Tallguide ® Linearity |

V_{p }is a function of frequency. As a consequence, all signals having a finite frequency spectrum will undergo dispersion, when transmitted through a length of waveguide. The phase relationship between the frequency components of the original signal at the launching point continually changes as the signal progresses along the waveguide. The analysis of these phenomena belongs in the domain of transient analysis.
For a signal containing only a narrow band of frequencies, the waveguide propagation constant b(w) may be expanded into a Taylor series about the center frequency w
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where
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where the phase velocity
V_{g} is called the group velocity, since it corresponds to the velocity with which the narrow band or groups of frequency components are propagated over the waveguide. Similarly, t, is the group delay for the waveguide length L. The group velocity is also equal to the velocity of energy propagation and is always less than the velocity of light. As an example, Figure 2 shows the group velocity of Tallguide TG31 compared to standard waveguide WR22. Note that the Tallguide group velocity is closer to C and more linear.
If the band of frequencies is too large for only the first two terms of the Taylor series expansion of b(w) to give a good approximation of b(w) throughout the band, then additional terms must be included. These higher order terms always lead to signal distortion. In general, these higher order terms are difficult to evaluate unless the modulation envelope is a simple function with an inverse transform. For a unit pulse modulation envelope typical of radar with pulse width T, the pulse spectra is give by
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M. P. Forrer, R. S. Elliott and others have shown that the terms up to and including the second derivative of the b(w) Taylor series expansion are needed.
To see the significance of dispersion distortion, we follow the unit pulse as it moves over a 20-ft. waveguide length. Following the computational methods of R. S. Elliott, C. M. Knop and G. I. Cohn, the output 38 GHz pulse envelope is plotted for various pulse widths. For WR22 and TG31, the Figure 4 series compares the output pulses for 5-ns (10 | ||||||||||||

Our next task is to examine the influence of higher order waveguide modes on signal linearity. For standard waveguide frequency bands, waveguide dimensions are chosen so that only the single mode TE
Without some form of mode suppression, the unwanted higher order modes are trapped between the two Tallguide transition ends. As shown in Figure 5, the trapping occurs, because at some point, the Tallguide transitions cutoff (narrows at point 1 and 5) to single mode waveguide operation. Depending on the signal frequency | ||||||||||||

In all practical installations, the Tallguide run length is many times the wavelength. Therefore the trapped resonate frequencies form a series of very fine comb lines. Even though residual higher order Tallguide mode generation is very week (typically –60 dB or less), trapped mode conversion affects linearity whenever the operating frequency coincides with one of the comb lines. The exact process causes small wiggles in the group delay at the comb line frequencies. It is for this purpose that the mode suppressor is introduced. With the mode suppressor, all higher order mode energy is absorbed, thereby removing the unwanted-trapped energy from the Tallguide system and removing the wiggles from the group delay. With the mode suppressor, Tallguide linearity is controlled by dispersion. Further from the above Figures, since the Tallguide wavelength is shorter than the wavelength in standard waveguide and with a more linear propagation constant, Tallguide linearity is 3 to 6 times superior to standard waveguide. What this means is that for the same pulse degradation, Tallguide run lengths may be 3 to 6 times longer than standard WR waveguide. Tallguide has been tested on numerous communications and radar systems in both narrow and broad band signal modulation modes. No negative linearity effects are measured for data, video, multi-carrier video, FM, phase modulation, frequency hoping formats and ultra short pulse radar signals.
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