*2.2. CRO Reverts EAE-Induced Motor Impairment*

To evaluate the efficacy of CRO after the onset of motor impairment, CRO was administered for five consecutive days (one dose by day), starting from the 12th day of immunization. The effectiveness of this protocol was compared with the single-dose protocol. The EAE groups showed a progressive increment in clinical score from the 11th day after immunization, peaking at the 16th day. Both groups treated with CRO showed lower clinical signs scores when compared to the untreated group, showing the potential of CRO to interfere with motor impairment even after its onset as well as to prevent it (Figure 2A,B). At this point, the analgesic effect of CRO was not evaluated, since it is not possible to apply the nociceptive test due to the motor impairment. The body weight of the animals was measured during the course of the disease and, as expected, EAE interfered with the weight gain of the animals (Figure 2C). Crotalphine did not alter the EAE-induced weight loss (Figure 2C).

**Figure 2.** Evaluation of CRO effect on clinical signs and body weight of animals immunized with MOG35–55 and treated before or after motor impairment. Animals were immunized with MOG35–55 and treated with CRO in a single dose on the fifth day after immunization (blue arrow), or in five doses (green arrows, one daily dose for five consecutive days starting on the 12th day after immunization). Clinical signs were evaluated daily (**A**), and, for statistical analysis, the area under the curve was evaluated (**B**). Body weight (g) was measured during the course of the disease (**C**). Data represent mean ± SEM 8–10 animals per group. \* *p* < 0.05 compared to the CFA group. # *p* < 0.05 compared to the untreated group (EAE). A one-way ANOVA test was used, followed by Tukey's post-hoc test in the area under the curve.


*1.1. Related Works*

The OFDM waveform for sensing can be processed either by the conventional correlationbased approach [24,25], or by OFDM symbol-based processing [26]. Correlation-based sensing is usually performed by cross-correlation in the delay and Doppler domains between the transmitted and received pulses, and different schemes have been proposed to improve sensing performance. For example, a good approximation of the transmitted signal is generated at the receiver for removing clutter in the correlation-based target detection [15]. Work in [25] proposes to use the information of data symbols for ambiguity suppression, and circular correlation for range extension up to an OFDM symbol duration. Different correlation-based OFDM radar receiver schemes have been compared in [27], in terms of complexity, signal-to-interference-plus-noise-ratio, and robustness against ground clutter.

Alternatively, similar to OFDM-based communication, OFDM-based sensing can also use IFFT/FFT operations to extract range and speed information. Based on this approach, a 77 GHz OFDM-based sensing system with a bandwidth of 200 MHz demonstrated a sensing resolution of 0.75 m with the maximum range of 150 m [28]. Another OFDM-based radar at 77 GHz used a stepped carrier approach to achieve a sensing resolution of 0.146 m with a bandwidth of 1.024 GHz, while the maximum range is 60 m [29]. Moreover, the authors implemented OFDM-based radar processing for automotive scenario by using a relatively longer interval of 128 ms to achieve speed resolution of 0.22 m/s, while the range resolution was 1.87 m for a bandwidth of 80 MHz at 5.2 GHz [30].

These two sensing processing approaches were employed in the development of OFDM-based radars, while from the viewpoint of converging OFDM-based communication and sensing, OFDM symbol-based sensing processing is more attractive, provided that a sensing receiver is synchronized with the transmitter and the transmitted data are readily available for sensing processing. Some interesting research has been done on OFDM-based convergence in the microwave band. By using OFDM waveforms which are designed for 3GPP-LTE and 5G-NR at 2.4 GHz with a bandwidth of 98.28 MHz, OFDM-based sensing supports a sensing resolution of 1.5 m and a maximum range of 350 m and performs an algorithm for self-interference cancellation in the full-duplex mode [31]. Authors in [32] provide measurement results for the indoor mapping using a 28 GHz carrier frequency for the 5G-NR with a bandwidth of 400 MHz and achieve a sensing resolution of 0.4 m. Another work in [33] shows results of mmWave demonstration testbed for joint sensing and communication; measurements were performed at 26 GHz with a bandwidth of 10 MHz to identify the angular location of different targets using beamforming technique. The work in [34] also presents a range resolution of 1.61 m and a maximum range of 206 m within 93 MHz bandwidth at the 24 GHz band. In addition, authors in [35] provide a parameter selection criterion for joint OFDM radar and communication systems by considering vehicular communication scenarios, such as CPI, subcarriers spacing, and coherence time of the channel.

### *1.2. Motivation and Contribution*

Please note that enabling the sensing functionality of the OFDM waveform (which is designed for wireless communication) does not provide the flexibility of parameter adjustment according to the sensing requirements. Furthermore, the ISI cancellation/compensation techniques proposed for OFDM wireless communication are not differently applicable for OFDM-based sensing because the transformation or truncation-based equalization destructs the sensing information. Ideally, the delay of an echo for sensing should fall within

the CPI, and the Doppler frequency normalized over OFDM waveform interval should be an integer. However, in a real scenario for sensing, a target is located randomly and moves with an arbitrary speed. Consequently, an OFDM waveform designed for communication shows limitation in obtaining high sensing resolution and a large detection range.

As we know, the detection range of a single target is determined by the detectable OFDM signal strength and an adjustment of delay offset. In the case of multiple echoes with delay beyond the CPI, the OFDM-based sensing is mainly limited by the ISI, free-spacepath-loss (FSPL), and processing gain. Echoes outside the CPI cause ISI as previous OFDM symbols interfere with current OFDM symbol in the processing window, which increases the threshold for target detection. In addition, echoes with delay longer than the CPI will achieve less processing gain, which reduces linearly with the delay. This loss of processing gain along with the ISI makes it difficult for OFDM-based sensing to detect targets outside the CPI, particularly in the millimeter-wave region featuring large bandwidth and high FSPL. Therefore, the extension of sensing range beyond the conventional limit of CPI is one of the important issues in developing communication and sensing converged systems for applications such as indoor mapping, digital health monitoring, unmanned aerial vehicles, and residential security.

In this work, we propose and experimentally demonstrate a converged communication and sensing system operating at 97 GHz using the same 16-QAM (quardrature amplitude modulation) OFDM waveform. An approach based on zero-delay shift is proposed to extend the detectable range by compensating for the IFFT processing gain for echoes outside the CPI. In the proposed method, we extended the range of an OFDM-based sensing, while the simplicity of operations for range and speed estimation is achieved using IFFT/FFT operations. The proposed method uses delay-shifts in the received signal before processing a received OFDM symbol. Active subcarriers in the received OFDM symbol are divided by the active subcarriers in the current and previous transmitted OFDM symbols (employed number of transmitted OFDM symbols determine the rang extension), and IFFT operations are used after each delay-shift to generate matrices in the delay and delay-shift domains (delay domain is the result of IFFT operation). Delay-shift rows at delay zero are concatenated to extend the delay-shift domain. Concatenation of delay-shift rows for different received OFDM symbols provides a matrix in delay-shift and time domain, and FFT operations over time domain provide the speed estimation. An experiment with a heterodyne W-band transmitter/receiver is performed, and both sensing and communication performance are measured in terms of range/speed profile and bit-error-rate (BER). The proposed approach for range extension is verified for distances well beyond the CPI and provides a range resolution of 0.042 m, and speed resolution of 0.79 m/s using a single OFDM waveform, which is promising in driving OFDM-based converged systems for future applications.

The rest of this paper is organized as follows. Section 2 presents the model for the OFDM-based converged system to provide the details of extracting sensing information from the received OFDM waveform. Section 3 details the proposed method for range extension in an OFDM-based converged system. Section 4 provides simulation results, while Section 5 is dedicated to experimental measurement results and discussions. Section 6 provides the conclusion of this work.

#### **2. Communication and Sensing Convergence Using OFDM Waveforms**

Motivated by the OFDM-based sensing presented in [26,34], a reference system model for the convergence of communication and sensing is presented here. An OFDM waveform for communication purposes consists of several OFDM symbols, each with orthogonal subcarriers modulated by data symbols and cyclically extended by appending the last part of the signal at the beginning called cyclic prefix (CP). If Δ*f* represents the subcarriers spacing, *N* the number of orthogonal subcarriers, *T* the OFDM symbol duration, *T*cp as the CPI, *T*s = *T*cp + *T* the effective duration of the OFDM symbol, and *M* the number of OFDM symbols, then the analytical expression of the transmitted OFDM waveform is [34],

$$s(t) = \sum\_{\mu=0}^{M-1} \sum\_{n=0}^{N-1} S(\mu N + n) e^{\left(j2\pi n \Delta f (t - \mu T\_\mathrm{s})\right)} e^{\left(-j2\pi n \Delta f T\_\mathrm{cp}\right)} \text{rect}\left(\frac{t - \mu T\_\mathrm{s}}{T\_\mathrm{s}}\right),\tag{1}$$

where *S*(*μN* + *n*) is the data symbol at *n*th subcarrier of *μ*th OFDM symbol. The rect(*t*) in (1) is the rectangular pulse shape, such that rect(*t*) = 1 for *t* ∈ [0 1] and 0 otherwise. The term exp −*j*2*πn*Δ*f T*cp appears due to the cyclic extension of OFDM symbols by the CP.

In order to fulfill the orthogonality among subcarriers, over the interval *T*, the following condition must be held:

$$
\Delta f = \frac{1}{T'} \tag{2}
$$

and *T*cp should accommodate the maximum expected delay caused by the radio channel. The baseband signal *s*(*t*) is up-converted by a carrier frequency *f*c to form *s*(*t*) for transmission,

$$
\widetilde{s}(t) = s(t)e^{j2\pi f\_\xi t}.\tag{3}
$$

The received signal *a*(*t*) at the sensing receiver is the sum of echoes from different targets. Using point-target channel model for *L* number of targets,

$$
\widetilde{a}(t) = \sum\_{l=1}^{L} b\_l \widetilde{s}(t - \tau\_l) \, . \tag{4}
$$

where *τl* and *bl* represent delay and attenuation related to the *l*th target, respectively. If *l*th target is located at a distance *Rl* and moving with a speed of *vl*, delay *τl* in the received echo can be expressed as

$$
\tau\_l = \frac{\mathbf{2}(R\_l - v\_l t)}{c\_0},
\tag{5}
$$

and *bl* [34],

$$b\_l = \sqrt{\frac{c\_0^2 G\_{\text{TX}} G\_{\text{RX}} \sigma\_{\text{RCS}}}{(4\pi)^3 R\_l^4 f\_\text{c}^2}},\tag{6}$$

where in (6), *c*0 is the speed of light in free space; *σ*RCS*l* is the radar cross-section of the *l*th target; and *G*Tx, *G*Rx represent transmitting and receiving antenna gain, respectively.

For the communication link, the signal attenuation *b*com is

$$b\_{\rm com} = \sqrt{\frac{c\_0^2 G\_{\rm Tx} G\_{\rm Rx}}{(4\pi)^2 R\_{\rm com}^2 f\_{\rm c}^2}}\tag{7}$$

where *R*com indicates the distance of the communication link.

For sensing processing, a single target is sufficient for mathematical derivations due to the linear operation in (1). The analytical expression for the received echo from a target, located at a distance *R*, moving with the speed of *v*, and attenuated by ˆ *b* (assuming constant attenuation factor for frequencies within the bandwidth) is obtained by using delay *τ* = (2*R* − 2*vt*)/*c*0 in (1), i.e.,

$$\begin{split} \widetilde{a}(t) &= \sum\_{\mu=0}^{M-1} \sum\_{n=0}^{N-1} \widehat{b}S(\mu N + n) e^{\left(j2\pi n \Delta f \left(t - \frac{(2R - 2vt)}{c\_0} - \mu T\_\mathrm{s} - T\_\mathrm{cp}\right)\right)} \\ &\cdot e^{\left(j2\pi f\_c \left(t - \frac{(2R - 2vt)}{c\_0}\right)\right)} \mathrm{rect}\left(\frac{t - \left(\frac{2R - 2vt}{c\_0}\right) - \mu T\_\mathrm{s}}{T\_\mathrm{s}}\right) + \mathcal{2}(t) \end{split} \tag{8}$$

where *z*ˆ(*t*) is to account for the additive white Gaussian noise (AWGN). Since *f*c is usually very high compared to the bandwidth of the signal, in particular in the millimeter-wave band, the Doppler shift (*n*Δ*f* 2*v*)/*c*0 is negligible for the subcarriers and the overall Doppler shift appears only caused by (2*v f*c)/*c*0.

The received signal is down-converted to baseband, which is equivalent to

$$a(t) = \sum\_{\mu=0}^{M-1} \sum\_{n=0}^{N-1} bS(\mu N + n)e^{\left(j2\pi n\Lambda f(t - \frac{(2R)}{c\_0} - \mu T\_\text{s} - T\_\text{cp})\right)} e^{\left(j2\pi \frac{2\mu \xi\_c}{c\_0} t\right)} \text{rect}\left(\frac{t - \left(\frac{2R}{c\_0}\right) - \mu T\_\text{s}}{T\_\text{s}}\right) + z(t), \tag{9}$$

where *b* and *z*(*t*) represent ˆ *b*exp(−*j*2*π f*c2*R*/*c*0) and *z*ˆ(*t*)exp(−*j*2*π f*c*t*), respectively.

Finally, the signal *a*(*t*) is sampled, the CP part is removed before it is converted into the frequency domain by using FFT operation,

$$\begin{split} A(\mu N + n) &= bS(\mu N + n)e^{\left(-j2\pi n \Delta f \frac{2R}{\epsilon\_0}\right)} e^{\left(j2\pi \frac{2\eta f\_c}{\epsilon\_0} \mu T\_8\right)} + Z(\mu N + n), \\ n &\in [0, N - 1], \quad \mu \in [0, M - 1] \end{split} \tag{10}$$

where *A*(*μN* + *n*) and *Z*(*μN* + *n*) are frequency domain equivalents of *a*(*t*) and *z*(*t*).

Once the received signal is translated back into the frequency domain, the elementwise division of the received OFDM symbol by the respective transmitted OFDM symbol is performed to construct the channel matrix **H**, i.e.,

$$H(\mu N + n) = be^{\left(-j2\pi n \Delta f \frac{2R}{c\_0}\right)} e^{\left(j2\pi \frac{2vf}{c\_0} \mu T\_s\right)} + \frac{Z(\mu N + n)}{S(\mu N + n)},\tag{11}$$

where *H*(*μN* + *n*) represents the *μ*th column and *n*th row of the channel matrix **H**, and *Z*(*μN* + *n*)/*S*(*μN* + *n*) defines the noise floor that depends on the digital modulation, e.g., a 16-QAM mapping affects the noise floor by approx 2.7 dB [36]. The IFFT of **H**, along subcarriers, provides the range information,

$$r(d) = e^{\left(j2\pi \frac{2vf\_c}{c\_0} \mu T\_s\right)} \frac{b}{N} \sum\_{n=0}^{N-1} e^{\left(-j2\pi n \Delta f \frac{2R}{c\_0}\right)} e^{\left(j\frac{2\pi}{N} nd\right)} + \mathfrak{z}(d), \tag{12}$$
  $d \in [0, N-1]$

where *z*ˇ(*d*) represents the noise part.

The |*r*(*d*)| shows a peak value under the following condition:

$$d = \left\lfloor \frac{2R\Delta fN}{c\_0} \right\rfloor,\tag{13}$$

i.e., the value of *d* corresponding to the maximum of |*r*(*d*)| holds the information of the target range, and the range resolution Δ*R* (minimum distinguishable distance between the two targets) is defined as

$$
\Delta R = \frac{c\_0}{2\Delta fN}.\tag{14}
$$

Similarly, the FFT operation over different OFDM symbols in **H** (over *μ* domain in (11)) provides the information about the speed of the target and can be recognized by using

$$p = \left\lfloor \frac{2vf\_{\text{c}}T\_{\text{s}}M}{c\_{0}} \right\rfloor, \quad p \in [0, M-1] \tag{15}$$

whereas the speed resolution Δ*v* can be calculated by setting *p* = 1,

$$
\Delta v = \frac{\mathcal{L}\_0}{2f\_\text{c}T\_\text{s}M}.\tag{16}
$$

The IFFT/FFT operations on **H** provide processing gain due to coherent addition of signals, and the overall processing gain is

$$G = NM.\tag{17}$$

If there are *N*´ guardband subcarriers on each side of the OFDM symbol, then the processing gain reduces to (*N* − 2*N*´ )*M*. Here, it is important to note that the guardband subcarriers reduce the bandwidth of the OFDM waveform, and consequently the value of Δ*R* increases in (14) when *N* is replaced by (*N* − 2*N*´ ). Although Δ*R* increases due to guardband subcarriers, improvement in the range accuracy (resolution of IFFT) is linked to the size of IFFT [37].

Figure 1 highlights the sensing processing using **H**. Figure 1a shows the real part of the channel matrix **H**, which has sinusoidal variations due to the range and speed of a single target. The IFFT operation, along with subcarriers, identifies the delay associated with the range, as shown in Figure 1b. Afterwards, the FFT operation provides the sensing information in the delay-Doppler profile, as shown in Figure 1c,d.

It is clear that the sensing performance depends on the OFDM waveform parameters because bandwidth defines the range resolution, and the duration of the OFDM waveform determines speed resolution. For the speed, the upper limit is selected as Δ*f* > 20 *f*c*v*/*c*0 to maintain the acceptable level of orthogonality among the subcarriers [35].

**Figure 1.** OFDM–based sensing from the channel matrix **H**. (**a**) IFFT operation over subcarriers. (**b**) FFT operation over OFDM symbols. (**c**) 3–D plot of the delay–Doppler profile. (**d**) Radar image, indicating the delay associated to the range and the Doppler frequency related to the speed of the target.

## **3. Proposed Method for Range Extension**

In OFDM-based sensing, the maximum range is limited by the CPI [28,35] as echoes falling outside the CPI cause ISI and suffer in processing gain. We propose a zero-delay shift method to compensate for delay *τ* in an echo to maintain its processing gain *G* during IFFT operation for OFDM-based sensing.

Using sampling intervals Δ*T* = 1/*F*s and Δ*f* = 1/(*N*Δ*T*), the sampled version of (9) is

$$a(k\Delta T) = \sum\_{\mu=0}^{M-1} \sum\_{n=0}^{N-1} b\mathcal{S}(\mu N + n) e^{\left(j2\pi n \frac{1}{\left(N\Delta T\right)} \left(k\Delta T - \frac{2R}{c\_0\Delta T} - \mu \frac{T\_8}{\Delta T} - \frac{T\_{\text{CP}}}{\Delta T}\right)\right)} \tag{18}$$

$$\cdot e^{\left(j2\pi \frac{2vf\_c}{c\_0}k\Delta T\right)} \text{rect}\left(\frac{k\Delta T - \frac{2R}{c\_0} - \mu \frac{T\_8}{\Delta T}}{\frac{T\_8}{\Delta T}}\right) + z(k\Delta T)\_s$$

where *k* is the sampled time index. Using *F*s/Δ*f* = *T*/Δ*T* = *N*, *T*s/Δ*T* = *N*s, *T*cp/Δ*T* = *N*cp, *m* = (2*R*)/(*c*0Δ*T*), and *a*(*k*), *z*(*k*) to represent *a*(*k*Δ*T*) and *z*(*k*Δ*T*) respectively,

$$a(k) = \sum\_{\mu=0}^{M-1} \sum\_{n=0}^{N-1} bS(\mu N + n)e^{\left(j2\pi \frac{n}{N}(k - m - \mu N\_{\rm s} - N\_{\rm cp})\right)}$$

$$\cdot e^{\left(j2\pi \frac{2vf\_{\rm s}}{c}k\Lambda T\right)} \text{rect}\left(\frac{k - m - \mu N\_{\rm s}}{N\_{\rm s}}\right) + z(k). \tag{19}$$

$$k \in [0, MN\_{\rm s} - 1]$$

A delay-shift in *k* by *m* samples shifts the target at zero on the delay axis. Since *m* is unknown, sequentially increasing the delay-shift in *k* identifies *m* when a peak appears at delay zero. This process can identify echoes with delay longer than the CP, provided they arrive with detectable signal strength. If we extend the sensing range up to *Q* number of OFDM symbols, the proposed method can be described in following steps:

Using the above process, a matrix (in the delay-shift and time domains) of size *QN*s × *M* is constructed, which requires an *M*-point FFT operation to complete the range/speed plot.

Figure 2 shows different steps in the proposed method to detect two targets separated by more than one OFDM symbol duration; *Q* = 2 is used, and the current OFDM symbol number is *q*. Figure 2a,b are obtained using steps 1–4 of the proposed method; Figure 2c is the plot of step 5 and using *M* = 12 for step 6; Figure 2d is the final range/speed plot, where the range is extended up to two OFDM symbols. A schematic diagram of the proposed method is presented in Figure 3. Delay shifts are used in the sampled version of the incoming OFDM waveform to get the frequency domain signal *Yq*. Element-wise division of *Yq* is performed with the current OFDM symbol *Sq* and previous OFDM symbols for sensing and combining.

We use periodogram to compare the performance of the proposed method with conventional OFDM-based sensing. Periodogram of the conventional OFDM-based sensing is defined as [31],

$$\begin{aligned} D\_{\text{conv}(d,p)} &= \left| \sum\_{\mu=0}^{M-1} r(d) e^{\frac{-j2\pi\mu p}{M}} \right|^2 \\ &\quad d \in [0, N-1] \quad p \in [0, M-1] \end{aligned} \tag{20}$$

where *r*(*d*) is defined in (12). A target is detected if the peak in *D*conv(*d*,*p*) is above a threshold level (usually defined by the minimum detectable signal strength). For the

range/speed plot, **D** is often transformed to normalized power, and in dB scale using 10 log10 (**D**/*max*[**D**]), where *max*[**D**] represents the maximum value of **D**.

**Figure 2.** Explanation of the proposed method when range extension is up to two OFDM symbols. (**a**,**b**) Steps 1–4 of the proposed method provide two matrices. (**c**) Delay–zero rows of the matrices in (**a**,**b**) are concatenated according to the step 5. (**d**) Range/speed plot is completed using *M*–point FFT operation over time domain.

**Figure 3.** Schematic of the proposed range extension method to detect targets beyond the range limit in the conventional OFDM–based sensing.

Similarly, the periodogram of the proposed method is

$$D\_{\text{pro}(\mathcal{J},p)} = \left| \sum\_{\mu=0}^{M-1} \hat{r}\_{\mathcal{J}}(0,\mu) e^{\frac{-j2\pi\mu p}{M}} \right|^2, \quad \hat{d} \in [0,(Q-1)N\_s - 1] \quad p \in [0,M-1] \tag{21}$$

where ˆ*d* represents the delay-shift domain and *r*ˆ ˆ*d*(0, *μ*) is obtained by concatenation of *Q* segments as defined in step 5 of the proposed method, i.e.,

$$\mathcal{F}\_{\vec{d}}(0,\mu) = [r\_{\vec{d}}(0,\mu), r\_{\vec{d}}(0,\mu - 1), \dots, r\_{\vec{d}}(0,\mu - (Q - 1))], \qquad \vec{d} \in [0, N\_{\rm s} - 1] \tag{22}$$

where *r* ´*d*(0, *μ*) is obtained by using *d* = 0 in *r* ´*d*(*d*, *μ*),

$$r\_{\vec{d}}(d,\mu) = \frac{1}{N} \sum\_{n=0}^{N-1} H\_{\vec{d}}(\mu N + n) e^{\frac{j2\pi nd}{N}}, \qquad d \in [0, N\_{\sf s} - 1] \tag{23}$$

i.e.,

$$r\_d(0, \mu) = \frac{1}{N} \sum\_{n=0}^{N-1} H\_d(\mu N + n). \tag{24}$$

If we represent *m* = *gN*s + *m*ˆ where *g* ∈ [0, *Q* − 2] and *m*ˆ ∈ [0, *N*cp − 1], received *q*th OFDM symbol and transmitted OFDM symbols provide

$$\mathbf{H}\_{\vec{d},(q-i)} = \frac{\mathbf{Y}\_{d,q}}{\mathbf{S}\_{(q-i)}},\tag{25}$$

where **H** ´*d*,(*q*−*i*) is taken as simplified notation for *H* ´*d*((*q* − *i*)*N* + *n*), *i* ∈ [0, *Q* − 1], and **Y** ´*d*,*q* = FFT(*A* ´*d*(*k*)), where *A* ´*d*(*k*) is the delay-shift of *A*(*k*) by ´*d* and *k* ∈ [ ´*d* + (*q*)*N*s − *gN*s − *m*ˆ +, ´*d* + (*q* + 1)*N*s − *gN*s − *m*ˆ − *N*cp] (interval of the N-samples of the waveform is selected at the initial step of the proposed method). It is clear that at ´*d* = ´*d*0 = *m*ˆ + *N*cp, *A* ´*d*0 (*k*) represents (*q* − *g*)th OFDM symbol without *N*cp; hence, (25) changes to

$$\mathbf{H}\_{\dot{d}\_{0\prime}(q-i)} = \frac{b\mathbf{S}\_{(q-g)} + \mathbf{Z}\_{(q-g)}}{\mathbf{S}\_{(q-i)}},\tag{26}$$

where **Z**(*q*−*g*) represents noise part in the (*q* − *g*)th OFDM symbol. Similarly, at ´*d* = ´*d*1 = (*m*ˆ + *N*), *A* ´*d*(*k*) consists of last *N*cp samples of the (*q* − *g*)th OFDM symbol and *N* − *N*cp samples of (*q* − *g* + 1)th OFDM symbol; therefore,

$$\mathbf{H}\_{\mathbf{d}\_{1},(q-i)} = \frac{N - N\_{\rm cp}}{N \mathbf{S}\_{(q-i)}} b \mathbf{S}\_{(q-g)} e^{-\frac{j2\pi n}{N} \mathbf{N}\_{\rm cp}} + \frac{N\_{\rm cp}}{N \mathbf{S}\_{(q-i)}} b \mathbf{S}\_{(q-g+1)} + \frac{\mathbf{Z}\_{(q-g)}}{\mathbf{S}\_{(q-i)}}.\tag{27}$$

Using (26) in (24) provides the maximum of *r* ´*d*(0, *μ*), which is same as *r*(*d*) in (20), whereas (27) indicates the additional peak with height reduced by a factor of *N*cp/*N* and affected by the ISI. Similar to *D*conv(*d*,*p*), where a processing of *NM* is assigned to a peak, *D* pro( ˆ*d*,*p*) also provides the same processing gain when *i* = *g* in (26); otherwise, **H** ´*d*,(*q*−*i*) in (26) is interference. In (27), contrary to interference term, *N*cp samples are coherently added when used in (24) and the processing gain is 10log10(*N*2 cp/(*N* − *N*cp)).

In a generalized scenario, there can be *L* echoes with delays not limited to CPI; the received signal *y*(*k*) is the summation of all echoes, each represented by the (19),

$$\begin{split} y(k) &= \sum\_{l=0}^{L-1} \sum\_{\mu=0}^{M-1} \sum\_{n=0}^{N-1} b\_l \mathcal{S} \left( \mu N + n \right) e^{\left( j2\pi \frac{n}{N} \left( k - m\_l - \mu N\_s - N\_{\rm cp} \right) \right)} \\ &\cdot e^{\left( j2\pi \frac{2v\_l \zeta\_c}{c} k \Delta T \right)} \text{rect} \left( \frac{k - m\_l - \mu N\_s}{N\_{\rm s}} \right) + z(k), \end{split} \tag{28}$$

where *ml* represents the delay associated with *l*th echo. Based on the delay *ml*, we split the *y*(*k*) into three portions such as *y*1(*k*) for *ml* ≤ *N*cp, *y*2(*k*) for *N*cp < *ml* ≤ *N*s, and *y*3(*k*) for *ml* > *N*s, i.e.,

$$y(k) = y\_1(k) + y\_2(k) + y\_3(k) + z(k). \tag{29}$$

Since *y*3 is formed by the summation of echoes that are outside the current OFDM symbol, therefore this part is only ISI. Unlike *y*3(*k*), the ISI part of *y*2(*k*) increases as *ml* approaches to *N*s. The detection of the echoes in *y*2(*k*) and *y*3(*k*) is possible if the processing gain *G* is sufficient to overcome the related ISI and noise.


**6. The principles of food regulation in the use of cellulose derivatives**

The Code of Federal Regulations (CFR) is an arrangement and codification of general, customary, and everlasting regulations published in the Federal Register by federal government agencies, supervisory departments, and businesses. In relation to the legal guidelines related to the consumption of special raw materials in the food industry, considerable codes have been provided that present appropriate information to industrial producers [66]. In the case of drugs for human use, such as ophthalmic demulcents, the concentrations percentage of each cellulose derivative (NaCMC, HEC, HPMC-P, and MC) has been established within 0.2 to 2.5% in accordance with the standard of 21CFR349.12 [67]. The use of ethyl cellulose in food and feed is stated in the legal standards of 21CFR172.868 and 21CFR573.420, respectively. Ethyl cellulose as food additive may be safely used in foods under the stated conditions: In clause "a"—The food additive is a cellulose ether containing ethoxy groups (OC2H5) linked by an ether bond and containing not more than 2.6 ethoxy groups per anhydro glucose unit on an anhydrous basis. In clause "b"—Ethyl cellulose is used or intended for use as a binder and filler in dry vitamin preparations, as part of protective coatings for vitamin and mineral tablets, and finally in the role of stabilizer in flavoring compounds. For the use of ethyl cellulose as animal feed, it must meet the previously stated conditions of clause "a" in the same way as in clause "b–"—its uses are presented as a binder or filler in dry vitamin preparations to be incorporated into animal feed [68, 69]. Usage rules for hydroxypropyl cellulose are provided in 21CFR172.870. This standard separates HPC with a high degree of substitution (which contains no more than 4.6 hydroxypropyl groups per anhydro glucose unit) and a low degree of substitution (which contains on average 0.1 to 0.4 hydroxypropyl groups per anhydro glucose unit). High substituted HPC may be used as an emulsifier, film former, protective colloid, stabilizer, suspending agent, and thickener according to good manufacturing practice (GMP). HPC with low substitution can be used as a binder and disintegrator in tablets or wafers containing dietary supplements according to GMP. FDA indicated that the proposed use of high-substituted HPC is safe with a minimum viscosity of 10 centipoises and for same using as a binder in dietary supplements similar to low-substituted HPC will not result in an increased intake or harm to human health under the established conditions of use and significantly it is

not expected to have different biological properties [70]. Finally, for HPC based on federal regulation of 75FR17928, there is no significant effect on the environment and thus an environmental impact statement is not required [71]. The specific labeling requirements for the use of various hydrophilic gums such as NaCMC in specific drug products are noted in 21CFR201.319 [72].

The prescribed conditions for the safe use of methyl ethyl cellulose are provided in the standard of 21CFR172.872: In clause "a"—The general formula of cellulose ether is as [C6H(10-x-y) O5(CH3)x(C2H5)y]n. In this chemical formula, x is the number of methyl groups and y is the number of ethyl groups. The average value of x is 0.3 and the average value of y is 0.7. In clause "b"—This additive composition must have the following conditions: The methoxy content shall be not less than 3.5% and not more than 6.5%, calculated as OCH3, and the ethoxy content shall be not less than 14.5% and not more than 19%, calculated as OC2H5, both measured on the dry sample. The viscosity of an aqueous solution, 2.5 grams of the material in 100 milliliters of water, at 20°C, is 20 to 60 centipoises. The ash content on a dry basis has a maximum of 0.6%. In clause "c"—The food additive is used as an aerating, emulsifying, and foaming agent, in an amount not in excess of that reasonably required to produce its intended effect [73].

The specified conditions for safely using "Hydroxyethyl cellulose film-water insoluble" for packaging food are stated in accordance with the regulation code of 21CFR177.1400. In clause "a"—Water-insoluble hydroxyethyl cellulose film consists of a base sheet manufactured by the ethoxylation of cellulose under controlled conditions, to which may be added certain optional substances of a grade of purity suitable for use in food packaging as constituents of the base sheet or as coatings applied to impart desired technological properties. In clause "b"—The optional substances that are identified as suitable in terms of food safety can be used in the base sheet of film production and coating as components of water-insoluble hydroxyethyl cellulose film. In clause "c"—Any substance employed in the production of the water-insoluble hydroxyethyl cellulose film described in this section [74].

### **7. Innovations of the cellulosic application in the food industry**

Studies discuss the interrelation between the chemical structure of cellulose and its source and its various physicochemical characteristics. Although cellulose extracted from plants has been most investigated, cellulose purified from microorganisms and animals with special structural features has received increasing attention [75].

Heretofore, enzymatic hydrolysis procedure, TEMPO oxidation reaction (2,2,6,6-Tetramethylpiperidine-1-oxyl), and carboxymethylation process have been widely used to assist in defibrillating cellulose during processing into nanocellulose, which not only helps decrease consumption of energy but also provides additional functional groups for the final products [76].

Acidic hydrolysis, which includes inorganic and organic acids, can remove and eliminate amorphous regions, resulting in cellulose nanocrystal (CNC), although highly corrosive conditions and low CNC yield are persistent issues. Through mechanical treatments such as refining, homogenization, microfluidization, sonication, ball milling, and the aqueous counter collision (ACC) technique, cellulose nanofibrils (CNF) can be produced, however, the very high input energy prohibits the commercialization of these methods [77, 78].

Bacterial cellulose (BC), a special nanocellulose derived from bacteria, has currently attracted numerous research interests. Its higher aspect ratio and larger

#### *Perspective Chapter: Cellulose in Food Production – Principles and Innovations DOI: http://dx.doi.org/10.5772/intechopen.109204*

diameter make it a promising material for food packaging applications. In order to facilitate the application of nanocellulose in food packaging, it is always processed using different manufacturing technologies, including solution casting, layer-by-layer (LBL) assembly, extrusion, coating, gel-forming, spray drying, electrostatic spinning, adsorption, with the aim of producing different forms of materials such as film, gel, coating membrane, and emulsions [79, 80].

Due to their non-toxicity, proper biodegradability and biocompatibility, high aspect ratio, low coefficient of thermal expansion, extremely good mechanical strength, and special optical properties, nanocellulose-based food packaging materials are broadly used for fruit packaging, meat products, fast foods, dairy products, and beverages. Since nanocellulose and functional fillers in cellulose-based nanocomposites provide excellent barrier and mechanical properties, antibacterial activity and stimuli-responsive performance, therefore noticeably improve food quality stability and shelf life [81, 82].

Nanocellulose and its derived nanocomposite have turned out to be a hotspot of research in food packaging due to its great properties including excessive strength, large specific surface area, excellent barrier properties and proper biocompatibility, safety, non-toxicity, and degradability. In food packaging materials, nanocellulosebased nanocomposites can be used as fresh and antibacterial packaging materials, smart packaging materials, and high-barrier packaging materials, which indicates the excessive utility potential of nanocellulose-based composites. Therefore, nanocellulose-based composites, as a type of renewable and environmentally friendly packaging material, enhance the protection and quality of food and are one of the important paths to understand the improvement of **"**eco-friendly industry**"** in the food industry [83].

Recently, biopolymer-based hydrogels have been attracting growing attention due to the fact of their promising applications in drug release, biosensors, superabsorbent materials, tissue engineering, and many others [84]. Hydrogels are water-insoluble polymers that have the ability to hold a large amount of water in their network [85, 86]. The considerable hydrophilic groups with hydroxyl, carboxyl, and aldehyde form in the structure of native cellulose or cellulose derivatives make them suitable to prepare hydrogels without difficulty with fascinating constructions and properties for biomedical and food packaging and applications [87, 88].

Regarding the progress of cellulose and its derivatives in the food industry, especially packaging, the following should be mentioned [89, 90]:

water usage, large amount of polluted wastewater, high demand for energy, and low efficiency have largely prohibited the industrially feasible production of nanocellulose. Therefore, more work efforts should be made to develop novel methods for the preparation of nanocellulose, such as those based on organic acids, which have already been shown to be a green approach (not environmentally harmful strategy) for the preparation of functionalized derivatives as nanocellulose.


4. Magnetic water treatment

Magnetic water treatment (MWT) is a new technique which is promising in environmental remediation in addition to its increased application in the area of medicine, agriculture and industrial process. The water molecules acquire unique physicochemical characteristics under the influence of the magnetic fields (MFs). It is a non-chemical method and the water molecules undergo change from their cluster of many loosely bound water molecules into very small, uniform and hexagonally organized clusters of molecules under the magnetic treatment [90]. These features of the magnetized water prevent the polluting agents to enter in to its cluster and also make their easy passage through the cells of plant as well as of animals. Moreover, the MFs have antimicrobial activity on water. Therefore, the magnetized water molecules depict as bio-friendly and eco-friendly compounds to environmental management as well as to plant and animal cells.


**Abstract**

Malaria driven pathophysiology inimically conjoined to systemic inflammation response cascade in a vicious feed-forward cycle destined to a terrible debilitation or demise of the host. The *Plasmodium* parasite initiates physiological changes when it is transmitted into the human host by intermediate host and vector. Sporozoites injection elicits immunological and inflammatory response suppression facilitating movement into the blood stream undetected, destined to hepatocyte. Subsequently, hepatocyte invasion culminates in intracellular growth and conversion of the parasites rapturing hepatocytes releasing merozoites into the extrahepatic circulation. Inflammatory and immunological response initiation results in overt malarial disease symptoms. Initially, inflammatory response alleviates and curtails infection. Activation of leukocytes, lymphocytes, monocytes, and phagocytes secretes inflammatory mediators, chemokines, cytokines cytoadhering molecules which accelerate infection patency. Hormonal processes influence disease tolerance without necessarily interfering with parasitemia. Current treatment is anti-parasitic. Phytotherapeutic intervention in malaria is anti-parasitic and anti-disease effects that terminate the vicious cycle and alleviating disease. The phytochemicals, in malarial experimental and clinical work, include asiatic acid, maslinic acid, oleanolic acid, and inflammatory and immunological aberrations evolving in malaria and the effects of phytochemical therapeutics in the alleviation of the disease to enable leverage of future treatment regimens through harnessing existing plants materials is explored.

**Keywords:** malaria inflammation, phytochemicals, Asiatic acid, Maslinic acid, Oleanolic acid, anti-parasitic, anti-disease, *Plasmodium falciparum*, *Plasmodium berghei*, pathophysiology


**Alan Melcher**

Professor Melcher is a clinician scientist, and currently Professor of Translational Immunotherapy at The Institute of Cancer Research, London, and Honorary Consultant Oncologist at The Royal Marsden NHS Foundation Trust. He graduated in medicine from the University of Oxford and trained in Clinical Oncology (Radiotherapy and Chemotherapy) in Cardiff, London and Leeds. Following completion of his PhD at the Imperial Cancer Research Fund (now Cancer Research UK) in London, he was a post-doctoral research fellow at the Mayo Clinic, Minnesota, before returning to the UK, where in 2007, he became Professor of Clinical Oncology and Biotherapy at Leeds, before moving to London in 2016. Professor Melcher's laboratory and translational research is focused on oncolytic viruses, radiotherapy and immunotherapy for the treatment of cancer. He and his team are investigating how to improve the ability of oncolytic viruses to trigger immunogenic cell death in tumours.


**Author details**

Pai-Yen Chen1 \*, Mohamed Farhat2 , Zhilu Ye1 , Muhammad Amin3 , Hakan Bagci1 and Danilo Erricolo2

1 Department of Electrical and Computer Engineering, University of Illinois Chicago, Chicago, IL, USA

2 Computer, Electrical, and Mathematical Science and Engineering (CEMSE) Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia

3 College of Engineering, Taibah University, Madinah, Saudi Arabia

\*Address all correspondence to<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Artificial Surfaces and Media for Electromagnetic Absorption and Interference Shielding DOI: http://dx.doi.org/10.5772/intechopen.99338*


**3. Endoscopic facelift (forehead lift, brow lift, midface lift)**

As humans age, lines and wrinkles naturally form on the forehead due to constant muscle movement, making one look older than he/she would like. Additionally, those horizontal lines across the forehead, or vertical lines between the brows, can cause one to look angry, stressed, or simply unpleasant and unapproachable. Fortunately, with the help of endoscopic surgery, one can achieve a fresh-faced, smooth, youthful appearance.

#### **3.1. Technique**

In preparation for a classic forehead lift, the hair is tied back with rubber bands in front and behind the incision area. An incision is usually made across the top of the head, just behind the hairline. Forehead skin is gently lifted and portions of facial muscle and excess skin are removed. The incision is then closed with stitches or clips. The result of a forehead lift is a younger, more rested look (Figure 4).

In an endoscopic forehead lift, the muscles and tissues that cause the furrowing or drooping are removed or altered to smooth the forehead, raise the eyebrows and minimize frown lines. Surgeons may use the conventional surgical method, in which the incision is hidden just behind the hairline; or it may be performed with the use of an endoscope. Both techniques yield similar results, smoother forehead skin and a more animated appearance.

Low, heavy "V" shaped eyebrows create a tired, older, masculine, unfriendly appearance. Opening up the eyes and brows and smoothing the forehead is both powerful and subtle. Patients look more awake, fresh, healthy and youthful. Forehead surgery is normally done in combination with an eye lift (blepharoplasty) for best results.

In preparation for a classic forehead lift, the hair is tied back with rubber bands in front and

behind the incision area. An incision is usually made across the top of the head, just behind the

hairline. Forehead skin is gently lifted and portions of facial muscle and excess skin are removed.

The incision is then closed with stitches or clips. The result of a forehead lift is a younger, more

#### **Figure 4.** Classic forehead lift incision

Before the operation, motivations and demands of the patients must be analyzed. A careful study of the upper facial region and its relations with the rest of the face should be made. A preoperative assessment is normally conducted as required. The anesthesiologist will be seen in consultation at the latest 48 hours before surgery. No medication containing aspirin should be taken within 10 days prior to surgery. Smoking cessation is strongly recommended at least one month before and one month after surgery. An antiseptic shampoo should be used the night before and / or in the morning. It is essential to fast (not eat or drink) 6 hours before surgery. **Figure 4 : Classic forehead lift incision** In an endoscopic forehead lift, the muscles and tissues that cause the furrowing or drooping are removed or altered to smooth the forehead, raise the eyebrows and minimize frown lines. Surgeons may use the conventional surgical method, in which the incision is hidden just behind the hairline; or it may be performed with the use of an endoscope. Both techniques yield similar

#### **3.2. Type of anesthesia** results, smoother forehead skin and a more animated appearance.

Two methods are possible: Low, heavy "V" shaped eyebrows create a tired, older, masculine, unfriendly appearance.

9

The choice between these different techniques will be the result of a discussion between patient, surgeon and the anesthesiologist. Patients look more awake, fresh, healthy and youthful. Forehead surgery is normally done in combination with an eye lift (blepharoplasty) for best results.

Hospitalization is short. The admission is in the morning (or even the day before in the afternoon) and the discharge is permitted either in the evening or the day after the operation. Before the operation, motivations and demands of the patients must be analyzed. A careful

#### **3.3. Technique of endoscopic forehead and eyebrow lift** study of the upper facial region and its relations with the rest of the face should be made. A

Each surgeon adopts his/her own technique that he/she adapts to in each case in order to obtain the best results. However, some common basic principles are as follows: preoperative assessment is normally conducted as required. The anesthesiologist will be seen in

Incisions are between 5 and 10 mm long, are three to five in number and are placed in the scalp, a few centimeters behind the forehead hairline. One of them will allow the passage of the endoscope connected to a mini video camera, the other giving way to the different instruments consultation at the latest 48 hours before surgery. No medication containing aspirin should be taken within 10 days prior to surgery. Smoking cessation is strongly recommended at least one

specifically adapted to endoscopic surgery. The path of these incisions is of course the future location of scars, which are therefore virtually invisible since they are very short and hidden in the hair. Detachment includes the temples and facial bones (Figures 5 and 6). specifically adapted to endoscopic surgery. The path of these incisions is of course the future location of scars, which are therefore virtually invisible since they are very short and hidden in the hair. Detachment includes the temples and facial bones (**Figures 5 and 6**).

month before and one month after surgery. An antiseptic shampoo should be used the night

The choice between these different techniques will be the result of a discussion between

Hospitalization is short. The admission is in the morning (or even the day before in the

Each surgeon adopts his/her own technique that he/she adapts to in each case in order to

Incisions are between 5 and 10 mm long, are three to five in number and are placed in the

obtain the best results. However, some common basic principles are as follows:

afternoon) and the discharge is permitted either in the evening or the day after the operation.

before and / or in the morning. It is essential to fast (not eat or drink) 6 hours before surgery.

**Figure 5.** Incision sites for endoscopic forehead (brow) lift surgery

**Figure 5: Incision sites for endoscopic forehead (brow) lift surgery**

10

**Type of anesthesia**

Two methods are possible:

General anesthesia

patient, surgeon and the anesthesiologist.

**Technique of endoscopic forehead and eyebrow lift**

Local anesthesia deepened by intravenous tranquilizer

Before the operation, motivations and demands of the patients must be analyzed. A careful study of the upper facial region and its relations with the rest of the face should be made. A preoperative assessment is normally conducted as required. The anesthesiologist will be seen in consultation at the latest 48 hours before surgery. No medication containing aspirin should be taken within 10 days prior to surgery. Smoking cessation is strongly recommended at least one month before and one month after surgery. An antiseptic shampoo should be used the night before and / or in the morning. It is essential to fast (not eat or drink) 6 hours before

In preparation for a classic forehead lift, the hair is tied back with rubber bands in front and

behind the incision area. An incision is usually made across the top of the head, just behind the

hairline. Forehead skin is gently lifted and portions of facial muscle and excess skin are removed.

The incision is then closed with stitches or clips. The result of a forehead lift is a younger, more

In an endoscopic forehead lift, the muscles and tissues that cause the furrowing or drooping are

removed or altered to smooth the forehead, raise the eyebrows and minimize frown lines.

Surgeons may use the conventional surgical method, in which the incision is hidden just behind

the hairline; or it may be performed with the use of an endoscope. Both techniques yield similar

Low, heavy "V" shaped eyebrows create a tired, older, masculine, unfriendly appearance.

Opening up the eyes and brows and smoothing the forehead is both powerful and subtle.

Patients look more awake, fresh, healthy and youthful. Forehead surgery is normally done in

Before the operation, motivations and demands of the patients must be analyzed. A careful

study of the upper facial region and its relations with the rest of the face should be made. A

preoperative assessment is normally conducted as required. The anesthesiologist will be seen in

consultation at the latest 48 hours before surgery. No medication containing aspirin should be

The choice between these different techniques will be the result of a discussion between patient,

results, smoother forehead skin and a more animated appearance.

Hospitalization is short. The admission is in the morning (or even the day before in the afternoon) and the discharge is permitted either in the evening or the day after the operation.

combination with an eye lift (blepharoplasty) for best results.

Each surgeon adopts his/her own technique that he/she adapts to in each case in order to obtain

Incisions are between 5 and 10 mm long, are three to five in number and are placed in the scalp, a few centimeters behind the forehead hairline. One of them will allow the passage of the endoscope connected to a mini video camera, the other giving way to the different instruments

surgery.

**3.2. Type of anesthesia**

**•** General anesthesia

9

Two methods are possible:

**Figure 4.** Classic forehead lift incision

rested look (**Figure 4**).

494 A Textbook of Advanced Oral and Maxillofacial Surgery Volume 2

surgeon and the anesthesiologist.

**•** Local anesthesia deepened by intravenous tranquilizer

**Figure 4 : Classic forehead lift incision**

**3.3. Technique of endoscopic forehead and eyebrow lift**

the best results. However, some common basic principles are as follows:

Replacement: Loose tissue will be retightened to soften the "crow's feet", move the tail of the eyebrows upward, and above all the cheek and fat under the eyes that had accumulated over

**Sutures**: The small incisions are closed, often with skin staples that are easily removed or with

taken within 10 days prior to surgery. Smoking cessation is strongly recommended at least one **Figure 6: Dissection and suturing during endoscopic surgery Figure 6.** Dissection and suturing during endoscopic surgery

buried absorbable sutures.

the nasolabial folds will be held in position by deep fixation.

11

Replacement: Loose tissue will be retightened to soften the "crow's feet", move the tail of the eyebrows upward, and above all the cheek and fat under the eyes that had accumulated over the nasolabial folds will be held in position by deep fixation.

**Sutures**: The small incisions are closed, often with skin staples that are easily removed or with buried absorbable sutures.

Depending on the surgeon, the extent of improvements and the possible need for additional procedures, the intervention may take 2 to 3 hours. Possibly some discomfort with a feeling of tension on the temples and cheek may occur. The postoperative course is mainly marked by the appearance of edema (swelling) and ecchymosis (bruising) the size and duration of which is highly variable from one individual to another. The dressing should be removed between the 1st and 3rd days. Staples are removed between the 8th and 15th day. The stigma of the intervention will diminish gradually, allowing the return to normal social and profes‐ sional life after a few more days (10-20 days depending on the magnitude of the surgery). Some numbness of the operated area, possibly some itching on the skull, may be observed during the first weeks. They gradually disappear. A delay of 3 to 6 months is necessary to assess the final outcome. This is the time for all of the edema to be reabsorbed and for the tissues to regain their flexibility. In most cases, intervention results in improvement and significant rejuvena‐ tion of the upper face, with an attenuation of nasolabial folds, padding the area under the eyes and cheeks (with disappearance of the "valley tears") and a decrease of the lower eyelid height.

The results are generally durable, although the aging process is not stopped by the interven‐ tion, the benefit of the lift will be present many years after.

#### **3.4. Ideal candidates**

Most patients opting for lifting are aged between 40 and 50 years, when brow lines and eyelids begin to sag noticeably and wrinkles or creases begin to appear along the forehead. Heredity sometimes causes these problems for people in their 20s and 30s, in which case a brow lift can help. Anyone considering this procedure should have a thorough understanding of what it can and cannot accomplish. After an in-depth discussion, some decide that a brow lift performed in conjunction with other procedures (e.g. a facelift (rhytidectomy) or eyelid surgery (**blepharoplasty**) will provide the best results

### **3.5. Facelift complications**

All surgical procedures carry some uncertainty and risk. Even in the best hands, complications do occur. Fortunately, these are usually treatable. Patients vary in their anatomy, physical reaction to surgery, anesthesia, and healing capabilities, so that the outcome is never com‐ pletely predictable. Surgeons know from experience that two operations in different patients, done almost exactly the same way, may have very different outcomes. Even operations on two sides of the same face or body can have different outcomes, particularly in terms of discomfort, bruising and swelling. Patients are often surprised at this.

It is best if patients anticipate having a complication, and if they do not that is a bonus. There is a well-known phrase in surgery: "The only way to avoid complications is by not operating." Experienced surgeons, particularly toward the end of their careers, are often very candid and admit that they've seen just about every complication in their practice over the years. It is important for the patient and doctor to have a mutual trustful relationship to manage com‐ plications when they develop.

A complication rate of 1% is commonly quoted. It seems small, only one in a hundred, and perhaps this is a rate that is comfortable from a psychological standpoint, an event that sometimes happens to other people. But it should not be too reassuring, even if it is correct. If patients encounter a complication, it's 100 percent as far as they are concerned. They have to understand that it could happen to them. They should have the surgery only if they can tolerate the risks.

#### **Facelift risks and complications may include:**

Replacement: Loose tissue will be retightened to soften the "crow's feet", move the tail of the eyebrows upward, and above all the cheek and fat under the eyes that had accumulated over

**Sutures**: The small incisions are closed, often with skin staples that are easily removed or with

Depending on the surgeon, the extent of improvements and the possible need for additional procedures, the intervention may take 2 to 3 hours. Possibly some discomfort with a feeling of tension on the temples and cheek may occur. The postoperative course is mainly marked by the appearance of edema (swelling) and ecchymosis (bruising) the size and duration of which is highly variable from one individual to another. The dressing should be removed between the 1st and 3rd days. Staples are removed between the 8th and 15th day. The stigma of the intervention will diminish gradually, allowing the return to normal social and profes‐ sional life after a few more days (10-20 days depending on the magnitude of the surgery). Some numbness of the operated area, possibly some itching on the skull, may be observed during the first weeks. They gradually disappear. A delay of 3 to 6 months is necessary to assess the final outcome. This is the time for all of the edema to be reabsorbed and for the tissues to regain their flexibility. In most cases, intervention results in improvement and significant rejuvena‐ tion of the upper face, with an attenuation of nasolabial folds, padding the area under the eyes and cheeks (with disappearance of the "valley tears") and a decrease of the lower eyelid height. The results are generally durable, although the aging process is not stopped by the interven‐

Most patients opting for lifting are aged between 40 and 50 years, when brow lines and eyelids begin to sag noticeably and wrinkles or creases begin to appear along the forehead. Heredity sometimes causes these problems for people in their 20s and 30s, in which case a brow lift can help. Anyone considering this procedure should have a thorough understanding of what it can and cannot accomplish. After an in-depth discussion, some decide that a brow lift performed in conjunction with other procedures (e.g. a facelift (rhytidectomy) or eyelid

All surgical procedures carry some uncertainty and risk. Even in the best hands, complications do occur. Fortunately, these are usually treatable. Patients vary in their anatomy, physical reaction to surgery, anesthesia, and healing capabilities, so that the outcome is never com‐ pletely predictable. Surgeons know from experience that two operations in different patients, done almost exactly the same way, may have very different outcomes. Even operations on two sides of the same face or body can have different outcomes, particularly in terms of discomfort,

It is best if patients anticipate having a complication, and if they do not that is a bonus. There is a well-known phrase in surgery: "The only way to avoid complications is by not operating."

the nasolabial folds will be held in position by deep fixation.

496 A Textbook of Advanced Oral and Maxillofacial Surgery Volume 2

tion, the benefit of the lift will be present many years after.

surgery (**blepharoplasty**) will provide the best results

bruising and swelling. Patients are often surprised at this.

buried absorbable sutures.

**3.4. Ideal candidates**

**3.5. Facelift complications**

**8.** General dissatisfaction with the cosmetic results, possibility of revision surgery, depres‐ sion or emotional mood changes may also develop.

#### **3.6. Preoperative instructions**

Before undergoing brow lift surgery, we must provide pre-operative instructions; these may include:

#### **3.7. Benefits of brow lift surgery**

All men and women over the age of 40 see signs of aging in the face. The forehead is usually one of the first places where lines and wrinkles appear due to excessive muscle movement. Fortunately, brow lift surgery can do away with a number of cosmetic flaws on the upper third portion of the face. The many benefits of brow lift surgery include: Increase confidence with enhanced appearance, rejuvenated appearance, alleviation of tension in the forehead muscles, causes minimal side effects, fast recovery, excellent, long-lasting results (up to 10 years or more), incisions are well hidden and scarring is minimal, natural-looking results and few potential risks or complications.


*Article* **A Resonant Ring Topology Approach to Power Line Communication Systems within Photovoltaic Plants**

**José Ignacio Morales-Aragonés 1, Matthew St. Michael Williams 2, Víctor Alonso Gómez 1, Sara Gallardo-Saavedra 3, Alberto Redondo-Plaza 3, Diego Fernández-Martínez 3, Francisco José Sánchez-Pacheco 4, Juan Gabriel Fajardo Cuadro 5 and Luis Hernández-Callejo 6,\***

**Abstract:** Within this study, single-cable propagation facilitated by PV strings' wiring characteristics is considered for an adapted design of PLC electronics. We propose to close the communications signal path, resulting in a ring topology where a resonance condition could be implemented. A PLC topology using the resulting circular closed-loop path of a PV series string as its physical communication support is designed and leveraged for practical use. When the path length or the number of transceivers is changed, the resonance properties that come with the circular path as the physical support are affected but are shown to be preserved with the application of automatic adjustable tuning. This automatic tuning guarantees that the resonance improves propagation parameters and reverts the system to its optimal values at the chosen carrier frequency.

**Keywords:** loop antenna; power line communication; resonance; single-wire transmission; tuning

#### **1. Introduction**

Monitoring and maintenance tasks within solar plants are becoming the focus of many research efforts, and a growing number of sensors and measuring devices are proposed to be installed along different points of the solar module associations, even within each solar module [1]. In this scenario, communications between solar modules and centralization points (combiner boxes) become an essential subject for research. Considering the year-on-year growing amount of solar modules within modern solar plants, the cost of the communications elements (module transceivers, wiring, etc.) becomes a key point in constructing optimal designs for future practical communication implementations. Regarding the cabling, an ideal solution would be a power line communication (PLC) system in order to use the same power cables already installed as a communications physical support, bypassing the need for extra communications wiring.

Some authors have developed works where PLC is used as an automatic transfer switch (ATS); ATS selects the electrical connection circuit in the solar plant [2]. In [3], PLC is used to send the data from the photovoltaic plant through the AC power line. Ref. [4] employs a PLC-based system to avoid the islanding of the PV solar plant; in this work, the authors propose the control of the connection and disconnection devices. Ref. [5] employs a PLC-based communication and control system to control cascade inverters.

Most of the literature regarding PLC over the DC power lines within a photovoltaic (PV) plant makes use of circuitry and several components designed initially for the standard

**Citation:** Morales-Aragonés, J.I.; Williams, M.S.M.; Gómez, V.A.; Gallardo-Saavedra, S.; Redondo-Plaza, A.; Fernández-Martínez, D.; Sánchez-Pacheco, F.J.; Cuadro, J.G.F.; Hernández-Callejo, L. A Resonant Ring Topology Approach to Power Line Communication Systems within Photovoltaic Plants. *Appl. Sci.* **2022**, *12*, 7973. https://doi.org/10.3390/

Academic Editor: Gaetano Zizzo

Received: 18 July 2022 Accepted: 8 August 2022 Published: 9 August 2022

app12167973

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physical support of traditional PLC systems [6,7], namely power wires with two conductors that run parallel to each other. Transmission in these kinds of lines is performed by means of TEM or quasi-TEM modes, and the traditional transmission lines theory is applicable, with of course some limitations, such as the nonuniformity of the distributed parameters. Ref. [8] presents an intelligent PV module monitoring scheme based on a parallel resonant coupling unit, which uses the DC bus as the communication channel and modulates the monitoring data into a 200 KHz carrier for communication. However, the topology of the power cables in each string of PV plants is essentially different since there is a single cable connecting the PV modules in series that runs away from other sections of the line, at least in parts of it. This part of the power line can be modelled as a single cable line, where the propagation mode cannot be TEM and where the classic transmission line theory is not applicable. This difference suggests that the optimal electronics, carrier frequencies and general strategy could be different than the ones intended for traditional PLC systems.

This single-wire topology is imposed by the inherent characteristics of the power wiring within each PV string. As such, in this work, we propose an adapted strategy with electronics for implementing PLC communications over this cabling topology of a single PV string, where we start considering this essential difference from classic PLC standards, since the two-wire physical support common for classic PLC applications is absent in this configuration.

One of the first studies focused within the area of single-cable transmission was performed by G. Goubau [9] in 1950, based on a previous study of A. Sommerfeld from 1899 [10]. These studies showed the possibility of radiofrequency propagation via a surface wave guided by a single conductor, in conjunction with the formulation of a TM propagation mode for the signal. By 2008, Corridor Systems, Inc. (Santa Rosa, United States)registered a patent application [11] for a single-cable transmission line proposed for carrier frequencies from 50 MHz to 20 GHz. Later studies have been published adding updated formulations of the single-cable transmission phenomena [12] and complementing the theory with the calculation of ohmic currents' distributions, losses and characteristic impedance or even creating a classic two-wire-line equivalent model for the single-cable propagation [13]. One of the most interesting conclusions of these works is the possibility of a very-low-loss propagation over a single cable. Therefore, this study evaluates the performance and accompanying possible benefit of the propagation mode of the PV plant single-cable segment and the need for compensatory electronics to sustain the innate benefits of the behaviour of the mode in the event where the cable is altered.

Our proposal for the PV string PLC communications system is to close the single-cable signal path by means of a capacitor connected between the combiner box terminals, in such a way that the line becomes a ring-shaped path for the communications signal, susceptible to being pushed to a loop-antenna-like resonance, improving the signal levels along the line. This work is structured as follows: Section 2 shows the theoretical frame and materials, Section 3 presents the results and Section 4 shows the conclusions and future work.

#### **2. Theoretical Frame and Materials**

This section presents the theoretical framework on which the presented work is based as well as the materials used in it.

#### *2.1. Theoretical Frame*

The previous documents mentioned regarding single-cable transmission in Section 1 considered frequencies of transmission above 50 MHz (higher than the ones we worked with in this first demonstration stage for our PV–PLC system), whose current distribution is expected to be flowing superficially or in a thin layer close to the surface of the cable (skin effect), with propagation described to be carried out by a surface wave whose phase velocity is c (the speed of light). Our direct measurements of the phase velocity over a line of single PV cable at a frequency of 20 MHz showed speeds around 0.6 c, closer to what is observed in typical coaxial cables [14], even when the propagation mode is different in our single-cable medium (TM) than the one in coaxial cables (TEM). The lower frequency used in our single-cable support suggests that the current distribution flows in a thicker layer inside the conductor, and the influence of the material lowers the phase velocity with respect to the previously mentioned Sommerfeld surface wave. As a result, the single-cable analogy applied to the PV plant cable cannot allow us to assume the same propagation mode described in Section 1, and since our aim with this document is not to establish a theoretical background but to develop a practical approach for implementing a working PLC system specific for PV plants, we assumed the measured phase velocity of 0.6 c and tried to start from a simple model to characterize our system.

The influence of the topology of the physical wiring in the previous literature on PLC systems for PV strings is not usually discussed, probably because the low-frequency carriers proposed do not show limitations related to higher frequencies, such as interferences or resonance issues. Some previous works use an open line topology [7,15,16] and some others propose a current loop topology [17]. The frequencies are normally in the order of 100 kHz or less, that is to say, considering the assumed phase velocity (0.6 c) wavelengths are around 1800 m, much bigger than the usual length of the string. With this work, we try to explore the possibility of setting the carriers of higher frequencies (from 1 MHz on), analysing the effects of the increased frequency and offering a practical solution, which inevitably leads to considering the physical topology of the wiring.

In a single PV string, the power wires starting from a combiner box return to the same box after connecting the modules in series. In essence, it is easy to establish a circular communications path by means of a capacitor connected between the two cables arriving at the combiner box and to bypass capacitors connected through each PV module. This allows for a cable loop configuration to be a communications physical support for a single string. The choice of a closed-loop configuration for the signal path has several advantages for communications purposes. This topology sets all the points along the circular line at the same level regarding attenuation, so differences in reception levels are reduced to a minimum and it allows for a resonance condition to be established for the signal along the loop, since there is a natural reactive impedance associated with a cable loop depending on the relationship between the wavelength and the physical length of the loop, which can be compensated for by some added lumped reactive impedance, leaving only a low-resistance path for the signal.

Adding the ring topology proposed to the aforementioned assumption about phase velocity = 0.6 c, a simple propagation model can be considered. Our starting point is the schematic in Figure 1.

**Figure 1.** Schematic of the communications loop (signal path) excited by a current generator (I), with a perimeter d.

The cable ring of perimeter d represents a simplified sketch of the signal path, including the PV cable line and bypass capacitors (with enough capacitance for presenting a very low impedance at our working frequency), where the I/O impedance of the transceivers located along the ring is neglected for a first approximation. It is excited by a current generator (which in practice could be the secondary binding of a transformer). A general expression of the current wave along this loop is:

$$I(\mathbf{x}) = I\left(A\,\boldsymbol{\varepsilon}^{-jk\mathbf{x}} + B\,\boldsymbol{\varepsilon}^{jk\mathbf{x}}\right) \tag{1}$$

Representing the sum of two waves moving in opposite directions along the ring, where I is the current amplitude with its time dependency:

$$I = I\_0 \ e^{-jwt} \tag{2}$$

Here, x is a coordinate indicating the distance along the loop measured clockwise from the generator position and k is the wavevector depending on the frequency (f) and phase velocity (0.6 c) and A and B are constants (which could be complex) to be determined.

The boundary conditions imposed are related to the continuity of the current at the generator thus:

$$I(0) = I\left(A + B\right) = I(d) = I\left(A \, e^{-jkd} + B \, e^{jkd}\right) = I\tag{3}$$

leading to

$$A + B = 1 \; ; \; A \; e^{-jkd} + B \; e^{jkd} = 1 \tag{4}$$

In general, the solutions of this system of equations lead to (complex) values of A and B different from zero and thus to a stationary wave pattern for the current distribution. These solutions are not desirable to implement a communications system because stationary waves give rise to maximum and minimum current amplitude points along the loop, which means different reception levels since a transceiver could be located at any point in the ring. For the case where

$$\mathbf{kd} = \pi (1 + 2\pi) \tag{5}$$

where n is an integer value, this system of equations is incompatible and there is no solution, representing a destructive interference between clockwise and anticlockwise waves. The optimal solutions for our purpose are those where A = 0 or B = 0, which leads to a travelling wave solution of the form:

$$I(\mathbf{x}) = I \ e^{-jkx} \text{ or } I(\mathbf{x}) = I \ e^{jkx} \tag{6}$$

not presenting maximum or minimum current amplitude points. To obtain these kinds of solutions, it is mandatory that:

$$kd = 2\text{ }\pi\text{ }n\text{ }\tag{7}$$

that is to say, the perimeter of the loop is an integer multiple of the wavelength.

However, even when the above condition is satisfied, there are stationary wave solutions (A and B = zero) satisfying only the extra condition A + B = 1. In order to determine the actual spatial current distribution over a typical PV cable loop, we built a setup comprising 20 m of cable from our real test PV plant (Figure 6, show later) and measured and assessed the string as one single conductor line travelling in a straight fashion from the positive lead of one signal generator to the end of the PV array arrangement where it then turned around, coming back as a loop at a distance of one metre apart from the initiated point at the positive lead, finishing in the negative lead of the signal generator. The topology of the circuit is thus a loop-like one, but the shape is elongated from a circular one. The generator was adjusted for a sinusoidal signal of 9.142 MHz (determined as the signal corresponding to a wavelength equal to the loop length, fulfilling the above condition) and

10 volts of amplitude. The validation of the system in short wire installations is interesting, since for longer installation lengths resonance can be achieved at the same frequency by means of higher-order modes, where more than one wavelength is present in the line. Essentially, if it works for our 20 m loop, it will work also in loops which are 40 m, 60 m, etc., and the fine adjusting for intermediate lengths can be easily achieved by the tuning circuit designed (see Section 2.2).

The current measurements were made in a low-invasive fashion at different points along the loop, sensing the AC magnetic field associated by means of a toroidal ferrite core surrounding the cable, with a 30-turn enamelled cable wiring. This way, an induced AC voltage proportional to the AC current in the line can be measured with an oscilloscope across the terminals of the wiring. The high input impedance of the oscilloscope guarantees that a very low current will flow through the wiring, so a negligible inductance was added to the loop during measurements. Figure 2 shows the results of these measurements taken every metre along the loop, and it shows a clear stationary wave pattern. These results agree with the literature about the current distribution on loop antennas, the theory of which is close to the one here considered.

**Figure 2.** Current amplitude distribution along the loop (normalised (%); measurement points and fitting to a stationary wave envelope function).

The difference between the maximum (100%) and minimum (21%) current amplitude levels from the measurements represents 13.55 dB, which can be managed easily by an automatic gain control (AGC) within receptors. There are two possibilities for fully exploiting the advantages of a resonant loop for communications avoiding significant differences in the signal levels along the loop: (I) Find a simple way to excite only the travelling wave mode over a one-wavelength ring (optimal). (II) Work at carrier frequencies low enough in a fashion that the loop length is a fraction of 1 ⁄4 of the wavelength or less. This is the slower option, but it still leads to carrier frequencies over 2 MHz (assuming a propagation speed of 0.6 c and a loop length of 20 m), significantly higher than the average previously reported.

Regarding solution I, some authors have faced the theory of travelling wave solutions for loop antennas [18], compared with standing wave solutions [19], and even have determined the necessary conditions for exciting the travelling wave modes [11]. All this work, however, is focused on antenna design and consequently looks for the best radiation properties. For our application, radiation losses are not desired, since they mean power losses and could affect the electromagnetic compatibility of the system. Fortunately, the drastic reduction in the loop area due to the particular shape of our setup will prevent the system from great radiation losses, since radiation integrals obtain contributions of opposite current elements much closer to each other [20]. The travelling wave or quasitravelling

wave mode of propagation for our system could be achieved by fulfilling some of the conditions exposed in [18,21].

However, these conditions are not easily applicable in a practical environment, so the insertion in series of a nonreciprocal device is proposed. These kinds of devices will attenuate the waves travelling in one direction, leaving unaffected ones travelling in the opposite direction, leading to a travelling wave propagation mode. Some of the possible practical devices that could accomplish this task are magnetic-circulator-based isolators or unity gain amplifiers referenced to Earth in such a way that waves arriving towards the output will find very low impedances to Earth, being attenuated, but the ones arriving towards the input will find very high impedances and will progress to the output almost unaffected. In this work, we focus on resonance control, and isolator insertion is left for future research.

Regarding solution II, if we work at wavelengths four times the length of the loop or bigger, the phase changes along the loop in *π*/4 radians maximum. For a loop length of 1 ⁄4 wavelength, the general solution for its current wave is:

$$A = \frac{1+f}{2} \; , \; B = \frac{1-f}{2} \; , \; I(\mathbf{x}) = I \left( A e^{-j\mathbf{k}\mathbf{x}} + B e^{j\mathbf{k}\mathbf{x}} \right) \tag{8}$$

where kx goes from 0 to *π*/2 along the loop length, so the maximum change in the current wave amplitude is:

$$\frac{I\_{\text{max}}}{I\_{\text{min}}} = \sqrt{2} \text{ , } \frac{I\_{\text{max}}}{I\_{\text{min}}} = 1.5 \text{ dB} \tag{9}$$

This value is small enough to avoid AGC systems in receptors and simplifies the electronics, allowing carrier frequencies over 2 MHz as explained before. This carrier (depending on the modulation system) can lead to baud rates around 200 kbps, which are higher than the previous baud rates reported in the literature for PLC within PV plants, so even when this mode of propagation represents the lower baud rate for our model, it still supposedly should provide an improvement on the speeds previously reported.

In addition, the resonance condition can still be achieved for this case because even when the impedance variations related to auto interference are almost not present, there is an inductance associated with the line and reactive impedances representing the transceivers (capacitive or inductive depending on the coupling chosen) that must be compensated for with a lumped element in order to push the loop to resonance. For the higher-frequency (lower-wavelength) option, as a starting point, we can consider a model of signal propagation along a closed loop similar to the ones previously mentioned regarding loop antennas, which show series resonances (impedance close to zero) at frequencies whose wavelengths are integer fractions of the loop lengths [20]. In this way, a constructive interference gives rise to a spatial resonance, and a maximum in the signal amplitude is observed. Since one key goal of a communications system is the integrity of the signal, we must satisfy the above condition in our cable loop in order to work at an optimal point with the best SNR possible.

For a chosen carrier frequency, a loop length is fixed to fulfil the above condition; however, the length of the loop is an imposed parameter depending on the physical dimensions of the installation, and therefore it is necessary to find a way to adjust the natural loop resonance to match the frequency of the carrier. The insertion of a coil in series with the cable loop has the effect of increasing the electrical length seen by the signal (length expressed as a wavelength multiple), that is to say, the loop will resonate at lower frequencies. The opposite of this behaviour is seen with the insertion of a capacitor. As such, the insertion of a reactive component in series with the loop could be used to perform the matching between the carrier and loop resonance frequencies. This effect is shown in Figure 3 from our measurements over a typical PV string cable loop 20 m long with a vector network analyser (VNA) connected to the loop, where the resonance condition is recognized by the minimum in the modulus of the S11 scattering parameter (maximum power sent to the loop) and a sudden change in its phase. Figure 3 shows curves around

the first resonance frequency (9.192 MHz without compensation) corresponding to the connection in series of a coil, three values of capacitors and the raw cable.

**Figure 3.** The shift of the loop resonance frequency with the addition of a reactance in series: the modulus (**a**) and phase (**b**) of the scattering parameter-1 measured with a VNA connected to the raw cable loop and with the addition in series of a coil and three increasing values of capacitors.

These measurements have been used to determine more precisely the phase velocity in our PV cable. Since the first cable resonance (9.192 MHz) corresponds to one wavelength in the 20 m long cable:

$$
\lambda = \frac{V\_f}{f} \Rightarrow V\_f = 20 \text{m} \\
\text{x} f = 20 \ast 9192000 = 0.613c \tag{10}
$$

#### *2.2. Materials*

Even though a preinstallation length compensation is feasible (installing a fixed reactive series component), employing automatic adjustable tuning would more so be convenient in confining the transmission around an optimal point, in order to account for the inevitable occurrence of small variations in the loop (for example, the addition of one more PV module to a string, which would increase the loop physical length). For this purpose, a simple tuning circuit was designed which was able to show either capacitive or inductive impedance by means of a control voltage. The basic variable component used was a varicap diode whose capacity could be adjusted depending on the inverse voltage applied. The circuit is shown in Figure 4a, and it is composed of a toroidal transformer with the primary (L2) connected to the cable loop and the secondary (L1) connected to the variable capacitor (C) (voltage controlled). The actual implementation circuit for the voltage-controlled capacitor is shown in Figure 4b.

**Figure 4.** Schematic of tuning circuit in (**a**) its generic representation and (**b**) actual implementation, and (**c**) schematic of voltage doubler detection circuit.

The network analysis of the circuit in Figure 4a leads to an impedance seen from the primary port:

$$Z = jwL\_2(1 - w2\,L\_1\mathbb{C}\,\left(1 - K2\right)) \div \left(1 - w2L\_1\mathbb{C}\right) \tag{11}$$

where the mutual inductance coefficient in the transformer is expressed by:

$$M = K\sqrt{L\_1 L\_2} \tag{12}$$

and *K* is the coupling coefficient, showing a parallel resonance at

$$w\_1 = 1 \div \sqrt{L\_1 C} \tag{13}$$

and a series resonance at

$$w\_2 = w\_1 \div \sqrt{1 - K2} \tag{14}$$

This impedance has two inductive regions, (*w* < *w*1) and (*w* > *w*2), and one capacitive region: (*w*1 < *w* < *w*2). In the centre of the capacitive region with a good coupling in the transformer (1 − *K*2 << 1), we have (1 >> *w*2 *L*1*C* (1 − *K*2) and (1 << *w*2*L*1*C*), so

$$Z \approx 1 \div \left( jw \mathbf{C} \frac{L\_1}{L\_2} \right) \tag{15}$$

and our circuit works as a capacitor multiplier by the factor *L*1 *L*2 , which can be very useful for loops requiring high-capacitive compensation with values higher than the maximum achieved by the varicap diode, for example, for loops with high inductance in series (the inductive coupling of the transceivers).

For loops with low series inductance (the capacitive coupling of transceivers), the usual length of a typical PV string and carrier frequencies over 5 MHz, our circuit is better used in the region around the higher frequency of resonance *w*2, where the impedance is close to zero, and for frequencies lower than *w*2 the impedance is capacitive, and for frequencies higher than *w*2 the impedance is inductive. Around this region and (1 *w*2*L*1*C*), the impedance can be expressed as:

$$Z = jwL\_2(1 - K2) - jL\_2 \div (wL\_1C) \tag{16}$$

equivalent to a series LC circuit with

$$L\_{equ} = L\_2(1 - \text{K2})\tag{17}$$

and

$$\mathbb{C}\_{equ} = \frac{L\_1}{L\_2}\mathbb{C} \tag{18}$$

resonant at *w*2. Since the capacitor *C* can be dynamically adjusted, connecting this circuit in series with the cable loop, we can add series inductance, capacitance or none of them depending on what is required by the loop, and the dynamic adjusting range can be selected with the value of *L*2 since it is a common factor in the expression of Z around *w*2. The possibility of the capacitance control varying a biasing inverse voltage on the varicap diode allows us to implement a microcontroller-based tuning system that will also require some kind of detection of the resonance condition in the loop.

The carrier amplitude through the primary coil in the circuit in Figure 4a will show a maximum if the loop is pushed to resonance, so if this signal is used as an input for a voltage doubler detection circuit (Figure 4c), we will obtain at the output a DC voltage proportional to the amplitude of the carrier in the loop and the resonance can be detected as a maximum in the DC voltage output. Finally, automatic resonance adjusting can be implemented by sampling the detector DC output with an analogue-to-digital converter (ADC) integrated in the microcontroller (MCU), where the convenient firmware will search for a maximum outputting a DC voltage sweep towards the tuning circuit.

Figure 5 shows the real implementation of the circuits proposed, with all the components labelled. Figure 5a shows the front side of the board and Figure 5b shows the back side.

**Figure 5.** Picture of the electronics developed for loop automatic tuning: (**a**) front side; (**b**) back side.

The PV plant used is shown in Figure 6. This plant is located on the facilities of the Duques de Soria campus of the University of Valladolid. The campus is in the city of Soria, Spain. The modules used in this article for the communication line are those on the upper row. Each module has the characteristics shown in Table 1.

**Figure 6.** PV plant on Duques de Soria campus of the University of Valladolid.

**Table 1.** Technical characteristics of the PV module.