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 analysed by R. Zheng and X. Chen [1] is dominated by metal and therefore much more robust. 

Structure of the folded waveguide.
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 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.

Dispersion diagram of a single period.
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 50mA.

Particle emission surface.
Figure 3: Particle emission surface.

The input signal is a monofrequent sinus with an input power of 2.5mW and a frequency of 230GHz. 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 480ps with an amplitude of 0.514 which results in a gain of 20.24dB. This agrees quite well to the gain of 20.9dB given by Pierce small signal theory (see page 282 in [2]).

The frequency spectrum of the output signal has a peak as well at 230GHz. 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.

Time signals of RF in and out (left) and frequency spectrum of output signal (right).
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.

Particle trajectory and zoom into end section.
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.

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


[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.

CST Article "Microfabricated Folded Waveguide for Broadband Traveling Wave Tube Application"
last modified 26. Jun 2013 4:27
printed 31. Mar 2015 2:13, Article ID 473

All rights reserved.
Without prior written permission of CST, no part of this publication may be reproduced by any method, be stored or transferred into an electronic data processing system, neither mechanical or by any other method.


4 of 4 people found this article useful

Did you find this article useful?

Other Articles

Heat Sink Design Flow for EMC

Heat Sink Design Flow for EMC Document type
Heatsinks are large conductive objects which are typically ungrounded and placed above ASICs or other ICs. They may pickup and enhance radiation. With today's SerDes line rates, wavelength sizes in the system are now comparable to heatsink sizes. A design flow is proposed that will allow quick and systematic simulations of heatsink for EMI. Read full article..

Radar Cross Section and Farfield Simulation of an Aircraft

Radar Cross Section and Farfield Simulation of an Aircraft
The article describes the RCS and farfield simulation of a large airplane at a frequency of 4GHz. The simulation is performed with the new Integral Equation solver of CST MICROWAVE STUDIO®. The length and width of the airplane is about 27 meters, and the total height is about 8 meters. The excitation is done by a plane wave from the front. In total, the calculation for the airplane is approximately 350 wavelengths in size. We perform a monostatic RCS calculation and we show the farfield and surface current distributions for the airplane. Read full article..

Using CST MWS for Signal Integrity problems

Using CST MWS for Signal Integrity problems
This article is concerned with the important issue of Signal Integrity and the application of CST MICROWAVE STUDIO® to the investigation of the characterisation of an SMA connector on a multi-layer PCB. Read full article..

Sirona cuts development costs of dental X-Ray equipment with the aid of 3D EM Simulation

Sirona cuts development costs of dental X-Ray equipment with the aid of 3D EM Simulation Document type
Electromagnetic simulation using CST EMS is now established at the heart of these significant improvements to the development and manufacturing processes. The software is extremely reliable, robust and efficient. The CST EMS development team reacts swiftly to our needs and feature requests and is always receptive to new ideas and suggestions. As a consequence, we believe that product support, in addition to the software‘s powerful features, has contributed to the success of EM simulation at Sirona Read full article..

Characterization of Photonic Structures with CST MICROWAVE STUDIO

Characterization of Photonic Structures with CST MICROWAVE STUDIO Document type
Stefan Prorok, Hamburg University of Technology We present an overview of our current research activities in silicon photonics and thermal barrier coatings. Doing so, we will comment on how CST Microwave Studio can be used to design strip waveguides, micro ring resonators, as well as 2-D and 3-D photonic crystal structures. Particularly we will concentrate on the discussion of photonic crystal micro cavities which can be used as electro-optic modulators. It will be shown that MWS provides all the functionality to optimize and characterize optical micro cavities. The appearance of resonant modes is adjusted through eigenmode calculation of the photonic crystal waveguide modes. Time domain simulation with discrete port excitation is applied to calculate the intrinsic Q-factor of the cavity. Waveguide ports are used to model experimental conditions of excitation with strip waveguide modes. Field monitors help to understand the mechanism of energy loss from the cavity. The simulation results are compared to measurements on fabricated structures. As possible application we will show a hybrid silicon organic hetero structure cavity for GHz electro-optic modulation. Read full article..
Back Back  

Your session has expired. Redirecting you to the login page...