DocumentCode :
1187821
Title :
Note on a Logarithmic Approximation for Use with Singularity Plots
Author :
Tompkins, H.E.
Volume :
2
Issue :
2
fYear :
1955
fDate :
6/1/1955 12:00:00 AM
Firstpage :
203
Lastpage :
208
Abstract :
The analysis or synthesis of band-pass networks using plots of the singularities \\dagger of their transfer functions[1].[2],[3] can often be shortened and simplified by using a suitable logarithmic transformation of the complex-frequency s -plane which permits a simple approximate calculation of the transfer function. This approximation is good for over-all-bandwidth ratios of 2 to 1 or less as compared with a usable bandwidth ratio of 1.2 to 1 for the conventional narrow-band approximation. This transformation is not intended for use with an electrolytic tank, for which better methods have been described in the literature[4],[5],[6] It does not have the power of certain conformal transformations,[8],[9] but is considerably simpler. Unlike the wide-band low-pass to band-pass transformations it is not limited to pole and zero patterns of particular symmetry. This approximation also has interesting properties as an aid in the factoring of network polynomials.
Keywords :
1955 IRE-AIEE Conference transistor circuit papers; Differential equations; Filtering theory; Frequency estimation; Frequency synchronization; Impedance; Least squares approximation; Nonlinear equations; Nonlinear filters; Poles and zeros; Switches;
fLanguage :
English
Journal_Title :
Circuit Theory, IRE Transactions on
Publisher :
ieee
ISSN :
0096-2007
Type :
jour
DOI :
10.1109/TCT.1955.1085235
Filename :
1085235
Link To Document :
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