CST – Computer Simulation Technology

Microfabricated Folded Waveguide for Broadband Traveling Wave Tube Application

As in most other technical areas, microfabrication is becoming more and more popular in the vacuum tube community. The reason is the need for miniaturization when going to higher frequencies. Circuits created by conventional fabrication techniques suffer from fragility. To circumvent this problem the structure suggested and analyzed by R. Zheng and X. Chen [1] is dominated by metal and therefore much more robust.



Figure 1: Structure of the folded waveguide

The slow wave structure is realized by a 50 period folded waveguide as shown in figure 1. The structure is fed at the RF input via waveguide ports known from CST MICROWAVE STUDIO® (CST MWS). Likewise the obtained output power is recorded at RF output with waveguide ports. The particles are traveling perpendicular to the waveguide as indicated by the arrow in figure 1....



Figure 2: Dispersion diagram of a single period

A cold test simulation of a single period performed with CST MWS Eigenmode solver (see Slow Wave Article) gives the dispersion diagram shown in figure 2 (see also [1]). The normalized phase velocity in this frequency band is about 0.255. Therefore the particles are emitted from the surface shown in figure 3 with a slightly higher beta of 0.2556 in order to transfer EM power from the electron beam to the RF-structure. The emitted beam current is 50 mA.



Figure 3: Particle emission surface

The input signal is a monofrequent sinus with an input power of 2.5 mW and a frequency of 230 GHz. The port amplitudes are wave amplitudes and in units sqrt(Power). Therefore the input signal (red) illustrated in figure 4 shows an amplitude of 0.05. The output signal saturates at 480 ps with an amplitude of 0.514 which results in a gain of 20.24 dB. This agrees quite well to the gain of 20.9 dB given by Pierce small signal theory (see page 282 in [2]).

The frequency spectrum of the output signal has a peak as well at 230 GHz. The additional ripples are resulting due to a finite simulation time which is in time domain a multiplication with a rectangular pulse. In frequency domain this is equivalent to the convolution with an SI function which is seen in figure 4.



Figure 4: Time signals of RF in and out (left) and frequency spectrum of output signal (right)

The particle trajectory is illustrated in figure 5. A zoom into the end section shows very nicely the sections with low and high velocity. This indicates the velocity modulation and the interaction of the beam with the electromagnetic wave which finally amplifies the RF input signal.



Figure 5: Particle trajectory and zoom into end section

The small signal analysis has been carried out by R. Zheng and X. Chen [1] for the complete frequency band of interest and compared to Pierce small signal theory. The comparison shows a reasonable agreement with respect to the validity of Pierce theory (see figure 6) which could be violated by space charge effects and electron bunching.



Figure 6: Comparison of CST PS PIC analysis and Pierce small signal theory (courtesy of R. Zheng and X. Chen [1])

The article shows the cold and hot test simulation of a slow wave structure by means of CST MWS Eigenmode solver and CST PARTICLE STUDIO® (CST PS) PIC solver. The results are in good agreement with theoretical values. Compared to a CST MWS model, which often is already existent after cold test simulations, only slight modifications have to be made to include the particles. The output power is directly provided by waveguide ports known from CST MWS. The signals can conveniently be postprocessed into gain and frequency spectrum inside the CST template based postprocessing.

References

[1] R. Zheng and X. Chen, "Design and 3-D Simulation of Microfabricated Folded Waveguide for a 220GHz Broadband Travelling-Wave Tube Application", Proceedings of the IVEC 2009, Rome, Italy, April 28-30, pp. 135-136, 2009.

[2] A. S. Gilmour, Jr., "Principles of Travelling Wave Tubes", Artech House, Inc, Norwood, MA, USA, 1994.

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