# Introduction

Before designing any reproduction of Shawyer’s cavity, it was necessary to make sure two important parts of the design process were understood. The first part was the basic simulation properties of Computer Simulation Technology’s (CST) Microwave Studio. The best method of confirming the simulation was to build a known structure and test it on the lab bench. By going from a 3D simulation model to a real working device, all parts of our design, modeling and fabrication process could be tested and documented. For example, it was realized half-way through the simulations that a 64bit machine with 8Gb of memory was necessary for large structures.

The second part was to understand and verify all the commercial parts purchased for the reproduction. For example, a thorough understanding of the magnetron including how to match it properly to a waveguide. Other components included a circulator with water load and waveguide-to-N pieces where each were tested to make sure they produced expected results.

# Theory

The target frequency is $f_o=2.45Ghz$ and the wavelength in free space is $c/f_o=\lambda_o=3x10^{11}/2.65x10^9=122.45mm$

For a rectangular waveguide with sides “$a$” and “$b$” compliant with the WR340 waveguide standard size, then $a=86.36mm$ and $b=43.18mm$ and $\lambda_c=2a=172.72mm$.

The wavelength in an enclosed waveguide is then $\lambda_g = \left ( \frac{\lambda_o}{\sqrt{1-(\lambda_o / \lambda_c)^2}} \right ) =173.62mm$

The length of the waveguide for a half wavelength should be $L= \left ( \frac{\lambda_g}{2} \right)= 86.81mm$

The cut-off frequency is then $f_c = \left ( \frac{c}{2a} \right)=\left ( \frac{3x10^{11}}{172.72} \right)=1.73Ghz$

# Simple Waveguide with Two Ports

The two port waveguide is shown below and was designed to be a half wavelength in length.

The S1,1 plot is relevant because it shows how much energy is reflected, i.e. if the line is at zero, that means all the energy was reflected at the frequency or if there is a significant dip, i.e. $> -10db$, then the energy was actually transmitted.

## Simulation at Cut-off

CST makes this comment about simulations below cut-off

Should I start the frequency band from 0 if I am exciting a waveguide? (Faq #27) (Last modified: 1/23/2007 )

No. For waveguides, it is important to operate above the cutoff frequency to avoid calculations of zero propagation constant. Use the frequency band of the waveguide. 

# Simple Waveguide with Three Ports

The ports are one at either end of the waveguide and a probe at the $\lambda=1/4\lambda_g$ point. The waveguide in this example was lengthened to be one wavelength long, or $\lambda_g$.

# Simple Waveguide with Two Ports

With this test, one end was shorted with a wall and a 50$\omega$ probe was used to inject the signal into a waveguide which exited via the port at the far end of the waveguide. The waveguide was again one wavelength in length.

# Reverse Engineered Microwave Launcher

Part of the problem with using commercial grade magnetrons is determining what the magnetron’s probe impedance is. Impedance matching is critical to making sure energy from the magnetron probe actually passes through the launcher into the cavity. It is a bit like the ground hog coming out at spring and unless the conditions are just right, it just heads right back. Unfortunately, googling for the typical impedance of commercial magnetron did not produce any usable results, even looking at datasheets for common types of magnetrons.

The only other option was to attempt to model the launcher and magnetron probe in MWS and see if we could determine the impedance match as expected by the dimensions of the waveguide, the location of the probe from the closest shorted wall and the dimensions of the probe. This “reverse engineering” was complicated by unknowns, for example what exactly is the epsilon of the dielectric for the magnetron’s probe, and how thick is it? The dielectric’s epsilon and thickness are necessary to calculate the impedance.

Below are pictures, figures 7 through 11, of a typical magnetron partially dissembled to show the parts. Two magnetrons, one by Toshiba and one by Matsushita were cut apart in order to understand how the probe was designed.

Note that the dielectric of the probe was the vacuum around the copper lead coming from the magnetron’s resonating chambers. Changing the dielectric constant of the pink ceramic insulator visible from outside the probe (approximately 1.4mm thick) had negligible effect on the impedance of the magnetron probe. The pink ceramic insulator is used to isolate the voltage between the probe and ground.

As a check, we measured the copper lead coming from the inner cavity of the magnetron in order to check the surface area. The Toshiba magnetron was a rectangular probe at 2.86mm by 1.30mm compared to the Matsushita magnetron which was a copper wire 2.55mm in diameter.

• The surface area for the rectangular copper lead is $2*2.86mm + 2*1.3mm = 8.32mm$ and the surface area of the copper wire is $2 * \pi * 2.55/2 = 8.01mm$

The surface area compared between the rectangular and circular copper wire, both leading from the resonating chambers of their respective magnetron are very similar (8.32mm vs 8.01mm) which makes sense. The energy of high frequency EM waves is only carried within the first few micro-meters of the surface of a conductor and is also the reason why the probe tip was modeled as a solid copper block.

The probe models results are shown in figures 12 to 15 including the S plot and line impedance.

The model ran about 15,000 mesh cells.

# Pyramidal Antenna

Having characterized and successfully modeled the magnetron probe, the next step was to model and build a simple form of Pyramid antenna. The objective of this section is to verify in a working real-life model that the results we get from our models are achievable. The first step was to model a pyramid antenna, attempt to build one and then test it in Faraday cage. If the magnetron probe plus antenna could heat water, then the matching of the magnetron to the waveguide and horn antenna could be assumed to be working.

As the first step, a horn antenna was designed and simulated in MWS .

Next, the probe model generated in the previous steps were added to the pyramid antenna and the results checked. In order for the launcher with magnetron probe to be attached to the antenna, it first had to remodelled with a thin shell exterior instead of a vacuum. The new probe model results are shown in figures 21 to 23 including the S plot and line impedance and the final model, after adaptive meshing, was based on 117,300 mesh cells with the Transient Domain solver.

The probe distance from the waveguide’s back wall short was optimized in order to get a reasonable S1,1 parameter, i.e. -15dB or better.

Once the shelled waveguide launcher was properly modeled, it was then added to the pyramid antenna and the entire object was simulated with 5.3 million mesh cells with the Transient Domain solver. Because of the ready availability of galvanized sheet metal, zinc was used as the metal for the waveguide in the simulations.

The resulting calculated Q was 38,817.

Because the Frequency Domain (or FD) solver is generally more accurate, the same model was simulated with the FD solver. After adaptive meshing, the number of Tetrahedral mesh cells was over 300,000 (required to meet the minimum error criteria as specified by MWS) and was too large to run in a 32 bit environment limited to 4GB of memory. The computer was upgraded to 64Bit and 8Gigs of RAM.

In order for the FD solver to operate properly, the model was modified to include a grounding plane behind the port and the thickness of the waveguide was changed from an infinitely thin sheet to 1mm thick. For the waveguide made up of Zinc, modeled as lossy metal, the following results were obtained:

The results are nearly identical with the Time Domain solver results shown previously, which gives us confidence nothing has been overlooked.