Measurement of Resonant Frequency of Radio Frequency Converter
under Conditions of Significant Electromagnetic Losses
ZAAL AZMAIPARASHVILI, NONA OTKHOZORIA, IRAKLI STEPNADZE, TENGIZ
TORIASHVILI
Faculty of Informatics and Control system
Georgian Technical University
Kostava 77, Tbilisi
GEORGIA
Abstract: -The measurement of resonant frequency in radio wave converter under conditions of high
electromagnetic losses presents a formidable challenge. This frequency serves as a crucial parameter directly
linked to non-electronic quantities, such as spatial separation thresholds or substance consumption levels.
Consequently, accurate measurement of these non-electric variables necessitates precise determination of the
transmitter's resonant frequency. However, when electromagnetic losses escalate due to control environment
properties, achieving such precision becomes daunting. Common methodologies often hinge on assessing
resonant frequency via the transmitter's amplitude-frequency characteristic. However, conventional
approaches, typically reliant on electron beam tubes with intricate control mechanisms, falter in accuracy
amidst substantial electromagnetic transmission losses. This inadequacy undermines the efficacy of current
devices. This paper introduces an unconventional method for resonance frequency measurement and
underscores the benefits of the device developed through this novel approach compared to existing ones. The
proposed method ensures sustained high measurement accuracy even in the face of significant transmitter
electromagnetic losses. Central to this method is the measurement of frequencies ω₁ and ω₂ proximate to the
resonant circuit's extreme value at points characterized by identical transmission coefficients. Resonant
frequency is then determined as the half-sum of these frequencies during symmetrical frequency modulation.
This innovative approach promises to overcome the limitations of traditional resonance frequency
measurement methods, offering enhanced precision and reliability in challenging electromagnetic
environments.
Key-Words: - Resonant frequency measurement, Frequency modulation, Amplitude-frequency
characteristic, Q factor
Received: March 16, 2023. Revised: May 5, 2024. Accepted: June 7, 2024. Published: July 23, 2024.
1 Introduction
The radio frequency transmitter converter functions
as a distributed-parameter oscillating system (RS),
characterized by several key parameters such as
resonance frequency, electromagnetic losses
(measured by the Q factor), passband, amplitude,
and shape of the resonance curve. Among these, the
primary parameter of interest is the resonance
frequency. This is because, owing to the nature of
electromagnetic waves, the resonant frequency of
the oscillating system directly correlates with the
significance of the controlled non-electric quantity.
For instance, it plays a crucial role in delineating
boundaries between different environments or
quantifying substance consumption (1).
Consequently, when employing a radio frequency
converter, the measurement of non-electric
quantities essentially boils down to determining the
resonant frequency of the radio frequency
oscillating system. However, under conditions
where electromagnetic losses of the radio frequency
converter increase—often due to the properties of
the controlled environment—achieving precise
measurements of the resonant frequency becomes a
challenging task.
[1] [2].
2 Problem Formulation
One common method frequently employed in
practice involves determining the resonance
frequency through the amplitude-frequency
characteristic [2], [3]. To achieve this, in many
cases, an oscilloscope or an electron-ray tube with
its intricate control scheme is utilized. These devices
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2024.3.4
Zaal Azmaiparashvili, Nona Otkhozoria,
Irakli Stepnadze, Tengiz Toriashvili
E-ISSN: 2945-0489
22
Volume 3, 2024
allow for the visual determination of research
information parameters on the screen. However,
they often lack the capability to provide high
accuracy, especially when confronted with
significant electromagnetic transmission losses. This
limitation restricts the usefulness of existing
devices. [3].
3 Problem Solution
This paper proposes an unconventional method for
measuring resonance frequency and highlights the
advantages of the device developed through this
approach compared to existing ones.
Figure 1 Factors affecting the result of measuring OS resonant
frequency: a) effect of a change in OS Q-factor and its
maximum AFC on measurement accuracy;
b) effect of time delays operating for individual units of the
layout on the measured result.
The proposed method ensures the maintenance of
high measurement accuracy under conditions of
substantial electromagnetic losses of the
transmitter[4] [5]. The essence of this method lies in
measuring frequencies and near the extreme
value of the resonant curve at points with the same
transmission coefficient and determining the
resonant frequency as their half-sum during
symmetrical frequency modulation.
Fig. 1a depicts the core concept of the
proposed method, while Fig.2 demonstrates
how the resonance curve of the radio frequency
converter alters with an increase in
electromagnetic losses (where suitability is small
with and amplitude is 6-10 times). The
visible frequency measurement cycle comprises two
stages: firstly, measuring the frequency while
linearly increasing the output frequency of the
driving generator, and secondly, measuring the
frequency while decreasing linearly at the same
rate as point a and point b of . At both the first
and second levels, recorded by the peak detector
integrated into the device.
The device, based on the proposed method, presents
several advantages over existing ones, notably: the
elimination of non-linearity resulting from the error
of the linear variable generator due to direct
measurement of frequencies and .
Figure 2 Measurement of resonant frequency with symmetrical
frequency modulation of the controlled voltage oscillator: a)
dependence of tuning frequency on time; b) signal
corresponding to the OS AFC in a dynamic regime; 1) static
resonance curve that on the frequency scale corresponds to a
static OS AFC; 2, 3) dynamic OS AFC.
The change in the amplitude of the resonant curve
of the transmitter has less effect on the result of gas
heating because the peak detector included in the
device always detects the extreme dimness in the
vicinity of the amplitude value, and the closer the
extreme value is to the amplitude mark, the smaller
the difference, which in turn reduces the error
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2024.3.4
Zaal Azmaiparashvili, Nona Otkhozoria,
Irakli Stepnadze, Tengiz Toriashvili
E-ISSN: 2945-0489
23
Volume 3, 2024
caused by non-peaking of the modulation
characteristic of the controlled generator.
The error caused by the asymmetry of the
transmission resonance curve is reduced.
The following graph (Fig. 3) shows the results of the
methodical error analysis of the existing (Fig. 4,
curve-1) and proposed (Fig. 3, curve 2) methods for
reducing the suitability of the supplier (4≤Q≤20).
The analysis is carried out taking into account the
following ratio:
The approximate equation of the amplitude-
frequency characteristic of the transmitter is:
(1)
Asymmetry coefficient
(2)
where is the transmitter resonance curve
amplitude, and frequencies, at the start and
end points of the radio transmitter's passband.
If the resonance curve of the transmission is
symmetrical, then the coefficient of asymmetry is
equal to L=1, and in the case of asymmetry, L≠1.
The analysis was carried out for the case when the
asymmetry coefficient was equal to L=0.5. The
extreme value that was obtained experimentally
corresponded to the level K=0.25-0.5 dB. From the
obtained graph, it can be seen that the
methodological error caused by the asymmetry of
the resonance curve based on the existing method
reaches 4% when reducing the suitability of the
transmitter (4≤Q≤20). When the methodological
error of the proposed method does not exceed 1%
under the same conditions.
In the proposed method, the use of symmetric
frequency modulation in the realization device
allows compensation for the dynamic error.
Dynamic errors stem from the delay threshold time
of individual device blocks and the displacement of
the amplitude-frequency characteristic. In dynamic
mode, the relative change of the displacement
concerning the static resonance curve is directly
proportional to the frequency rate of change β and
the transmitter's suitability Q, calculated by the
formula:
And the relative change of the transmission band is
proportional to the square of the frequency and the
fourth power of the fit, which is calculated by the
formula:
where is the conduction band of the transmitter in
static mode and ) is the displaced conduction
band in dynamic mode.The device based on the
existing method has the errors defined by formulas
in dynamic mode, and in the device based on the
discussed method, such errors are compensated,
which is shown in Figure 3 below. This can be
explained as follows:
In the proposed device (4) symmetric frequency
modulation is used, and in both stages of
measurement, the frequency of the controlled
generator is changed at the same rate B. The
deviation of the dynamic resonance curve of the
transmitter with respect to the static one and the
delay of the individual blocks included in the device
are the integral quantities in both I and II
measurement stages (see Fig. 3).
When determining the half-sum of and , the
shifted quantities included in them have opposite
signs, which are canceled during summation, and
the dynamic resonant frequency of the
Figure 3
Figure 4
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2024.3.4
Zaal Azmaiparashvili, Nona Otkhozoria,
Irakli Stepnadze, Tengiz Toriashvili
E-ISSN: 2945-0489
24
Volume 3, 2024
transmission will be equal to the static resonant
frequency .
which proves dynamic error compensation.
Thus, the considered method and the resonant
frequency measuring device based on it have a
number of advantages, compared to the existing
ones, and these advantages are especially evident
when using a radio wave transmitter.
Fig.5 presents the functional scheme of the device
implementing the improved method of determining
the resonant frequency, the principle of operation of
which is based on the above-mentioned algorithm.
Fig. 6 shows the time diagrams explaining the
working principle.
The diagram shows the following components: 1:
rectangular meander generator; 2: triangular pulse
shaper; 3: "select-store" elements; 4: controlled
(high-frequency) generator; 5: frequency measuring
block, which includes measuring time interval
generator 24, key 25, and pulse counter 20; research
object - an oscillating system connected to the
device by means of the first and second clamps; 6:
amplitude detector; 7: amplifier; 8: peak detectors;
9: comparators; 11: differential amplifier; 15: "D"
triggers; 17, 22: delay lines; 14, 18: "and-not"
logical elements; 21, 26—differentiators; 19:
memory register; 23: indicator block.
The device described above determines the
resonance frequency with high accuracy, even with
low suitability, in the case of a symmetrical
amplitude-frequency characteristic and a linear
function characteristic of voltage-controlled
generator conversion into frequency. In practice, the
characteristic of the controlled generator is non-
linear, making it difficult to determine the exact
value of the resonant frequency with high accuracy.
To eliminate this shortcoming, it is necessary to
approach the extreme value of the resonant
frequency and measure the frequencies f1 and f2 in
its vicinity. However, near the extreme value, the
instability of the comparator is revealed, caused by
the sharp smoothness of the resonance curve,
ultimately leading to the instability of the
measurement result.
In the proposed device (Fig. 5), the oscillating
system is supplied with a frequency signal that
increases linearly over time, which is modulated
according to the amplitude-frequency characteristic
of the oscillating system. After detection, in the first
stage, the extreme value of the amplitude-frequency
characteristic of the oscillating system is "roughly"
fixed and stored. The difference signal between the
stored value and the extremum is amplified in
amplitude, resulting in a steep waveform
corresponding to the smooth amplitude-frequency
characteristic caused by the low suitability of the
oscillating system in the extremum region. In the
second stage, the "exact" value of the extremum of
the obtained amplitude-frequency characteristic is
fixed, followed by the fixing of the instantaneous
value of the frequency acting on the oscillating
system at that moment. The first frequency f1 is set
and the value is memorized.
Figure 6 Timing Diagrams Explaining the Working Principle of
the Resonant Frequency Determination Device
Figure 5 Functional scheme of the device implementing
the resonance frequency determination method.
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2024.3.4
Zaal Azmaiparashvili, Nona Otkhozoria,
Irakli Stepnadze, Tengiz Toriashvili
E-ISSN: 2945-0489
25
Volume 3, 2024
In the second cycle, a similar process occurs, and
the second frequency f2 is determined, with the
difference that the frequency of the signal acting on
the oscillating system decreases linearly. The
average value of the determined frequencies f1 and
f2 determines the natural frequency of the
oscillating system.
Figure 7 Experimental output characteristic of the object
The device described above was realized and
implemented in a factory producing plastic
products, where the object was a chemical reactor
with axial mixing. In this reactor, a liquid chemical
(high-temperature plastic substance) was placed,
and the technological process (synthesis) occurred
under high pressure.
Figure 8 Construction of the object (chemical reactor)
In many cases, it is difficult to control the
technological process inside such reactors,
necessitating the use of methods involving external
exposure to harmful radiation, which is challenging,
environmentally unjustified, and harmful to service
personnel. The proposed method is environmentally
justified, and the determination of technological
parameters is simpler and more reliable.
On the mentioned object, the mechanical
construction of which is shown in Fig. 8, studies
were conducted, resulting in the experimental
(output) characteristic of the dependence of the
amount (level) of the liquid medium in the chemical
reactor on the resonance frequency .
The maximum value of the resonance frequency
was f01=33.9MHz, which corresponded to the state
of the chemical reactor without a liquid medium. In
the case of the reactor fully filled with liquid
medium, the resonance frequency was f02=15.4MHz.
The advantage of this approach is the use of the
mechanical construction of the research object itself
as a source of primary information. There is
practically no need to use special sensors, which
simplifies the process of converting a non-electrical
physical quantity into an electrical quantity and
increases the reliability of determining technological
parameters.
4 Conclusion
The measuring devices based on the proposed radio
frequency method feature straightforward
functionality, employing simple iron or steel
constructions as sensitive elements. Implementation
of this method in practical applications ensures the
maintenance of requisite measurement accuracy for
informational parameters, even when the sensitive
element exhibits significant electromagnetic losses
and operates under challenging conditions.
Moreover, the proposed approach offers the
advantage of utilizing the mechanical structure of
the research object itself as a primary source of
information. This minimizes the need for
specialized sensors, simplifying the process of
converting non-electrical physical quantities into
electrical ones and enhancing the reliability of
technological parameter determination. This method
can be applied in situations where existing methods
fail to provide sufficient accuracy or are generally
unsuitable. Particularly, it finds utility in scenarios
involving elevated or low temperatures, aggressive
environments, increased vibration intensity, and
other challenging conditions, such as radiation
exposure, determining technological parameters of
liquid metals and low-temperature cryogenic
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2024.3.4
Zaal Azmaiparashvili, Nona Otkhozoria,
Irakli Stepnadze, Tengiz Toriashvili
E-ISSN: 2945-0489
26
Volume 3, 2024
substances, monitoring the volume of loose matter,
as well as assessing geometric dimensions, among
others.
Declaration of Generative AI and AI-assisted
technologies in the writing process
During the preparation of this work the
author(s) used ChatGPT and
www.scribbr.com//Free Online Proofreader, only
to improve readability and language.
After using this tool/service, the author(s)
reviewed and edited the content as needed and
take(s) full responsibility for the content of the
publication.
References
[1] Z Azmaiparashvili, N Otkhozoria (2021)
“Mathematical Model for Studying the
Accuracy Characteristics of Devices for
Measuring the Resonant Frequency of
scillatory Systems New Approaches in
Engineering Research” 121-131
doi.org/10.9734/bpi/naer/v5/10242D.
[2] Zaal Azmaiparashvili, Nona Otkhozoria,
Alexander Maltsev. Analytic-Imitation Model
for Determination of the Natural Frequency of
Oscillatory Systems and Its Research.
Engineering and Technology. Vol. 4, No. 6,
2017, pp. 82-87.
http://www.aascit.org/journal/archive2?journal
Id=896&paperId=5986
[3] A. Akhmedova. Determination of oscillating
circuit resonance frequency with account
for eddy current losses. Russian Electrical
Engineering, Volume 82, Issue 12, (2011)
688-690
[4] N. Otkhozoria, Z. Azmaiparashvili, L.
Petriashvili, V. Otkhozoria, & E. Akhlouri.
(2023). Labview In The Research Of Fractal
Properties Of The Topology Of Networks And
Stochastic Processes. World Science, (3(81).
https://doi.org/10.31435/rsglobal_ws/30092023
/8020
[5] Bernard P. Zeigler, Hessam S. Sarjoughian,
Guide to Modeling and Simulation of Systems
of systems (Simulation Foundations, Methods
and Applications) Springer-Verlag, 2012.
[6] Lunkin B. V. Mishenin V. I. Azmaiparashvili Z.
A. Efendiev I. M., (1991). Patent No. 1673862
A1. Devices for measuring the liquid level in a
tank with an axial stirrer.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2024.3.4
Zaal Azmaiparashvili, Nona Otkhozoria,
Irakli Stepnadze, Tengiz Toriashvili
E-ISSN: 2945-0489
27
Volume 3, 2024
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
