On the Application of Waveguide Slow-Wave Systems for Measuring Dielectric Parameters
Abstract Generated abstract
The paper considers the use of waveguide slow-wave systems as broadband measuring resonators for determining dielectric permittivity and loss tangent in the microwave range. It describes a comparison method in which samples of the unknown and reference dielectrics are alternately placed on the resonator axis, while resonant-frequency shifts and quality-factor changes are measured visually under pulsed excitation with an oscilloscope. Modified formulas are given for calculating dielectric loss from transient-response amplitude ratios, under the assumption that frequency shifts are small. The reported measurement accuracy is about 10 percent for permittivity and 20 percent for loss tangent, with tests on paraffin and organic glass showing discrepancies below 9 percent and 17 percent, respectively.
Full Text
ON THE APPLICATION OF WAVEGUIDE SLOW-WAVE SYSTEMS FOR MEASURING THE PARAMETERS OF DIELECTRICS
P. I. GOSKOV
In [1], for the investigation of the properties of dielectrics in the microwave range, various waveguide slow-wave systems were used as broadband measuring resonators. In this case, the parameters of the dielectrics under investigation are determined by comparing the results of the effect on the resonant properties of the measuring resonator of samples of identical shape and geometrical dimensions made of the investigated dielectric (with unknown \(\varepsilon_x\) and \(\operatorname{tg}\delta_x\)) and of the reference dielectric (with known \(\varepsilon_{\mathrm{e}}\) and \(\operatorname{tg}\delta_{\mathrm{e}}\)), placed alternately on the axis of the waveguide slow-wave system.
Although in [1] the measurements were carried out in the continuous-generation mode, in this case it is more convenient to use visual methods. This is explained by the fact that measuring resonators based on waveguide slow-wave systems are multiresonant systems. Therefore, determining these resonances visually (with the aid of an oscilloscope) will be considerably simpler than in the continuous-generation mode. For this purpose we used the pulsed-excitation mode described in [2].
The expressions for determining the losses and permittivity of dielectrics by the comparison method through the parameters of the measuring resonator and the parameters of the reference dielectric, according to [3], at constant input voltage on the resonator, are written as
\[ \operatorname{tg}\delta_x = \frac{\varepsilon_{\mathrm{e}}}{\varepsilon_x} \frac{\left(Q_0/Q_x - 1\right)}{\left(Q_0/Q_{\mathrm{e}} - 1\right)} \operatorname{tg}\delta_{\mathrm{e}}, \tag{1} \]
\[ \varepsilon_x = (\varepsilon_{\mathrm{e}} - 1) \frac{\Delta f_{px}}{\Delta f_{p\mathrm{e}}} + 1, \tag{2} \]
where \(Q_0\) is the quality factor of the measuring resonator without a dielectric, and
\(Q_x\) is that with the investigated dielectric and \(Q_{\mathrm{e}}\) that with the reference dielectric;
\(\Delta f_{px}\) and \(\Delta f_{p\mathrm{e}}\) are the shifts of the resonant frequency when samples of the investigated and reference dielectrics are introduced into the measuring resonator, determined with the aid of a wavemeter.
Tuning to resonance was carried out by the maximum of the transmission characteristic on the oscilloscope screen. The values of the quality factor of the measuring resonator \(Q_0\), \(Q_x\), and \(Q_{\mathrm{e}}\) were determined according to [3],
i.e., the ratio of the maximum amplitude of the transient characteristic \(A_0\) to the amplitude at an arbitrary level \(A_3\) was used; this level was accurately fixed by suppressing part of the transient characteristic when a negative pulse was applied to the modulating electrode of the oscilloscope. In this case, the expression \(\operatorname{tg}\delta_x\), taking into account that \(\Delta f_{px,\text{э}}/f_p \ll 1\), will have the form:
\[ \operatorname{tg}\delta_x = \frac{\varepsilon_{\text{э}}}{\varepsilon_x} \frac{\left(\lg N_x / \lg N_0 - 1\right)} {\left(\lg N_{\text{э}} / \lg N_0 - 1\right)} \operatorname{tg}\delta_{\text{э}}, \tag{3} \]
where the coefficients \(N_0\), \(N_x\), and \(N_{\text{э}}\), when a square-law detector is used, are equal to
\[ N_0=\sqrt{\frac{A_0}{A_3}}, \quad N_x=\sqrt{\frac{A_{0x}}{A_{3x}}}, \quad \text{and} \quad N_{\text{э}}=\sqrt{\frac{A_{0\text{э}}}{A_{3\text{э}}}}. \]
In this case the error in determining \(\varepsilon_x\) is of the order of 10%, and for \(\operatorname{tg}\delta_x\) of the order of 20%. In particular, when measuring the parameters of the same specimens of paraffin and organic glass as in [1], the discrepancy for \(\varepsilon\) was \(<9\%\), and for (1), less than 17%.
REFERENCES
- P. I. Goskov. Izv. vuz., “Radiotekhnika,” VIII, 3, 368, 1965.
- P. I. Goskov. Izv. vuz., “Fizika,” 3, 61, 1965.
- P. I. Goskov. Izv. vuz., “Fizika,” 4, 5, 1965.