Use MatLab to derive the frequency response of the Low and High-Pass Filters.MatLab Calculation of Frequency Response Using a Smith chart, determine the SWR of each filter using hand analysis.Design the both the Chebyshev Low and High-Pass Filters for N = 3 with 3 dB ripple in the passband using discrete elements with a cutoff frequency of 550 MHz.Hand analysis of discrete element filters The transformed value takes into account the terminations and the cutoff frequency. Transformations to Actual Capacitor and Inductor Values from the Low-Pass Prototype Normalized Component As is shown in Figure 3 for high pass filter design, the capacitors and inductors are interchanged, and a transformation is applied to the values of the components. The Coefficients for the Low-Pass Butterworth, Linear Phase, Chebyshev (3 db ripple) and Chebyshev (0.5 db ripple) filters are shown in Tables 5-2, 5-3, 5-4(a), and 5-4(b), respectively.ELEC 412 Laboratory Exercise 8 4 The transformation between Low-Pass and other types of filters, including High-Pass, are provided in tabular form in FigureELEC 412 Laboratory Exercise 8 5 Figure 3. The normalized inductors and capacitors are denormalized using: 2nCCCfR=π (5) and 2nCLRLf=π, (6) where Cn is the normalized capacitor value,ELEC 412 Laboratory Exercise 8 3 Ln is the normalized inductor value, C is the denormalized (actual) capacitor value, L is the denormalized (actual) inductor value, and R is the final load resistor. (4) Normalized Butterworth (Maximally Flat), Linear Phase, and Chebyshev LC lowpass filters are presented in tabular form on the following pages. The closeness of the impedance match between the source resistance RS and filter input resistance Rfin is frequency expressed as a return loss defined as: 120logAρ=ρ. Two Ladder Network Configurations for LC Filters Figure 2. Generic representations of the LC low-pass filter are shown in Figure 2.ELEC 412 Laboratory Exercise 8 2 vsRSC1L1C2L2 RLvsRSC1L1C2L2RL(a) (b) Figure 1. The component values in the tables are normalized with respect to the termination ratio and cutoff frequency. Tabulated "normalized" values for the inductors and capacitors for varying termination ratios are available to the design engineer. Note that the values of the capacitors and inductors changes with varying input and output resistances. Two section (or second order) filters are shown in Figure 1. Each "section" consists of an L-C pair, with each section corresponding to the order of the filter. Two common low-pass LC filter configurations are shown in Figures 1 (a) and (b). In this laboratory, passive LC filters at radio frequencies (RF) will be designed and tested. The values of the inductors and capacitors are varied depending on the type of filter, frequency specifications, and terminations. LC ladder networks are commonly used as building blocks for passive filters at RF. The two types of frequency selective circuit configurations most commonly used in communication systems are the passive LC filter (low, high, and bandpass responses) and the tuned amplifier (bandpass response). However, due to their limited gain-bandwidth product, active filters using OpAmps see little use in communication system design where the operational frequencies are orders of magnitude higher than the audio frequency range. One of the advantages of using active filters included the addition of some gain. In electronic circuits, active filter concepts using OpAmps were introduced. Other radio stations occupying frequencies close to the selected radio station are eliminated. In simple amplitude modulation (AM) radio receivers, for example, the user selects one radio station using a bandpass filter techniques. The isolation or elimination of information contained in frequency ranges is of critical importance. INTRODUCTION Signal filtering is often central to the design of many communication subsystems. Design a third order high-pass Chebyshev filter with a cutoff frequency of 5500 MHz and 3 dB ripple with equal terminations of 50 Ω using: (a) discrete components (pick reasonable values for the capacitors) (b) What is the SWR of the filter in the passband (pick 200 MHz and 550 MHz)? (c) What does the SWR do outside the passband? II. Design a third order (N = 3) low-pass Chebyshev filter with a cutoff frequency of 550 MHz and 3 dB ripple with equal terminations of 50 Ω using: (a) discrete components (pick reasonable values for the capacitors) (b) What is the SWR of the filter in the passband (pick 200 MHz and 550 MHz)? B. Laboratory #8: Low Pass RF Filter DesignELEC 412 Laboratory Exercise 8 1 Laboratory #8: Low Pass RF Filter Design I.
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