Design of a Microwave Quadrature Hybrid Coupler with Harmonic Suppression Using Artificial Neural Networks

In this paper


Introduction
Lowpass flters (LPFs) are devices that permit low-frequency signals to pass while reducing the strength of high-frequency signals.Te LPFs are commonly used in microwave and communication systems for the applications, in which the desired low frequency signal should be separated from higher frequencies signals [1].Several types of flters have been used in microwave circuits, such as active [2] and passive LPFs [3,4].
On the other hand, couplers are devices that are used to distribute power between diferent transmission lines or components in communication systems and microwave applications [5].Te couplers enable splitting or combining signals, while maintain the desired properties such as impedance matching, isolation, and power division [6][7][8].Tere are several types of couplers, which are widely used in microwave and communication systems, such as QHCs [9] and rat-race couplers [10].A QHC is also known as a branch line coupler (BLC).In this type of coupler, the input signal is split into two output signals, while maintaining a phase diference of 90 degrees between the outputs.A QHC consists of four λ/4 transmission lines arranged in a rectangular shape [11].
Recently, there are several approaches that have been used to provide harmonic suppression and rejection band in microwave devices, such as couplers and power dividers.In [12], an electromagnetic bandgap (EBG) technique is used to design a U-shaped microstrip LPF.Circular EBG structure is exploited in this work to fatten the pass band and widen the rejection band.Also, defected ground structure (DGS) is another technique, which have been applied on the ground plane of the flters to improve the device performance [13][14][15][16].In [16], interdigital DGS structures are incorporated to design LPF with 3 GHz cut of frequency, which can provide two transmission zeros for rejection band.DGS structure, meandered lines, and squared resonators are applied in [15] to design a flter with frequency of 2.4 GHz, which can provide fve poles; however, the suppression band has not high level of attenuation and the pass band is not fat.Te efects of DGS structures on performance of LPFs are investigated in [14], where the results of this work showed that the length of three-pole flter with DGS structure is reduced 67%, compared to the conventional three-pole device.Moreover, a flter with squared DGS structures is presented in [13] in order to obtained high rejection stopband in the frequency response, which shows 30 dB attenuation level in the suppression band.Hairpin resonators with coupler lines are incorporated in [17] to design an LPF at 2.5 GHz, in which the insertion loss of 20 dB is obtained.
Te similar techniques have been considered in the couplers to achieve higher performance in the terms of harmonic suppression and wide rejection band.Te EBG and DGS techniques are also used to design couplers and power dividers [18,19].Te EBG squared units are presented in [18] to design a wide band QHC operating at mm wave applications.Wide isolation and matching band is obtained in [18] with the presented unit cells.A planar coupler is presented in [20] using E-shape impedance transformer for dual-band functionality.Dual-band operation is achieved in this device using closed-form design equations based on ABCD matrices [20].In [21], the folded transmission lines and coupled lines are incorporated to design a dual-band QHC with compact structure.Tis coupler operates at 1 GHz and 2 GHz and features compact size, compared to the conventional coupler [21].Using open stubs [6,22] and diferent shaped resonators [7] are also common techniques for obtaining rejection band in the couplers and power dividers.Each open stub can provide a transmission zero, which its frequency is dependent on its length [23].In [24], four open stubs are used in middle of the QHC main branches to obtain rejection band for the designed device, which operates at 0.9 and 2 GHz frequencies.Also, optical couplers have been presented [25] for higher frequencies using crystal photonic structures [26][27][28].
Te presented BLC in [29] integrates open stubs and resonators to achieve enhanced performance, which can suppress unwanted harmonics.A dual-band BLC featuring a wide rejection band for harmonics is developed in [30], operating at 2.6 and 4 GHz.Tis design incorporates four low-pass flters and four open-ended stubs to enable dual frequencies and reject harmonics at higher frequencies.In [31], a technique is presented for swiftly redesigning miniaturized microstrip couplers to accommodate various operating conditions and dielectric substrate material properties.Tis dimension scaling method relies on preoptimized reference designs derived from an equivalent circuit model of the coupler.Tis approach facilitates scaling across a broad range of operating conditions and substrate parameters.A BLC characterized by compact dimensions and efective harmonic suppression achieved through nonperiodic reactively loaded artifcial lines is presented in [32].Tese lines incorporate step impedance shunt stubs (SISSs) as reactive loading elements, which introduce transmission zeros crucial for mitigating harmonic interference.Additionally, the reactive loading imparts a desirable slow wave efect to the artifcial lines, facilitating device miniaturization [32].
In addition, the applications of artifcial neural network (ANN) and artifcial intelligence (AI) models have become prevalent in solving engineering challenges [33][34][35][36].Machine learning and optimization strategies have introduced as potential techniques for dealing with several problems [37][38][39][40][41]. Trough the training of ANNs on data collected from complicated systems, the underlying behaviors can be captured, facilitating precise predictions and refned control over these systems [42][43][44].AI tools have been also widely used in designing of electronics and microwave devices, such as antennas, couplers, and power dividers [8,[45][46][47].
As mentioned, and explained in the literature, all of the previous approaches have used additional process, such as EBG and DGS structures or used extra resonators, which complicates the coupler structure.In this paper, simple elliptic LPFs are designed and optimized using neural networks.Ten, the proposed flters are used in the conventional QHC structure to improve the features of the device.According to the obtained results, the proposed approach has improved the obtained performance of the coupler signifcantly.

The Proposed LPF Design Steps
A rectangular-shaped and a radial-shaped resonator are used to design the proposed LPF.Also, neural network approach has been exploited to design the device with high performances.Te structure and frequency responses of diferent square shaped resonators are investigated, as shown in Figure 1.As result shown, the middle high-impedance line can be used to improve the resonator response and sharpen the transition band.As seen in Figure 1, three steps to create the basic LPF are shown.In Figure 1(a), simple high-low impedance resonators are used to shape a simple flter.In this structure, the length of the high-impedance line is too short.Te frequency response of this simple flter is depicted in Figure 1(b), which has a 3.3 GHz cut of frequency and provides a transmission zero at 6.7 GHz.In this structure, the length of the high-impedance line is too short, which this length is increased for the performance improvement, as shown Figure1(c).Te frequency response of this LPF is depicted in Figure 1(d), which has a 2.24 GHz cut of frequency and provides a transmission zero at 2.9 GHz.As result shown, this flter has better performance, compared 2 Active and Passive Electronic Components with the depicted structure in Figure 1(a).To further improvement, the length of this high-impedance line is increased again as depicted in Figure 1(e).Te bended lines are used to reduce circuit size, such that all these three structures occupied same size.Te frequency response of the proposed basic LPF with rectangular resonators is depicted in Figure 1(f ), which has 1.92 GHz cut of frequency and provides a transmission zero at 2.37 GHz, which has the best performance compared with other depicted flters.All simulations in this paper are executed using momentum and schematic environments of ADS (advanced design system) software.Te mentioned parameters of L1, L2, W1, W2, and D1 will be set as the neural network inputs, while the important parameters of elliptic LPF, which are cut-of frequency, fc (GHz), bandwidth, BW (GHz), suppression factor, SF (dB), and roll-of rate, Ro (ζ dB/GHz), will be assumed as the ANN model outputs.Te presented model incorporates a multi-layer feedforward ANN capable of forecasting the flter parameters by taking into account the input parameters.Tis presented model functions as a predictor tool for the presented elliptic flter.Figure 3 illustrates the architecture of the applied multi-layer perceptron (MLP) network, which is a feed forward ANN.As depicted in the fgure, the input nodes are connected to the outputs through two hidden layers, which each layer containing fve neurons.Sigmoid activation function (Tansig) is used in the hidden layers, while the linear activation function (Purelin) is used at the output of the presented model.

LPF Design Steps
In comparison with the traditional optimization methods, it should be noted that the ANNs do not require equations for modeling.In contrast, optimization methods rely on equations, and in complex structures, it may be challenging to extract all the necessary equations.Optimization methods often require a predefned mathematical model of the system, which may not accurately represent the real-world complexity of certain problems, while ANNs are data-driven models that adapt to the patterns present in the training data.Tey can handle situations where the underlying system is not well understood or described by a clear mathematical formulation.
In addition, many optimization techniques assume linear relationships between input parameters and output responses.In cases where the relationships are nonlinear, traditional methods may struggle to accurately model and optimize the system, while ANNs are appropriate for tasks where complex dependencies exist between input and output variable.Moreover, the complexity of the design problem with intricate relationships between input parameters and output performance metrics makes ANNs well-suited for capturing and optimizing these relationships.Additionally, the fexibility of ANNs in handling nonlinearities provides a valuable tool in scenarios where traditional optimization methods may fall short.
Te data used for training and testing procedures of the presented ANN model is listed in Table 1.As seen, the important parameters of L1, L2, W1, W2, and D1, which are depicted in Figure 2, are assumed as input parameters and impact of these parameters on the outputs parameters like cut of frequency, bandwidth, suppression factor level, and sharpness are investigated.Among the 33 samples of data set, frst 27 samples are selected for training procedure, the next 5 samples are selected for test procedure, and the last sample is considered as the verifcation sample.
In Figure 4, predicted and real values of the output parameters of cut-of frequency, fc (GHz), bandwidth, BW(GHz), suppression factor, SF(dB), and roll-of rate, Ro (ζ dB/GHz), are depicted.As can be concluded from this fgure, the important output parameters of the flter are predicted successfully and the predicted values are close to the real values.So, the proposed model can be used to design and optimize the proposed elliptic flter.In Figure 4, the performance of the proposed model can be analyzed.In regression plots, the relationship between the input variables and the predicted output values can be seen, in both training and testing procedures.Te obtained regression plots show that the model can efectively generalize to unseen data and make accurate predictions.In Figure 5, mean square error (MSE) of the fc (GHz), BW (GHz), SF(dB), and Ro (ζ dB/GHz) output parameters in train process of the presented model are shown.As seen, the MSE decreases as the proposed model iteratively adjusts its weights and biases to minimize prediction errors on the training data, which shows that the proposed model is converging towards optimal parameter values.Also, the rapid decrease in MSE plots of fc and Ro parameters shows efective learning in training process of these two parameters.2, which shows acceptable performance of the proposed model.As results show, the proposed model can predict the resonator performance, precisely.So, the best performance predicted by ANN can be used to design the resonator with optimized performances.According to the ANN model, best performance of the presented LPF is obtained for W1 � 4.4 mm, L1 � 3.6 mm, D1 � 6 mm, W2 � 0.2 mm and L2 � 7.4 mm.Tese circuit parameters extracted from the proposed ANN model, used to design the resonator with best performance.Te frequency response of the fnal proposed elliptic flter, with the obtained dimensions from ANN, are illustrated in Figure 6.As results shown the proposed device has cut-of frequency of 2.2 GHz, stop-band bandwidth of 10.24 GHz with more than 20 dB suppression level.Te proposed LPF provides very sharp response of 158.3 dB/GHz.
Te transition band sharpness which also called, roll-of rate, is written in equation (1) as follows: In equation ( 1), the minimum and maximum values of α represent 3 dB and 60 dB attenuation levels, respectively, with the corresponding frequencies of f c and f s .Te roll-of rate value is calculated as 158.3 dB/GHz with corresponding frequencies of f c and f s equal to 2.2 GHz to 2.56 GHz.
Moreover, suppression factor of an LPF, which is also known as stopband attenuation, refers to the level of attenuation that the low-pass flter applies to frequencies beyond its cutof frequency.Typically, the suppression factor is expressed in decibels (dB) and indicates the ratio of the strength of the unwanted signal (higher frequencies) to the strength of the desired signal (lower frequencies).A higher suppression factor means that the flter can attenuate the unwanted frequencies more efectively, resulting in better signal quality.
Figure 7 shows current distribution of the proposed elliptic LPF including a rectangular and a radial resonator.Te rectangular resonator exhibits concentrated currents along its edges, emphasizing the resonator role in confning and guiding the electrical energy through the flter.Te radial resonator demonstrates a more difuse and outwardly propagating current distribution, Te LC equivalent circuit and its S-parameters for the presented elliptic LPF is extracted as shown in Figure 8. Two transmission zeroes are provided near 3 GHz and 9 GHz, which have provided wide suppression band.Te values of l O1 and l O2 have the most efects on the 9 GHz and 3 GHz transmission zeros, respectively.
Te provided LC circuit is analyzed for better investigation of the flter behavior.As seen the value of seen impedance from two points are shown with Z A and Z B , which extracted in equations ( 2)-(4).
After calculating Z A and Z B , the transfer function of the elliptic flter can be achieved as written in equation.
After fnding the transfer function of the presented elliptic flter, the frequency representation of the transfer function can be drawn as shown in

The Proposed Coupler Design and Results
In this section it will be explained that how the designed elliptic flter is incorporated in the proposed QHC structure to improve the performance of the coupler and also to    Active and Passive Electronic Components provide the fltering response and harmonic suppression ability for the coupler.At the frst step the conventional QHC is briefy investigated as explained in the next subsection.

Conventional QHC Design.
A conventional QHC is a specifc type of microwave coupler that is commonly used in various applications.Te design of a coupler typically involves four microstrip or stripline branches, and the Sparameters for such a coupler should exhibit specifc characteristics to ensure its proper operation.Ideally, the S 11 , refection coefcient at port one, should be as close to zero as possible, indicating minimal signal refection at port one.Tis ensures that most of the input signal is efciently coupled into the output ports and that there is little energy refected back to the source.Also, theoretically, the S 21 , and S 31 , transmission coefcients from port 1 to port 2, and port 2 to port 3, should be as close to −3 dB (0.707) as possible.A value of −3 dB indicates that half of the input power is transferred to Port 2, while the other half continues to Port 3.Moreover, the S 41 , transmission coefcient from Port 1 to Port 4, typically represents the isolation between Port 1 and Port 4. Ideally, S 41 should be as close to zero as possible, indicating that there is minimal direct coupling between these ports.Te structure and simulated frequency response of a conventional QHC operating at the frequency of 1 GHz is illustrated in Figure 9. Te results show that the frequency response of the simulated conventional QHC is close to ideal one which verifes the design.

Proposed Coupler Design.
Te harmonics presence in the frequency response is a common problem in QHC devices.
Harmonics are unwanted signal components that occur at integer multiples of the main frequency.Te presence of harmonics in the frequency response can be result of nonlinearities in the circuit, and they can degrade the performance of the overall circuit in various ways.As mentioned in the proposed approach, elliptic flter is proposed to mitigate the undesirable issue of harmonics in the QHC by incorporating the flter into the coupler structure.By designing the elliptic flter to have a wide stopband that encompasses the harmonic frequencies of interest, it can efectively attenuate these harmonics.Tis approach reduces the harmonic content in the output signal of the QHC.Te basic circuit structure of the proposed QHC and its simulated frequency response is shown in       Active and Passive Electronic Components very close to ideal QHC results.Also there is a suppression band from 2.25 GHz up to more than 14 GHz, which can efectively provide a desirable harmonic suppression for the designed QHC.
After circuit simulation and obtaining the desired results, the layout of the proposed coupler is simulated, which the results are shown in Figure 11.Te obtained magnitudes of S 11 , S 21 , S 31 , and S 41 , are −26.1 dB, −3.06 dB, −3.07 dB, and −23.1 dB respectively, for the simulated layout of the proposed QHC.A suppression band of 2.25 GHz up 14 GHz is achieved according to the layout simulation results, which can efectively provide a desirable harmonic suppression for 3 rd to 14 th harmonics.
A fabricated prototype the proposed QHC and the measured frequency response are shown in Figure 12.Te device is simulated and fabricated with RTduroid 5880 substrate and ε r of 2.2 and the fabricated prototype is measured using 8720B network analyzer.Te simulated and measured frequency response of the presented coupler is compared in Figure 13.A good agreement can be seen between the experimental results and simulation data.Te obtained magnitudes of S 11 , S 21 , S 31 , and S 41 , are −21 dB, −3.4 dB, −3.3 dB, and −22.5 dB respectively, for the measured layout of the proposed QHC.Te bandwidth of the proposed BLC is 300 MHz, considering 10 dB attenuation for isolation and return loss.Tis bandwidth starts from 800 MHz up to 1100 MHz, which shows more than 31% of bandwidth.
Te performance results of the proposed coupler are compared with similar works and listed in Table 3. Te results show the superior performance of the proposed coupler.A wide suppression band from 2.2 GHz up to 14 GHz is obtained for the proposed QHC which can provide 3 rd and 14 th harmonic suppression.Also, the other       Active and Passive Electronic Components parameters of the designed coupler, such as isolation and return loss are desirable.

Conclusion
Tis paper presents a novel approach to address the problem of harmonic suppression in microwave coupler applications, particularly in QHCs.Te key contributions of this work include the incorporation of simple elliptic LPFs, a radial resonator, and a rectangular resonator into the QHC structure, as well as the utilization of neural networks for device design optimization.Previous approaches to harmonic suppression often involved complex structures, such as EBG and DGS confgurations, which could complicate the coupler design.However, this paper introduces an efective approach by integrating simple LPFs directly into the conventional coupler structure.Tis innovative strategy leads to a signifcant improvement in coupler performance, particularly in terms of harmonic suppression.Te flters are designed using both rectangular-shaped and radial-shaped resonators.Furthermore, neural networks are employed to optimize the LPF design, resulting in enhanced performance and sharper transition bands.Also, the proposed device structure is analyzed and the LC equivalent circuit and its transfer function is extracted.Te proposed flter has cut-of frequency of 2.2 GHz, stop-band bandwidth of 10.24 GHz with more than 20 dB suppression level.Te proposed LPF provides very sharp response of 158.3 dB/GHz.Te impedance analysis of the circuit further validates the simulation results.Te conventional QHC design is analyzed and compared with the results of the proposed device.Te results of the proposed coupler are desirable, which the simulated S-parameters are close to the desired ideal values.A wide suppression band from 2.25 GHz up to more than 14 GHz efectively addresses the issue of harmonics, providing desirable harmonic suppression for higher-order harmonics.Te results of the proposed QHC and its performances are compared with similar devices, which show desirable results of the proposed device.

Figure 1 :
Figure 1: Tree steps of creating the basic LPF.(a) Te initial structure of the basic LPF.(b) Te frequency response for the LPF in step 1, in which the basic LPF only consists of an open-stub and a high impedance line located in a T-shaped structure.Te structures and frequency responses for the designed basic LPF in step 2 and step 3 are shown in subfgures (c)-(f ).In steps 2 and 3, the middle high impedance line is bended, resulted in size reduction and also performance improvement of the LPF.

Figure 2 :Figure 3 :
Figure 2: Te basic structure of the proposed elliptic LPF incorporated with rectangular-shaped and radial-shaped resonators.

Figure 5 :
Figure 5: Mean square error (MSE) of the fc (GHz), BW (GHz), SF (dB), and Ro (ζ dB/GHz) output parameters in train process of the presented ANN model.

Figure 8 (
Figure 8(c).As shown, the frequency response of the transfer function, obtained from analyses, verifes the simulation results.

Figure 6 :
Figure 6: Te frequency response of the fnal proposed elliptic LPF incorporated with radial-shaped and rectangular-shaped resonators.

Figure 7 :
Figure 7: Te (a) 3D structure and (b) current distribution of the proposed elliptic LPF.In the rectangular resonator, the current distribution occurs along the edges of the patch.Also, in the circular resonators, the current distribution is concentrated around the perimeter of the circular structure.Te high impedance line ensures that the signal paths remain separate, allowing the LPF to efectively flter out highfrequency components, while allowing low-frequency signals to pass through from input to output.

Figure 8 :
Figure 8: Te (a) LC equivalent circuit of the designed elliptic LPF.(b) Te S-parameters for the presented elliptic LPF, which is obtained by simulation of the LC equivalent circuit.(c) Te frequency response of the presented elliptic flter, extracted from analyses, according to equation (5).

Figure 10 :
Figure 10: Te basic (a) circuit structure of the proposed QHC and (b) its simulated frequency response.

Figure 9 :
Figure 9: Te (a) structure and (b) simulated frequency response of a conventional QHC operating at the frequency of 1 GHz.

Figure 11 :
Figure 11: Te (a) layout structure of the proposed QHC and (b) its simulated frequency response.

Figure 12 :
Figure 12: Te (a) fabricated prototype the proposed QHC and (b) the measured frequency response.

Figure 13 :
Figure 13: Te simulated and measured frequency response of the proposed coupler.

Table 1 :
Data used for training and testing procedures of the presented ANN model.

Table 2 :
Te calculated errors of the presented ANN model.

Table 3 :
Performance summary of the presented coupler and similar works.