Eşikaltında çalışan CMOS OTA-C süzgeç tasarımı ve tıp elektroniği alanına uygulanması

Abstract

Bu çalışmada, eşikaltında çalışan geçiş iletkenliği kuvvetlendiricileri COT AD ve kapasite elemanları ile kurulan, dördüncü ve sekizinci dereceden süzgeçlerin tasarımı ele alındı. Bu tür süzgeçlerin tıp elektroniği uygulamalarına elverişli olduğu, EEG işaretlerinin elde edilmesi örneğiyle gösterilmeye çalışıldı. Çalışılan akımlar çok küçük olduğundan, OTA' 1 arın geçiş iletkenlikleri de çok küçük olmaktadır ki, bu da a, fi, O ve 6 bandlarının yer aldığı 1Hz - 40Hz aralığında gerçekleştirilecek süzgeç yapıları için, 19 -260 pF mertebesindeki küçük kapasite değerlerinin kullanılabilmesi olanağını getirmektedir. Böylece, dört süzgeci kapsayan bir yapının tümleçtir ilebilecek boyutlarda gerçekleştirilebilmesi mümkün olmaktadır. Tasarlanan band geçiren süzgeci er, ikinci dereceden alçak ve yüksek geçiren süzgeçlerin ardarda bağlanması ile oluşturulmuştur. Ayrıca, bu süzgeçlerin doğrudan kurulmaları durumunda elde edilen sonuçlarla kar şılaştırılmıştır. öteyandan, elektrodlar yardımıyla algılanan bu düşük genlikli işaretlerin, kuvvetlendirilmesinde kullanılabilecek.düşük gürültülü işlemsel kuvvetlendirici yapısı önerilmiştir. Tasarlanan devrelerin SPICE simülasyonları yapılarak elde edilen sonuçlar tartışılmıştır.

In recent years, ampl i f iers in which transistors operate in the subthreshold regionCweak inversion region!) become important day by day. The reason for this is the need for low-power devices in battery-powered, human implantible biomedical instruments. In the preceding sections, the definition of subthreshold region and SPICE model small signal equations for MOS transistors have been given Cl]-C4]. In the electrical circuit simulation programs, deri vati ve of current and voltage equations are needed. However, in SPICE model, the derivative of drain current with respect to gate voltage is discontinous along the transition region between the subthreshold and strong inversion regions. To eliminate this problem» in the SGS version of SPICE, a more precise model for subthtreshol d and transition region was proposed [ 5], C63. This model is based on the separate calculation of the contributions of the drift and diffusion currents which are then simply added together, without distinguishing between the regions of weak and strong inversion. Fur thermore, conti nous current-voltage equations exist which represents MOS transistor in this three distinct operation region [7] -[£)]. In subsection 2.3, current-voltage equations are defined for the transistors operating in subthreshold region which forms simply the OTA structure [10]. The symmetrical CMOS OTA, illustrated in Fig. 5.1 is a widely used building block in the IC tecnique and suitable for several applications. OTA' s do not behave linearly as in practice when output voltage saturates. In this situation, a clipped signal at the output terminal is obtained. If output current saturates, saw-tooth waveforms at the output is seen because of the slew-rate problem [11]. In section 3, an equation has been proposed which determines the maximum input signal level so as not to cause clipping and slew-rate limitations [12]. In this thesis, signals with low frequencies such as EEG signals can be extracted with subthtreshold region operating OTA-C filters which can be integrated on a single VLSI chip. EEG frequency bands are normally classified into four categories as shown below. Al phaC cO BetaC/33 The t aC 03 Del taC 6D 8 - 12H: 13 - 40Hi 4 - 8Hz 1 - 4Hz EEG signals are sensed by small surfaced electrodes which are placed at specific points of head. Magnitude, phase and frequency of this signal depends on the placement of the electrode [13]. The meaning of these different frequencies is not completely known. However, alpha activity is less than 1 O/jV peak to peak, and reasonably stabl eC devi ati ng less than 0.5 Hz D. These signals arise from the posterior brain in the waking person with eyes closed. Opening the eyes and focusing attention greatly reduces alpha waves. Beta activity is less than 20^iV peak to peak arise over the entire brain but is most predominant over the central region at rest. High states of weakf ulness and desynchronized alpha patterns produce beta waves. Theta and delta act i vi tyCless than 1 00/jV peak to peakD are strongest over the central region and are indications of sleep. In literature, OTA-C filters are mostly used for strong inversion region in various applications. However, in this thesis, the OTA-C filters operating in subtreshold region has been designed to extract EEG signal s. Moreover, it has been shown that this type of filters are suitable for medical electronics applications. The frequecy bands that are to be chosen is so low that large valued capacity elements are required if classical approach is applied to the active filter design. However, the capacity values used in OTA-C filters operating in subthreshold region are in the range of 19-260 pF and this valued capacity elements can be integrated in CMOS technology with operational transcon- ductance amplifier C OT AD. Thus, this results filter structures with small dimensions to be real i zed. While designing OTA-C fil ters, the topologies proposed by Acar, Anday and Kuntman and design principles are taken into consideration [12]. In section S, fourth and eighth order filter structures are designed for ot,/3,0 and 6 frequency bands. In this f i 1 ters, symmetrical transconductance CMOS amplifier topology have been used as an active element [14] Two topologies are proposed for the design of band-pass fil ters: Connecting second order low pass and high pass Butterworth filters cascade; connect i ng second order band pass filters di recti y. While connecting second order band pass filters to design high order f i Iters, design equations proposed by Gönül eren have been used [16]. VI To provide simplicity in the realization of the filters which are obtained by connecting second order low pass and high pass filters cascade, the transconductances G, of the OTAs in each cell, were set equal to each mı M other. Designed band- pass filters were simulated with PSPICE for symmetrical supply voltages of ± 5 V. Simulation results of this filters have been compared. It can be easily observed that each of the characteristics fullfills the main requirements in the pass band. The deviations from theoretical results in the stop-band are caused by the OTA non-idealities which can be easily neg lected since they arise in frequency regions far from the pass -band where the input signal is attenuated more than 60 dB. Recently it was shown that the maximum input signal level of an OTA-C filter is limited dominantı y by the slew-rate arising from the current saturation at the output of the OTAs. In the same work a simple formula was derived for the input signal amplitude not causing any clipping and slew-rate limiting promblems E 12]. Applying the derived formula to the designed active-filter structures, the maximum input signal level of the filters SPICE simulation performing transient anal yses. Thi s is caused by the low level of the dc operating currents, which results in slew-rate at the output signal even though at low load capacitance values of the order of several ten picofarads. Fortunately, the EEG signals are small enough and therefore there is no need of taking any measure to over come this limiting problem. The output signals of the filters must be applied to following amplifier stages to obtain meaningful 1 levels for signal processing. Low-noise op amps are important in several respects. A large percentage of applications for analog CMOS circuits is in the area of telecommunications were the signal -to- noise ratioCS/ND is important. The lower the noise, the better the value of S/N for a given signal level. Another way of looking at this characteristic is from the viewpoint of dynamic range. The dynamic range of a circuit is the ratio of the largest-to-smallest signal that can be processed without distort i on. The upper level is typically established by the power supplies and the large-signal swing limits. The lower level is established by the noise or the rippel injected by the power -suppl y. As the magnitudes of EEG signals are so low, the incoming signal has to be amplified before filtering. Furthermore, as one works with small magnitude signals, he has to take consideration the effect of noise. Preamp- lifying procedure may be maintained by the low noise CMOS amplifier structure given in section 6 [17]. VII Design of low-frequency QTA-C filters: The symmetrical CMOS OTA, il lustrated in Fig. 1, is a widely used building block in the IC technique and suitable for several applications. The current -vol t age relation of a MOS transistor operating in sub-threshold region can be expressed in terms of exponential functions rather then the quadratic function which is only valid for operation in strong inversion. As a result, the transconductance of the OTA structure can be written as. G = K m B CI 5 T for the subthreshold operation where Vt is the thermal voltage, K is a multiplier and Ib is the biasing current of the OTA. From eq. 1 it can be easily observed that the OTA transconductance Gm is proportional to the biasing current Ib in sub-threshold operation and shows a different character than the operation in the stroncj Û 5 inversion region where Gm is proportional to CIb3 '. Starting from the filter topologies and design considerations given by ACAR.ANDAY, and KUNTMAN, fourth order band pass filters for a,/?,0 and 6 bands of the EEG signal were designed by cascading low- and high -pass But ter worth filters. Each filter contains six OTAs and four capacitors. The basic filter structure is shown in Fig. 2. The transfer function of the band-pass filter is gi ven by, Pi HCs3 = "g 2 ; + C oj. /Q,'Js + to. pi pi pi ; + Cw.-,-"Q 'J s * <,/^., pd p<£ pc=. C23 \00 = f-£V O VSS=-ÇV Figure 1. Symmetrical CMOS OTA VI 1 1 Design equations of the band-pass filter obtained as. Ci = G mi Q. ? <^, pi pi C3D C.o= ma' Qpl "pi C43 G m3 C5*} C6D where GmtC i =1.. 6D represents the transconductance of the ith OTA, wpi, <:op2,Qpi and Qp2 are the pole-frequencies and the quality factors of the low- and high-pass fil ters, respecti vely. The quality factors of. Butterworth filters are given as Qpi=Qp2=Qp=C 1,-'2D '. the Vi '-\U u T ± cz r X _4- X" -o »o Figure 2. Fourth order band-pass OTA-C filter.