Properties of Helical Structures with Internal Anisotropic Shields

Properties of the helical structures with internal anisotropic shields are considered in the paper. Models of systems based on the multiconductor line method and the CST Microwave Studio software package are used. The expressions for the retardation factor and the input impedance of the system are derived using the multiconductor line method. Analysis of the retardation factor allowed to show that there are possibilities to design helical structures with internal anisotropic shields having good dispersion properties and relatively high characteristic impedance. Simulation made using the CST Microwave Studio package confirmed the properties of the systems revealed using the multiconductor line method. Furthermore, in addition it allowed the detection of parasitic resonances that are available in helical systems with anisotropic internal shields. Synergy of various methods can be effectively used at analysis and design of wide-band periodic structures. DOI: http://dx.doi.org/10.5755/j01.eee.19.1.3256


I. INTRODUCTION
Helical structures are applied for retardation of electromagnetic waves in traveling-wave tubes, travelingwave cathode-ray tubes, delay lines and other electronic devices [1]- [4].Models of helical systems are proposed and their properties are described in [5]- [14] and other monographs and papers.Properties of helical systems with internal shields are investigated in [8].This work shows that retardation factor dependency on frequency can be reduced and the pass-band of system can be extended by using internal shields.If the thickness of the internal shield is increased, the retardation factor in the low frequency band increases.At a certain thickness of the internal shield the systems retardation factor becomes constant over a wide frequency range.However, in this case, the characteristic impedance of system decreases.Other known method for increasing the retardation factor at lower frequencies uses an internal anisotropic shield [9].
In this paper, the investigation results of helical delay systems with internal anisotropic shields are presented.Multiconductor line method and numerical method based MicroWave Studio software package are used in this investigation.The pass-band extension options are revealed.

II. THE MODEL OF THE HELICAL STRUCTURE WITH INTERNAL ANISOTROPIC SHIELDS
In order to investigate influence of the internal anisotropic shield on the helical system characteristics, let us firstly consider and examine characteristics of a simplified version of the system (Fig. 1).
This figure shows the system internal and external shields located symmetrically in relation to the helix.Let us assume that the helix conductors are in vacuum.The model of system based on multiconductor line method [10] is shown in Fig. 2.
The following dispersion equation and characteristic impedance expressions can be obtained for the investigated simplified model [8]:  ( ) ( ) ) where ( ) is the wavenumber, ω is the angular frequency, 0 c is the speed of light in the free space.The internal shield gap, whose width is a 2 , is placed symmetrically, so 1 3 a a = .
Retardation factor and characteristic impedance expressions at low frequencies can be obtained from ( 1) and (2) where R s k is the structural retardation factor.
At high frequencies, as in other systems, where conductors are in vacuum, R HF R s , It follows from presented expressions that the gap in the internal shield affects the system retardation factor at low and medium frequencies.When the gap is narrow ( 2 a h << ), expression (3) can be simplified and written as where The last expression shows that the retardation factor R LF k is dependent on characteristic admittance ratios.An assessment is needed that at low frequencies 0 When the internal shield is thin, According to (3) − ( 5) and investigation of other helical structures [10], the different influence of the gap onto systems dispersion properties can be explained as follows.On one hand, electromagnetic fields interaction between the flat helix parts arises because of the gap and this decreases Characteristics of the helix system with internal anisotropic shield calculated using (1) and ( 2) are shown in Fig. 3.
The above characteristics indicate that thickening the internal shield of the helical system with a longitudinal gap really can increase the system retardation factor in the low frequency range (Fig. 3(b), curves 3 and 4), and at the same time allows to reduce the phase delay dispersion in a wide frequency range and to widen the pass-band of the system.In order to reduce the system's input impedance dependency on frequency, its value should be reduced in the low-frequency range and increased in the high frequency range.This can be achieved by bringing the shields closer to the helix (Fig. 3(b), curve 4).

III. SIMULATION USING THE PACKAGE MICROWAVE STUDIO
The multiconductor line method allows us to simulate infinitively long slow-wave systems.Besides, changes of characteristic impedances of vertical parts of the helical wires (Fig. 1) are not taken into account when the simplest model (Fig. 2) is used.In order to verify the conclusions, based on the multiconductor method, the CST software package Microwave Studio was used for simulation of the system presented in Fig. 4.
The model of helical system with an internal anisotropic shield model was created by using the package graphical editor.The methodology of simulation is described in [10].The calculated system retardation factor versus frequency is presented in Fig. 5.
Analysis of the calculation results shows that thickening the internal shield really allows to increase the retardation factor in the low frequency range (Fig. 5, curves 1 and 3).Gap in the internal shield also increases the system retardation factor in the low frequency range (Fig. 5, curves 4 and 5).The thick shield with a gap gives the biggest effect (Fig. 5, curve 4).
Thus, the results obtained using the software package Microwave Studio confirmed the results obtained using multiconductor line method.At the same time, it is important to notice that using Microwave Studio package internal resonances were detected in the systems with anisotropic shield, when the shield gap width is greater than the distance between the helix and the internal shield ( ) 2 1 2 a w p > − (Fig. 6).
We can consider the anisotropic internal shield as a twowire line short-circuited at its ends.Then the first resonance is possible at wavelength 2l, where l is the length of the twowire line (like in other helical systems [10]).According to this, at l = 44 mm, the first resonant frequency must be approximately 3.4 GHz.According to Fig. 5 (curve 4), the first resonance occurs at twice less frequency.
We can explain the last effect taking into account that the current that is returning along the internal anisotropic shield cannot repeat the current path that is flowing in the helix conductor, and the return path in the internal shield has almost twice the length.
Examination of the distribution of the current density in the internal shield confirms this idea (Fig. 6).
At small gap in the anisotropic shield, resonant effects have less influence onto characteristics of the helical system (Fig. 5, curve 4, and Fig. 7, curve 1).
Thus, when using broadband helical delay systems with anisotropic internal shields attention should be given to the possible parasitic resonances that may affect the system performance.The following investigations of the electromagnetic field distribution in the system cross-section and frequency characteristics have shown that resonance can be avoided by reducing the thickness of the internal anisotropic shield (by increasing the gap between the helix and the internal shield).However, this is followed by decrease the retardation factor in low frequency range.Parasitic resonance effect can be also reduced by reducing the internal anisotropic shield gap area 5-th curve in Fig. 5.When It is also important that, according to (6), it is possible to avoid resonances due to parts of the internal shield using a thin conductor shortening them (using H-type internal shield).

IV. CONCLUSIONS
Properties of the helical line with internal anisotropic shields are revealed using the multiconductor line method and the CST software package Microwave Studio.
The multiconductor line method allowed us to show that there are possibilities to design the helical asymmetrical systems (Fig. 4) or symmetrical systems with internal anisotropic shields having good dispersion properties and relatively high characteristic impedance.
Simulation made using the package CST Microwave Studio confirmed the properties of the systems discovered using the multiconductor line method.At the same time, using the Microwave Studio we were able to detect a possibility of parasitic resonances occurring in such systems.Possible methods to avoid the mentioned resonances are showed.

Fig. 2 .Fig. 1 .
Fig. 2. The model of the helical line (a); cross-section (b): 1 -conductor of the multiconductor line, 2, 3 -shields, xi -multiconductor line section end coordinate, h -half the length of the helix coil, ai -dimensions of the internal parts of the system.

=
the characteristic admittance of the one-row multiconductor line in the model, are dual-row multiconductor line characteristic admittance in the gap area of the shield, along the helix conductor, and because of this increases R LF k .

Fig. 7 .
Fig. 7.The amplitude-frequency responses of the helical system: 1curve corresponds to the system, which retardation factor is shown in Fig. 5 by curve 5, and characteristic 2 -by curve 4.