Randall W. Rhea's HF Filter Design and Computer Simulation PDF

By Randall W. Rhea

ISBN-10: 1884932258

ISBN-13: 9781884932250

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Next these results are substituted in the expression for the input impedance of the terminated network to be synthesized and we have Zi= s3+2s2+2s+1-s3 [ $+&2+2s+l+s3 ]=[ ,z~zi+1] (4% This expression for the impedance of the terminated network is used to find the network element values. First we rationalize the numerator Zi= 1 23+2s2+2s+l (43) 2s2+2s+1 Next we continually divide the lower order polynomial into the higher order polynomial and invert the remainder. 01 dB corner cutoff attenuation at a frequency of 1 radian per second.

I+ : . + . -12 + + ,L . -.. + + + t + Figure 2-7 Amplitude transmission and return loss for 5thorder (dashed) and 7th-order (solid) lowpass Butterworth (UL), Chebyshev (UR), Bessel (LL) and Cauer-Chebyshev (LR) filters. The Bessel transfer function has excellent group delay properties but poor selectivity. 17 Bessel Approximation Just as a maximally flat amplitude response is approximated by Butterworth, a maximally flat group-delay response is approximated by the Bessel transfer function.

13 Chebyshev Approximation If the poles of the Butterworth polynomial are moved toward the imaginary axis of the complex-frequency plane by multiplying their real parts by a constant factor iFz,< 1, the poles then lie on an ellipse and the maximally flat amplitude response of the Butterworth develops equal-attenuation ripples which increase with increased pole shifting. The resulting amplitude response becomes more zonal and the selectivity increases. Even a small amount of ripple can significantly improve the selectivity.

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HF Filter Design and Computer Simulation by Randall W. Rhea

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