# Automated Cavity Perturbation Method for Measurement of Dielectric Constant

#### The cavity perturbation method is a well established technique for the measurement of dielectric properties of materials at microwave frequencies. This article presents an automated cavity perturbation technique at X-Band, using a VNA and LabVIEW softw...

Cavity perturbation techniques^{1,2} have been widely used for the measurement of dielectric properties at microwave frequencies. The fundamental concept of this technique is that the presence of a small volume of dielectric sample in the resonant cavity will not significantly perturb the electromagnetic field around the loaded sample and the shift in resonant frequency of the loaded cavity has been computed with these assumptions. The dielectric constant and loss tangent of the specimen can be calculated from the shifts of resonant frequency and the change in quality factor.^{1,2}

LabVIEW^{3} is a high level graphical programming language that is designed for data acquisition and control. This article describes an automated procedure based on LabVIEW software to measure the dielectric properties of the material, which are dielectric constant and loss tangent. The measurement setup uses a rectangular waveguide TE_{103} cavity resonator, an HP8510 Network Analyzer and a personal computer.

### Cavity Perturbation Technique

In the cavity perturbation method, the sample under test is positioned at the maximum electric field in the resonant cavity then the change in resonant frequency and Q of the cavity in loaded and unloaded conditions is measured using a standard resonant rectangular cavity in the TE_{103} mode. The sample under test is fabricated in the form of a thin rod. A weak circular aperture coupling to the cavity is used to enhance the Q of the cavity. ε_{r} = ε_{r}' − j ε_{r}" is the relative complex permittivity. The real and imaginary parts of the relative permittivity are calculated from measurable quantities as follows:_{2}

**Figure 1** Cavity resonator.

where f_{c} and f_{s} are the resonant frequencies without and with the sample, respectively, and Q_{c} and Q_{s} are the quality factors of the cavity without and with the sample inside the cavity, respectively, V_{c} and V_{s} are the volumes of cavity and the sample, respectively.

The rectangular X-Band waveguide cavity used in this work is shown in **Figure 1**. The cavity is coupled to a WR90 (X-Band) waveguide through circular inductive irises at both ends of the cavity. The sample is inserted through a non-radiating hole at the center of the broad side of the cavity. The resonant frequency and Q of the cavity with and without the sample are measured and ε_{r}' and tan δ are computed from Equations 1 to 4. The Q is calculated from the following relation

where f_{0} is the resonant frequency and f_{2} and f_{1} are the frequencies at the −3 dB points.

**Figure 2** Block diagram of the test set-up.

### Design Methodology

The measurement system, shown in **Figure 2**, is composed of the following:

- HP 8510C Network Analyzer
- LabVIEW Version 8.2
- Computer with GPIB card
- TE
_{103}cavity

The computer is interfaced with the network analyzer through the GPIB port. The cavity resonator is connected to the two ports of the HP 8510 S-parameter test set with standard waveguide to coax adaptors. The resonance properties, that is the resonant frequency and the 3 dB frequency points are observed with the VNA for the loaded and unloaded cavity.

**Figure 3** Flow chart of the software.

The program for the measurement of dielectric constant and loss tangent using a VNA has been developed using LabVIEW, which controls every stage of the measurement process. The program performs the tasks of instrument control, data acquisition and post processing of data. The computer plays the roles of talker (writes a control string to the instrument with the address), listener (receive data string from the instrument with the address) and controller (GPIB). The devised program has a simple and user friendly input panel, where the details of the measurement set up like frequency range, number of points and dimensions of sample can be entered. The measured data and results are displayed in the output panel. The program flowchart is shown in **Figure 3**. In designing this measurement software, a modular approach has been chosen. In LabVIEW, these modules are called virtual instruments (VI). The main VI, automated cavity perturbation (ACP) measurements, consists of various sub-VIs, which are designed for specific tasks as shown in **Figure 4**. These sub-VIs can be executed and debugged independently. The functions of various sub-VI are as follows:

**Figure 4** Main VI and sub VIs.

- Initialize.VI: This VI initializes the system by taking information from the input panel as start frequency, stop frequency, number of points, parameter and scale.
- −3 dB.VI: This VI measures the resonance frequencies and −3 dB points on either side of the resonance curve, first for the unloaded cavity as well as for the cavity loaded with the sample.
- Cal.VI: This VI calculates the dielectric parameters, that is the dielectric constant (ε
_{r}') and loss tangent (tan δ) from the recorded data, using Equations 1 to 4. - Plot_Gen.VI: This VI presents the resonance curves for the empty cavity and for the loaded cavity.
- Waveformgraph.VI: This is used to present the waveform in the desired format.
- Sum2xcl.VI: This saves and presents the results in an EXCEL sheet.
- Printgraph.VI: This VI is used to print the graphs and provide a hard copy of the data.

**Figure 5** Resonant frequency curves (a) unloaded cavity and (b) loaded cavity.

**Figure 5** shows the measured resonance curves for the unloaded cavity and the loaded cavity.

### Conclusion

The software for automated measurement of dielectric constant and loss tangent of dielectric materials at X-Band, using a VNA and LabVIEW, has been successfully developed. The method is simple and flexible as the VIs can be adapted to meet changing requirements, if any, very quickly. The system is routinely used for our work on ceramic and ferrite.

### Acknowledgment

The authors express their gratitude to the Director, SSPL, for his encouragement and permission to publish this work.

### References

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