Chebyshev circuit

The schematic in Fig. 3.44 of the Chebyshev band pass filter utilized the predicted values from the MathCAD file, where lab resources allowed. Close approximations were used, to which the circuit performance was extremely sensitive. Any deviations from the values predicted in the MathCAD file resulted in gain in the pass band. Using SPICE to test possible circuit realizations greatly reduces the time to implement hardware. SPICE will predict if a given circuit realization will perform as desired with available parts, before actual hardware measurements are made. This is helpful because Chebyshev circuit realization can be difficult small changes in the circuit elements can result in undesired performance. The simulated AC results from IsSpice, PSpice, and Micro-Cap are shown in Figs. 3.45, 3.46, and 3.47, respectively. The measured breadboard AC response of the filter is shown... 

Chaise-current four vector, 545 Chebyshev approximation, 96 Chebychev inequality, 124 Chemoft, H., 102,151 Cholesky method, 67 Circuit, 256 matrix, 262... 

The Chebyshev low pass filter shown in Fig. 3.53 was constructed in all three simulators as well as in hardware. The circuit values in Fig. 3.53 were used in all cases. A MathCAD file that was used to design the Chebyshev low pass filter is located in the Chebyshev directory of the CD, which accompanies this book. This file can easily be modified to accommodate designs that use a Sallen-Key circuit for each stage of the filter (see Fig. 3.54). The schematic of the circuit that was used in each simulator is shown in Fig. 3.53. The measured breadboard results are shown in Fig. 3.55, and the simulated results are shown in Figs. 3.56, 3.57, and 3.58. 

The Chebyshev filter offers higher attenuation and a steeper roll-off near the cutoff frequency than the Butterworth filter. There is a tradeoff to achieve the higher attenuation. The cost of utilizing a Chebyshev filter is higher values of Q, which leads to difficulties in hardware realization, and nonlinear phase characteristics, which can result in difficulties in predicting circuit performance. 

The results from the three simulators are shown in Figs. 3.62, 3.63, 3.64, and 3.65. All of the simulators accurately predict the phase and gain of the Chebyshev high pass circuit. 

Active filters utilize an operational amplifier as part of the circuit and allow the design of any RLC filter without the need of an inductance. Filters of this type include Buttersworth and Chebyshev filters. 

Parks, T.W. and McClellan, J.H. 1972a. Chebyshev approximations for non recursive digital filters with linear phase. IEEE Trans. Circuit Theory CT-19 189-194. 

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