Instrumentation & Measurement Magazine 23-9 - 16

optimization carried out by CST. The final structure deriving from the simulations has an air transmission coefficient
S21 shown in Fig. 2, with a quality factor equal to about 160. It
has been realized with a milling machine, and the prototype is
shown in Fig. 1b.

Preliminary Validation

Fig. 2. Simulated transmission coefficient of the SRR in air.

requirements for measurement. For the latter, it is easy to understand that the greater the thickness, the greater the strength
of the resonator. In fact, it is essential not to bend the resonator,
to ensure a good repeatability of the measurements and, above
all, to preserve a high accuracy. To determine the suitable substrate, simulations were performed with CST software, using
various substrates available in the laboratory. From the analysis of the transmission coefficient (S21) and the quality factor,
the Duroid RT-5870 with thickness h = 1.19 mm was chosen.
The characteristics of the RT Duroid 5870 substrate are: εr= 2.5;
loss tangent = 0.0012; t = 0.035 mm, where t is the thickness of
the copper.
The feeding microstrip width is defined following the formulas in [30], and the radius of the circular crowns is derived
from [22]. The remaining quantities are determined on the basis of the limits imposed by the prototyping machine present
in the laboratory, and above all, by the results obtained by the

The SRR is simulated in contact with a concrete block, whose
dielectric parameters (εr and loss tangent) have been found
through measurements on a real concrete sample (Fig. 3a)
C25/30 class (UNI 11104). The concrete is classified in strength
classes, based on compressive strength, expressed as characteristic strength fck or Rck; for each resistance class, the first of
the two values represents fck (25 in this case) defined on cylindrical samples, and the second Rck (30) defined on cubic
samples, both expressed in N/mm2.
The simulated transmission coefficient, i.e., the ratio of the
power transmitted at the output port (port 2) to that of the input power (port 1) at the resonator, is shown in Fig. 4a. The
figure shows both the results with a whole concrete block and
with the same block with one crack of variable width. The considered simulated crack is 3 cm in length, 10 mm deep and has
a width of 1 mm or 2.5 mm.
In order to validate simulation results, measurements have
been conducted with a Keysight E8363C PNA Vector Analyzer. The experimental set-up, composed by the PNA and the
SRR in contact with the block with a 2-kg mass placed on the
ground plane, is depicted in Fig. 3b. Even if in this preliminary
validation the resonator is not embedded in the concrete, but
only in contact with it, this is representative of realistic conditions since the material behind the ground plane does not
influence the resonance. Ten repeated measurements on the
whole concrete block have been carried out, showing a mean
resonant frequency of 1.7774 GHz with a standard deviation of
the mean σM = 2.5 MHz. These results confirm simulation results represented in Fig. 4a. Then the block was damaged to
create a crack that is approximately 2.5 mm wide. Repeated
measurements have been conducted that highlighted a mean
resonance frequency equal
to 1.8436 GHz with a σM =
1.4 MHz, with a frequency
shift of about 66 MHz. Results are shown in Fig. 4b.

SRR network

Fig. 3. (a) Picture of the concrete block with the crack; (b) Experimental set-up composed by a Keysight E8363C PNA
Vector Analyzer and the SRR in contact with the block with a 2-kg mass placed on the ground plane.
16	

IEEE Instrumentation & Measurement Magazine	

In order to discriminate
the localization of the
crack in the concrete, a SRR
network that consists of
different resonators, each
one with a different resonance frequency, is studied.
In particular, simulations
of a network composed of
two split ring resonators
are proposed for simplicity.
December 2020



Instrumentation & Measurement Magazine 23-9

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