Wide Band Tunable Filter Design Implemented in CMOS W. Matthew Anderson and Bogdan M. Wilamowski Electrical & Computer Engineering Dept. Auburn University, AL 36849 anderwm@auburn.edu, wilambm@auburn.edu G¨ unhan D¨ undar Electrical and Electronic Engineering Bogazici University Istanbul, Turkey dundar@boun.edu.tr Abstract— Generation of filters using operational transconduc- tance amplifiers and capacitors (OTA-C) has become more and more popular over recent years. A simple yet effective method of analytical synthesis is presented that makes use of ladder circuits, which are much more widely understood. Given the ladder circuit of a filter of any order, an equivalent OTA-C filter can be easily synthesized. The synthesis process is shown for both a low pass and a band pass filter. Higher order filters can easily be synthesized by extending the design process described. The design of the band pass filter is implemented in CMOS with a linearly tunable OTA to show the effect of non-ideal elements. The CMOS filter implementation is capable of linear center frequency tuning across three degrees of magnitude. Because of the wide band width tunability, this type of design lends itself to intelligent frequency scanning techniques. Such a system, to be used in military applications, is presented as an application of this filter design. I. I NTRODUCTION The design of a passive ladder filter circuit based on stan- dard filter specifications is well documented [1]. The design process is straightforward, and as such, software also exists that will calculate the necessary values of circuit elements based on given design specifications [2]. The simplicity of the ladder network provides a springboard to more complicated filter designs. This paper shows the process of transforming any ladder type circuit into an equivalent circuit containing only operational transconductance amplifiers (OTA’s) and ca- pacitors. In Section II a low pass filter (LPF) is analyzed and synthesized into an OTA-C circuit. Section III transforms the low pass prototype from Section II to a band pass filter and the new circuit is synthesized into its OTA-C equivalent. Section IV discusses the CMOS implementation of this circuit topology and shows simulations conducted with non ideal elements. An OTA is presented that is linearly tunable by varying the reference current. This OTA is used to create a band pass filter that is tunable across a wide range of frequencies. The ability to tune a filter across a very wide frequency range is advantageous in many intelligent radio systems used in the military as well as commercially. A concept for a high speed frequency scanner will be shown that is capable of using a neural network to interpret the traffic on a system. Fig. 1. Low pass filter LC implementation II. LOW PASS FILTER SYNTHESIS A. LC Ladder Circuit The implementation of a third order Chebyshev low pass filter is sufficient to show the design process. The ladder circuit for such a filter, designed for minimum capacitance, is shown in figure 1. For simplicity, values for the passive elements are chosen to set the cut-off frequency at 1 Hz. The frequency response of such a circuit is shown in figure 2. Fig. 2. Frequency response of 3 rd order prototype Chebyshev LPF B. OTA-C Transformation Using the current and voltage conventions defined in Figure 1, one can easily write the state space equations for this particular circuit. 219 1-4244-1148-3/07/$25.00 ©2007 IEEE. Authorized licensed use limited to: Auburn University. Downloaded on March 9, 2009 at 09:45 from IEEE Xplore. Restrictions apply.