Interdigital Lines Research Articles

Design and implementation of a lumped-element multipole HTS filter at 15 MHz

We have designed a three-pole bandpass filter operating at 15 MHz. The parameters of the filter include high Q, narrow band, low insertion loss and a return loss of 20 dB. The filter was fabricated from double-sided YBCO thin film on a two inch LAO substrate. The design utilizes individual HTS lumped elements (interdigital capacitors and meander line inductors) to realise the poles of the filter. The design and modeling of the filter are discussed in detail. Experimental results from the S-parameter measurements will be presented. Good agreement has been found between the simulation results and experimental data.

Quasi-optical Josephson-junction oscillator arrays

Josephson junctions are natural voltage-controlled oscillators capable of generating submillimeter-wave-length radiation, but a single junction usually can produce only 100 nW of power and often has a broad spectral linewidth. The authors are investigating 2-D quasi-optical power combining arrays of 10/sup 3/ and 10/sup 4/ NbN/MgO/NbN and Nb/Al-AlO/sub x//Nb junctions to overcome these limitations. The junctions are DC biased in parallel and are distributed along interdigitated lines. The arrays couple to a resonant mode of a Fabry-Perot cavity to achieve mutual phase-locking. The array configuration has a relatively low impedance, which should allow the capacitance of the junctions to be tuned out at the oscillation frequency. >

Replication of 50-nm-linewidth device patterns using proximity x-ray lithography at large gaps

We demonstrate the replication of device patterns consisting of interdigital lines ∼50 nm wide on 100 nm pitch using 1.32 nm x rays at a mask-to-substrate gap of 2.72 μm. The exposure latitude exceeds the factor 2.3 at this gap. From the expression that relates gap, G, linewidth, W, and wavelength λ (i.e., G=αW2/λ), we obtain α=1.44, which is well beyond the predictions of previous theoretical analyses based on the Kirchhoff boundary conditions. We attribute this disparity to the fact that an x-ray absorber is a lossy dielectric, hundreds of wavelengths thick, and hence the Kirchhoff boundary conditions are not applicable.

Graph Transformations of Nonuniform Coupled Transmission Line Networks and Their Application (Short Paper)

The graph transformation method of [5] has been extended to apply for a class of coupled nonuniform transmission lines whose self and mutual line constants have the same functional dependence along the direction of propagation, and it is assumed that the mode of propagation is TEM. First, the graph representation of such nonuniform coupled two-wire transmission lines is derived by decomposition of the 4 X 4 admittance matrix. This leads to three-port equivalent circuits of nonuniform coupled two-wire line networks. Then, the multiport graph transformations of networks consisting of nonuniform transmission lines and nonuniform stubs are shown. By using the graph transformation of n-wire nonuniform coupled lines, the equivalent circuits for the nonuniform interdigital line and the nonuniform meander line are given. Finally, a meander-line low-pass filter consisting of parabolic tapered coupled transmission lines designed on this equivalent circuit is shown.

Amplification by Interdigital Excitation of Space-Charge Waves in Semiconductors

A new concept of amplification of the electromagnetic (EM) wave as a consequence of its interaction with a space-charge wave in a semiconductor is analyzed. The EM wave is applied to an interdigital line which in turn excites a space-charge wave in a high-resistivity silicon. The theoretical calculations are carried out by means of the least-square boundary residual method, where a theoretical gain of 84 dB is obtained at synchronism of the third harmonic of the wave. The experimental device exhibits a net gain of 13 dB at synchronism. The mobility of the carriers in the semiconductor is deduced out of the experimental results.

Dispersive propagation in surface-acoustic-wave pulse-compression filters

The phase response of a dispersive interdigital delay line is shown to be affected by dispersion of the surface wave. A device with a time–bandwidth product of 850 and a nonlinear group-delay characteristic gave results consistent with dispersion due to mass loading and topographic effects.

Meander and interdigital lines as periodic slow-wave structure. II. Applications to slow-wave structures

In this part, the dispersion law of meander and interdigital lines is determined by the imposition of the boundary conditions relative to each slow-wave structure. Having established the transmission matrix of the unit cell, the iterative impedance of the line can be found.

Meander and interdigital lines as periodic slow-wave structures. Part I. Characteristics of waves propagating along an infinite array

This paper consists of two parts. In part I, in a quasi-TEM approximation, the complex charge and potential distributions are determined, and then the other characteristics of an infinite array of parallel strips are analysed. The effects of the coupling, shielding and the dielectric constant of the substrate on the characteristics of the propagated waves ore discussed.

Explicit formulae for the dispersion diagram of a triplate interdigital line in a homogeneous dielectric medium

The interdigital line is frequently employed in diverse appliances involving the interaction of microwaves with photons or phonons. Classical theoretical studies (Fletcher 1952, Walling 1957) of their dispersive characteristics lead to calculations which are too complex to be feasible. Simpler formulae can be obtained when only the coupling to the adjacent and to the next but one neighbouring bar is considered. As a result, the capacitance matrix becomes a band matrix which, when accompanied by extremely simple boundary conditions, gives rise to a recurrent equation for the potential of the nth bar. The existence of forward and backward waves is obtained from the solution of this equation. A study of the dispersion diagram as well as the width of the attenuation band of these waves is presented.

Design of Transmission-Line Reactance Networks for Equalizer Applications

Synthesis techniques are presented for realizing arbitrary transmission-line reactance functions in four common forms of arrays of coupled lines, together with minor variations of these forms. These are two types of interdigital lines and dual forms of half-wave parallel-coupled lines. Design examples are presented for each form of coupled-line network and variations. Although the synthesis procedures are developed from the point of view of applications to equalizers, the procedures are completely general.

Generalized Interdigital Linear Phase Filter

The design theory is presented for narrow-band generalized interdigital linear phase filters which consist of a pair of identical cross-coupled interdigital lines. The procedure for the determination of the characteristic admittances of the elements which describe the structure based upon the element values of the low-pass linear phase prototype network is given, from which the physical dimensions of the filter may readily be obtained. The measured performance characteristics of two filters are presented. The first is a 2.5 percent bandwidth 14-element filter based upon the maximally flat prototype operating in L-band, and the second is a 1 percent bandwidth 18-element version based upon the finite band prototype in S-band. Both filters are shown to be in excellent agreement with theory, with the latter exhibiting transfer characteristics considerably superior to those obtainable from any form of conventionally equalized filter of similar overall degree.

Generalized interdigital linear phase networks with optimum maximally flat amplitude characteristics

The closed-form solution is presented for microwave bandpass nonminimum phase transfer functions that exhibit an optimum passband maximally flat amplitude characteristic while maintaining a maximally flat group-delay response about band center. There are two basic transfer functions obtained depending upon whether the degree of the resulting network is even or odd. The transfer characteristics are shown to be capable of being realized by resistively terminated symmetrical generalized interdigital networks. Synthesis procedures are presented for the case of n odd corresponding to the input and output ports being situated at the same physical end of the generalized interdigital line and for the case n even where the ports are at opposite ends. These procedures are based upon the one-port synthesis of the even- and odd-mode forms. Finally, the synthesis procedure is illustrated for the case of n = 6 , and typical transfer characteristics are shown for this example.

The Theory of Generalized Interdigital Networks

A theory for two-port generalized interdigital networks is presented. Initially, after the definition of an arbitrary generalized interdigital network, properties of admittance scaling and transformations of general interdigital lines are formulated. The necessary and sufficient conditions are then presented for the individual realization of any admittance parameter of such a network. The results obtained in this section influence the choice of a compact set of sufficiency conditions for the realization of any arbitrary twoport admittance matrix by this class of networks. These sufficiency conditions are also shown to imply simple sufficiency conditions on the insertion-loss function of a resistively terminated, two-port generalized interdigital network.

Microwave Allpass Networks - Part II

Synthesis procedures are developed for the direct realization of a complete microwave allpass network without the reduction of the network to cascades of C- and D-type sections which include interdigital line structures. The application of microwave allpass networks to the phase correction of conventional microwave filters and to the construction of delay networks with linear delay characteristics is also presented.

A theoretical study of the optimal design of bar lines

The dispersion characteristics of all bar-type slow-wave structures and filters can be derived in terms of a common bar admittance function. This admittance function, so far known only in infinite series form, is made amenable to direct numerical use by a transformation in the complex plane. The utilization of this result in the optimal design of bar lines is demonstrated with the example of the interdigital line.

Phase-velocity Tapering in Crossed-field Devices†

ABSTRACT The possibility of increasing the power output of injected-beam crossed-field devices by tapering of circuit phase velocity and beam velocity is investigated theoretically and experimentally. The hard-kernel-bunch model of the electron beam is used to derive practical circuit tapers which lead to conversion of beam kinetic energy besides the conversion of electron potential energy normally taking place in crossed-field devices. An experimental S-band crossed-field amplifier was constructed with a uniform and a tapered interdigital line and an improvement in power output between 1 and 2 dB was noted.

Exact Theory of Interdigital Band-Pass Filters and Related Coupled Band-Pass Structures

An exact theory of interdigital line networks and related coupled structures is presented. The theory of parallel-coupled line arrays is reviewed briefly, and the derivation of exact equivalent circuits from the impedance matrix using modem network synthesis techniques is discussed. A simplified theory of equivalent coupled structures is introduced in order to avoid the lengthy analysis required when using the impedance matrix approach. Equivalent networks for the interdigital line are obtained by inspection, using a transformed capacitance matrix associated with the two-dimensional geometry of the conductors and ground planes. The techniques presented are simple to apply and allow a given transmission response to be obtained in a variety of line configurations. A practical design example and experimental results are given to illustrate the simplicity of the approach, along with general criteria for the design of practical filter networks with optimum transmission characteristics. The paper is directed toward the design of interdigital band-pass filters; however, the techniques presented can be used to analyze and design a much broader class of microwave networks. The relationship of the exact theory to existing approximate theory is discussed.

Crossed-field backward-wave oscillators above X-band

The extension of crossed-field, or M-type, backward-wave oscillators into frequency ranges above X-band is described. Two tube types cover ranges of 10.8 to 15 Gc and 14.9 to 18.1 Gc, respectively, with minimum power outputs of 120 and 80 watts being achieved across these respective bands. Design criteria usually applied to such tubes were not practical in a number of important respects. For example, operation at 18.1 Gc takes place with a magnetic field substantially less than critical value. Basic dimensions of a representative X-band device in terms of wavelengths are compared with these two higher frequency models. New approaches to optics, output, and gun mount designs are described which are also applicable to lower frequency tubes. For example, the interdigital delay line structure converts to a single ridge waveguide output instead of the coax used in the aforementioned X-band device.

A high gain broadband crossed-field amplifier for X band

A Broadband, Crossed-Field Amplifier with 20 db gain and peak power output of several hundred kilowatts will be described. The amplifier uses a choke supported interdigital line for a slow wave circuit and a secondary emitting cold cathode with re-entrant electron stream. The use of programmed interaction space geometry has given results superior to those obtained with symmetrical structures. Programmed interaction space geometry is accomplished by changing the RF properties of the circuit and/or the dc electron optics along the active circuit length. Proper programming of the variation requires maintaining a constant optimum value for Feinstein's spoke stabilization factor. This factor is essentially the ratio of the RF electric field intensity at the hub surface to the incremental dc electric field intensity above the synchronous field. It attempts to correlate the facts that (1) the RF field intensity limits the amount of space charge that can be phase focussed to the anode in the presence of space charge debunching forces and (2) the dc electric field intensity above the synchronous value determines the amount of space charge entering the base of the electron spoke. Theoretical considerations influencing the proper programming of the interaction space geometry will be discussed and some of the methods which have been employed for realizing the desired variation will be described.

A broad-band slow-wave structure for a millimeter traveling-wave tube amplifier

A new filter-type slow-wave structure, which is considered as an interdigital line loaded with inductance in shunt, is described in this paper. The results of the cold-test study of the structure are presented in terms of the phase velocity and impedance measurements. For the structure studied, interaction takes place between multiple electron streams and the axial electric field of the +1 space harmonic. The circuit has broad-band properties of phase and interaction impedance as a circuit for a traveling-wave amplifier. The maximum deviation of the phase velocity for a 30 per cent bandwidth has a value on the order of ±0.3 per cent. The structure is suitable for use as a high-power amplifier operating with a 20 per cent bandwidth in the millimeter-wave region.