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Waveguide and
Tallguide Linearity

EHF Band Tallguide TG31
Tallguide TG31 for 33 to 55 GHz.
TG31 replaces WR22 waveguide.
Signal linearity is key in communication and radar systems. Any distortions introduced into the communications path degrade overall signal quality. Subsequent signals processing, down conversions, remodulation or retransmission strategies do not improve or perfect signal clarity for the end user. For waveguide, signal distortions are introduced into the waveguide run by dispersion and by excitation of higher order waveguide modes. In particular, this paper will show that ultra low transmission loss Tallguide transmission lines have superior linearity over standard waveguide. As an example, standard WR22 waveguide is compared to Tallguide TG31 over the 33 to 55 GHz frequency range.

Figure 1. Propagation constants for Waveguide WR22 and Tallguide TG31.
Figure 1. Propagation constants for
Waveguide WR22 and Tallguide TG31.
In any waveguide system, the phase velocity Vp 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 w0. The propagation constants for waveguide WR22 and Tallguide TG31 are shown in Figure 1.

Propagation constant Taylor series.


For a signal containing only a narrow band of frequencies, we retain only the terms up to the first derivative term linear in frequency. To this order of approximation, the original modulation is reproduced without any distortion but is delayed in time by an amount

Group delay.

where L is the waveguide length. The velocity with which the signal propagates through the waveguide is equal to the waveguide length L divided by the time delay and therefore:

Group Velocity
Propagation constant second derivative

where the phase velocity Vp = w0/b0 , C is the velocity of light and wc is the waveguide cutoff frequency.
Figure 2. Group velocity comparison for waveguide WR22 and Tallguide TG31.
Figure 2. Group velocity comparison for
waveguide WR22 and Tallguide TG31.
The definition of signal velocity Vg 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

Pulse spectra of unit pulse modulation envelop.

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.
Figure 3. Ratio of second derivatives for Tallguide TG31 to waveguide WR22.
Figure 3. Ratio of propagation constant second derivatives for Tallguide TG31 to waveguide WR22 = b''(TG31)/b''(WR22).
As a second example appearing in Figure 3, the distortion causing second derivative of b(w) for Tallguide TG31 is compared to standard WR22 waveguide. To simplify the comparison, the ratio of the second derivatives is plotted in Figure 3. Note that Tallguide TG31 distortion is 18 percent to 40 percent of that of waveguide WR22.

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 (10-9 second), 2-ns and 1-ns input pulse widths. For convenience, the input unit pulse and output pulses are plotted on the same set of curves taking into account the 28.7-ns delay for WR22 and 23.5-ns for TG31. Note that for a 1-ns pulse width, the WR22 output unit pulse shape has completely distorted into a smooth curve.

Figure 4. Unit Pulse Output Waveforms
for WR22 and TG31 at 20-ft. Waveguide Length and 38 GHz
5-ns Pulse Width2-ns Pulse Width
5-ns Pulse Width2-ns Pulse Width
1-ns Pulse Width
1-ns Pulse Width

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 TE10 will propagate. Small manufacturing waveguide tolerance flaws and minor installation errors excite higher order modes, but these waveguide modes are evanescent and do not propagate. For Tallguide, however, the story is different. Even with precise electroform component manufacturing, no matter how insignificant the mode conversion energy is in the Tallguide interfacility run, the possibility still remains that some unwanted higher order waveguide modes may be excited. Tallguide transmission line dimensions often allow 15 or more higher order modes to propagate.

Figure 5.  Schematic representation of a Tallguide run with transition units from waveguide into and out of Tallguide with mode suppressor in-between.
Figure 5. Schematic representation of a Tallguide run with transition units from waveguide into and out of Tallguide with mode suppressor in-between.

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 f, higher order mode waveguide wavelength l and Tallguide run length L, the trapped energy forms a series of cavity frequencies with resonate frequency spacing df.

Resonate frequency spacing.

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.

AFC manufactures, markets and sells worldwide satellite dish antennas, conical horn antennas, radomes, antenna feeds, microwave and waveguide components, ultra low loss waveguide transmission line Tallguide, and shelters. Our customers serve the broadcast, communications, radar, weather and cable industry, defense, government, and government agencies worldwide. AFC's quality control manufacturing standards are certified under ISO 9001 : 2008.

For additional Tallguide information, please refer to the Tallguide home page, which is the starting point for all Tallguide information. A complete AFC Internet WWW site index may be found in Antennas for Communications (AFC) Home Page Document Summary List.

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