# 0.5 V, nW-Range Universal Filter Based on Multiple-Input Transconductor for Biosignals Processing

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## Abstract

**:**

_{m}) in filter application, in terms of topology simplification, increasing filter functions, and minimizing the count of needed active blocks and their consumed power. Further, the filter enjoys high input impedance, uses three MI-G

_{m}s and two grounded capacitors, and it offers both inverting and non-inverting versions of low-pass (LPF), high-pass (HPF), band-pass (BPF), band-stop (BS) and all-pass (AP) functions. The filter operates under a supply voltage of 0.5 V and consumes 37 nW, hence it is suitable for extremely low-voltage low-power applications like biosignals processing. The circuit was designed in a Cadence environment using 180 nm CMOS technology from Taiwan Semiconductor Manufacturing Company (TSMC). The post-layout simulation results, including Monte Carlo and process, voltage, temperature (PVT) corners for the proposed filter correlate well with the theoretical results that confirm attractive features of the developed filter based on MI-G

_{m}.

## 1. Introduction

_{m}stage), is a basic block for electronic applications like filters and oscillators [5,6,7,8,9,10]. Unlike the standard and well-known single-input OTA, the multiple-input OTA/transconductor (MI-OTA/MI-G

_{m}) offers increased arithmetic operation at the input that results in a reduced number of active elements, power consumption, and simplification of the filter topology. It is worth noting that for designers in CMOS, it is a challenge to design a circuit operating with supply voltage V

_{DD}around or even below the threshold voltage V

_{TH}of the MOS transistor without scarifying the performance of the circuit. The use of multiple-input transconductors to reduce the number of components in the design of OTA-C filters was confirmed in the literature [5,6]. It was shown that the multiple-input OTA can reduce the number of components, silicon area, and power dissipation by approximately factor k, where k is the number of OTA inputs [5]. Multiple-input transconductor can be obtained by the following techniques: 1. using extra differential pairs [5,6], or 2. using a multiple-input floating-gate transistor (MIFG) [7,8,9,10]. While the first technique increases the count of transistors, current branches, and the complexity of the design, the second technique suffers from the high-voltage offset, incapability of processing DC signals, and becomes unsuitable for modern deep-nanoscale CMOS technology with gate leakage [11]. A promising technique that offers multiple-input OTA without the above-mentioned limitations is the multiple-input MOS transistor (MI-MOS), firstly presented and experimentally confirmed in [12,13,14]. The multiple-input MOS transistor is shown in Figure 2. The multiple-input terminals V

_{1}, V

_{2}, etc. can be obtained from: a. the gate while the bulk is biased by voltage V

_{BB}, b. from the bulk while the gate is biased by V

_{BG}, c. from the bulk-gate (known as dynamic threshold MOS transistor “DTMOS”) without biasing or d. from the bulk-gate (known as quasi-floating-gate “QFG”) with different biasing voltages V

_{BB}and V

_{BG}for bulk and gate, respectively [15].

_{i}(i = 1,…,N) connected to the bulk terminal of a MOS transistor. To provide proper biasing of the bulk terminal for DC operation, the high resistance resistors R

_{MOS}is used. These R

_{MOS}are realized as the anti-parallel connection of two minimum-size transistors M

_{L}, operating with V

_{GS}= 0. For AC signals, and for frequencies f >> 1/2πC

_{i}R

_{MOSi}, i = 1…N, resistors R

_{MOS}are shunted by capacitances C

_{i}, which create an analog voltage divider/voltage summing circuit, with the gain coefficients determined solely by the ratio of capacitances [15].

_{m}to build a multiple-input voltage-mode analog filter. As a result, the number of used active devices is reduced while offering more filtering responses compared to conventional G

_{m}-based filters.

## 2. Methods

_{m}and the universal filter based on it will be described.

#### 2.1. The Multiple-Input G_{m}

_{m}stage are shown in Figure 4a,b, respectively. In an ideal case, the transfer characteristic of the MI-G

_{m}stage of Figure 4a can be expressed by:

_{m}is the transconductance gain, V

_{+}

_{1}and V

_{+}

_{2}are signals at the non-inverting inputs, V

_{−}

_{1}, V

_{−}

_{2}are signals at the inverting inputs, and I

_{out}is the output current.

_{m}stage discussed here was first presented and experimentally verified in [15]. The circuit employs the MI-bulk-driven differential pair M

_{1}, M

_{2}, with the source-degenerative bulk-driven transistors M

_{11}, M

_{12}, which operate in the triode region and improve the circuit linearity. Note, that V

_{GS}as well as V

_{BS}voltages for M

_{11}, M

_{12}and M

_{1}, M

_{2}are identical for any common-mode input voltage and biasing current. The single-input gate-driven counterpart of the input stage was first proposed in [16], and its weak-inversion version was discussed in [17]. Here, due to the use of bulk-driven transistors, and an additional capacitive voltage divider, both, the input linear range, as well as the input common-mode range are significantly increased, as compared with the conventional gate-driven (GD) version operating in a weak-inversion region. Moreover, the application of MI transistors allows realizing MI-G

_{m}s without multiplying the input differential pair, as in classical solutions, which saves power and simplifies the overall structure of such circuits.

_{T}is the technology current, W and L are the transistor channel width and length, respectively, n

_{p}is the subthreshold slope factor, U

_{T}is the thermal potential and V

_{TH}is the threshold voltage, which can be linearly approximated as:

_{TO}is the threshold voltage for V

_{BS}= 0.

_{m}can be expressed as:

_{p}− 1)=g

_{mb}

_{1,2}/g

_{m}

_{1,2}at the operating point, m= (W

_{11}/L

_{12})⁄(W

_{1}/L

_{1}) is the relative aspect ratio of the two matched transistor pairs M

_{11}–M

_{12}and M

_{1}–M

_{2.}β

_{i}is the voltage gain of the input capacitive divider from one input, which neglects the second order effects and for f >> 1/C

_{i}R

_{MOSi}can be approximated as:

_{set}[17].

_{i}η, which for the discussed case (β

_{i}= 0.5, η = 0.34) means that the linear range is extended around 6 times.

_{m}can be calculated from Equation (4) as:

_{1}and M

_{2}, multiplied by a factor of [4m⁄(4m + 1)] β

_{i}η, which for the proposed design in the optimal case (m = 0.5) is equal to around 1⁄9.

_{m}can be approximated as:

_{m}. On the other hand, however, self-cascode connections allow for enlarging the output resistance of the MI-G

_{m}, thus improving its voltage gain and at least partially compensating the losses caused by the input capacitive divider and the small bulk transconductance of MOS transistors.

_{OX}is the oxide capacitance per unit area and K is the flicker noise constant, the input-referred noise of the MI-G

_{m}, referred to as one of the differential inputs, is given by:

_{ds}

_{11}||r

_{ds}

_{12}) at the operating point.

_{m}is increased, as compared to its single-input GD counterpart, due to the lower transconductance G

_{m}. However, the input noise is increased in the same proportion as the input linear range, therefore, the dynamic range will not be affected and remains the same in both realizations.

#### 2.2. Universal Filter Design

_{m}blocks, and two grounded capacitors and it offers five standard filtering functions [26]. In this work, a multiple-input voltage-mode analog filter using multiple-input transconductors MI-G

_{m}is proposed as shown in Figure 5b. The structure will show that the multiple-input G

_{m}-based filter can reduce the number of used active devices and can offer more filtering responses compared with conventional G

_{m}-based filters. The filter employs three multiple-input G

_{m}stages and two grounded capacitors, which is desirable in integrated solutions. Thanks to the MI-G

_{m}elements that offer noninverting/inverting multiple-input terminals, noninverting/inverting transfer functions of five types of filtering responses, namely, low-pass, high-pass, band-pass, band-stop, and all-pass can be easily obtained. Moreover, the input signals are connected to the high-impedance inputs of MI-G

_{m}, hence the additional buffer circuits to avoid the loading effects are not required. It is worth noting that although both filters in Figure 5a,b offer the five standard filtering functions, the count of active elements is reduced from 5 to 3 thanks to the MI-G

_{m}. This results in power consumption reduction and filter topology simplification, and in offering more transfer functions (including both non-inverting and inverting versions of five standard filtering functions).

_{o}) and the quality factor (Q) are given by:

_{o}can be controlled electronically by G

_{m}

_{1}= G

_{m}

_{2}while the parameter Q is controllable orthogonally by the ratio of C

_{2}/C

_{1}.

_{m}, there are three major non-idealities that should be considered [29]: (i) the frequency-dependent transconductance, (ii) the input parasitic resistances and capacitances, (iii) the output parasitic resistances and capacitances.

_{m}, where R

_{+}, R

_{−}, C

_{+}, C

_{−}are the input parasitic resistances and capacitances, and R

_{o}, C

_{o}is the output parasitic resistance and capacitance, respectively. Considering Figure 5b the parasitic resistances at nodes V

_{o}

_{1}and V

_{o}

_{2}are, respectively, R

_{o}

_{1}//R

_{+}

_{1}and R

_{o}

_{2}//R

_{+}

_{3}, thus the value of these parallel resistances is very high and can be neglected. Consider the parasitic capacitances at nodes V

_{o}

_{1}and V

_{o}

_{2}, they can be expressed respectively as ${C}_{1}^{\prime}={C}_{1}+{C}_{o1}+{C}_{+2}$ and ${C}_{2}^{\prime}={C}_{2}+{C}_{o2}+{C}_{-1}+{C}_{+3}$.

_{mnj}is the non-ideal transconductance gain of the j-th MI-G

_{m}that is frequency-dependent, and can be approximately given by [29,30]:

_{o}and Q become as follows:

_{o}as compared to the ideal case.

## 3. Results and Discussion

_{m}stage first presented in [15] was used. The transistor aspect ratios W/L are presented in Table 2. The input metal-insulator-metal (MIM) capacitor C

_{i}with a capacitance value of 0.5 pF was used. The layout of the MI-G

_{m}is shown in Figure 7, with a silicon area of 116.3 µm × 99.2 µm.

_{m}for I

_{set}= [2, 5, 10, 15, 20, 25] nA are shown in Figure 8. The enhanced linearity in the V

_{in}range of ±500 mV is clearly observable.

_{1}= C

_{2}= 15 pF and the setting current I

_{set}= 5 nA. The simulated cut-off frequency value of 153 Hz is very close to the calculated value of 154.9 Hz. The power consumption of the filter was 37 nW.

_{1}= C

_{2}= 15 pF. The setting current was I

_{set}= 2 nA, 5 nA, 10nA, and 20 nA and the cut-off frequency values were 62.3 Hz, 153 Hz, 301.9 Hz, and 595.6 Hz, respectively. Results shown in Figure 10 confirm the wide tuning capability of the proposed filter for low-frequency biomedical applications.

_{DD}± 10%, and the temperature corners were 0 °C and 70 °C.

_{pp}@ 50Hz and its output spectrum. The total harmonic distortion (THD) of 0.33% was achieved, which was kept still below 1% for the input signal of 200 mV

_{pp}@ 50 Hz. The output integrated noise of the LPF was 220 µV

_{rms}which resulted in a 50 dB dynamic range (DR = 20 × log (V

_{rms-max}/V

_{rms-onoise})) of the filter with 1% THD.

_{m}stage in filter applications mainly by means of reducing the count of active blocks and power consumption. The figure of merit (FoM) is also presented, where a lower FoM implies the better performance of the filter.

## 4. Conclusions

_{m}in filter application, in terms of topology simplification, increasing filter functions, and minimizing the count of the needed active blocks and their power consumption. Therefore, the developed circuit is a good candidate for extremely low-power low-voltage applications like biosignals processing. The filter application offers the largest amount of filtering functions with a minimum count of active elements. The post-layout simulations prove the presented advantages of MI-G

_{m}.

## Author Contributions

## Funding

## Conflicts of Interest

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Filtering Function | Input | Output | |
---|---|---|---|

LP | Non-inverting | ${V}_{in4}\phantom{\rule{0ex}{0ex}}{V}_{in5}\phantom{\rule{0ex}{0ex}}{V}_{in1}\phantom{\rule{0ex}{0ex}}{V}_{in1}$ | ${V}_{o1}\phantom{\rule{0ex}{0ex}}{V}_{o1}\phantom{\rule{0ex}{0ex}}{V}_{o2}\phantom{\rule{0ex}{0ex}}{V}_{o3}$ |

Inverting | ${V}_{in3}\phantom{\rule{0ex}{0ex}}{V}_{in6}\phantom{\rule{0ex}{0ex}}{V}_{in1}\phantom{\rule{0ex}{0ex}}{V}_{in2}$ | ${V}_{o1}\phantom{\rule{0ex}{0ex}}{V}_{o1}\phantom{\rule{0ex}{0ex}}{V}_{o2}\phantom{\rule{0ex}{0ex}}{V}_{o3}$ | |

BP | Non-inverting | ${V}_{in1}$ and ${V}_{in6}$ ${V}_{in3}\phantom{\rule{0ex}{0ex}}{V}_{in6}\phantom{\rule{0ex}{0ex}}{V}_{in3}$ | ${V}_{o1}\phantom{\rule{0ex}{0ex}}{V}_{o2}\phantom{\rule{0ex}{0ex}}{V}_{o2}\phantom{\rule{0ex}{0ex}}{V}_{o3}$ |

Inverting | ${V}_{in2}$ and ${V}_{in5}$ ${V}_{in4}\phantom{\rule{0ex}{0ex}}{V}_{in5}\phantom{\rule{0ex}{0ex}}{V}_{in4}$ | ${V}_{o1}\phantom{\rule{0ex}{0ex}}{V}_{o2}\phantom{\rule{0ex}{0ex}}{V}_{o2}\phantom{\rule{0ex}{0ex}}{V}_{o3}$ | |

HP | Non-inverting | ${V}_{in5}\text{}\mathrm{and}\text{}{V}_{in2}$ | ${V}_{o3}$ |

Inverting | ${V}_{in6}\text{}\mathrm{and}\text{}{V}_{in1}$ | ${V}_{o2}$ | |

BS | Non-inverting | ${V}_{in5}$ | ${V}_{o3}$ |

Inverting | ${V}_{in6}$ | ${V}_{o3}$ | |

AP | Non-inverting | ${V}_{in5}\text{}\mathrm{and}\text{}{V}_{in4}$ | ${V}_{o3}$ |

Inverting | ${V}_{in5}\text{}\mathrm{and}\text{}{V}_{in3}$ | ${V}_{o3}$ |

Device Name | W/L (µm⁄µm) |
---|---|

M_{1}, M_{2}, M_{7}–M_{10}, M_{13} | 2 × 15/1 |

M_{3}–M_{6} | 2 × 10/1 |

M_{3c}–M_{6c} | 10/1 |

M_{7c}–M_{10c}, M_{13c}, M_{11}, M_{12} | 15/1 |

M_{L} | 5/4 |

This Work | [26] | [27] | [28] | |
---|---|---|---|---|

Technology (nm) | 180 | commercial IC | 180 | 180 |

V_{DD} (V) | 0.5 | ±15 | 1.2 | ±0.3 |

Power consumption (nW) | 37 | 860 × 10^{6} | 0.96 × 10^{6} | 5770 |

DR (dB) | 50 | 53.2 | ||

Fter function | 22 (VM) | 13 (VM) | 22(VM) | 20 (MM) |

Offer inverting and non-inverting of five standard responses | Yes | No | Yes | No |

Natural frequency (kHz) | 0.153 | 217 | 1 | 5 |

Number of active and passive element | 3-OTA, 2-C | 5-OTA, 2-C | 4-OTA, 2-C | 8-OTA, 2-C |

Total harmonic distortion (%) | 0.33@100 mV_{pp} | 1.93@200 mV_{pp} | 1.67@600 mV_{pp} | <2@200 mV_{pp} |

$FOM=\frac{{P}_{diss}}{{f}_{o}\times N\times DR}$ | 2.41 × 10^{−12} | - | 78.6 | 1.26 × 10^{−12} |

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**MDPI and ACS Style**

Khateb, F.; Kumngern, M.; Kulej, T.; Akbari, M.; Stopjakova, V.
0.5 V, nW-Range Universal Filter Based on Multiple-Input Transconductor for Biosignals Processing. *Sensors* **2022**, *22*, 8619.
https://doi.org/10.3390/s22228619

**AMA Style**

Khateb F, Kumngern M, Kulej T, Akbari M, Stopjakova V.
0.5 V, nW-Range Universal Filter Based on Multiple-Input Transconductor for Biosignals Processing. *Sensors*. 2022; 22(22):8619.
https://doi.org/10.3390/s22228619

**Chicago/Turabian Style**

Khateb, Fabian, Montree Kumngern, Tomasz Kulej, Meysam Akbari, and Viera Stopjakova.
2022. "0.5 V, nW-Range Universal Filter Based on Multiple-Input Transconductor for Biosignals Processing" *Sensors* 22, no. 22: 8619.
https://doi.org/10.3390/s22228619