# Design and Validation of a Ten-Port Waveguide Reflectometer Sensor: Application to Efficiency Measurement and Optimization of Microwave-Heating Ovens

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Basic Theory and design principles for a ten-port reflectometer

#### 2.1. Six-port reflectometer review

_{i}signals go always into the i

^{th}port and b

_{i}signals go out from the i

^{th}port. Ports ranging from 3 to 6 are matched and therefore no reflected wave is considered there. In this scheme, Port 1 is the input port where the EM source is connected, whereas Port 2 is the output port of the sensor.

_{11}scattering parameter, provides a relationship between the incident wave amplitude at Port 1 (a

_{1}) and the reflected wave amplitude (b

_{1}) at the input port (Port 1 in Figure 1). The bigger the magnitude of Γ, the more energy is reflected to the EM source, thus less energy is absorbed by the load.

_{i}and N

_{i}are complex constants. As described earlier, several calibration methods and load standards can be used.

#### 2.2. Ten-port description

- 1)
- The microwave source provides the incident wave (a
_{1}) to the port. - 2)
- The electromagnetic energy propagates along the waveguide reflectometer until it reaches the sample.
- 3)
- A reflected wave (b
_{2}) is generated at the variable load thus generating a standing wave within the reflectometer. - 4)
- The power sensors sample the energy of this microwave standing wave and convert the detected power into voltage in a logarithmic way.
- 5)
- Simultaneously, a VNA measures the reference value for the reflection coefficient.
- 6)
- These voltages obtained from power detectors and the reference reflection coefficient value are then introduced to a neural network. This neural network learns the relationship between the reference value of the reflection coefficient (output of the network) and the output voltages from power detectors (fed as inputs to the neural net).

#### 2.3. Simulation of ten-port performance and design principles

_{10}mode, which is the first propagating or fundamental mode of the rectangular waveguide, propagates along the ten-port whose rectangular cross section is a=8.6 cm and b=4.3 and the working frequency is 2.45 GHz. Figure 4 shows the electric field distribution of the TE

_{10}mode. Figure 4a) shows the electric field distribution at the cross-section perpendicular to the propagation direction and Figure 4b) the distribution for this propagation direction. It can be observed that the maximum value for the electric field is located at the center of the waveguide and that the polarization of the electric field is oriented in the same way that the coaxial probes. Therefore, a good coupling is obtained between the sampling coaxial probes and the electric field.

_{10}mode spatial distribution.

#### 2.4. Power sensors and microstrip board circuits

#### 2.5. Neural network for calibration

_{i}Gaussian activation functions of the neurons are combined to provide the S

_{11}parameter at the working frequency. These functions are defined by the

**c**

_{i}adaptive centroids and a constant variance value for all the Gaussians.

**c**

_{i}centroids determine the segmentation of the input space of the

**x**input vector. The components x

_{i}of vector

**x**are fed as inputs to the neural network. This input is processed by the Gaussians to give G

_{i}, the output of the hidden level. The output of the network is obtained by means of the vectorial expression

**W· G**in the output linear level,

**W**being the weights of the linear layer. In this case, the input vector is formed by the eight voltage values provided by the LTC5530 detectors, whereas the output of the network estimates |S

_{11}|. A similar scheme is used for the estimation of S

_{11}phase.

_{11}(

**x**),

**x**={x

_{1},.., x

_{8}}, considered in this work –see Figure 14– since it does not have a linear behaviour. Although the activation of the neurons in the RBF model is carried out by radial basis functions, this model has a linear expression for the estimation of S

_{11}. Therefore, for each input vector

**x**(k), the estimation of S

_{11}is given by equations (2) and (3).

_{j}(k) is the output of the j

^{th}Gaussian radial function at input

**x**(k), c

_{j}and σ

_{j}are the centre and standard deviation of G

_{j}(k), w

_{j}is the weight value associated to G

_{j}, k is the training example and M the number of neurons of the network.

_{j}is carried out by using the gradient descent algorithm to minimize the cost function described in Equation (4).

^{T}

_{11}(k) and S

^{M}

_{11}(k) represent the theoretical and measured values for the parameter S

_{11}, for both magnitude and phase. N is the number of examples used for training the neural network.

_{11}permits to obtain, after the training stage, the optimal values for w

_{j}. In the operation stage, equation (2) supplies the approximation of S

_{11}(k) from DC voltages provided by power sensors.

## 3. Experimental set-up

^{3}cavity has been employed for testing the sensor under low power conditions, and to provide different S

_{11}values for calibration purposes. Two DC supply sources were employed for biasing the LTC5530 power sensors.

_{11}value provided by the VNA and the value computed by the neural network as shown in Equation (2). This error was minimized when optimal w

_{j}values were found after the optimization process.

_{11}provided by the VNA. A variable load provided different values for S

_{11}The phase and magnitude of training data for the S

_{11}covered the ranges [0, 2π] and [0, 1], respectively. The number of Gaussian neurons was fixed to 60. This number was selected after some trials, because it gave an adequate balance between learning and generalization. The centers of the Gaussian neurons were chosen to be equally spaced, covering the whole range of the inputs. For all the neurons, σ

_{j}was set to 0.3466. That is equivalent to say that the spread factor of the Gaussians is of 0.1, inside of the hypercube of the normalized inputs.

## 4. Results and Discussion

_{11}parameter provided by the VNA. These reference data are represented in the so called Smith chart that shows S

_{11}both in magnitude and phase. Once the network has been trained, the weights of the RBF neural network are optimized and the sensor is ready to estimate the value of S

_{11}only from the output values of the power sensors.

_{11}estimated values provided by the ten-port reflectometer have been compared to the ones measured by the VNA, both in magnitude and phase. Figure 15 shows the absolute error obtained for this comparison, resulting in average absolute error of 6.2 × 10

^{-3}for the magnitude and of 2.3×10

^{-2}for the phase of S

_{11}. As it can be observed in Figure 15, this error is very small and therefore very accurate measurements can be made with the proposed reflectometer. The phase error is bigger than the magnitude one, since phase can vary from 0 to 2π radians whereas magnitude variation ranges from 0 to 1.

_{11}. The output of the faulty detectors is defined as a constant value for all the training positions. The defective sensors were chosen in a random way. Some of the results obtained for the absolute error of |S

_{11}| when compared to VNA measurements are represented in Figure 16, where 255 training patterns and 74 validation measurements have been considered.

_{11}function even when some detectors do not work properly, provided that the working detectors allow an appropriate sampling of the stationary wave, as stated by the Shannon theorem [16]. It is noticeable that the error observed when all the power sensors are working is lower than those obtained with 4 power sensors, which is the configuration of a conventional SPR. However, the error observed when only two power detectors are in use is not acceptable and a minimum of 4 power detectors should be used when carrying out the measurements. This is an expected result, because at least four samples along its wavelength are needed to correctly sample a wave without losing information. Therefore, these results show that it is possible to reconfigure the sensor software structure by training again the RBF neural network in order to correctly operate even when some of the power sensors are broken or faulty.

## 5. Sensor application to microwave oven optimization

^{3}microwave oven. The sensor was used to monitor the value of the S

_{11}magnitude in real time for different positions of a 250 cm

^{3}cylindrical water sample. Figure 17 shows the scheme of the employed cavity. As it can be observed, the optimization process is focused only on one dimension along the main axis of the oven. It gives a partial solution to the problem for the considered oven because the optimization process is completed only when the three dimensions are considered for the algorithm. Although the symmetry of the process permits to consider the y-axis as the dimension in which the maximum variations for the electromagnetic field are produced, a more accurate result can be found for experimental platforms with a cartload displacing along the 3 axis inside the oven.

_{11}magnitude when 0.5 watts were employed as microwave power source and the sample was moved with the PTFE carrying system. The movement was carried out by placing the sample as near as possible to the WR-340 coupling aperture and then moving the sample away from that position. As it can be observed in Figure 18, values lower than 0.2 can be obtained for S

_{11}magnitude for sample distances around 46 cm away from the coupling aperture. On the contrary, other sample positions may lead to reflection coefficient values up to 0.75. Therefore, the employment of this ten-port reflectometer allows, once it is calibrated, the monitoring of the reflection coefficient of microwave ovens in real time. It implies to improve the energy use and to protect the microwave sources from undesired reflections that may damage them.

## 6. Conclusions

## References and Notes

- Judah, S.R.; Holmes, W. A novel sixport calibration incorporating diode detector non-linearity. IEEE Instrumentation and Measurement Technology Conference
**1998**, 1, 592–595. [Google Scholar] - Moreau, J.; El ldrissi, A.; Tibaudo, C. Permittivity measurements of materials during heating by microwaves. Meas. Sci. Technol.
**1994**, 5, 996–1001. [Google Scholar] - Roussy, G.; Pearce, J.A. Foundations and industrial applications of microwave and radio frequency fields: Physical and chemical processes; John Wiley & Sons: West Sussex, UK, 1995. [Google Scholar]
- Yakabe, T.; Kinoshita, M.; Yabe, H. Complete calibration of a six-port reflectometer with one sliding load and one short. IEEE T. Microw. Theory
**1994**, 42, 2035–2039. [Google Scholar] - Yakabe, T.; Ghannouchi, F.M.; Eid, E.E.; Fujii, K.; Yabe, H. Six-port self-calibration based on active loads synthesis. IEEE T. Microw. Theory
**2002**, 50, 1237–1239. [Google Scholar] - Rangel de Sousa, F.; Huyart, B.; de Lima, R.N. A new method for automatic calibration of 5-port reflectometers. Journal of Microwaves and Optoelectronics
**2004**, 3, 135–144. [Google Scholar] - Engen, G.F. Calibrating the six-port reflectometer by means of sliding terminations. IEEE T. Microw. Theory
**1978**, 26, 951–957. [Google Scholar] - Hoer, C.A. Performance of a dual six-port network analyzer. IEEE T. Microw. Theory
**1979**, 27, 993–998. [Google Scholar] - Wiedmann, F.; Huyart, B.; Bergeault, E.; Jallet, L. A new robust method for six-port reflectometer calibration. IEEE T. Microw. Theory
**1999**, 48, 927–931. [Google Scholar] - Wiedmann, F.; Huyart, B.; Bergeault, E.; Jallet, L. New structure for a six-port reflectometer in monolithic microwave integrated-circuit technology. IEEE T. Microw. Theory
**1997**, 46, 527–530. [Google Scholar] - Hesselbarth, J.; Wiedmann, F.; Huyart, B. Two new six-port reflectometers covering very large bandwidths. IEEE T. Microw. Theory
**1997**, 46, 966–969. [Google Scholar] - Liu, Y. Calibrating an industrial microwave six-port instrument using the artificial neural network technique. IEEE T. Instrum. Meas.
**1996**, 45, 651–656. [Google Scholar] - Pedreño-Molina, J.L.; Pinzolas-Prado, M.; Monzó-Cabrera, J. A new methodology for in-situ calibration of a neural network-based software sensor for S-parameter prediction in six-port reflectometers. Neurocomputing
**2006**, 69, 2451–2455. [Google Scholar] - Requena-Pérez, M.E.; Pedreño-Molina, J.L.; Monzó-Cabrera, J.; Díaz-Morcillo, A. Multimode cavity efficiency optimization by optimum load location: Experimental approach. IEEE T. Microw. Theory
**2005**, 53, 2838–2845. [Google Scholar] - Broomhead, D.; Lowe, D. Multivariable functional interpolation and adaptive networks. Complex Systems
**1988**, 2, 322–355. [Google Scholar] - Shannon, C.E. Communication in the presence of noise. Proc. Institute of Radio Engineers
**1949**, 37, 10–21. [Google Scholar]

**Figure 2.**Ten port scheme with input and output ports and sampling coaxial ports, d being the distance between consecutive coaxial probes within the waveguide.

**Figure 4.**Electric field distribution for TE

_{10}mode at the waveguide. (a) Perpendicular cross section. (b) Along the propagating direction.

**Figure 12.**a) Manufactured power sensor boards. b) Rack disposition with biasing and ground connections.

**Figure 14.**Smith chart representation of S

_{11}complex data used in the experimental training stage.

**Figure 15.**Validation error for 74 different validation patterns. (a) S

_{11}magnitude. (b) S

_{11}phase.

© 2008 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Pedreño-Molina, J.L.; Monzó-Cabrera, J.; Lozano-Guerrero, A.; Toledo-Moreo, A.
Design and Validation of a Ten-Port Waveguide Reflectometer Sensor: Application to Efficiency Measurement and Optimization of Microwave-Heating Ovens. *Sensors* **2008**, *8*, 7833-7849.
https://doi.org/10.3390/s8127833

**AMA Style**

Pedreño-Molina JL, Monzó-Cabrera J, Lozano-Guerrero A, Toledo-Moreo A.
Design and Validation of a Ten-Port Waveguide Reflectometer Sensor: Application to Efficiency Measurement and Optimization of Microwave-Heating Ovens. *Sensors*. 2008; 8(12):7833-7849.
https://doi.org/10.3390/s8127833

**Chicago/Turabian Style**

Pedreño-Molina, Juan L., Juan Monzó-Cabrera, Antonio Lozano-Guerrero, and Ana Toledo-Moreo.
2008. "Design and Validation of a Ten-Port Waveguide Reflectometer Sensor: Application to Efficiency Measurement and Optimization of Microwave-Heating Ovens" *Sensors* 8, no. 12: 7833-7849.
https://doi.org/10.3390/s8127833