Setup for Measuring the Relative Electric Field Strength in Cavity Resonators
Abstract Generated abstract
This paper describes an apparatus for measuring relative electric field intensity in cavity resonators using the small perturbing body method, in which resonant frequency shifts are related to local field strength. The authors address the difficulty of accurately measuring small frequency shifts, especially in low quality factor resonators, by combining visual tuning on an oscilloscope with beat frequency measurement. The setup uses limiting, amplification, sweep scale enlargement, and a frequency marker to enlarge the observed resonance peak and improve effective selectivity. Reported performance includes frequency shift measurement errors below 1 kHz and an example in which a resonator with quality factor 750 is observed with an equivalent quality factor of about 15000.
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SETUP FOR MEASURING THE RELATIVE ELECTRIC FIELD STRENGTH IN CAVITY RESONATORS
L. A. Kovrigin, A. P. Olshanskii, E. V. Padusova
(Presented by the scientific seminar of the Radio Engineering Faculty)
Measuring the absolute value of the strength of an electromagnetic field is associated with considerable difficulties, especially when studying weak electromagnetic fields. In a number of cases it is sufficient to measure the relative strength of the electromagnetic field, which is called the relative intensity and, for the electric field, is determined by the relation
\[ I=\frac{E^{2}}{W}, \]
where \(E\) is the electric component of the electromagnetic-field strength;
\(W\) is the energy of the electromagnetic field stored in the system.
The field intensities in a waveguide and in the corresponding waveguide resonator are equal in magnitude. In view of this, measurement of the field intensity in waveguides can be carried out on resonant models using the method of small perturbing bodies.
The essence of the method is that, when a small perturbing body is placed in a resonator, a shift of the resonant frequency occurs that is proportional to the field intensity at the given point.
If the sensitivity of the probe used, \(A\), and the shift of the resonant frequency, \(\Delta f_{0}\), are known, then the field intensity is determined by the formula
\[ I=\frac{\Delta f_{0}/f_{0}}{A}. \]
The sensitivity of the probe \(A\) is calculated theoretically or determined experimentally by calibrating the probe in a special resonator, the field intensity in which can be calculated.
The main difficulty in using this method, especially in the case of low quality factors of the systems under study, is the measurement of small frequency shifts. Various setups may be used to measure small shifts of the resonant frequency; these reduce essentially to two types of circuits.
In the first circuit [2], automatic tuning of the klystron generator frequency to the frequency of the perturbed resonator is used. The oscillation frequencies of the klystron and reference generators are compared with one another by the beat method, which ensures high measurement accuracy. The accuracy of measuring the frequency shift is 1 kHz, with the corresponding frequency stability of the generators. However, the circuit is difficult to adjust, requires careful matching of the circuit elements at a fixed frequency, and therefore is poorly suited for operation over a frequency range. In the second circuit [1, 3], a visual method is used, which makes it possible to measure the frequency shift from the resonance curve observed on the screen of an oscilloscope by means of a high-\(Q\) resonant wavemeter. The disadvantage of this circuit is the low accuracy of the measurements, especially when studying resonators with low \(Q\).
We have developed a setup (Fig. 1) that makes it possible to obtain high accuracy in measuring small frequency shifts (error less than 1 kHz) while remaining comparatively simple. This is achieved by the fact that
Fig. 1. Block diagram of the setup. 1—Oscilloscope. 2—Limiter. 3—Amplifier. 4—Reference generator. 5—Pulse circuit. 6—Sawtooth-voltage generator. 7—Frequency meter. 8—Mixer. 9—Klystron generator. 10—Attenuator. 11—Resonator under study.
the resonator under study is tuned visually according to the frequency characteristic observed on the oscilloscope screen, while the frequency shift is measured by the beat method. Successive limiting and amplification of the signal reproducing the resonance characteristic of the resonator, and enlargement of the frequency scale of the sweep, make it possible to observe the top of the resonance curve on an enlarged scale, which is equivalent to an increase in \(Q\). In this case the resonator under study may be characterized by an equivalent \(Q\)
\[ Q_{\mathrm{eq}}=\frac{Q}{\sqrt{\left(\frac{1}{c}\right)^2-1}}, \]
where \(Q\) is the \(Q\) of the resonator under study;
\(c\) is the limiting level.
The limiting level is determined by the ratio of signal to noise at the amplifier input. When studying a resonator with \(Q = 750\) (passband \(\Delta F = 4\) MHz), the top of the resonance curve observed on the oscilloscope screen had a width \(\Delta f = 200\) kHz, which corresponded to the limiting level used, 0.998. The equivalent \(Q\) of the resonator in this case is 15000.
To measure the frequency shifts when a perturbing body is introduced into the resonator, a method was developed for producing a frequency marker, the essence of which is as follows. A sawtooth voltage is applied to the klystron reflector through a capacitor; therefore, at the moments when the sawtooth voltage passes through zero \((t_1, t_2,\) etc.), the oscillation frequency of the klystron \(f\) is equal to the oscillation frequency in continuous operation. By changing the dc voltage applied to the klystron reflector, this frequency can be made equal to the resonant frequency of the system under investigation. At the times \(t_1, t_2,\) etc., the pulse circuit generates short negative-polarity pulses, which are applied to the modulating electrode of the tube and cause a dark marker to appear on the oscilloscope sweep. When the klystron frequency is equal to the resonant frequency of the system, the marker will be located at the top of the resonance curve. When the modulating voltage is switched off, the klystron frequency \(f\) remains equal to the resonant frequency of the system. The measurement of the frequency shift between the resonant frequency of the perturbed resonator and the frequency of the reference generator is carried out by the beat method.
The frequency scale of the horizontal sweep obtained by us was \(1.6\ \text{kc/mm}\). The width of the marker was \(1\ \text{mm}\). The klystron generator was powered from batteries, while the power supply of the remaining circuits of the setup was stabilized by ferroresonant stabilizers.
The accuracy of measuring the frequency shift depends on the accuracy with which the beat frequency is measured and on the accuracy with which the system is tuned to resonance. The beat frequency is measured with a heterodyne wavemeter with the accuracy guaranteed by the instrument specifications. The accuracy of tuning to resonance depends mainly on the frequency scale of the image obtained on the oscilloscope screen:
\[ \delta f = \frac{\Delta f_{\mathrm{e}}\cdot x}{l}, \]
where
\[ \Delta f_{\mathrm{e}} \simeq \sqrt{\frac{2\Delta U}{U}}\,\Delta f_0 \]
is the bandwidth of the equivalent resonator;
\(l\) is the length of the oscilloscope sweep;
\(x\) is a quantity characterizing the accuracy with which the marker is set at the top of the resonance curve;
\(\Delta f_0\) is the passband of the resonator under investigation;
\(U\) is the voltage at the amplifier output without limiting;
\(\Delta U\) is the voltage corresponding to the top of the resonance curve.
For a given amplifier gain and electron-tube sensitivity, the frequency band of the equivalent resonator may be determined as
\[ \Delta f_{\mathrm{e}} \simeq \Delta f_0 \sqrt{\frac{2\Delta U_{\mathrm{sh}}h}{Ud}}, \]
where \(h\) is the vertical size of the image of the resonance curve,
\(d\) is the width of the noise band on the oscilloscope sweep.
The ratio
\[ \frac{U_{\mathrm{sh}}}{U} = \frac{1}{p} \]
may be specified arbitrarily.
In its final form, the formula determining the error in measuring the frequency shift may be written as follows:
\[ \delta f \simeq \frac{\Delta f_0 x}{l}\sqrt{\frac{2h}{pd}}, \]
the quantity \(\sqrt{\frac{2h}{pd}} < 1\) characterizes the reduction in the error of the visual method due to the use of limiting of the resonance curve.
References
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G. N. Rapoport. Measurement of electric-field strength in end vibrators by the method of shifting the resonant frequency with a dielectric probe, Radiotekhnika, vol. 12, No. 6, 1957.
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L. C. Maier, I. S. Slater. Field strength measurement in Resonant Cavities, J. Appl. Phys., vol. 23, No. 1, 1952.
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S. I. Tetelbaum, G. I. Gladyshev, G. N. Rapoport. On certain methods for measuring the strength of electric fields in resonators and waveguides at microwave frequencies, Collected Works of the Institute of Electrical Engineering, Academy of Sciences of the Ukrainian SSR, issue 12, 1955.