High-Frequency Low-Current Second-Order Bandpass Active Filter Topology and Its Design in 28-nm FD-SOI CMOS

: Fully Depleted Silicon on Insulator (FD-SOI) CMOS technology o ﬀ ers the possibility of circuit performance optimization with reduction of both topology complexity and power consumption. These advantages are fully exploited in this paper in order to develop a new topology of active continuous-time second-order bandpass ﬁlter with maximum resonant frequency in the range of 1 GHz and wide electrically tunable quality factor requiring a very limited quiescent current consumption below 10 µ A. Preliminary simulations that were carried out using the 28-nm FD-SOI technology from STMicroelectronics show that the designed example can operate up to 1.3 GHz of resonant frequency with tunable Q ranging from 90 to 370, while only requiring 6 µ A standby current under 1-V supply.


Introduction
Fully Depleted Silicon on Insulator (FD-SOI) CMOS technologies provide several advantages in comparison to bulk CMOS, namely: (1) unparallel threshold voltage tuning range from the back gate, which allows effective trimming strategies for process and temperature compensation, (2) better threshold voltage matching, (3) low parasitic capacitances, (4) high transition frequency, f T , of hundreds of gigahertz, and (5) improved intrinsic dc gain [1]. These behaviors, together with the increased flexibility offered by the MOS "fourth terminal", have enabled many ingenious and innovative integrated-circuit (IC) solutions in analog, radio frequency (RF), millimeter wave (mW), and mixed-signal systems also for automotive, IoT, 5G, and emerging applications [2][3][4][5].
Ubiquitous RF portable communications need ultra-low-power IC solutions that are able to prolong battery life and recharging cycles in energy harvested devices [6][7][8]. In these applications fundamental building blocks are continuous-time filters with tunable cutoff frequency and small fractional bandwidth. At this purpose, several IC implementations have been developed that exploit inductors, transformers, resonators, transmission lines, etc. [9][10][11][12][13][14][15][16]. These solutions usually require current consumptions in the order of several milliamperes in order to provide the required high frequency performance and frequently exploit nonstandard approaches for the CMOS technology.
This paper addresses the problem of designing a monolithic inductorless second-order band-pass active filter that is suitable for RF portable applications providing electrical tunability of both the resonant frequency and quality factor, under a very limited quiescent current budget constraint of a few microamperes. This result is achieved thanks to the low parasitic capacitances and high f T offered by the FD-SOI CMOS technology and through the extensive use, as a design option, of the body terminals of transistor devices [17][18][19]. No particular application has been targeted, as the purpose of this document is simply to introduce a new topology and show its potential. To this end, a preliminary Figure 1 shows the circuit schematic of the proposed band-pass filter. It is made up of common source transistor M1 implementing a first (inverting) gain stage biased by current generator M5. The input signal is AC coupled to the gate of M1 through capacitor C IN and the output of the filter is taken at the drain of M1 which drives also the second (noninverting) gain stage made up of common source transistor M2 and unitary current mirror M3-M4 biased by current generator M6. Transistors M7-M11 are used for biasing purposes. Negative feedback is accomplished by connecting the second stage output (drains of M4 and M6) to the bulk of M1. This loop also provides DC stabilization by setting the second stage output voltage to around V G11 thanks to the gate-bulk connection of M11 and circuit symmetry. The bulk of M2 is used for tuning the filter quality factor, Q, through voltage V B , as we will show in the followings.
J. Low Power Electron. Appl. 2020, 10, x FOR PEER REVIEW 2 of 10 purpose of this document is simply to introduce a new topology and show its potential. To this end, a preliminary design example was developed and simulated while using STMicroelectronics 28-nm process. The filter consumes 6 μA of dc current from a single 1-V power supply while providing a resonant frequency of 1.3 GHz and tunable quality factor ranging from 90 to 370. Simulated 1-dB compression point, P1dB, and input referred third-order intercept point, IIP3, were −20.5 dBm and −9.23 dBm, respectively. The noise Figure was found to be 31 dB. Figure 1 shows the circuit schematic of the proposed band-pass filter. It is made up of common source transistor M1 implementing a first (inverting) gain stage biased by current generator M5. The input signal is AC coupled to the gate of M1 through capacitor CIN and the output of the filter is taken at the drain of M1 which drives also the second (noninverting) gain stage made up of common source transistor M2 and unitary current mirror M3-M4 biased by current generator M6. Transistors M7-M11 are used for biasing purposes. Negative feedback is accomplished by connecting the second stage output (drains of M4 and M6) to the bulk of M1. This loop also provides DC stabilization by setting the second stage output voltage to around VG11 thanks to the gate-bulk connection of M11 and circuit symmetry. The bulk of M2 is used for tuning the filter quality factor, Q, through voltage VB, as we will show in the followings.  Figure 2 illustrates the simplified small-signal equivalent circuit of the proposed solution, where gmi and gmbi are the gate-source and source-bulk transconductances of the i-th transistor. Cdb1 is the drain-bulk capacitance of M1 and ro1, ro2 and Co1, Co2 are, respectively, the equivalent resistances and capacitances at the nodes o1 and o2 (being o1 the filter output terminal. The expressions of these small signal parameters are given below   Figure 2 illustrates the simplified small-signal equivalent circuit of the proposed solution, where g mi and g mbi are the gate-source and source-bulk transconductances of the i-th transistor. C db1 is the drain-bulk capacitance of M1 and r o1 , r o2 and C o1 , C o2 are, respectively, the equivalent resistances and capacitances at the nodes o1 and o2 (being o1 the filter output terminal. The expressions of these small signal parameters are given below r o1 = r d1 r d5 (1a) r o2 = r d4 r d6 (1b)

Circuit Analysis
We will show that Co1 and Co2 play an important role in setting the filter resonant frequency while Cdb1 is fundamental in the selection of Q. Observe that AC coupling capacitance CIN is neglected here, as its effect is well known; indeed, it introduces a zero at ω = 0 and a low-frequency pole 11 in the input-output transfer function. After standard calculation and neglecting higher-order terms, the resulting transfer function Vo1/Vi is given by Assuming gmb1gm2ro1ro2 >> 1, the outband filter gain, Hob, is from (2) which becomes conveniently less than 1, provided that gmb1ro2 > gm1/gm2, a condition that is usually met. Under the same assumption, gmb1gm2ro1ro2 >>1, the resonant angular frequency, ωo, and quality factor are respectively given by The above expressions can be further simplified as a result of the straightforward design strategy that takes advantage of similar transistor dimensions and bias currents for the two common-source stages in order to gain further insight into the above equations useful during the design phase. In this case, we can set ro1 = ro2 = ro1,2 and, somehow, oversimplifying, Co1  Co2 = Co1,2, yielding  Figure 1, v o1 = v o is the filter output.
We will show that C o1 and C o2 play an important role in setting the filter resonant frequency while C db1 is fundamental in the selection of Q. Observe that AC coupling capacitance C IN is neglected here, as its effect is well known; indeed, it introduces a zero at ω = 0 and a low-frequency pole After standard calculation and neglecting higher-order terms, the resulting transfer function V o1 /V i is given by and Assuming g mb1 g m2 r o1 r o2 >> 1, the outband filter gain, H ob , is from (2) H ob = g m1 r o1 1 + g mb1 g m2 r o1 r o2 ≈ g m1 g mb1 g m2 r o2 (4) which becomes conveniently less than 1, provided that g mb1 r o2 > g m1 /g m2 , a condition that is usually met. Under the same assumption, g mb1 g m2 r o1 r o2 >> 1, the resonant angular frequency, ω o , and quality factor are respectively given by The above expressions can be further simplified as a result of the straightforward design strategy that takes advantage of similar transistor dimensions and bias currents for the two common-source stages in order to gain further insight into the above equations useful during the design phase. In this case, we can set r o1 = r o2 = r o1,2 and, somehow, oversimplifying, C o1 ≈ C o2 = C o1,2 , yielding The approximated expression in (6a) shows that ω o is determined by the ratio of the square root of g mb1 g m2 to C o1,2 , as C db1 is intrinsically lower than C o1,2 and, consequently, 2C db1 /C o1,2 can be neglected with respect to the unity. This condition can be also ensured by adding parallel capacitances to C o1 and C o2 at the expense of a proportional reduction of ω o that, in this way, can be decreased by several decades, offering wide range of frequency application. Of course, C IN must be increased accordingly to set the input pole well below the resonant angular frequency. However, (6a) indicates that, to maximize ω o for a given transconductance level of g m2 and g mb1 (observe that g mb1 is a known fraction of g m1 ), the design effort should be aimed at minimizing C o1,2 .
It is also to be noted that ω o can be finely and continuously tuned by varying the transconductances in (6a) by varying, in turn, the DC current I B in Figure 1. Once ω o is set, (6b) shows that also Q is set because both ω o and Q depend on the same parameters. It is seen that, due to the minus sign in the denominator of (6b), very high Q values can be achieved. Indeed, the term proportional to g mb1 − g m2 is negative and tends to reduce the denominator. However, because Q must be positive to preserve stability, the following condition (7) must be ensured. In other words, Q tends to be infinitely large and then becomes negative if the first member of (7) approaches the second member and overtakes it. Additionally, in this case, if it is required to fulfil (7), additional capacitances in parallel to C o1,2 may be added.
Some of the above considerations can be gained with the aid of Figure 3a,b, which, respectively, depict the normalized resonant frequency, ω on , and normalized quality factor, Q n , defined in (8a) and (8b) versus C db1 /C o1,2 , and where g mb1 , g m2 , and r o1 were set to 1.4 µA/V, 19 µA/V, and 2 MΩ, respectively.

Validation Results
The proposed solution was designed in the 28-nm FDSOI technology provided by STMicroelectronics. Power supply was set to 1 V and transistor dimensions were set in order to achieve a resonant frequency of around 1 GHz with Q > 100, under a very limited current consumption of 6 μA (1 μA for each branch, including the reference one). The chosen design values and main small signal parameters are summarized in Tables 1 and 2, respectively.
Using the values in Table 2 and the expressions that are found in Sec. 2B, the low-frequency pole due to CIN results at around 14.4 MHz. The outband gain from (4) results to be 0.33 (−9.6dB). The expected resonant frequency from (5a) is 1.46 GHz with expected quality factor from (5b) of 180. Note that the inaccurate estimation of Co1,2 may lead to strong errors, given the extreme sensitivity of this parameter. Figure 4 depicts the Bode plots (magnitude and phase) of the simulated circuit transfer The light dependence of ω on on C db1 /C o1,2 can be appreciated from Figure 3a, which shows a 5% decrease as a result of a change in C db1 /C o1,2 from 0 to 0.06. In contrast, the strong dependence of Q n on C db1 /C o1,2 is apparent from Figure 3b, which shows the expected asymptote given by (7) when its first member equals the second member.
Because the high Q values achievable lead to a high circuit sensitivity to process tolerances and temperature variations, additional circuitry must be added to control this parameter, the development of which is beyond the scopes of this paper. From (6b) or (8b), it is seen that a possible way to provide continuous Q tunability is via g m2 , which, in turn, can be electrically varied through V B in Figure 1. Observe that changing g m2 has a limited impact onto ω o because g m2 >> g mb1 , as will be shown in the next simulations section.

Validation Results
The proposed solution was designed in the 28-nm FDSOI technology provided by STMicroelectronics. Power supply was set to 1 V and transistor dimensions were set in order to achieve a resonant frequency of around 1 GHz with Q > 100, under a very limited current consumption of 6 µA (1 µA for each branch, including the reference one). The chosen design values and main small signal parameters are summarized in Tables 1 and 2, respectively. Using the values in Table 2 and the expressions that are found in Section 2.2, the low-frequency pole due to C IN results at around 14.4 MHz. The outband gain from (4) results to be 0.33 (−9.6 dB). The expected resonant frequency from (5a) is 1.46 GHz with expected quality factor from (5b) of 180. Note that the inaccurate estimation of C o1,2 may lead to strong errors, given the extreme sensitivity of this parameter. Figure 4 depicts the Bode plots (magnitude and phase) of the simulated circuit transfer function, which shows 2πω o = 1.33 GHz and Q = 164. The peak gain is 54.5 dB and the outband gain is −13 dB. Figure 5a shows Bode plot magnitude for three different bias currents I B , namely 0.9 µA, 1 µA, and 1.1 µA. It is seen that the resonant frequency is shifted, respectively, from 1.24 GHz to 1.33 GHz and to 1.42 GHz. As an expected but unwanted effect of frequency tuning, the quality factor also changes from 312 to 164 and to 112. Equalization of the quality factors is possible through voltage V B , as explained in the previous section and illustrated in Figure 5b, where V B equal to 173 mV, 500 mV, and 904 mV is used to tune g m2 and achieve the same Q value of 164 in the three cases. Figure 6 shows the plot of achieved resonant frequency and quality factor as a function of voltage V B in the nominal condition I B = 1 µA in order to better appreciate the Q tuning interval offered by the proposed design. It is seen that Q can be varied from around 90 to 370, while no appreciable change in the resonant frequency is produced.
Using the values in Table 2 and the expressions that are found in Sec. 2B, the low-frequency pole due to CIN results at around 14.4 MHz. The outband gain from (4) results to be 0.33 (−9.6dB). The expected resonant frequency from (5a) is 1.46 GHz with expected quality factor from (5b) of 180. Note that the inaccurate estimation of Co1,2 may lead to strong errors, given the extreme sensitivity of this parameter. Figure 4 depicts the Bode plots (magnitude and phase) of the simulated circuit transfer function, which shows 2πωo = 1.33 GHz and Q = 164. The peak gain is 54.5 dB and the outband gain is -13dB.    Figure 5a shows Bode plot magnitude for three different bias currents IB, namely 0.9 μA, 1 μA, and 1.1 μA. It is seen that the resonant frequency is shifted, respectively, from 1.24 GHz to 1.33 GHz and to 1.42 GHz. As an expected but unwanted effect of frequency tuning, the quality factor also changes from 312 to 164 and to 112. Equalization of the quality factors is possible through voltage VB, as explained in the previous section and illustrated in Figure 5b, where VB equal to 173 mV, 500 mV, and 904 mV is used to tune gm2 and achieve the same Q value of 164 in the three cases.   Figure 6 shows the plot of achieved resonant frequency and quality factor as a function of voltage VB in the nominal condition IB = 1 μA in order to better appreciate the Q tuning interval offered by the proposed design. It is seen that Q can be varied from around 90 to 370, while no appreciable change in the resonant frequency is produced.  The effect of temperature was simulated under three different conditions, namely −10 • C, 27 • C, and 85 • C. The obtained magnitude Bode plots are shown in Figure 7a. ω o /2π and Q are respectively 1.43 GHz and 353@−10 • C, 1.33 GHz and 164@27 • C, and 1.20 GHz and 95@85 • C. These limited variations are within the tuning range seen before and they can be counteracted by the use of concurrent I B and V B tuning. Figure 7b shows the result after Q tuning to the value of 164 by setting V B equal to 17 mV@−10 • C, 500 mV@27 • C, and 963 mV@85 • C. The effect of temperature was simulated under three different conditions, namely −10 °C, 27 °C , and 85 °C. The obtained magnitude Bode plots are shown in Figure 7a. ωo/2π and Q are respectively 1.43 GHz and 353@−10 °C, 1.33 GHz and 164@27 °C , and 1.20 GHz and 95@85 °C. These limited variations are within the tuning range seen before and they can be counteracted by the use of concurrent IB and VB tuning. Figure 7b shows the result after Q tuning to the value of 164 by setting VB equal to 17 mV@−10 °C, 500 mV@27 °C , and 963 mV@85 °C.   Linearity was evaluated under −50 dB input power. The third-order intermodulation distortion, IMD3, was found to be −79 dBm and it was simulated by a two-tone test with 11 MHz spacing at 1.33 GHz, within the band of interest. Table 3 shows the summary and comparison of this work with other second-order band pass filters in the literature. A figure-of-  Linearity was evaluated under −50 dB input power. The third-order intermodulation distortion, IMD3, was found to be −79 dBm and it was simulated by a two-tone test with 11 MHz spacing at 1.33 GHz, within the band of interest. Table 3 shows the summary and comparison of this work with other second-order band pass filters in the literature. A figure-of-merit, FOM, is also used for overall performance comparison [20,21] where N is number of poles (filter order), P 1dB,W is the in-band 1-dB compression point in watts, f o is the resonant frequency, Q is the quality factor, P dc is dc power consumption in watts, and NF is the noise figure (not in decibels). Higher FOM mean better performance. The proposed solution exhibits the lowest power consumption and lowest supply voltage, with FOM being one of the highest.

Conclusions
Although the "fourth" MOS terminal has been used for decades in the digital domain and even in the analog one [17,18], the body-source biasing was limited to only around 300 mV in order to avoid junction turn on and, hence, restricting the designer options and/or compatible supply voltage. The advent of FD-SOI technologies has made possible the full exploitation of the body as an independent terminal available to the designer, so that new circuits schemes that use the bulk with much more flexibility and efficiency can be developed. In this paper, a new micropower bandpass filter topology that exploits the MOS bulk terminal in the dc stabilization loop and also as a means of quality factor tuning is proposed and preliminary simulations are presented to show its potential in terms of achievable operating frequencies and quality factors. No particular application or standard has been targeted. Lower filter resonant frequency can be achieved by adding two capacitors at nodes o1 and o2 in Figure 2, whereas higher resonant frequency can be achieved by increasing the standby current. The main advantage of the solution is its high frequency capability requiring only a few microamperes of current consumption. The main drawback is related to the dependence of ω o to the bulk transconductance, that is a fraction of the gate transconductance, thus limiting the maximum achievable ω o . Further investigation is currently carried out to avoid this drawback as well realize a higher-order filter function with automatic tuning control for specific applications.