State Variables Analysis of Passive Filters Ersoy KELEBEKLER Ali Bekir YILDIZ Technical Education Faculty Engineering Faculty Kocaeli University, Kocaeli - TURKEY Kocaeli University, Kocaeli - TURKEY e-mail: ersoy@kou.edu.tr e-mail: abyildiz@kou.edu.tr Abstract- In this paper, analysis of passive filters is achieved by using state variables technique. The transfer function and frequency-domain analysis of filters are obtained. Graphic User Interfaces (GUI) are prepared to implement analysis of the circuits and to get fundamental concepts of filters more comp- rehensible. Frequency-gain and frequency-output characteristics are given. Various passive filters are examined by using the prepared GUI. Two illustrative examples are included into the study. I. INTRODUCTION Frequency selective circuits are called filters because of their ability to filter out certain input signals on the basis of frequency. Filter circuits are designed according to response of inductance and capacitance whose reactance changes with frequency [1,2,3]. An electrical filter is a device designed to separate, pass or suppress a group of signals from a mixture of signals. On a larger scale, televisions and radios are typical examples of electrical filters. When a television or a radio is tuned to a particular channel, it will only pass those signal transmitted by that channel and will block all other signals. On a smaller scale, filters are basic electronic components used in the design of communication systems such as telephone, television, radio, radar and computer [4]. In [5], analysis of passive and active filters is obtained by using Modified Nodal Analysis (MNA). Passive filter design is realized with genetic algorithms in [6]. In this study, different passive filter circuits have been examined. The state variable equations of each circuit have been obtained. Using these equations, the circuits have been analyzed on Matlab interpreter. Analysis results which include output voltage in time and frequency-gain curve in decibel have been given. Additionally, the transfer functions of the circuits have been obtained and added into the study. Besides, Graphic User Interfaces (GUI) have been prepared to implement analysis of the circuits and to help user to understand fundamental concepts of the passive filters. The GUI includes information about selected circuit like its figure, the values of the circuit’s components and results like cutoff or center frequency of the circuit, transfer function of the circuit, output voltage in time and frequency-gain curve in decibel. In this paper, we present the state variables analysis of passive filters. In section II, the fundamental properties and advantages of passive filters are given. Section III is about state model and transfer function of systems. We offer two illustrative examples of circuits in section IV and give Graphic User Interface in section V. Conclusions are given in section VI. II. PASSIVE FILTERS Electrical filters may be classified in a number of ways. Analog filter is a filter used to process analog or continuous time signals, whereas a digital filter is used to process discrete time or digital signals. Analog filters may further be divided into two groups as passive filters and active filters. Passive filters don’t have any active components like transistors or op-amps. They consist of passive component like resistor (R), inductor (L), capacitor (C) and transformer. The output signal can never have greater than the input signal to passive filters, because resistors, inductors and capacitors have no gain themselves. If a filter includes one or more transistors or operational amplifiers, it is called active filter. The output signal can have greater than input signal for active filters. The passive filters have several advantages over active filters: • Highly selective when losses are low • The response is highly resonant • Guaranteed stability • For linear filters, generally, more linear than filters including active (and therefore non-linear) elements • Cheap Filters are generally classified in four groups according to their frequency response; • Low pass filters • High pass filters • Band pass filters • Band stop filters In this study, eight passive filters have been performed, which are RC and RL low pass filters, RC and RL high pass filters, serial resonant and parallel resonant band pass filters, serial resonant and parallel resonant band stop filters. III. STATE VARIABLE EQUATIONS and TRANSFER FUNCTION In circuit analysis, one of the most common used techniques is state variables analysis because it has min. variables. The derivation of state variable equations is based on the concept of a proper tree of circuit [7]. The state variables are branch capacitor voltages and link inductor currents. State variable equations and output equations are given in equation (1) and equation (2), respectively. They’re together called state model.