A 20-80 MHz Continuously Tunable Gm-C Low-Pass Filter for Ultra-Low Power WBAN Receiver Front-End

This paper presents a third-order Butterworth low-pass ﬁlter (LPF) with continuously tuning capability to be used in the receiver front-end for Wireless Body Area Network (WBAN). To realize the bandwidth tuning for multi-standard operation in WBAN receivers with ultra-low power consumption and minimized area, a novel transconductor-capacitor (Gm-C) ﬁlter is proposed. The proposed transconductor core uses an additional gain stage with regulated cascode structure to control the transconductance ( G m ) by tuning the drain-source voltage V ds of the input transistors operating in linear region. Based on fundamental analysis, V ds should be reduced to attenuate the nonlinear effects caused by higher-order harmonic components. This proposed transconductor circuit enables the G m tuning and widens the tuning range while maintaining good linearity with negligible power and area consumption. This work is then implemented into a third-order Butterworth LPF. Measurements show that with external control voltage varying from 450 mV to 550 mV, the cutoff frequency of the LPF can be continuously adjusted from 20 MHz to 80 MHz. This design is implemented in 40 nm CMOS process with 1.1 V supply voltage. The total power consumption of this work is below 2 mW with an active area of 0.0105 mm 2 . Its low power consumption and good area efﬁciency makes this LPF suitable for WBAN


I. INTRODUCTION
The rapid development in biomedical devices shows the rising public concern towards health topic. Moreover, the advancement in wireless technologies and radio frequency communications enables the evolution of ''e-health'' services, allowing healthcare providers to efficiently administer and deliver a great variety of healthcare services. Health information including vital signs and emotion statuses can be closely monitored at anytime, anywhere. Doctors may be alerted in case of emergencies [1].
One key technology that aligns with ''e-health'' concept, namely, wireless body area network (WBAN), describes the wireless network that builds the communication channel between tiny physiological signal sensors and central con- The associate editor coordinating the review of this manuscript and approving it for publication was Emrecan Demirors .
trolling unit for monitoring purpose [1]. Notably, for medical data transmission, it is crucial to carefully select and adjust the operating frequency bands to avoid loss of accuracy and reduce the latency of wireless data transfer. In-time transmission of data is always critical in medical data monitoring especially when alerting emergencies. Besides, power and area consumption are also important attributes for WBAN devices. Especially for those implanted WBAN devices, long battery life and miniature size can largely improve the quality of service (QoS). Supporting by IEEE 802.15.6 standard [2], a fully on-chip receiver front-end block shown in Fig. 1 undertakes the coordination task in between the central processing unit and the sensing front-end in the WBAN system. Receivers, as the entry block of the entire wireless transceiver systems, play a crucial role in quantifying system's performance and reliability [3]- [5]. In order to support multi-standard operation, passband reconfigurability of the filtering block in the WBAN receivers becomes necessary. Besides, the filter shall not add extra power and area expense to the entire receiver. This paper provides a low-pass reconfigurable filtering solution at high frequency while meeting the stringent power and area requirements for short-range WBAN communications.
Over the years, various low-voltage active filter designs have been well developed. Among these, active resistorcapacitor (active-RC) topology and transconductor-C (Gm-C) topology are popular choices in wireless communication applications. As illustrated in Fig. 2 (a), the active-RC topology shows good linearity performance, but the lack of local feedback around its active elements results in the limited filter's bandwidth [6]- [9]. Using resistive elements also results in high power and large area consumption, making such topology less attractive to today's WBAN market. On the contrary, as shown in Fig. 2 (b), the open-loop operation of the Gm-C topology suggests a reduction in power consumption as compared to the active-RC topology, even at high frequency. Moreover, previous works suggest that when the transconductance value G m or the capacitance value C are tuned, we can control the frequency response of the Gm-C filter for multi-standard wireless receiver systems [11], [15], [16]. The digitally configurable OTA in [16] allows continuous tuning of G m whereas the other capacitive tuning method in [15] adopts the programmable capacitor bank with control logic to digitally tune C. In fact, the digitally tuned OTAs in the former Gm-C topology employ powerhungry common-mode feedback circuitry and also show poor linearity. The large area occupied by the capacitor bank brings up the area concern for WBAN devices. For short-range WBAN devices or corresponding peripherals, power consumption, linearity performance and area efficiency are all important attributes. Therefore, this work addresses these issues where we propose a novel G m -tunable transconductor topology. The proposed circuit achieves tuning capability with improved linearity through the novel regulated cascode structure. The use of an additional gain stage with a cascode transistor regulates the drain-source voltage of the input transistor and also forms a feedback loop to boost the output impedance. In addition, a level shifter is added in between the gain stage and the input transistor to achieve wide tuning range and further improve the linearity. By using the single-stage amplifier as the gain stage and making the input transistors operating in linear region, ultra-low power is achieved in this work. Furthermore, the third-order Butterworth filter realized by the proposed transconductor occupies small chip area since the G m tuning scheme with fixed capacitors largely reduces the area as compared to those conventional designs with the capacitor bank.
This paper is structured into four sections. Firstly, section I serves as the introduction. Section II begins with the Butterworth filter design and continues with the proposed fully differential transconductor core with novel tuning structure. With the common-mode feedback, the complete fully differential third-order low-pass filter is shown with the proposed transconductor cells. Measurement results and comparison table are presented in Section III and conclusions are drawn in the last section.

II. PROPOSED THIRD-ORDER LPF WITH TUNING CAPABILITY
In this section, the Butterworth structure is first introduced to explain the filter's operation. Then the proposed tunable regulated cascode transconductor core is analyzed in detail. Lastly, the complete design is presented with common-mode feedback.

A. THIRD-ORDER BUTTERWORTH LOW-PASS FILTER
For a low-pass analog filter, the generalized transfer function is given as where the coefficients m, n and K are real numbers and the imaginary part s introduces the frequency components. The Contrarily, the slope of the magnitude curve will increase by the same ratio when coming across a zero frequency. Not surprisingly, numerous approximation methods on the frequency response have been raised such as elliptic, Chebyshev, Butterworth, and many others. Out of those classic methods, Butterworth filter is chosen due to its ''maximally flat'' response and hence most suitable in this low-pass filter VOLUME 9, 2021 design for the WBAN system [10], [11]. Higher-order Butterworth filters are constructed by cascading lower-order ones. Here, the proposed third-order low-pass filter begins with a lossy integrator as the first-order block and is cascaded by a biquadratic cell as the second-order block. The generalized transfer function is given as The first pole is created by the first-order Gm-C filter shown in Fig. 3 (a). The Kirchhoff's current law is applied on node X to obtain its first-order response as in (3). The fraction a in this design is set to zero so that the result follows a low-pass frequency response and create a pole in the final transfer function. The biquadratic cell, derived from the RLC ladder network prototype in Fig. 3 (b), contributes two poles to the final frequency response. As shown in Fig. 3 (c), G m1 performs voltage to current conversion but with a reversed polarity to obtain a positive output V 4 integrated from V x . G m2 replaces the resistor G while the capacitor C 1 stays unchanged. The subsequent gyrator cell formed by G m3 and G m4 together with another capacitor C 2 has an equivalent inductance as in (5).
To improve the system's stability, the final circuit is converted into fully differential structure. By integrating the transfer functions of the two stages, the final frequency response can then be derived with the device parameters.
In this work, identical transconductor cells are employed, implying the same G m values throughout the entire LPF block. In the lossy integrator stage, the dc gain is unity and the capacitance C 0 is chosen such that ω 0 C 0 G m , resulting in a negligible effect from C 0 over the bandwidth of interest. Then the biquadratic section contributes to the −3 dB attenuation at the passband corner, where we need |T 2 (s)| s 2 =−ω 2 0 = Q. The quality factor Q is √ 1/2 so we have 2C 1 = C 2 . In such way, the third-order low-pass filtering can be realized. Through the tuning of either G m or the capacitance value, the filter's cutoff frequency is determined. With such tunable frequency response, we can obtain the prototype of the bandwidthtunable third-order Butterworth LPF, where we propose a novel transconductor circuit to meet the WBAN network design requirements.

B. PROPOSED ULTRA-LOW POWER TUNABLE TRANSCONDUCTOR WITH ENHANCED LINEARITY
Tuning capability is crucial for the LPF in multi-standards WBAN applications. In the Gm-C filters, the cutoff frequency is proportional to the G m value and inversely proportional to the capacitance C. Literature mainly chose to tune the bandwidth with programmable capacitor arrays to prevent linearity distortion [14]- [16]. However, the capacitor array occupies large chip area and consumes extra power, which is less favorable to meet WBAN standards. In this work, the tuning scheme is fulfilled by tuning the G m values in the identical transconductor cells in the third-order Butterworth LPF.
In the transconductor cell, the conversion from the input voltages to the output currents is quantified by the linear transconductance factor G m . As illustrated in Fig. 4, the current flowing through the common-source transistors M1 where V i = V gs1 − V gs2 and β is the coefficient defined by the physical properties of the transistor. On such account, (6) shows that the transconductance I o /V i is linear only when V gs is large enough and reaches velocity saturation, which contrasts with the prerequisite of low power design. However, we can easily observe a linear relationship between input voltage and output current in (7). This value, corresponding to a constant V ds over the variation of V gs and I ds , defines the linear transconductance and is represented by G m (or g m in small-signal model).
As mentioned, the cutoff frequency in this work is tuned by varying individual G m in each transconductor simultaneously. Equation (8) indicates that G m can be controlled by the β factor or V ds . However, the β factor is hard to change as it is related to the transistor's sizing and physical constraints. Hence, G m value can only be tuned by controlling the drain-to-source voltage of the input transistors. As shown in Fig. 5 (a), the common-source transistor M2 functions as a negative feedback amplifier to fix V ds1 at a constant level so that the input transistor M1 operates in the triode region. The corresponding transfer characteristic should consider various factors including the second-order effects such as mobility degradation and parasitic capacitance. The Taylor expansion of the transistor model is applied to describe its I-V characteristic [12].
where the coefficient of the fundamental V ds1 term is given by a 1 ≈ β(V gs1 − V th ). As the even-order terms are cancelled out through adopting the fully differential structure, the third-order term V 3 ds1 becomes the main source of nonlinearity. To improve the linearity, one effective method is to reduce the V ds1 level to minimize higher-order terms in (9). Hence, one major drawback of this simple structure is the bias of the input transistors is restricted by V gs2 which leads to its modest linearity. Besides, its limited tuning range is another shortcoming of this structure, where V ds1_min = V th2 .
In this work, we propose a novel regulated cascode structure to allow a wider range of V ds1 tuning while lowering its value to improve linearity, as illustrated in Fig. 5 (b). The gain stage is an operational transconductance amplifier (OTA) that forms a feedback loop to achieve sufficiently large gain and hence boosts the output impedance of the transconductor. The output impedance is approximated as: R out = r o1 + r o3 + Ag m3 r o1 r o3 ≈Ag m3 r o1 r o3 (10) The PMOS source follower M2 functioning as a level shifter is inserted to the inverting input of the OTA. This level shifter reduces the V ds1_min of the input transistor M1 by an amount of V sg2 to widen the tuning range of the transconductor cell. As a result, we are able to tune the transconductance without degrading the linearity. Note that the body of M2 is connected to its own gate terminal with a floating well, so that voltage between its body and source V bs2 is zeroed, producing a constant threshold voltage V th2 for level shifting.
The amplifier together with the level shifter maintains V ds1 at a pre-determined level at (V ctrl − V sg2 ). In this way, the cascode amplifier ''regulates'' V ds1 and results in lesser variations in I out . Meanwhile, this regulating structure maintains the triode operation region of the input transistor M1, with a simplified expression of its drain current Finally, the transconductance becomes: (11) Therefore, the gain offered by the amplifier increases the effective transconductance of M3 by A times and hence reduces the linearity error 2I D1 /(Ag m3 V ds1 ). The level shifter widens the tuning range with V ds1_min = V ctrl − V sg2 , hence allowing the control of the voltage condition of M1 with better linearity. Continuous tuning of the passband is then possible by tuning V ctrl whereas literature realized the tuning scheme by complex programming capacitor arrays [15]. Besides, simulations on dc operations also showed reduced power as compared with other G m tuning designs [16]. Together with the simplified structure, this work realizes the tuning capability with good power and area efficiency.
In Fig. 6 (a), the proposed transconductor structure is transformed to fully differential structure to reduce the evenorder non-linear elements caused by interference. In addition, to hold the output common mode level at constant, the common-mode feedback (CMFB) loop is implemented with dual-differential pair (DDP) common-mode detector topology based on current-steering principle, as depicted in Fig. 6 (b).

III. MEASUREMENT RESULTS AND COMPARISON
The proposed third-order low-pass filter was designed and fabricated using TSMC 40 nm CMOS process. With input common-mode level at 550 mV (half of V DD ), the overall current consumption was 1.76 mA to 2.06 mA corresponding to the minimum and maximum V ctrl . As shown in Fig. 7, this design occupies a core area of 0.0105 mm 2 (0.07 mm × 0.15 mm) and a total die area of 0.18 mm 2 (0.36 mm × 0.5 mm) including decoupling capacitors and I/O pads.
Post-layout simulations in Cadence R Virtuoso ADE and on-PCB measurements were performed subsequently to evaluate the performance. The test-bench for the LPF prototype was fed with 100 differential input and 1.1 V supply. In the WBAN receiver front-end, the subsequent block following the filter is a variable gain amplifier (VGA) with extremely high input impedance. To preserve the consistency for the system design, the differential output in the test-bench is loaded with very high impedance, up to 100 k .
First, the tunable frequency response was examined. V ctrl represents the external control voltage that tunes the G m value of the transconductor. Fig. 8 (a) and (b) shows the frequency response under different V ctrl values for both post-layout simulation and on-PCB measurement. From the plot, we can observe 20 MHz passband frequency change with every 25 mV voltage change, ranging from 450 mV to 550 mV and from 20 MHz to 80 MHz and it allows continuous and precise tuning within the tuning range. The anticipated impacts caused by additional capacitance from the off-chip Balun and signal converters are the main reason of reduced cutoff frequencies in the measured results.
Other than the frequency response, the linearity of the filter was also evaluated. When the even-order harmonic terms are cancelled out in fully differential structure, the main source of nonlinearity is the third-order term. As shown in Fig. 8 (c), the input-referred third-order interception point (IIP3) is a hypothetical extrapolation point where the fundamental component intercepts with the third-order intermodulation products in the input-output power plot. The IIP3 value of this LPF is 7.67 dBm with 450 mV control voltage corresponding to the 20 MHz cutoff frequency.
In addition, a figure-of-merit (FoM) introduced in [13] is used to compare with relevant works.
where N is the number of poles and zeros, P C /N is the normalized power consumption, and SFDR · N 4/3 is the normalized spurious free dynamic range. With P N denotes the input-referred noise power, the spurious-free dynamic range (SFDR) measured in dBc defines the dynamic ratio between the power of the fundamental signal and that of the next most significant spurious signal in frequency domain, hence accounting for both the filter's linearity and noise performance.
The important parameters are summarized in Table. 1 with literature. The active-RC design in [14] shows good linearity but the power consumption is rather high with lower tunable bandwidth. In [15], although the Gm-C filter adopts the current-reuse amplifiers to achieve lower FoM, the filter's cutoff frequency has no tuning capability and its higher-order frequency response increases the power consumption and the chip area. In addition, the work in [16] uses similar G m tuning scheme, indicating that its nonlinear distortion is also caused by the triode-region input transistors. The FoM comparison suggests that this work achieves improved noise and linearity performance. To summarize, the proposed filter tunes the cutoff frequency continuously with wide tuning range. It also shows excellent power and area efficiency while maintaining comparable linearity. These features highlight the significance of this design in the WBAN receiver frontend implementation.

IV. CONCLUSION
In this paper, we have proposed an ultra-low power tunable third-order Butterworth Gm-C low-pass filter for multi-standard receivers for WBAN applications. By employing a novel regulated cascode OTA gain stage, the fully differential transconductor core allows continuous passband tuning from 20 MHz to 80 MHz while maintaining an IIP3 of 7.67 dBm. Fabricated in CMOS 40 nm process with 1.1 V supply voltage, measurements show that this design consumes 2 mW of power and occupies 0.0105 mm 2 of chip area. The low FoM of this work also shows its advantages in power consumption and noise performance. In conclusion, this design fulfills the filtering needs in advanced WBAN receivers.