Patent Grant
8866542
1. Field of the Invention
The present invention relates to active filters, and particularly to a low frequency filter for biomedical applications.
2. Description of the Related Art
Very low frequency filters have a wide range of applications in biomedical signal processing. The bandwidth of an Electroencephalogram (EEG), for example, refers to the monitored signal due to the brain activities, and of an Electrocardiogram (ECG), which is a test for the electrical activities that are being recorded due to heart beats, are 0.1-30 Hz and 0.01-100 Hz, respectively. Amplification and pre-filtering of these signals are mandatory before further digital signal processing (DSP). However, such very low frequency filters need large passive components values, which cannot be implemented in standard analog integrated circuit (IC) fabrication. Typical values for integrated resistors are from several ohms to 40 kΩ, and for capacitors are from 0.5 pF to 50 pF. This has been a challenging design problem due to the difficulty in developing efficient methods to achieve large time constants using integrated passive elements.
Thus, a low frequency filter for biomedical applications solving the aforementioned problems is desired.
The low frequency filter for biomedical applications uses a novel approach to scale down the pole frequency while accomplishing a 5-bit reduction in the cut off frequency. This is made possible through adding a passive resistor in the forward path of the op-amp-based integrator, introducing a difference term of the pole frequency. Moreover, the filter topology is modified to avoid changing the quality factor. An exemplary second-order low pass filter is designed and simulated. Simulation results show that the pole frequency is scaled down from 1.43 MHz to 4.97 kHz, while maintaining tuning of 30% around the nominal value by controlling only one resistor.
These and other features of the present invention will become readily apparent upon further review of the following specification and drawings.
Similar reference characters denote corresponding features consistently throughout the attached drawings.
The low frequency filter for biomedical applications uses a novel approach to scale down the pole frequency while accomplishing a 5-bit reduction in the cut off frequency. The amplitude and frequency ranges of some physiological signals are shown in plot 100 of
The present low frequency filter for biomedical applications 300 (shown in
where K is the gain of the filter, Q is the quality factor, BW represents the bandwidth and ω is the corner frequency (3-dB frequency). The corner frequency of the low pass filter is given by:
To get low frequencies in the range of a few hertz to few kilo-hertz, large capacitors and resistors are needed. One novel approach to scale down the frequency is to introduce a difference term of R1 and R2, m=R1−R2, in the ω term. So, as m decreases, the frequency is scaled down and a very low corner frequency can be obtained. The challenge in this approach in filter design is to introduce the difference term m, not only in the pole frequency ω, but also in the s-coefficient term, (Q/BW) to cancel the effect of m in Q, and hence the quality factor can be controlled via the ratio of resistors Rx/Ry independent of R1−R2. The filter topology is adjusted to resolve this problem by introducing a square of the difference term m2, in the pole frequency and m in the s-coefficient term, and hence the effect of m on the Q is cancelled. Also m2 is introduced in the numerator coefficient such that the gain is not disturbed.
A low pass filter can be obtained using the integrator shown in
From the above transfer function, and assuming Rf=R5=R, R1=R3, R2=R4, and C1=C2=C, we can obtain the DC gain, the corner frequency and the quality factor as follows:
In this topology, the DC gain, the quality factor, and the corner frequency can be controlled independently (Eqn. 4). Moreover, the corner frequency can be scaled down by exploiting the presence of the difference term of the resistors in the numerator. However, this technique suffers from high sensitivity (Equation 6). The sensitivity for the present filter 300 is given below:
SR
SPICE Simulation tests have been done using second-order low pass filter (LPF) with frequency scaling technique and values of C=100 pF, R1=10 KΩ for different cases of R2. Using Monte Carlo analysis, the filter has been extensively simulated for 100 runs with an applied resistance tolerance of 1% to R1 and R2 to check the reliability of the proposed filter. The frequency responses of three different cases, namely R2=9.41 kΩ, R2=5 kΩ and R2=1 kΩ, are provided in plot 400 of
The histogram 500 of
The inference drawn from Table 1 is that this technique can be used for both directions, upscaling and downscaling. Capacitor arrays can be incorporated to introduce a 30% tuning in the pole frequency. As a result, a 5-bit pole frequency reduction can be realized, as indicated in Table 1, giving a probability of p=0.76 and a 6-bit reduction if we allow 50% tuning. This technique can be combined with other techniques, an R2R approach, for example, to realize a very low pole frequency on the order of 0.1 Hz.
It is to be understood that the present invention is not limited to the embodiments described above, but encompasses any and all embodiments within the scope of the following claims.
| Number | Name | Date | Kind |
|---|---|---|---|
| 5175510 | Satomäki | Dec 1992 | A |
| 7023263 | Chang et al. | Apr 2006 | B2 |
| 7466192 | Nakabo et al. | Dec 2008 | B2 |
| 8368461 | Blanc | Feb 2013 | B2 |
| Entry |
|---|
| Yaqub Mahnashi and Hussain Alzahar, “Applying the Difference Term Approach for Low Frequency Biomedical Filter,” Published on Jun. 30, 2012. |
