Elliptic Function Filter Research Articles

Predistortion Techniques for Multicoupled Resonator Filters (Short Papers)

This paper presents predistorted, Iossy design techniques as applied to general, multicoupled, resonator networks. The analytical procedure predistorts the poles of the transfer function to recover the Iossless passband flatness at the expense of insertion loss. Experimental results on 4- and 6-pole elliptic-function filters confirm the validity of the theory. These techniques should lead to significant system efficiencies in applications such as satellite transponder input multiplexer.

Dual-Mode Dielectric Resonator Loaded Cavity Filters

A new miniature realization of dust-mode filters is presented. As a basic building element of the filter, the dielectric resonator axially mounted in a waveguide below cutoff and resonating in a hybrid, degenerate mode is used. A dramatic reduction in size and weight, and excellent temperature performance with minimum degradation of resonator Q was achieved. Dust-mode configuration, preferred in satellite applications, allows simple realization of high-performance elliptic function filters. Experimental results are presented and demonstrate excellent agreement with the theory. Bandpass filter configuration is discussed however, realizations of bandstop, directional, etc., filters are also possible.

Lowpass prototype elliptic function filter for T.V. transmission

Lowpass prototype elliptic function filter for T.V. transmission

Unsolved theoretical problem in design of optimal low-pass filter for harmonic suppression in radio-transmitter output

The author offers to cooperate in development of an optimal harmonic-suppression output filter for power amplifiers. The commonly used elliptic-function filter is not optimal for this purpose: less attenuation is needed at higher frequencies in the stopband. An improved design should provide a value of A_{\min} that varies with frequency as the harmonic output of the amplifier varies with frequency.

TEM Pseudoelliptic-Function Bandstop Filters Using Noncommensurate Lines

A synthesis procedure for distributed bandstop filters that approximate an elliptic-function response is described. Existing tables of lumped constant elliptic-function filters are used together with an approximate transform that exchanges commensurate Foster sections for noncommensurate pairs of stubs or coupled lines. The method is usable for all bandwidths up to about 100 percent, providing that networks with a relative bandwidth of more than 50 percent are considered to be pseudo-low-pass.

Filters with Single Transmission Zeros at Real or Imaginary Frequencies

A new unified theory is presented for the synthesis of exactly equiripple low-pass prototypes having: a) one simple pole of attenuation at a real frequency; or b) a single pair of real-axis transmission zeros (giving linear-phase performance). These types of filters may be regarded as representing the least possible degree of complication over the conventional Chebyshev filter, and are usually realized with one extra cross coupling in the structure. It is demonstrated that this gives much improved skirt selectivity in the case of a finite frequency pole, making it a viable intermediate case between the Chebyshev and elliptic function filters, while in the case of real-frequency zeros, very flat group delay over 50 percent of the passband is achieved with minimal cost in insertion loss and skirt rejection. Approximate and exact synthesis techniques are described, including results for the previously neglected odd-degree case. Experimental results demonstrate agreement with theory.

Prototype Characteristics for a Class of Dual-Mode Filters (Short Papers)

Selected prototype characteristics of nonequiripple antimetric elliptic-function filters which can be realized in orthogonal cascaded dual-mode circular or square waveguide structures are presented. Cavity-coupling data for 4-, 6-, and S-section 0.01- and 0.05-dB-ripple passband designs with variable stopband levels are tabulated. Quantitative comparisons of elliptic and Chebyshev filter designs are also discussed, indicating the superior characteristics of elliptic networks.

Tabulation of characteristics and active network design values for cauer elliptic function filters of order 2 to 9

Design values are given for active elliptic function filters realized with biquadratic sections in tandem; for networks of odd-order there is an additional linear section. The complete set of tables contains sixteen separate designs for filters of each order from second to ninth, with attenuation and phase characteristics for each design. Only one network order (8th) is included here: the full paper containing all the tables is published separately.

Waveguide Bandstop Elliptic Function Filters

Using the "natural prototype" for elliptic function filters, a design procedure is presented for a class of waveguide bandstop filters, which exhibit equiripple passband and stopband responses. Due to the availability of explicit formulas for element values in the natural prototype elliptic function filter, the design procedure is entirely analytic and does not require numerical synthesis techniques. The resulting physical structure is the familiar uniform guide with iris-coupled series stubs. Unlike the bandstop filters designed from maximally flat or Chebyshev prototypes, the elliptic function design results in stubs that are not exactly three-quarter-wave coupled.

Least-squares passband filters

The mathematical properties and design techniques of a novel low-pass filter type are described. A fifth-degree filter is designed, analyzed, and compared with its elliptic counterpart. This evaluation shows that the discrimination, phase, and delay properties of the two circuits are comparable; also, the time response of the proposed filter is substantially similar to that of an elliptic function filter. However, the loss responses are quite different: the loss of the least-squares filter is much less over the lower 90 percent of the passband. As a consequence, it is anticipated that the new circuit is best suited for the filtering of signals having most of their energies at lower frequencies.

Design of elliptic function filters using a double-layer RC distributed-active circuit

An active double-layer RC distributed circuit is analyzed. Design charts for realizing a second-order transfer function with real-frequency zeros and a pair of complex-conjugate poles are given using the dominant-pole approach. A fifth-order Cauer-Chebyshev-(CC) type low-pass filter with equiripple passband and stopband characteristics is realized using these charts.

Explicit formulas for element values in elliptic function prototype networks

Explicit formulas are derived for elliptic function prototype networks in a direct and simple manner without recourse to continued-fraction expansion techniques. The natural prototype for the - elliptic function filter incorporates the concept of frequency invariant reactances and impedance inverters from which relatively narrow bandwidth, bandpass, or bandstop filters may be readily derived using the reactance slope parameter method. Formulas are given for the general arbitrary gain case where the zeros of the reflection coefficient are located in one half-plane or equally distributed between the two half-planes, and the degenerate cases of maximum gain and operation from a zero impedance generator are specifically recovered. The corresponding results are also presented for the inverse Chebychev response.

Some explicit formulas for the components in low-pass ladder networks

The paper gives explicit formulas for the component values in a general low-pass ladder filter in terms of the coefficients of the polynomials of the open- or short-circuit input impedance and of the frequencies of infinite loss. The formulas are a direct generalization of the results given by Bader in: 1940 for the special case where all the loss poles are at infinite frequency and use determinants that are natural extensions of those due to Hurwitz. An alternative representation of these determinants has been found in the form of a double bialternant that provides a link with some recent work by Navot. One motivation for presenting these various formulas is the hope that they will help in discovering the explicit formulas for the elliptic-function filter.

Narrow-Bandwidth Elliptic-Function Filters

This paper describes the development of a practical circuit for realizing narrow-bandwidth elliptic-function filters at microwave frequencies. The design procedure is presented for TEM filters of any bandwidth up to about 10 percent. Experimental verification of the low-loss feature of the elliptic-function response is demonstrated with measured data on 1-percent-bandwidth strip-transmission-line S-band filters.

The Half-Wave Stepped Digital Elliptic Filter

A design procedure for narrow-band bandpass TEM-line elliptic-function filters is presented. The proposed realization is in the form of a stepped-impedance digital n-wire line which is one-half of a wavelength long at midband and short circuited to ground at both ends, where the digital line is stepped in impedance along any arbitrary prescribed plane in the filter. Due to its physical form and mode of electrical operation, the filter has been termed the half-wave stepped digital elliptic filter. A detailed design procedure for the construction of the two characteristic admittance matrices which describe the digital n-wire line from the low-pass prototype element values is presented. It is also shown that the normalized impedance values of the elements in the filter are all of the order of unity and independent of the actual bandwidth of the falter except for the input and output transformer elements. A numerical example and experimental results on a seventh-degree 1-percent bandwidth filter with a center frequency at 3.7 GHz are given, demonstrating the significant improvements which may be obtained from the half-wave stepped digital elliptic filter over most other known form of microwave TEM-line narrow-band bandpass filter.

The Stepped Digital Elliptic Filter

The design and synthesis of various types of microwave elliptic function filters has been accomplished by a number of authors. However, one problem in this field which remains is the realization of compact narrow-band bandpass elliptic function filters. In this paper, a procedure is presented which enables this class of filters to be constricted in a compact digital form. Since the physical realization is in the form of an n-wire line, one-quarter of a wavelength Iong at the center frequency of the passband, where the impedance levels are stepped along the center of the coupled lines, the filter has been termed the stepped digital elliptic filter. The absence of awkward interconnections in the filter due to the stepped digital structure inherently implies that reasonable insertion loss characteristics may be achieved in the X-band region and above, and also simplifies the mechanical construction. It is shown that the resonant elements in the filter, due to the design procedure adopted, are relatively insensitive to the absolute bandwidth of the filter, and consequently fractional bandwidths of approximately 30 percent and below may be readily achieved while the normalized impedance values of the elements in the network remain of the order of unity. This latter result is similar to that obtainable from conventional interdigital filters but in the case of narrow bandwidths the stepped digital filter is considerably smaller in physical size. A systematic procedure is also formulated for the inclusion of the parasitic lumped end effect capacitances into the overall design procedure in order to maintain the equiripple passband and stopband responses. Experimental results are presented for a five-element, 11 percent bandwidth filter and are shown to be in good agreement with theoretical predictions.

The Modern Network Theory Approach to Microwave Filter Design

A review of the modern network theory approach to microwave filter design based on Richards' transformation is given. Basic concepts are discussed, including the use of Kuroda's identities and the specialized theory of optimum filter forms. Applications of the theory presented to elliptic-function filters, special rejectiontype filters, and multiplexers are given. Throughout the presentation, emphasis is placed on basic methods and techniques rather than on detailed design procedures.

Transient Response of Elliptic Function Filters

Transient Response of Elliptic Function Filters

Optimum Elliptic-Function Filters for Distributed Constant Systems (Correspondence)

Optimum Elliptic-Function Filters for Distributed Constant Systems (Correspondence)

The Digital Elliptic Filter--A Compact Sharp-Cutoff Design for Wide Bandstop or Bandpass Requirements

Detailed design procedures are presented for a practical elliptic-function filter form capable of achieving high selectivity in a very compact configuration. This filter form, called the digital elliptic because of its digital construction and elliptic function response, can provide either bandpass or bandstop characteristics. Examples are given to illustrate typical design procedures for both bandpass and bandstop applications. Experimental results are presented for an octave bandstop design.