108-pA SUPPLY CURRENT Total harmonic distortion (THD) - 3-dB bandwidth Offset voltage Transconductance Fig. 9. Chip microphotograph. the process parameters extracted from this run and the parameters used in the original design. Most notable of these are: to, decreased by 20%, p-channel pC,, increased by 35%, and n-channel y decreased by 86%. Substituting the new process parameters in (8) and noting that the integrator capacitance is inversely proportional to to,, the combined effect of the various parameter changes is to decrease the resonant frequency of the filter by a factor of 0.85. This works out to be approximately 305 kHz. Four chips were received from MOSIS in which the measured resonant frequencies ranged from 283 to 300 kHz. The performance characteristics of the OTA buffer and the tracking biquad filter are summarized in Tables I1 and 111, respectively. The total harmonic distortion measurements are obtained using a balanced-driven input and an off-chip differential-to-single-ended converter. For the tracking notch depth measurement, the dc offset is trimmed using an off-chip current source attached to the 0.31% at Vi, = 1 VP-,, 100 kHz 0.69% at Vi, = 2 Vp-p, 100 kHz 11.3 MHz 10" typical 1/10.4 k R appropriate terminal of C, in the correlator circuit of Fig. 7(a). Typical frequency responses of the OTA and the biquad (including off-chip differential-to-single-ended converters) are shown in Figs. 10 and 11, respectively. A scaled version of the gradient signal is measured by disconnecting the current feedback that controls the resonant frequency and biasing the filter with a fixed current. A 1-MR resistor is shunted across the correlator capacitance C, and the voltage across this resistor is tabulated for a sine-wave input of varying frequency.' The results are plotted in Fig. 12 for an input sinusoid of amplitude 0.5 V. The measured slope of the gradient is 1.2e-6 pA/rad, which is in close agreement with value of l.le-6 pA/rad calculated from (10). Note that the cumulative effect of all offsets in the system results in approximately 70 mV of offset at the correlator output. The measured magnitude and phase response of the tracking bandpass output of the biquad is shown in Fig. 13. For this measurement, the current controlling the resonant frequency of the biquad has two components. One component is fixed at 40 p A while the other is allowed to vary from 0 to 40 p A to adapt the resonant frequency of the biquad to that of an input sinusoid. The range of adaptation shown is determined by the second current component. In Fig. 14, the transient response of the adaptive biquad's notch output (with offset trimming) is shown while tracking the frequency of an FSK input. IV. NONIDEAL EFFECTS A practical implementation of an adaptive filter is often plagued by many nonideal effects, the major outcome being deviations from ideal filter response and tracking 'The actual gradient current is twice the current through the resistor due to the common-mode feedback to the current sources M22 and M23. KWAN AND MARTIN: ADAPTIVE ANALOG CONTINUOUS-TIME CMOS BIQUADRATIC FILTER 865 TABLE 111 TYPICAL ONDUC TANCE-C INTEGRATOR PERFORMANCE CHARACTERISTICS O F THE TRANS< A N D TRACKING BIQLJADRATIC FILTERFOR A IO-V SUPPLY VOITAGE Integrator: DC gain Q factor Tracking Filter: Notch frequency - 3-dB bandwidth Notch depth Tracking Error Tracking Notch Depth CMRR (bandpass output) CMRR (low-pass output) CMRR (notch output) Power supply rejection ratio ( + , - ) Bandpass Low pass Notch THD (notch output) THD (low-pass output) Power dissipation Chip Area R E F !LEVEL_ - - 3 0 .O O O d E 5 .OOOdB 180.000deg 45.000deg STAR1 /'DIV OF-FSET 1 1 333 O B S . 6 0 0 H Z Y.\G ( B / A ) - 2 . 965dB OFFSET 1 1 333 0 8 5 . 6 0 0 H Z PilASE (B/R) -127.769deg 1 000 OOOHZ STOP 100 0 0 0 0 0 0 O O O H Z 55 dB 707 291 kHz at I,, = 21.1 p A 132 kHz at I,, = 18.4 p A cf. 131 kHz theoretical 45 dB -7% without dc offset trimming - 0.28% with trimming 11 dB without dc offset trimming 39 dB with trimming 59.5 dB at 300 kHz 59.3 dB at 300 kHz 59.8 dB at 100 kHz 53.9 dB at 500 kHz 33.4 dB, 35.1 dB at 300 kHz 30.9 dB, 33.9 dB at 300 kHz 38.1 dB, 33.9 dB at 100 kHz 0.40% at V,, = 1 V , - , 30 kHz 0.81% at V,, = 2 VP-,,, 30 kHz 0.44% at V,,,= 1 Vp-p, 30 kHz 0.93% at V,, = 2 VP-,,. 30 kHz 6.84 mW 1741 p m X 1012 p m REF LEVEL /DIV OFFSET -15:. O O O d B I O . OOOdB MAG START 500 OOOHZ 29 1 2 9 7 . 4 7 1 H Z -45.499dB (UOF) STOP 10 0 0 0 0 0 0 O O O H Z Fig. 10. Measured OTA magnitude and phase response. Fig. 11. Measured magnltude response of the notch, bandpass, and low-pass outputs of the biquadratic filter. accuracy. For example, parasitic capacitances and integrators with finite Q's can contribute to finite notch depths, and dc offsets can lead to biases in the filter tracking behavior. In the following, we discuss the effect of finite integrator quality factor Q on notch filter performance and several factors that can contribute to tracking inaccuracies in which dc offsets are the most dominant. error (due to high-frequency parasitic poles or finite integrator dc gain) on filter performance can be estimated. For the biquad shown in Fig. 1, it can be shown that the is notch depth A. Finite Integrator Q Factor One measure of an integrator's nonideal performance is its quality factor [18]. By modeling an integrator with a finite Q factor, the effects of any integrator phase-shift 20" Enor =- BQI ( 12) where Q, is the quality factor of the integrators. To obtain a large notch depth at high frequencies, excess phase shift of high-frequency poles needs to be compensated. One solution is to insert a zero above the resonant IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 26, NO. 6, JUNE 1991 866 frequency of the biquad to introduce phase lead. To account for process and temperature variations, a master-slave tuning arrangement similar to most fixed filter tuning schemes [4], [5], [8], [16] can be used. ..... 100 B. DC Offset O t ! -100 = ' 9.. .." I 100 200 300 400 500 kHz Fig. 12. Measured gradient curve REF LEVEL -10.000dBm 0 . Odeg START ,,'DIV 5.000dB 22.500deg 100 0 0 0 . 0 0 0 H z STOP 1 0 0 0 000.000Hz Fig. 13. Measured magnitude and phase response of the tracking bandpass output of the biquadratic filter. Of all the potential problems in an all-analog implementation of the adaptive biquad, dc offset is one of the most serious. The cumulative effect of the dc offsets in the OTA's and the Gilbert multiplier results in a dc shift of the true gradient. The biquad will converge to a frequency at which the generated gradient will exactly cancel this dc offset, resulting in a bias in the tracking frequency. If the offset is large enough such that the generate gradient is not able to cancel it, then the biquad fails to adapt. Given the signal flow graph of the biquad in Fig. 1, we can calculate the worst-case notch and low-pass dc offsets by assuming the various sources of offsets can be lumped into an equivalent offset voltage at the input of each transconductance block. Let Vosl, l/;,,*, Vos3,and Vos4 represent the input-referred offset voltages of the transconductance blocks gmin, g m y , gmbp, and gm,p, respectively; then the worst-case offsets of the notch current and low-pass voltage outputs are The dominant source of dc offset in the gradient comes from the Gilbert multiplier. The multiplier was initially designed to have: 1) a large U,, bias across its input devices (M16-Ml9) to minimize the nonlinearity of the source couple pairs, and 2) a small multiplier gain to ensure algorithm stability, which resulted in less than optimal scaling in terms of its input-referred offset voltage. Worst-case SPICE simulations show that a 1% width mismatch of the multiplier input pairs (M16-Ml9) coupled with a dc offset of 10 mV for each OTA results in an offset that is twice as large as measured in experiment. If the offset of the multiplier is eliminated, the worst-case offset of the gradient (due to OTA's alone) is reduced by a factor of 60. The multiplier's gain needs to be increased dramatically to reduce its input-referred offset voltage. This increase in multiplier gain can then be compensated by scaling the gain in the following differential pair (M24, M 2 5 ) and current mirrors (M10-Ml3). C. Finite Gain of Correlator Integrator Fig. 14. Measured waveforms while tracking an FSK input signal (f, = 260 kHz, Af = 47 kHz): (a) FSK modulating input, (b) filter demodulated output, and (c) notch filter output. Since the "integrator" has only finite dc gain due to the finite impedance of the current sources surrounding Ci, a small amount of signal current is lost to leakage, which also contributes to a frequency bias in the tracking loop. This leakage current is directly proportional to the amplitude of the integrated voltage across the capacitor Ci. With a 1-V signal across Ci and an effective output KWAN AND MARTIN: ADAPTIVE ANALOG CONTINUOUS-TIME CMOS BIQUADRATIC FILTER impedance of 14 M O for the current sources, this leakage current is in the same order of magnitude as the measured dc offset current. A regulated current source that can lower the output conductance by an order of magnitude would be an ideal solution for this problem [12]. D. Harmonic Distortion Under perfect tracking of an input sinusoid, the notch filter's output becomes dominated by its second and third harmonic components since the fundamental is "notched out." These harmonics, depending on their relative phase, can produce a gradient error signal when correlated with the low-pass output. This is an additional source of bias in frequency tracking. For the OTA, one can improve the OTA's harmonic distortion at the expense of more circuitry and power dissipation. This can be accomplished by adding two extra source followers to bias the Vgs of M 5 and M5' in Fig. 4. fluctuation which is tied to This would eliminate M6's the output current in the present circuit. SPICE simulations of the modified circuit show a THD of 0.15%, an improvement of a factor of 4 for a 2-VP_, input. Cs T. Kwan and K. Martin, "A notch-filter-based frequency-difference detector and its applications," in 1990 IEEE ISCAS Proc., pp. 1343- 1346. A. P. Nedungadi and P. E. Allen, "Design of linear CMOS transconductance elements," IEEE Trans. Circuits Syst ., vol. CAS31, pp. 891-894, Oct. 1984. E. Sickinger and W. Guggenbiihl, "A versatile building block: The CMOS differential difference amplifier," IEEE J . Solid-State Circuits, vol. SC-22, pp. 287-294, Apr. 1987. E. Sackinger and W. Guggenbiihl, "A high-swing, high-impedance MOS cascode circuit," IEEE J . Solid-State Circuits, vol. 25, pp. 289-298, Feb. 1990. Y. Tsividis, Z. Czarnul, and S. C. Fang, "MOS transconductors and integrators with high linearity," Electron. Lett., vol. 22, pp. 245-246, 1986. M. Banu and Y. Tsividis, "Floating voltage-controlled resistors in CMOS technology," Elecfron. Left., vol. 18, pp. 678-679, 1982. S. Willingham, private communication, 1989. Y. T. Wang, "A 12.5 MHz CMOS continuous-time bandpass filter," Master thesis, Univ. of Calif., Los Angeles, 1989. R. Gregorian and G. C. Temes, Analog MOS Integrated Circuits for Signal Processing. New York: Wiley 1986. A. Sedra and P. 0. Brackett, Filter Theory and Design: Active and Passitv. Champaign. IL: Matrix, 1978. [I91 J. K. Roberge, Operational Amplifiers: Theory and Practice. New York: Wiley, 1975. Tom Kwan received the B.A.Sc. (hons.) degree from the University of Toronto, Toronto, Ont., Canada, in 1984, and the M.S. and Ph.D. degrees in electrical engineering from the University of California, Los Angeles, in 1986 and 1990, respectively. After graduation, he joined Analog Devices, Norwood, MA, as a Design Engineer in the Mixed-Signals group. His technical interests include analog and digital filter design, adaptive signal processing, and oversampled data ACKNOWLEDGMENT The authors would like to thank S. Willingham for numerous discussions and the anonymous reviewers for their useful and constructive comments, which improved the presentation of this paper. REFERENCES [1] B. Widrow and S. Stearns, Adaptice Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1985. [2] K. Bult and H. Wallinga, "A CMOS analog continuous-time delay line with adaptive delay-time control," IEEE J . Solid-State Circuits, vol. 23, pp. 759-766, June 1988. [ 3 ] D. A. Johns, W. M. Snelgrove, and A. S. Sedra, "Continuous-time analog adaptive recursive filters," in 1989 IEEE ISCAS Proc., pp. 667-670. [4] Y. Tsividis, M. Banu, and J. Khoury, "Continuous-time MOSFET-C filters in VLSI," IEEE Trans. Circuits Sysf., vol. CAS-33, pp. 125-39, Feb. 1986. [SI C.-F. Chiou and R. Schaumann, "Design and performance of a fully integrated bipolar 10.7-MHz analog bandpass filter," IEEE J . Solid-State Circuits, vol. SC-21, pp. 6-14, Feb. 1986. [6] A. P. Nedungadi and R. L. Geiger, "High-frequency voltage-controlled continuous-time lowpass filter using linearized CMOS integrators," Electron. Lett., vol. 22, pp. 729-731, Dec. 1986. [7] H. Khorramabadi and P. R. Gray, "High-frequency CMOS continuous-time filters," IEEE J . Solid-State Circuits, vol. SC-19, pp. 939-948, Dec. 1984. [8] C. S. Park and R. Schaumann, "Design of a 4-MHz analog integrated CMOS transconductance-C bandpass filter," IEEE J . SolidState Circuits, vol. 23, pp. 987-996, Aug. 1988. 867 converters. Kenneth Martin (S'75-M'SO-SM'89-F91) received the Ph.D. degree from the University of Toronto, Toronto, Ont., Canada, in 1980. He first worked for Bell-Northern Research in Ottawa, Ont., Canada Since 1980 he has been employed by the Electrical Engineering Department at the University of California, Los Angeles, where he presently IS a Full Professor He has also been a consultant to many hightechnology companies including Xerox Corporation, Hughes Aircraft Company, Intel Corporation, and Brooktree Corporation in the areas of high-speed analog and digital integrated circuit design. He has research interests in the areas of analog CMOS systems, high-speed GaAs circuits, and real-time IIR adaptive filters. Dr Martin was a member of the Administrative Committee of the IEEE Circuits and Systems Society from 1985 to 1988, and was an Associate Editor of the IEEE TRANSACTIONS ON CIRCUITS AND SY~TEMS from 1986 to 1988. He is a Fellow of the IEEE.
اگر آپ کے آلے پر ٹیلیگرام ایپلی کیشن انسٹال ہے، تو براہ کرم نیچے دیئے گئے بٹن پر کلک کریں اور ویب سائٹ کو ٹیلیگرام کھولنے کی اجازت دیں۔
براہ کرم ذیل میں صارف نام سے ہمارا ٹیلیگرام بوٹ تلاش کریں۔
پھر مندرجہ ذیل متن کو بوٹ پر بھیجیں۔
Source: https://ur.booksc.me/book/20717497/37ec07
Post a Comment for "T Kwan Adaptive Analog Continuous Time"