1. Introduction
With the increasing demand of medical electronics, the analog frond-end circuit has been given much importance to improve the quality of medical devices. Figure 1 shows an analog frond-end circuit of wearable bio-telemetry monitoring applications in a UWB wireless body area network[1]. In this circuit, a chopper operational amplifier is used as a preamplifier to amplify the input signal 100 times for the electrocardiogram (ECG) applications, and a low-pass filter (LPF) should be used to remove the undesirable noise. Then a variable gain amplifier (VGA) is needed to adjust the gain for the large dynamic input. Because the ECG signal possesses a small amplitude (0.1-4~mV) and low frequency (0.1-250 Hz), it is vulnerable to flicker noises, thermal noises, and other varieties of electromagnetic devices[1]. Thus a low-pass filter with a low cut-off frequency is applied to the system to decrease the out-of-band noise. For this reason, the LPF is the key part that can improve the performance of the ECG acquisition system. However, for low frequency biomedical applications, implementing an LPF with large time constant ($\tau$ $=$ RC) under an acceptable capacitance (typically < 10 pF) in an analog IC circuit requires a very large resistance, and this resistance is too large to be integrated. For instance, it requires a resistance close to 60 M$\Omega $ to realize an LPF with the cut-off frequency of 280 Hz ($\tau$ $\approx$ 6 $\times$ 10$^{-4}$ s) under the capacitance of 10 pF. Assuming that such a large resistance is implemented using the polysilicon in a SMIC 0.18-$\mu $m CMOS process, it will occupy 0.2 mm$^{2}$ area at least, and this would lead to a high cost.
Usually, an analog integrated filter can be realized by a switched-capacitor technique or continuous-time technique[2, 3, 4]. The switched-capacitor filter is not suitable for a situation that requires large time constant because of the leakage problem[2]. Therefore, the use of an OTA-C filter as one of continuous-time filters has been proposed to realize a very low transconductance ($G_{\rm m})$ by using several techniques in References [5, 6, 7, 8, 9, 10]. Although these OTA-based filters have been developed to implement very small $G_{\rm m}$ for biomedical applications, their linear range is still very narrow[5, 6, 7, 8, 9, 10].
This paper presents a fifth order fully differential OTA-C low-pass filter to meet the requirement of biomedical system shown in Figure 1. The source degeneration circuit based on Reference [5] is improved to further expand the linear range of OTA-C filter. An output structure of OTA is proposed to reduce the loss of the filter passband gain.
2. OTA circuit design
In this study the active filter is based on the fully differential OTA circuit, so the OTA cell as the building block will affect the active filter's performance, such as linearity, pass-band gain and cut-off frequency.
2.1 OTA linear range
In OTA-C filter the cut-off frequency equation is given by[6]
$f_{\rm c} =\frac{G_{\rm m}}{2\pi C}.$ |
(1) |
From Equation (1), it can be seen that $G_{\rm m}$ should be as low as a few nS because of very low cut-off frequency requirement for ECG applications. Considering factors such as area, power and noise, the small-$G_{\rm m}$ OTA circuit is usually implemented with three techniques, including current cancellation and current division as well as source degeneration for low frequency applications[5, 6, 7, 11]. However, the OTA realized in this way only provides a linear range of around 0.1 V$_{\rm PP}$. As a part of the system shown in Figure 1, the OTA-C filter will process the signal that has been amplified 100 times by the preamplifier. So a maximum signal level of around 0.4 V$_{\rm PP}$ will appear in the input terminal of the OTA. Unfortunately, such a highly linear range could not be provided in References [5, 6, 7, 8, 9, 10, 11]. To tackle this problem, this study, which is based on Reference [5], proposes a new structure, which is shown in Figure 2(a). Compared with Reference [5], two extra transistors are added to the source degeneration structure, and a cascode structure is employed to the output stage of the OTA circuit so that a highly linear range and less passband degradation can be obtained.
In this OTA the current division transistors MM are adopted to split most of the current from MR or MR'. Current cancellation transistors MN are used to further reduce the transconductance. Transistors MR and MR' of the source degeneration devices are utilized to improve the linearity with wide input range. The dimensions of transistors MM were designed to lead most of the current to flow to ground. Transistors MR and MR' are biased in the triode region, and other MOSFETs are operated in the weak inversion region to reduce their circuit power consumption. Figure 2(b) shows the common-mode feedback (CMFB) circuit of the fully differential OTA.
Ignoring the channel-length modulation and body effect, the small-signal equivalent is studied to show how an OTA circuit of highly linear range can be achieved. As shown in Figure 3, $M$ represents the transconductance ratio between MM and M1, while $N$ is defined as the $g_{\rm m} $ ratio between MN and M1. Transistors M5 and MNB match each other. The OTA transconductance can be calculated by
Gm=iovi=Ngm1vgs1−gm1vgs1vgs1+vs1=N−1M+N+1gm1(M+N+1)1+gm1(M+N+1)(1go_MR+1go_M′R). |
(2) |
If the p-MOSFETs MR and MR' are matched, we have $g_{\rm o\_MR} =g_{\rm o\_MR'}$. The $G_{\rm m}$ is then given by
$G_{\rm m} =\frac{N-1}{M+N+1}\frac{g_{\rm m1} (M+N+1)}{1+\dfrac{2g_{\rm m1} (M+N+1)}{g_{\rm o\_MR} }}, $ | (3) |
$g_{\rm o\_MR} =\mu _{\rm p} C_{\rm OX} \frac{W_{\rm MR } }{L_{\rm MR } }(v_{\rm sg} -V_{\rm th} -v_{\rm sd} ), $ | (4) |
$g_{\rm m} =\frac{I_{\rm D} }{nV_{\rm T} }=\frac{qI_{\rm D} }{n\kappa T}.$ |
(5) |
In the above equation, $q$ is the electron charge, $n$ is the slope factor, $ê$ is the Boltzmann's constant, and $T$ is the absolute temperature. By introducing these two p-channel transistors MR and MR', the circuit is easier to meet the condition $2g_{\rm m} (M+N+1)\gg g_{\rm o\_MR}$ rather than the condition $g_{\rm m} (M+N+1)\gg g_{\rm o\_MR}$ in Reference [5], so the source degeneration can further improve the OTA linear range. We can obtain the expressions as follows.
$G_{\rm m} \approx \frac{N-1}{M+N+1} \frac{g_{\rm o\_MR } }{2}, $ |
(6) |
$i_{\rm o} =G_{\rm m} v_{\rm id} =\frac{N-1}{M+N+1} \frac{g_{\rm o\_MR } }{2}v_{\rm id}.$ |
(7) |
From Equations (6) and (7), the OTA's $G_{\rm m}$ is linear to the conductance $g_{\rm o\_MR}$, and the output current ($i_{\rm o})$ is a linear function of the $G_{\rm m}$. This indicates that most of the change in differential input voltage $v_{\rm id}$ appears across the conductance $g_{\rm o\_MR}$, rather than as the gate-source overdrive voltage ($=v_{\rm SG} -V_{\rm th})$. Therefore, the linearity of the open-loop OTA can be improved with a wide dynamic range of the input signal. Meanwhile, the small-$G_{\rm m}$ can be achieved by selecting the proper factors $M$ and $N$.
2.2 The finite output resistance
Ideally, the OTA's output resistance is infinite, but in a real situation the non-idealities (such as the channel-length modulation) will result in a finite resistance, which has a significant influence on the passband gain of the OTA-C filter. Figure 4(a) shows the first-order fully differential low-pass filter with the infinite output resistance of the OTA, and its transfer function is given by
$\frac{V_{\rm o} }{V_{\rm id}}=-\frac{G_{\rm m1} }{sC_{\rm L} +G_{\rm m2}}.$ |
(8) |
With regard to the finite output resister $1/{g_{\rm o}}$, it can be seen in Figure 4(b) that the transfer function becomes
$\frac{V_{\rm o} }{V_{\rm id}}=-\frac{G_{\rm m1} }{sC_{\rm L} +G_{\rm m2} +g_{\rm o1} +g_{\rm o2} }.$ |
(9) |
From the above equation, it is apparent that the finite resistance leads to a reduction of the filter's gain.
In order to increase output resistance of the OTA circuit, the cascode structure is adopted as the output stage to decrease the loss in the passband of filter. By using the small signal analysis technique, the output resistor $r_{\rm o} (1/{g_{\rm o}})$ in Figure 2(a) can be computed as
$r_{\rm o} \approx (g_{\rm m4} r_{\rm o4} r_{\rm o5} )\parallel (g_{\rm m3} r_{\rm o3} r_{\rm o2} ),$ | (10) |
Figure 5 shows dc-sweep curve of OTA transconductance versus differential input voltage. It can be seen that the OTA transconductance is almost constant for $\pm $0.4 V input voltage since the transconductance only has a deviation of 0.4% (from 11.01 to 11.05 nS). This linear input range of the proposed OTA is good enough to meet the design requirement.
3. OTA-C filter implementation
According to the characteristics of the ECG signal and the fabrication variation, the cutoff frequency of the designed filter will be located at 280 Hz. In order to achieve a maximally flat amplitude within the passband of the filter, as well as to suppress the noise at out-of-band extremely, a fifth order Butterworth low-pass filter is selected for this design.
Methods to implement high order filter mainly include the cascade technique, the multi-loop feedback technique, and the passive LC ladder equivalent circuit technique. Because of the low sensitivity to the circuit components[13], the passive LC ladder equivalent structure is a popular method to implement the active filter. With the help of a filter design handbook[14], a fifth order passive LC ladder type filter is deduced, as shown in Figure 6(a). The normalized coefficients of the topology can also be determined and the corresponding denormalized coefficients of the active filter can be derived from the following math equations. In order to use the normalized coefficients, the frequency-scaling factor (FSF) as well as the impedance-scaling factor ($Z)$ is determined at first. The frequency-scaling factor is given by
${\rm FSF}=\frac{\rm desired \, reference\, frequency}{\rm existing\, reference \, frequency}.$ |
(11) |
The denormalized values are then given by
$R'=R Z, $ | (12) |
$L'=\frac{L Z}{\rm FSF}, $ | (13) |
$C'=\frac{C}{{\rm FSF} \times Z}, $ | (14) |
The topology of the fifth order differential OTA-C Butterworth type LPF is shown in Figure 6(b). In order to implement the circuit easily, the OTAs in the filter are designed to the same transconductance. In the structure, the OTA1 converts the voltage source to the current source, while the OTA2 (or OTA11) and OTA3-OTA6 (or OTA7-OTA10) are, respectively, used to realize the equivalent active resistor and inductor.
In order to evaluate the linear distortion of the filter utilizing the proposed OTA, a transient sinusoidal wave of 100~Hz and 0.8 V$_{\rm PP}$ is injected into this filter. The simulated power spectrum is then observed. Figure 7 shows a HD3 (third harmonic distortion) of $-62.53$ dB. Since we have adopted a fully differential structure which can effectively suppress the even order harmonic distortion, the linear distortion of filter is mainly decided by the HD3. Thus the THD of filter is approximately equal to the HD3.
4. Measured results
The low pass filter with a buffer was fabricated in a SMIC 1P6M 0.18-$\mu $m CMOS process. Using metal-insulator-metal technology, the capacitors have a long distance from the bulk, so that the parasitic capacitor has a negligible impact on the frequency response. The center symmetrical structure is used to implement the layout of the fully differential OTA to reduce the process error. The chip occupies an active area of 450 $\times$ 460 $\mu $m$^{2}$ (including the buffer), as shown in Figure 8.
The chip was tested with an Agilent audio analyzer U8903A and Tektronix oscilloscope TBS1104. The measured magnitude response for the filter is shown in Figure 9. It can be observed in this plot that the $-3$-dB frequency is 276 Hz and the passband gain is $-6.2$ dB. Moreover, the output power spectrum reveals the THD of $-56.8$ dB in Figure 10 by applying a differential sinusoidal signal of 100 Hz and 0.8 V$_{\rm PP}$. In order to verify the function of the filter for ECG applications, a real ECG signal with various noises, generated by another application-specific circuit, is put into the chip, the time-domain measured result is shown in Figure 11. It is obvious that the out-of-band noises are eliminated by our low-pass filter, as depicted in the lower half of this figure. The output signal still contains some interference because of in-band noises, such as instrumentation noise and power frequency. A performance comparison with other references is depicted in Table 2. It is obvious that the presented filter performance is superior in DC gain and THD.
5. Conclusion
In this paper a highly input linear range OTA with a large output equivalent resistor is presented to improve the THD of an active OTA-C filter. It has been shown that the highly linear range and lower loss passband gain of this filter can be obtained with the improvement of source degeneration and the optimization of the output stage in the OTA integrator. The measured results indicate that the presented filter provides a THD of $-56.8$ dB for a 0.8 V$_{\rm PP}$ sinusoidal wave input, a passband gain of $-6.2$ dB, and a bandwidth of 276 Hz. Thus this filter is suitable for the analog frond-end of the ECG system to remove the out-of-band noise.