EP2553757B1 - Coaxial conductor structure - Google Patents

Description

Technical area

The invention relates to a method for producing a coaxial conductor structure for the interference-free transmission of a single propagatable TEM mode of an RF signal wave within at least one band of frequency bands forming in the context of a dispersion relation. Furthermore, a use of the coaxial conductor structure will be described.

State of the art

The transmission quality of coaxial conductors for the TEM fundamental mode of RF signal waves decreases with increasing signal frequencies, especially as at higher frequencies by way of mode conversion processes along the coaxial line form undesirable, propagatable modes higher order, for example TE ₁₁ , TE ₂₁ modes, etc ., Which overlap with the TEM fundamental mode.

So goes, for example, from an article by Douglas E. Mode, "Spurious Modes in Coaxial Transmission Line Filters," Proceedings of the IRE, Vol. 38, 1950, p. 176-180 , DOI 10.1109 / JRPROC. 1950.230399 a study of the lower limit frequency of a disturbing forming the lowest TE mode along a coaxial line forth, along the so-called shunt inductors, in the form of the inner and outer conductors of the coaxial line connecting rods attached. For the analytical determination of the lower limit frequency, simplifying assumptions are made, for example, a coaxial line representing the modified rectangular waveguide is used. No dispersion relations are calculated for the TEM and TE ₁₁ modes.

In particular, with regard to future extensions or changes of existing transmission ranges for RF signals, which are defined in the frequency usage plan for the Federal Republic of Germany to higher frequencies, it is necessary to look for measures with which a trouble-free, high-frequency signal transmission of the TEM basic mode of RF signals via coaxial cables with the largest possible diameter possible.

The solution of the problem is specified in claim 1. Advantageous embodiments and further developments of the method according to the invention for producing a coaxial conductor structures are specified in the subclaims and the further description with reference to the exemplary embodiments.

The solution according to the method for producing a Koaxialleiterstruktur based on the finding that the transmission behavior of coaxial lines for RF signal waves changes significantly, provided between the outer and inner conductors in each periodically equidistant intervals along the coaxial line electrically conductive connection structures are introduced. If one considers the propagation behavior of the TEM fundamental mode along a conventional coaxial line, ie the outer and inner conductors are electrically insulated by the interposed dielectric, in the context of a dispersion diagram, it can be established that a linear relationship between the frequency or angular frequency ω and the propagation constant β of the RF signal wave is of the form e ^{j (ω t -β z )} , ie, w = cβ. This linear relationship is represented in a dispersion diagram ω (β) as a so-called sky of light speed. From a lower limit frequency - the so-called cut-off frequency (f _∞ ) for the TE ₁₁ mode - with increasing frequencies along the conventional coaxial line undesirable propagation modes of higher order, TE ₁₁ , TE ₂₁ , TE ₃₁ , TE ₄₁ , TM ₀₁ , TM _11, etc., so that at frequencies above f _∞ the TEM fundamental mode is always superimposed by modes of higher excitation order.

If, on the other hand, one sees electrically conductive structures in the manner indicated above between the outer and inner conductors of the coaxial line, frequency bands are formed in which the TEM fundamental mode is capable of propagation, as well as band gaps lying between the frequency bands, in which the TEM Basic mode evanescent, ie is not capable of spreading. This result appears disadvantageous at first glance, especially since the frequency-specific transmission range for the TEM fundamental mode is trimmed compared with a conventional coaxial conductor, although this disadvantage can be used in a solution-like manner.

Furthermore, it has been recognized that by adding the electrically conductive connection structures between the outer and inner conductors of the coaxial line the above outlined frequency windowing of the TEM fundamental mode in each concrete frequency bands capable of propagation also occurs in the higher order excitation modes, ie even in the higher excitation modes, TE _11th , TE _21, etc. form frequency ranges in which the modes are capable of propagation, and other frequency ranges in which they are evanescent.

The idea underlying the invention is based on the consideration that by a suitable choice of constructive design parameters for the formation of a coaxial line with electrically conductive connection structures between outer and inner conductors, a targeted or controlled influence on the frequency-dependent layers of the above-mentioned frequency bands is taken in such a way in that at least one frequency band in which the basic TEM mode is capable of propagation is overlapped with a frequency band or range in which all higher order excitation modes are evanescent.

For further conceptual definition, it is assumed that a number "n" of concrete frequency bands in which the basic TEM mode is capable of propagation is formed in the coaxial conductor structure produced in accordance with the invention. Here, the counting parameter "n" starts at one and represents a natural positive number. In the same way, "m" form concrete ones Frequency bands in which the TE ₁₁ mode is capable of propagation, where also "m" represents a positive natural number as a count parameter. A further discussion regarding the occurrence of higher-order excitation modes is discarded, especially since these occur at frequencies whose technical applicability is at least presently considered to be less relevant, nevertheless these excitation modes can also be taken into account in an equivalent application of the idea according to the solution.

1. a) einen kreisrunden Querschnitt aufweisenden Innenleiter mit einem Innenleiterdurchmesser D_i, denkbar sind jedoch auch an die Kreisform angenäherte Querschnittsformen, bspw. mit einer n-eckigen Umfangskontur,
2. b) einen Außenleiter, der den Innenleiter radial mit einem Außenleiterinnendurchmesser Da umgibt, vorzugsweise äquidistant radial umgibt, denkbar sind jedoch auch an die Kreisform angenäherte Querschnittsformen, bspw. mit einer n-eckigen Umfangskontur, und
3. c) einen sich axial erstreckenden gemeinsamen Leiterabschnitt von Innen- und Außenleiter, längs dem in äquidistanten Abständen p jeweils s ≥ 1 den Innen- mit dem Außenleiter elektrisch verbindende stabförmige Strukturen mit einem Stabdurchmesser D_s vorgesehen sind. Vorzugsweise eignen sich im Querschnitt kreisrunde Stäbe, gleichwohl können die Stabquerschnitte auch n-eckig o.ä. ausgestaltet sein. Für eine von höheren Anregungsmoden, die sich zumindest in Form einer TE₁₁-Mode innerhalb von m Frequenzbändern ausbilden, ungestörte Ausbreitung der TEM-Grundmode längs der Koaxialleiterstruktur sind die vorstehenden Parameter D_i, D_a, D_S, p, s derart zu wählen, dass die folgenden beiden Bedingungen erfüllt sind:
   1. i) Eine untere Grenzfrequenz f_u(TEM) des sich innerhalb eines n ≥ 2 2-ten Bandes ausbreitenden TEM-Modes ist gleich einer oberen Grenzfrequenz f_o(TE₁₁) des sich ausbildenden TE₁₁-Modes im m-ten Band, und
   2. ii) eine obere Grenzfrequenz f_o(TEM) des sich innerhalb des n ≥ 2-ten Bandes ausbreitenden TEM-Modes ist gleich einer unteren Grenzfrequenz f_u(TE₁₁) des sich innerhalb des (m+1)-ten Bandes ausbildenden TE₁₁-Modes ist.

A coaxial conductor structure produced in accordance with the invention for the interference-free transmission of a monomode TEM fundamental mode of an RF signal wave within at least one band of n frequency bands forming in the context of a dispersion relationship has the following components:

1. a) having a circular cross-section inner conductor with an inner conductor diameter D _i , but are also conceivable to the circular shape approximate cross-sectional shapes, for example. With an octagonal peripheral contour,
2. b) an outer conductor which surrounds the inner conductor radially with an outer conductor inner diameter Da, preferably equidistant radially surrounds, but are also conceivable to the circular shape approximate cross-sectional shapes, for example. With an n-angular peripheral contour, and
3. c) an axially extending common conductor section of inner and outer conductors, along which the inner and the outer conductor electrically connecting rod-shaped structures with a rod diameter D _{s are} provided at equidistant intervals p each s ≥ 1. Circular rods are preferably suitable in cross-section, however, the rod cross-sections can also be n-sided or similar. be designed. For one of higher excitation modes, which form at least in the form of a TE ₁₁ mode within m frequency bands, undisturbed propagation of the TEM fundamental mode along the coaxial conductor structure, the above parameters D _i , D _a , D _s , p, s are to be selected in such a way in that the following two conditions are met:
   1. i) A lower cutoff frequency f _u (TEM) of the TEM mode propagating within an n ≥ 2 2-th band is equal to an upper cutoff frequency f _o (TE ₁₁ ) of the forming TE ₁₁ mode in the mth band, and
   2. ii) an upper limit frequency f _o (TEM) of the TEM mode propagating within the n ≥ 2-th band is equal to a lower limit frequency f _u (TE ₁₁ ) of the TE ₁₁ forming within the (m + 1) th band -Modes is.

1. i) $$\left|f_u\left(\mathit{TEM}n\right)-f_o\left(\mathit{TE}11,m\right)\right|<\frac{1}{3}\left(f_o\left(\mathit{TEM}n\right)-f_u\left(\mathit{TEM}n\right)\right)$$
   
   
   sowie
2. ii) $$\left|f_o\left(\mathit{TEM}n\right)-f_u\left(\mathit{TE}11,m+1\right)\right|<\frac{1}{3}\left(f_o\left(\mathit{TEM}n\right)-f_u\left(\mathit{TEM}n\right)\right)$$
   

The above mathematical relational requirements are to be understood as somewhat softened in the sense of the solution, ie a technically acceptable single-mode propagation of the TEM mode can also be used if the following applies:

1. i) $$\left|f_u\left(\mathit{TEM}n\right)-f_O\left(\mathit{TE}11.m\right)\right|<\frac{1}{3}\left(f_O\left(\mathit{TEM}n\right)-f_u\left(\mathit{TEM}n\right)\right)$$
   
   
   such as
2. ii) $$\left|f_O\left(\mathit{TEM}n\right)-f_u\left(\mathit{TE}11.m+1\right)\right|<\frac{1}{3}\left(f_O\left(\mathit{TEM}n\right)-f_u\left(\mathit{TEM}n\right)\right)$$
   

It has been found that in an area in which there is a slight overlap of the propagatable TEM mode and TE ₁₁ modes, a technical use of the TEM mode without significant loss of quality is possible. This tolerance range Δf is at most 1/3 of the nth TEM bandwidth.

It has also been found that the measures according to the solution for creating a frequency window capable of propagating smoothly along a coaxial conductor structure for TEM mode can also be used successfully in a coaxial conductor structure in which the inner conductor and / or outer conductor cross section of the coaxial line deviates from the circular shape has the same characteristic impedance as the round coaxial line. For example, the outer and inner conductor cross-section can be formed n-angular. The further considerations, however, relate to each circular cross-sectional shapes.

As the further explanations will show, it is possible by appropriate choice of the design parameters D _i , D _a , D _S , p, s to define coaxial conductor structures which in frequency ranges above the cut-off frequency f _{∞ of} the TE ₁₁ mode a completely interference-free propagation of the TEM fundamental mode is possible without any higher-order excitation modes and this at such high frequencies at which higher-order excitation modes are unavoidable in the case of conventional coaxial conductors.

In the same way, it is possible by suitable constructive definition of the coaxial conductor structure produced in accordance with the solution to shift the cut-off frequency f _∞ to higher frequency values and in this way to expand the first frequency band in which the basic TEM mode is capable of single-mode propagation in the direction of higher frequencies ,

und ${\mathrm{f}}_{\mathrm{u}}\left({\mathrm{TE}}_{\mathrm{11}}\right)=\sqrt{\frac{6a}{3+a}{f}_0^2+f_{\mathit{co}}^2},$

so dass gilt $$\frac{c}{2p}\le \sqrt{\frac{6a}{3+a}{f}_0^2+f_{\mathit{co}}^2}\mathrm{.}$$

Such a coaxial conductor structure produced in accordance with the invention is distinguished by the constructive parameters D _i , D _a , D _s , p, s explained above, wherein these parameters are to be selected in such a way that an upper limit frequency f _o (TEM) of the inside of the first, ie n = 1, band propagating TEM mode is less than or equal to the lower limit frequency f _u (TE ₁₁ ) of the forming TE ₁₁ mode in the first band, ie m = 1, where: ${\mathrm{f}}_{\mathrm{O}}\left(\mathrm{TEM}\right)=\frac{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">c</figure-callout>}}{2p}$

and ${\mathrm{f}}_{\mathrm{u}}\left({\mathrm{TE}}_{\mathrm{11}}\right)=\sqrt{\frac{6a}{3+a}{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}^{\mathit{}}}.$

so that applies $$\frac{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">c</figure-callout>}}{2p}\le \sqrt{\frac{6a}{3+a}{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}^{\mathit{}}}\mathrm{,}$$

und $\mathit{a}=\frac{\mathit{s}{\mathit{Z}}_{\mathit{TEM}}\mathit{p}}{2{\mathit{cL}}_{\mathit{Stab}}}$

und $Z_{\mathit{TEM}}=\frac{1}{2\pi }\sqrt{\frac{\mu }{\epsilon }}\ln \frac{D_a}{D_i}$

Where: ${\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0=\frac{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">c</figure-callout>}}{2\mathit{\pi p}}.f_{\mathit{co}}\cong \frac{c}{\pi }\frac{2}{D_a+D_i}$

and $\mathit{a}=\frac{\mathit{s}{\mathit{Z}}_{\mathit{TEM}}\mathit{<figure-callout\; id="2"\; label="p"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">p</figure-callout>}}{2{\mathit{cL}}_{\mathit{Rod}}}$

and $Z_{\mathit{TEM}}=\frac{1}{2\pi }\sqrt{\frac{\mu }{\epsilon }}\ln \frac{D_a}{D_i}$

erhöht, vgl. mit f_u(TE₁₁) = f_co einer konventionellen Koaxialleitung.For the above relationships, assume that c represents the speed of light in the dielectric, usually air. It should be noted that the lower limit frequency of the TE ₁₁ mode in the first band and thus the single-mode TEM operation are the case for this coaxial conductor structure according to the invention ${\mathrm{f}}_{\mathrm{u}}\left({\mathrm{TE}}_{\mathrm{11}}\right)=\sqrt{\frac{6a}{3+a}{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}^{\mathit{}}}$

increased, cf. with f _u (TE ₁₁ ) = f _{co of} a conventional coaxial line.

In addition to the above-described design criteria for Koaxialleiterstrukturen that provide very much the use of the outer and inner conductors connecting electrically conductive structures and at least in certain frequency bands interference-free transmission characteristics exclusively for the TEM fundamental mode, just carry the electrically conductive structures to a targeted cooling of the Inner conductor, which is subject to considerable heat, especially in the transmission of high-power RF signals. Since the electrically conductive connection structures are preferably in the form of rod-shaped structures of a metallic material, preferably of the material of which the inner and / or outer conductor, they have a high thermal conductivity. Thus, electrically conductive materials are suitable for these structures, which have a particularly high thermal conductivity.

Brief description of the invention

Fig. 1

Darstellung eines Abschnittes einer lösungsgemäß ausgebildeten Koaxialleiterstruktur und

Fig. 2

TEM Dispersions-Diagramm,

Fig. 3

Diagrammdarstellung zur Bloch-Impedanz für TEM-Mode sowie

Fig. 4

Diagramm mit allen Dispersions-Relationen bis zu einer bestimmten Maximalfrequenz. Vergleich des Ersatz-Schaltbilds mit einer Vollwellen EM-Simulation.

The invention will now be described by way of example without limitation of the general inventive idea by means of embodiments with reference to the drawings. Show it:

Fig. 1

Representation of a portion of a solution according trained coaxial conductor structure and

Fig. 2

TEM dispersion diagram,

Fig. 3

Diagram showing the Bloch impedance for TEM mode as well

Fig. 4

Diagram with all dispersion relations up to a certain maximum frequency. Comparison of the replacement circuit diagram with a full wave EM simulation.

Ways to carry out the invention, industrial usability

In FIG. 1 a section of a solution according manufactured coaxial conductor structure is shown. The section represents a kind of unit cell for the construction of a coaxial line, which is ultimately characterized by a periodic return of the illustrated section. Inside the transparently illustrated outer conductor AL, which has an outer conductor inner diameter Da, an inner conductor IL of the length p with a circular conductor cross-section and an inner conductor diameter Di is inserted. Central to the longitudinal extent p of the inner conductor IL are s = 2 rod-shaped structures S are provided which produce an electrically conductive contact or an electrically conductive connection to the outer conductor AL. The rod-shaped structures S are made of an electrically and thermally highly conductive material, preferably metal, preferably made of the same material from which the inner or outer conductor are made. The structures S may have a circular or n-shaped cross section. For the further mathematical consideration, it is assumed that the structures have a diameter D _S.

Basically, it is possible a single, i. s = 1, to provide rod-shaped structure S per unit cell. Further considerations and corresponding calculations show that particularly favorable transmission properties of the coaxial line are achieved when s = 2, 3 or 4. In the case of s = 1 or s = 2, it is advisable to arrange the rod-shaped structures arranged at equidistant distances p along the coaxial line relative to the circumferential direction of the inner and outer conductors in such a way that the rod-shaped structures are in an axial projection to the axially extending common conductor section are each arranged congruently one behind the other, or in each case offset with an identical in the circumferential direction of the inner and outer conductor IL, AL oriented, identical angular offset .DELTA..alpha. For example. in the case of s = 1 or 2, it is advantageous to arrange two axially successive rod-shaped structures each rotated by Δα = 90 ° about the coaxial longitudinal axis to minimize any magnetic couplings between the rods.

Furthermore, based on the in FIG. 1 For the construction of a coaxial line produced in accordance with the invention, the unitary cell illustrated in the description of the electromagnetic design of such a line is described in order to obtain desired dispersion relations of the invention technically used TEM basic modes and the annoying TE11 mode tailoring. The aim is to design coaxial conductor structures with relatively large diameters Da, which in a desired frequency range, bounded by a lower f _u and upper limit frequency f _o , have only one single propagatable mode, namely the TEM fundamental mode. All other modes should be evanescent in this frequency range.

Ausbreitungskonstante $\gamma =j\frac{\omega }{c},$

und der Länge l= p / 2 und einer zwischengeschalteten Shunt-Admittanz Y =1/ jωL. Die Stäbe kann man näherungsweise durch eine Induktivität L beschreiben mit $L=\frac{L_{\mathit{Stab}}}{s},L_{\mathit{Stab}}\approx \frac{\left(D_a-D_i\right)}{2}\frac{\mu }{4\pi }\ln \frac{D_a}{D_s},$

wobei s die Anzahl der radialen Stäbe ist.In the FIG. 1 shown symmetrical unit cell has the advantage that their input impedances at the input E and output A are the same. The cell consists of two lines L1, L2 with the impedance $Z=Z_{\mathit{TEM}}=\frac{1}{2\pi }\sqrt{\frac{\mu }{\epsilon }}\ln \frac{D_a}{D_i}.$

propagation constant $\gamma =j\frac{\omega }{c}.$

and the length l = p / 2 and an interposed shunt admittance Y = 1 / jωL. The rods can be approximately described by an inductance L with $L=\frac{L_{\mathit{Rod}}}{s}.L_{\mathit{Rod}}\approx \frac{\left(D_a-{\mathrm{<figure-callout\; id="2"\; label="D\; i"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_i\right)}{2}\frac{\mathrm{<figure-callout\; id="4"\; label="\mu "\; filenames="imgf0003.png"\; state="\{\{state\}\}">\mu </figure-callout>}}{4\pi }\ln \frac{D_a}{D_s}.$

where s is the number of radial bars.

und die Shunt-Induktivität L durch $${\mathit{ABCD}}_{\mathit{L}}=\left(\begin{array}{cc}1& 0\\ \frac{1}{j\omega L}& 1\end{array}\right)\mathrm{.}$$

The individual sections of the unit cell, L1, L, L2, can be described by ABCD matrices, which can be simply switched one after the other by matrix multiplication. The ABCD matrix of line L1, L2 is given by $${\mathit{ABCD}}_{\mathit{TL}}=\left(\begin{array}{cc}\cosh \left(\mathit{\gamma l}\right)& Z\sinh \left(\mathit{\gamma l}\right)\\ \frac{1}{Z}\sinh \left(\mathit{\gamma l}\right)& \cosh \left(\mathit{\gamma l}\right)\end{array}\right).$$

and the shunt inductance L through $${\mathit{ABCD}}_{\mathit{L}}=\left(\begin{array}{cc}1& 0\\ \frac{1}{j\omega L}& 1\end{array}\right)\mathrm{,}$$

This gives you for the entire unit cell $${\mathit{ABCD}}_{\mathit{cell}}={\mathit{ABCD}}_{\mathit{TL}}{\mathit{ABCD}}_{\mathit{L}}{\mathit{ABCD}}_{\mathit{TL}}$$

und erkennt ein Eigenwertproblem mit zwei Eigenwerten e ^{jϕ _k} . Hier stellt sich heraus, däß gilt: ϕ₁ = ϕ₂ , d.h. man hat es mit je einer vor und einer rücklaufenden Welle zu tun. Für die Berechnung des Eigenwerts muß folgende Determinante verschwinden: $$\left|\begin{array}{cc}A-e^{j\varphi }& B\\ C& D-e^{j\varphi }\end{array}\right|=0$$

Now, the Bloch analysis can be performed using periodic boundary conditions, ie voltage + current at the output is equal to voltage + current at the input multiplied by a phase factor exp ( j φ). This gives you $$\left(\begin{array}{c}{U}_1\\ I_1\end{array}\right)={\mathit{ABCD}}_{\mathit{cell}}\left(\begin{array}{c}{U}_2\\ I_2\end{array}\right)=e^{j\phi }\left(\begin{array}{c}{U}_2\\ I_2\end{array}\right)$$

and recognizes an eigenvalue problem with two eigenvalues e ^{j φ _k} . Here it turns out that the following applies: φ ₁ = φ ₂ , ie one has to deal with one each before and one returning wave. The following determinant must disappear for the calculation of the eigenvalue: $$\left|\begin{array}{cc}A-e^{j\phi }& B\\ C& D-e^{j\phi }\end{array}\right|=0$$

After a long calculation you get $$\cos \frac{p\omega }{c}+\frac{\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Z</figure-callout>}}{2\omega L}\sin \frac{p\omega }{c}=\cos \phi$$

und man erhält $$\cos x+\frac{a}{x}\sin x=\cos \varphi$$

wobei $a=\frac{\mathit{Zp}}{2\mathit{cL}}$

einen dimensionslosen Parameter für die so genannte Störung durch L darstellt. Diese Gleichung (7) kann man nach ϕ auflösen. Trägt man x über $\varphi \left(x\right)=\arccos \left(\cos x+\frac{a}{x}\sin x\right)$

auf, so erhält man schließlich das in Figur 2 gezeigte TEM Dispersions-Diagramm, hier für verschiedene Werte von a gezeigt.Here it makes sense to normalize the frequency $x=\frac{p}{c}\omega =\frac{2\mathit{\pi p}}{c}f$

and you get $$\cos x+\frac{a}{x}\sin x=\cos \phi$$

in which $a=\frac{\mathit{<figure-callout\; id="2"\; label="Zp"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Zp</figure-callout>}}{2\mathit{cL}}$

represents a dimensionless parameter for the so-called disturbance by L. This equation (7) can be solved for φ. If you transfer x over $\phi \left(x\right)=\arccos \left(\cos x+\frac{a}{x}\sin x\right)$

on, so you finally get the in FIG. 2 shown TEM dispersion diagram, shown here for different values of a.

It can be clearly seen how bands B and band gaps BL are generated by the periodic shunt inductance. In bands B, a TEM wave propagates, but at frequencies within a band gap, the wave is evanescent and attenuated.

der ungestörten Koaxialleitung, die Zick-Zack in die erste Brillouin-Zone gefaltet wird. Der andere Extremfall ist bei α = ∞, L = 0: Dann erhält man ungekoppelte Leitungsresonatoren der Länge p mit den Resonanzfrequenzen x = nπ, d.h. λ/2-Resonatoren. Hier schrumpfen die Bänder auf Punktfrequenzen zusammen.For a = 0 (ie L becomes infinity, crossbars disappear, dashed curve) you get the typical speed of light line $f=\frac{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">c</figure-callout>}}{2\mathit{\pi p}}\phi$

undisturbed coaxial line folded zig-zag into the first Brillouin zone . The other extreme case is at α = ∞, L = 0: Then one obtains uncoupled line resonators of length p with the resonance frequencies x = nπ, ie λ / 2 resonators. Here the bands shrink to point frequencies together.

By extending the left-hand side of equation (7) up to the second order at the points x = n π and setting equal (-1) ", one can approximate for small perturbations a" 3n the cut-off frequencies (f _u , f _o ) calculate the individual bands and you get for the first band with the lowest frequency: $$\begin{array}{ll}{x}_{1.O}& =\pi \\ x_{1.u}& \cong \sqrt{\frac{6a}{3+a}}\approx \sqrt{2a}\end{array}$$

And for the nth band with n> 1: $$\begin{array}{ll}{x}_{n.O}& =\mathit{n\pi }\\ x_{n.u}& \cong \left(n-1\right)\pi +\frac{2a/\left(n-1\right)/\mathrm{<figure-callout\; id="1"\; label="\pi "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{1+2a/{\left(n-1\right)}^2/{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\pi </figure-callout>}}^2}\approx \left(n-1\right)\pi +\frac{2a}{\left(n-1\right)\pi }\end{array}$$

For very large perturbations a »3n, on the other hand, for the nth band (n> = 1) we obtain: $$\begin{array}{ll}{x}_{n.O}& =\mathit{n\pi }\\ x_{n.u}& \cong \mathit{n\pi }-\frac{\mathit{<figure-callout\; id="2"\; label="n\pi a\; n"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">n\pi a\; </figure-callout>}}{n^{}}\left(\sqrt{1+\frac{\mathrm{8th}}{a}+\frac{4{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">n</figure-callout>}}^2{\pi }^2}{a^2}}-1\right)\approx \mathit{n\pi }-\frac{2\mathit{n\pi }}{a}\end{array}$$

Thus, the TEM dispersion is fully characterized and can be tailored depending on the geometry. Typically, one will use a band for transmission so that the actual usable frequency range is significantly greater than the required one. Thus, manufacturing tolerances can be compensated, high insertion losses due to the vanishing group speed (slope = 0) are minimized at the band limits and high reflections due to the increasing deviation of the frequency-dependent Bloch impedance from the target impedance at the band boundaries are minimized.

The so-called Bloch impedance Z _B is the effective impedance of the periodic line - it is the input impedance of an infinitely long periodic structure. So that the periodic structure can be connected to a conventional coaxial line with the characteristic impedance Zw as free from reflection, Z _B should be as close as possible to Z _W.

The Bloch impedance can be calculated from the voltage and current of an elementary cell at periodic boundary conditions, ie the two components of the eigenvector of the eigenvalue problem (4): $$Z_B\left(\omega \right)=\frac{U_1}{I_1}=\frac{U_2}{I_2}=-\frac{B}{A-e^{j\phi }}=\frac{B}{\sqrt{A^2-1}}=Z_{\mathit{TEM}}\frac{\sin \frac{p\omega }{c}+\frac{{\mathrm{<figure-callout\; id="2"\; label="Z\; TEM"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Z\; </figure-callout>}}_{\mathit{TEM}}}{2\omega L_{\mathit{TEM}}}\left(1-\cos \frac{p\omega }{c}\right)}{\sqrt{1-{\left(\cos \frac{p\omega }{c}+\frac{{\mathrm{<figure-callout\; id="2"\; label="Z\; TEM"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Z\; </figure-callout>}}_{\mathit{TEM}}}{2\omega L_{\mathit{TEM}}}\sin \frac{p\omega }{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">c</figure-callout>}}\right)}^2}}$$

The strong frequency dependence of the Bloch impedance Z _B , which can deviate extremely from the impedance of the undisturbed coaxial line Z _TEM , shows the in FIG. 3 illustrated diagram. In this example we used a = 7.8, p = 72mm and Z _TEM = 28Ω.

In the band gaps BL, Z _{B is} purely imaginary, as it should be for a reactive load that does not absorb active power. On the other hand, in the transmission bands B, Z _{B is} real and, in the higher bands, where the perturbation by the inductances is weaker, approaches the value of the undisturbed line Z _TEM . It is also nice to see how in the even-numbered bands the Bloch impedance becomes negative, which is related to the negative group velocity (ie slope dω / dβ <0), so that the current changes its sign.

betragsmäßig kleiner bleibt als ein gegebenes r _max, beispielsweise |r|<r _max = 0,1. Dies stellt eine Nebenbedingung für das Bestimmen bzw. Optimieren der geometrischen Parameter dar.Preferably, a periodic structure will be designed so that in the transmission region B, the reflection $r=\frac{Z_B-Z_W}{Z_B+Z_W}$

in amount remains smaller than one given r _max , for example | r | < r _max = 0.1. This is a constraint for determining or optimizing the geometric parameters.

mit der genäherten TE₁₁-cutoff-Frequenz $f_{\mathit{co}}\cong \frac{c}{\pi }\frac{2}{D_a+D_i}\mathrm{.}$

The TE ₁₁ mode can be modeled similar to the TEM fundamental mode described above, especially since the structure of the unit cell and the equivalent equivalent circuit is the same as in the case of the TEM Gundmodes, only in the waveguides, the propagation constant and the impedance are highly frequency-dependent: $$\begin{array}{r}Z\left(f\right)=\frac{\ln \frac{D_a}{D_i}}{\pi }\sqrt{\frac{\mu }{\epsilon }}\frac{1}{\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}^{\mathit{}}/{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}}.\\ \gamma \left(f\right)=j\frac{2\mathit{\pi f}}{c}\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}^{\mathit{}}/{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}.\end{array}$$

with the approximated TE ₁₁ cutoff frequency $f_{\mathit{co}}\cong \frac{c}{\pi }\frac{2}{D_a+D_i}\mathrm{,}$

If one carries out the same calculation as in the TEM case analogously to (6), one obtains the following equation for the TE ₁₁ mode: $$\cos \frac{p\omega }{c}\sqrt{1-{{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}}^2/{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}+\frac{2Z_{\mathit{TEM}}/\sqrt{1-{{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}}^2/{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}}{2\omega L_{\mathit{TE}}}\sin \frac{p\omega }{c}\sqrt{1-{{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}}^2/{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}=\cos \phi$$

nun jedoch mit der normierten Frequenz $x_{\mathit{TE}}=\frac{2\mathit{\pi p}}{c}\sqrt{f^2-f_{\mathit{co}}^2},$

bzw. $f=\sqrt{{\left(\frac{x_{\mathit{TE}}c}{2\mathit{\pi p}}\right)}^2+f_{\mathit{co}}^2}$

und mit der Störung ${\mathit{a}}_{\mathit{TE}}=\frac{{\mathit{Z}}_{\mathit{TEM}}\mathit{p}}{\mathit{c}{\mathit{L}}_{\mathit{TE}}}\mathit{.}$

Since the same root appears in the impedance and in the propagation constant, one can transform to a normalized frequency x as in the TEM case and in fact get the same equation again $$\cos x_{\mathit{TE}}+\frac{{\mathit{a}}_{\mathit{TE}}}{{\mathit{x}}_{\mathit{TE}}}\sin x_{\mathit{TE}}=\cos \phi .$$

but now with the normalized frequency $x_{\mathit{TE}}=\frac{2\mathit{\pi p}}{c}\sqrt{f^2-{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}^{\mathit{}}}.$

respectively. $f=\sqrt{{\left(\frac{x_{\mathit{TE}}c}{2\mathit{\pi p}}\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}^{\mathit{}}}$

and with the disorder ${\mathit{a}}_{\mathit{TE}}=\frac{{\mathit{Z}}_{\mathit{TEM}}\mathit{p}}{\mathit{c}{\mathit{L}}_{\mathit{TE}}}\mathit{,}$

was wiederum bedeutet, dass auch die normierten Grenzfrequenzen (x_u, x_o) der TEM- und TE11-Bänder gleich sind!If, as in a preferred application, four, ie s = 4, radial rods are used to prevent mode conversion TEM <-> TE11, then L _TEM = L _bar / 4 and L _TE = L _bar / 2, as the TE11 wave "sees" only two bars parallel to the E-field. But this will equal the disturbance parameter in both cases: ${\mathit{a}}_{\mathit{TEM}}={\mathit{a}}_{\mathit{TE}}=\frac{2{\mathit{Z}}_{\mathit{TEM}}\mathit{p}}{\mathit{c}{\mathit{L}}_{\mathit{Rod}}}.$

which in turn means that the normalized cutoff frequencies (x _u , x _o ) of the TEM and TE11 bands are the same!

The quintessence is thus: The dispersions of TEM and TE11 modes in periodic structures with four interconnects are very closely linked. The only parameter that allows for individual influencing of both modes is the cut-off frequency f _{co of} the TE11 mode in the coaxial line, which shifts the TE11 bands upwards.

π f ₀ n $$\left(\left(n-1\right)\pi +\frac{2a/\left(n-1\right)/\pi }{1+2a/{\left(n-1\right)}^2/{\pi }^2}\right)f_0$$

nπ f ₀ TE₁₁ 1 $$\sqrt{\frac{6a}{3+a}{f}_0^2+f_{\mathit{co}}^2}$$

$$\sqrt{{\left(\pi f_0\right)}^2+f_{\mathit{co}}^2}$$

m $$\sqrt{{\left(\left(n-1\right)\pi +\frac{2a/\left(n-1\right)/\pi }{1+2a/{\left(n-1\right)}^2/{\pi }^2}\right)}^2{f}_0^2+f_{\mathit{co}}^2}$$

$$\sqrt{{\left(\pi f_0\right)}^2+f_{\mathit{co}}^2}$$

Große Störung a>>3n Mode Band Untere Grenzfrequenz Obere Grenzfrequenz TEM n $$\left(\mathit{n\pi }-\frac{n\mathit{\pi }a}{n^2{\pi }^2+2a}\left(\sqrt{1+\frac{8}{a}+\frac{4n^2{\pi }^2}{a^2}}-1\right)\right)f_0$$

nπ f ₀ TE₁₁ m $$\sqrt{f_{\mathit{TEM},u,n}^2+f_{\mathit{co}}^2}$$

$$\sqrt{{\left(\mathit{n\pi }{f}_0\right)}^2+f_{\mathit{co}}^2}$$

wobei $f_0=\frac{c}{2\mathit{\pi p}},f_{\mathit{co}}\cong \frac{c}{\pi }\frac{2}{D_a+D_i}$

und die Störung $\mathit{a}=\frac{2{\mathit{Z}}_{\mathit{TEM}}\mathit{p}}{\mathit{c}{\mathit{L}}_{\mathit{Stab}}}$

ist.The following tables summarize the (non-normalized) cutoff frequencies of the TEM and TE ₁₁ bands of 4-bar geometries: Little disturbance a << 3 n Fashion tape Lower limit frequency Upper limit frequency TEM 1 $$\sqrt{\frac{6a}{3+a}}{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0$$

π f ₀ n $$\left(\left(n-1\right)\pi +\frac{2a/\left(n-1\right)/\mathrm{<figure-callout\; id="1"\; label="\pi "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{1+2a/{\left(n-1\right)}^2/{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\pi </figure-callout>}}^2}\right){\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0$$

nπ f ₀ TE ₁₁ 1 $$\sqrt{\frac{6a}{3+a}{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}^{\mathit{}}}$$

$$\sqrt{{\left(\pi {\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0\right)}^2+f_{\mathit{co}}^2}$$

m $$\sqrt{{\left(\left(n-1\right)\pi +\frac{2a/\left(n-1\right)/\mathrm{<figure-callout\; id="1"\; label="\pi "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{1+2a/{\left(n-1\right)}^2/{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\pi </figure-callout>}}^2}\right)}^2{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}^{\mathit{}}}$$

$$\sqrt{{\left(\pi {\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}^{\mathit{}}}$$

Great disturbance a >> 3 n Fashion tape Lower limit frequency Upper limit frequency TEM n $$\left(\mathit{n\pi }-\frac{n\mathit{\pi }a}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">n</figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\pi </figure-callout>}}^2+2a}\left(\sqrt{1+\frac{\mathrm{8th}}{a}+\frac{4{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">n</figure-callout>}}^2{\pi }^2}{a^2}}-1\right)\right){\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0$$

nπ f ₀ TE ₁₁ m $$\sqrt{f_{\mathit{TEM}.u.\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}^{\mathit{}}}$$

$$\sqrt{{\left(\mathit{n\pi }{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="f\; co"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{\mathit{co}}^{\mathit{}}}$$

in which ${\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0=\frac{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">c</figure-callout>}}{2\mathit{\pi p}}.f_{\mathit{co}}\cong \frac{c}{\pi }\frac{2}{D_a+D_i}$

and the disorder $\mathit{a}=\frac{2{\mathit{Z}}_{\mathit{TEM}}\mathit{p}}{\mathit{c}{\mathit{L}}_{\mathit{Rod}}}$

is.

For Z _TEM : $Z_{\mathit{TEM}}=\frac{1}{2\pi }\sqrt{\frac{\mu }{\epsilon }}\ln \frac{D_a}{D_i}$

In the FIG. 4 shown dispersion relation shows an excellent match of the equivalent circuit diagram description with a full wave simulation for a Koaxialleiterstruktur with four connecting rods per unit cell and the other dimensions D _a = 36mm, D _i = 22.8mm, p = 72mm, D _s ≈1.5mm, with pure rectangular bar with 1x2mm; Here, L _Stab = 1.68nH was extracted from a numerical model using CST (Computer Simulation Technique). The solid curves correspond to the TEM dispersion bands n = 1, 2, 3, 4 and the dashed curves show the TE ₁₁ dispersion bands m = 1, 2, 3, 4, with both a CST simulation, as well as ESB calculations (ESB: equivalent circuit diagram) have been carried out. Especially the four lowest bands are modeled almost on line width exactly!

At the in FIG. 4 The dispersion ratio shown here makes it possible to use the 3rd TEM band (n = 3) for the transmission, more precisely the much smaller frequency range FB of 5.4 to 5.9 GHz.

Since one usually wants the largest possible single-mode frequency range, the TEM band used should be as wide as possible and at the same time the TE11 band gap as wide as possible. Since one but, as shown above, the TEM mode can not affect independently of the TE11 mode, the compromise to a disturbance a in the transitional area a ≈ will result in 3 n, so that band-width and band gap are approximately equal. With such a conductor geometry, the perturbation with a = 7.8 is exactly in the transition region, where both approximation formulas, as summarized in the table above, become inaccurate for the cutoff frequencies. Nevertheless, the cutoff frequencies of the two lowest bands can preferably be calculated using the formula for the large perturbation. At the higher bands with n> 2, the formulas for the small disturbance are more accurate. Exact results of course provides a numerical method, for example the Newton method.

LIST OF REFERENCE NUMBERS

CST

Computer Simulation Technology

ESB

Equivalent circuit

e

entrance

A

output

L1, L2

lead inductance

L

Shunt admittance

S

Structure, connection structure

AL

outer conductor

IL

inner conductor

D _a

Outer conductor inner diameter

D _i

Inner conductor (outside) diameter

D _s

Bar diameter

p

Unit cell length

BL

bandgap

B

tape

Claims (9)

1. Method for producing a coaxial conductor structure for interference-free transmission of a TEM mode, which is the only mode capable of propagation, of an HF-signal wave within at least one band of n frequency bands forming in the context of a dispersion relation, with n as a positive natural number, with

   a) an internal conductor having a circular cross-section with an inner conductor diameter D_i,

   b) an external conductor which equidistantly radially surrounds the internal conductor with an internal diameter D_a of the external conductor,

   c) an axially extending common conductor section of the internal and the external conductor, along which in each case s ≥ 1 rod-shaped structures having a rod diameter D_s, which electrically connect the internal conductor to the external conductor are provided at equidistant intervals p,

   characterized in that
   for a propagation of the single TEM mode along the coaxial conductor structure undisturbed by higher excitation modes, which form at least in the form of a TE₁₁ mode within m frequency bands, the parameters D_i, D_a, D_s, p, s are selected such that

   (i) a lower cutoff frequency f_u(TEM) of the single TEM mode propagating within a n ≥ 2-th band is equal to an upper cutoff frequency f_o(TE₁₁) of the TE₁₁ mode forming in the m-th band ± a tolerance range Δf, and

   (ii) an upper cutoff frequency f_o(TEM) of the single TEM mode propagating within the n ≥ 2-th band is equal to a lower cutoff frequency f_u(TE₁₁) of the TE₁₁ mode forming inside the (m+1) -th band ± a tolerance range Δf, where n and m are positive natural numbers and that 1/3 of the bandwidth of the n-th TEM mode is selected as the tolerance range Δf,
   i.e. $\left|\mathrm{\Delta }f\right|<\frac{1}{3}\left(f_{o,\mathit{TEM},n}-f_{u,\mathit{TEM},n}\right)\mathrm{.}$

   
2. Method according to Claim 1,
   characterized in that
   s is chosen to be equal to 3 or 4.
3. The method according to Claim 1 or 2,
   characterized in that
   the following applies to (i): $${\mathrm{f}}_{\mathrm{u}}\left(\mathrm{TEM}\right)={\mathrm{f}}_{\mathrm{o}}\left(\mathrm{TE}11\right)\pm \left|\mathrm{\Delta f}\right|$$

   

   
   with $${\mathrm{f}}_{\mathrm{u}}\left(\mathrm{TEM}\right)=\left(\left(n-1\right)\pi +\frac{2a/\left(n-1\right)/\pi }{1+2a/{\left(n-1\right)}^2/{\pi }^2}\right)f_0$$

   

   $${\mathrm{f}}_{\mathrm{o}}\left(\mathrm{TE}11\right)=\sqrt{{\left(\mathit{m\pi }{f}_0\right)}^2+f_{\mathit{co}}^2}$$

   

   
   and $$\left|\mathrm{\Delta }f\right|<\frac{1}{3}\left(f_{o,\mathit{TEM},n}-f_{u,\mathit{TEM},n}\right)$$

   

   
   and
   that the following applies to (ii): $${\mathrm{f}}_{\mathrm{o}}\left(\mathrm{TEM}\right)={\mathrm{f}}_{\mathrm{u}}\left({\mathrm{TE}}_{11}\right)\pm \left|\mathrm{\Delta f}\right|$$

   

   with $${\mathrm{f}}_{\mathrm{o}}\left(\mathrm{TEM}\right)=\mathrm{n\; \pi }{\mathrm{f}}_{\mathrm{0}}=\frac{\mathit{nc}}{2p}$$

   

   
   and $${\mathrm{f}}_{\mathrm{u}}\left({\mathrm{TE}}_{\mathrm{11}}\right)=\sqrt{{\left(\mathit{m\pi }+\frac{2a/m/\pi }{1+2a/m^2/{\pi }^2}\right)}^2{f}_0^2+f_{\mathit{co}}^2}$$

   

   
   and with
   Perturbation: $a=\frac{\mathit{Zp}}{2\mathit{cL}};$

   

   
   Characteristic Impedance: $Z=\frac{1}{2\pi }\sqrt{\frac{\mu }{\epsilon }}\ln \frac{D_a}{D_i};$

   

   
   Inductance: $L\cong \frac{1}{s}\frac{D_a-D_i}{2}\frac{\mu }{4\pi }\ln \frac{D_a}{D_s};$

   

   
   Cutoff frequency: $f_0=\frac{c}{2\mathit{\pi p}},$

   

   
   Cut-off frequency of the TE₁₁ Mode: $f_{\mathit{co}}\cong \frac{c}{\pi }\frac{2}{D_a+D_i};$

   

   
   where c:= velocity of light, µ:= magnetic permeability, ε:= dielectric permittivity.
4. The method according to any one of Claims 1 to 3,
   characterized in that
   the rod-shaped structures, which are positioned in each case at equidistant intervals p, are arranged relative to the circumferential direction of the inner and outer conductor such that
   the rod-shaped structures are each arranged such that they are aligned identically one behind the other in an axial projection to the axially extending common conductor section, or the rod-shaped structures are arranged in axial sequence such that they are each offset by an identical angular offset Δα oriented in the circumferential direction of the internal and external conductor.
5. Method according to Claim 4,
   characterized in that
   Δα is chosen equal to 90°.
6. Method according to any one of Claims 1 to 4,
   characterized in that
   the rod-shaped structures are selected from a metallic material, preferably from the material from which the internal and/or the external conductor is composed.
7. Method according to Claims 1 to 6,
   characterized in that
   the cross-section of the internal conductor and/or the external conductor of the coaxial conductor is designed in a manner deviating from the circular shape with a characteristic impedance equal to that of a circular coaxial cable.
8. Use of a coaxial conductor structure produced according to the method according to any one of Claims 1 to 7, for interference-free signal transmission of a single TEM mode of an HF-signal wave within a frequency band in which higher excitation modes are not capable of propagating, with simultaneous use of local cooling of the internal conductor by provision of thermally and electrically conductive rod-shaped structures between the internal and external conductor.
9. Use of a coaxial conductor structure for interference-free transmission of a TEM mode, which is the only mode capable of propagation, of an HF-signal wave within at least one band of n frequency bands forming in the context of a dispersion relation, with n as a positive natural number, with

   a) an internal conductor having a circular cross-section with an inner conductor diameter D_i,

   b) an external conductor which equidistantly radially surrounds the internal conductor with an internal diameter D_a of the external conductor,

   c) an axially extending common conductor section of the internal and the external conductor, along which in each case s ≥ 1 rod-shaped structures having a rod diameter D_s, which electrically connect the internal conductor to the external conductor, are provided at equidistant intervals P,

   characterized in that
   for a propagation of the single TEM mode along the coaxial conductor structure undisturbed by higher excitation modes, which form at least in the form of a TE₁₁ mode within m frequency bands, the parameters D_i, D_a, D_s, p, s are selected such that

   (i) a lower cutoff frequency f_u(TEM) of the single TEM mode propagating within a n ≥ 2-th band is equal to an upper cutoff frequency f_o(TE₁₁) of the TE₁₁ mode forming in the m-th band ± a tolerance range Δf, and

   (ii) an upper cutoff frequency f_o(TEM) of the single TEM mode propagating within the n ≥ 2-th band is equal to a lower cutoff frequency f_U(TE₁₁) of the TE₁₁ mode forming inside the (m+1)-th band ± a tolerance range Δf, where n and m are positive natural numbers and that 1/3 of the bandwidth of the n-th TEM mode is selected as the tolerance range Δf,

   i.e. $\left|\mathrm{\Delta }f\right|<\frac{1}{3}\left(f_{o,\mathit{TEM},n}-f_{u,\mathit{TEM},n}\right)\mathrm{.}$

   

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