# 0.5 V Fifth-Order Butterworth Low-Pass Filter Using Multiple-Input OTA for ECG Applications

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

## 1. Introduction

_{2}and L

_{4}are simulated using OTA-based gyrators. The resistors R

_{S}and R

_{L}are simulated using OTAs as well. It should be noted that the filter in [7] employs eleven FD-OTAs and consumes 453 nW of power. The number of active devices that are used to realize this fifth-order Butterworth filter can be reduced by using multiple-output fully differential OTA (MOFD-OTA) as shown in Figure 3b [8,9], or fully differential-difference transconductance (FDDA) (a multiple-input active device) as shown in Figure 3c [10]. The structures in [8,9] employ six MOFD-OTA while the structure in [10] employs five FDDAs and one OTA. The filter in [8] consumes 350 nW of power and offers a 49.9 dB dynamic range while the filter in [9] consumes 41 nW of power and offers a 61.2 dB dynamic range. The filter in [10] consumes 453 nW of power and offers a 50 dB dynamic range.

## 2. Fifth-Order Butterworth Low Pass Filter

#### 2.1. Multiple-Input Gate-Driven OTA

_{1}and M

_{2}were used to create a multiple-input differential pair, biased by the self-cascode current sources M

_{7,7c}and M

_{8,8c}. The drain currents of the input differential pair are transferred to the outputs (I

_{o+}and I

_{o-}) through the current mirrors composed of the self-cascode transistors M

_{3/3c}-M

_{4/4c}and M

_{5,5c}-M

_{6,6c}. The current mirrors are loaded with the self-cascode current sources M

_{10,10c}and M

_{9,9c}. Note that the tail node that supplies the differential pair in Figure 6 is drawn with two branches for esthetic reasons. The application of self-cascode connections in this design allows for an increase in the output resistance of the OTA, which entails increasing the DC voltage gain of this circuit. The transistors M

_{9c}-M

_{11c}form a simple common-mode feedback circuit (CMFB) circuit, which forces the output common-mode level to be equal to the reference potential V

_{CM}. All the transistors operate in a subthreshold triode region. If the common-mode level is increasing/decreasing, the channel resistances of M

_{10C1,c2}are increasing/decreasing as well, thus lowering the currents flowing through M

_{10}and M

_{9}, and consequently, decreasing/increasing the common-mode level to the desired value. The transistors M

_{9c}and M

_{10c}are divided into two devices, which makes the circuit insensitive to the output differential signals of the OTA, at least for small amplitudes of the signal. For larger amplitudes of the output signals, one can observe nonlinear components of the drain currents I

_{D9}and I

_{D10}, caused by the differential output voltage of the OTA. However, this nonlinear effect is not apparent at the differential output of OTA, since variation of I

_{D9}and I

_{D10}are identical. This effect, however, causes variation of the output common-mode level. Figure 7 illustrates the large signal transfer characteristics and the common-mode level variation for unloaded OTA in Figure 6 controlled with differential signals. Note, moderate nonlinear effects are caused by the nonlinear output conductance of the OTA rather than that of the CMFB. Variations of the common-mode output voltage are maintained at an acceptable level.

_{9c}–M

_{11c}and variations of the output common-mode level caused by differential signals. However, the negative effects can be maintained at an acceptable level.

_{ieff}= (WL

_{i}∙WL

_{ic})/(WL

_{i}+ WL

_{ic}), i = 3…10, WL

_{9,10c}= WL

_{9,10c1}+ WL

_{9-10c2}, K

_{Fn}and K

_{Fp}are the flicker noise constants for n- and p-channel transistors, respectively, and C

_{OX}is the oxide capacitance per unit area.

#### 2.2. Proposed Filter

_{0}, OTA

_{1}in Figure 3b and OTA

_{0}, FDDA

_{1}in Figure 3c, it can be noted that these devices are used to realize a floating resistor [9]. In this work these components together with the capacitor C

_{1}create a lossy integrator as shown in Figure 9a [8], Figure 9b [10]. The ideal transfer function of these circuits can be expressed as:

_{0}in Figure 3b,c can be removed by using multiple-input OTA. This application can only be realized using multiple-input OTA and it is not possible by using conventional OTA. It should be noted that only the parts mentioned above in Figure 9a of [8], Figure 9b of [10] are modified, the other parts (OTA

_{2-5}or FDDA

_{2-5}) are not changed and the feedback connection is still similar to the filters in [8,10].

## 3. Results and Discussion

_{B}= 3.3 nA consumes 8.25 nW under a 0.5 V supply voltage. The isolation between OTA inputs is assured by the large value resistance of the MOS transistor operating in a cutoff region. The input currents are well below 100 pA for input range rail-to rail.

_{S}= R

_{L}= 1 Ω, C

_{1}= C

_{5}= 393.4 µF, C

_{3}= 1.27 mF, and L

_{2}= L

_{4}= 1.03 mH. For the OTA-C filter C

_{1}= C

_{5}= 5.43 pF, C

_{2}= C

_{4}= 14.2 pF, C

_{3}= 17.57 pF, and the bias current for each OTA was I

_{B}= 3.3 nA. Note that the bias current circuit serves to bias all OTAs hence the maximum power consumption of the filter is 34.65 nW. Figure 10 shows the frequency responses of the RLC and the proposed filter. The gain magnitude at low frequency was −6 dB and −6.4 dB and the cut-off frequency (f

_{c}) was 250.2 Hz and 250.4 for the RLC and OTA filters, respectively. Both curves are in good agreement up to −70 dB. Figure 11 shows the frequency response of the filter with different bias currents ranging from 0.1 nA to 3.3 nA while the f

_{c}was in the range of 17.11 Hz to 250.4 Hz. The tuning capability and the linear relation between f

_{c}and I

_{B}are demonstrated in Figure 12. The transient response of the filter for the input sine wave of V

_{inpp}= 100 mV and 10-Hz frequency are illustrated in in Figure 13. The total harmonic distortion (THD) was 1%.

_{rms}. Figure 18 shows the performance of the proposed filter in processing the ECG signal where (a) depicts the ECG signal with a distortion signal (5 mV/500 Hz) that was applied at the input of the filter and (b) depicts the filtered output signal.

_{DD}of fifth-order low-pass filters are shown in Figure 19. Compared with the works in [7,8,10], the proposed filter offers clearly better FOM. The FOM is even slightly lower than the one in [9] with half the value of V

_{DD}. It is worth noting that the estimated chip area of 2-inputs and 3-inputs OTA based on the MIGD technique is increased by approximately 5% and 8%, respectively, compared to that of a single-input conventional OTA with the same transistor dimensions. This confirms the advantage of this technique of saving chip area. Note, a similar conclusion of this advantage based on experimental results is stated in [11]. The small chip area of the proposed filter is evident in Table 1 compared with that of [10] that used off-chip capacitors for filter realization.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

_{B}, and a multiple-input OTA composed of n identical OTAs of the same structure, but biased with currents of I

_{B}/n (Figure A1b). For simplicity, let us consider only the thermal noise.

_{inmax}) to the i-th input referred noise, then for the multiple-input OTA in Figure A1b we have:

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**Figure 7.**Output differential voltage and common-mode level versus input differential voltage for unloaded OTA in Figure 6.

**Figure 13.**The transient response of the filter for input sine wave with V

_{inpp}= 100 mV and 10 Hz.

**Figure 14.**The frequency response of the proposed filter under process, voltage and temperature (PVT) corners.

**Table 1.**Performance comparison between the proposed filter and other fifth-order low-pass filters for ECG signal acquisition.

Symbol | This Work | MEJ (2019) [10] | IEEE TBioCAS (2019) [9] | IEEE TCAS-II (2018) [8] | IEEE TBioCAS (2009) [7] |
---|---|---|---|---|---|

V_{DD} [V] | 0.5 | 0.25 | 1 | 1 | 1 |

Tech [um] | 0.18 | 0.13 | 0.18 | 0.18 | 0.18 |

V_{TH} [V] | 0.5 | 0.44 | 0.5 | 0.5 | 0.5 |

Order (N) | 5 | 5 | 5 | 5 | 5 |

No. of active device | 5 MIGD-OTAs | 6 FDDTAs | 6 OTAs | 6 OTAs | 11 OTAs |

Structure | G_{m}-C fully-diff. | G_{m}-C fully-diff. | G_{m}-C fully-diff. | G_{m}-C fully-diff. | G_{m}-C fully-diff. |

BW [Hz] | 250 | 100 | 250 | 250 | 250 |

IRN [µV_{rms}] | 167 | 4.7 | 134 | 100 | 300 |

DR [dB] | 63.24 | 57.00 | 61.2 | 49.9 | 50 |

Power (P) [nW] | 34.65 | 603 | 41 | 350 | 453 |

FOM = P/(N * BW * DR) [pJ] | 0.0191 | 1.7 | 0.0286 | 0.896 | 1.15 |

LV capability = V_{TH}/V_{DD} * 100 [%] | 100 | 176 | 50 | 50 | 50 |

Area [mm^{2}] | 0.08 (estim.) (off-chip cap.) | 0.67 (off-chip cap.) | 0.24 | 0.12 | 0.13 |

Obtained results | Simulation | Measured | Measured | Measured | Measured |

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**MDPI and ACS Style**

Kumngern, M.; Aupithak, N.; Khateb, F.; Kulej, T. 0.5 V Fifth-Order Butterworth Low-Pass Filter Using Multiple-Input OTA for ECG Applications. *Sensors* **2020**, *20*, 7343.
https://doi.org/10.3390/s20247343

**AMA Style**

Kumngern M, Aupithak N, Khateb F, Kulej T. 0.5 V Fifth-Order Butterworth Low-Pass Filter Using Multiple-Input OTA for ECG Applications. *Sensors*. 2020; 20(24):7343.
https://doi.org/10.3390/s20247343

**Chicago/Turabian Style**

Kumngern, Montree, Nattharinee Aupithak, Fabian Khateb, and Tomasz Kulej. 2020. "0.5 V Fifth-Order Butterworth Low-Pass Filter Using Multiple-Input OTA for ECG Applications" *Sensors* 20, no. 24: 7343.
https://doi.org/10.3390/s20247343