1 Introduction

Diplexers are important blocks in microwave circuits and communication devices [1,2,3,4,5,6,7,8] like; GSM [9], GPS and WLAN [10, 11], antenna [12], radars [13], multiple-frequency devices [14], Diplexers consist of three-ports, which separates input signals into two different pathways. The usual method to design and construct of diplexers is connecting filters together. Also hairpin resonators [15], ring resonators [16] coupled step Impedance [17], bended lines [18], Folded step resonators [19], Dual mode substrate resonators [20] and slotline step Impedance [21] have been recently used to design diplexers.

The recently designed diplexers have several disadvantages. For instance, in [22], a diplexer is reported by using the packaging technique and metal cavities in the triple mode for LTE application, which can operate at two different frequencies but has a complex structure. In [23], by using coupled lines and coupled resonators, a low pass-band pass diplexer is reported but using coupled lines caused decrement in the Q factor of the diplexer. In [24], an electromagnetic waveguide filter with a rectangular ring is reported to design a diplexer but the diplexer has inappropriate insertion loss in lower and upper passbands. In [25], a bandstop–bandstop low loss diplexer using a stepped-impedance resonator and inter-digital capacitor for mobile communication is reported, which has not excellent characteristics. In [26], a diplexer using the defected ground structure and T-shaped resonator is reported, but the insertion loss parameter is not acceptable. In [27], a tunable dual bandpass-bandpass diplexer is reported that is designed in C band frequency for satellite communication system but the dimensions and insertion loss of the diplexer are inappropriate.

Power amplifiers (PAs) are devices that increase the input signal power to drive loads directly as a final block in the amplifier chain [28,29,30,31,32,33]. The hybrid power amplifier (HPA) is the combination of two PAs in parallel, series, and envelope configuration that enabling them to be employed in new applications [34]. The major problem in the power amplifier design is harmonic conflict in class F and F−1 concurrently.

In this work, for the first time two diplexers are designed based on connecting filters together and using L, T and rectangular-shaped resonators, which are applied to design a novel HPA to solve the harmonic conflict in class F and F−1 concurrently. The proposed diplexers simulation and measured results are in good agreement together.

2 Method

To design the HPA, which can operate in class F and F−1 at two different frequencies concurrently, one method is to use a resonant circuit at the beginning of each path. In this case, each path is active at one frequency and the main problem is that the resonant circuit branches cannot provide perfect dividing and coupling of signals between two paths. Band-pass filters can be used instead of the resonant circuits. Using band-pass filters is more effective than the resonant circuit technique, but this method cannot solve the prefect dividing of signals, to solve this problem and matching at the point where the paths end, a circuit was applied after the output matching networks (OMN)to eliminate the harmonic conflict, as shown in Fig. 1.

Fig. 1
figure 1

Proposed HPA structure with filters

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A diplexer can be used instead of two band-pass filters, which creates better isolation between the stages. So, a diplexer is placed at the beginning and at the end of the output matching network (OMN) to achieve an HPA structure, which can operate in two different classes and at two frequencies, as shown in Fig. 2.

Fig. 2
figure 2

HPA proposed structure with diplexers

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3 Design procedure of the diplexers

The frequency of the proposed HPA structure is considered as 1.5 GHz and 2.1 GHz to operate in class F and F−1, respectively. Therefore, in the OMN, the dividing diplexer and the coupling diplexer should both operate at both 1.5 GHz and 2.1 GHz frequencies. The final proposed OMN structure is shown in Fig. 3. Based on this plan, the design procedure of the two diplexers will be discussed in the next sub-sections. Given that the types of diplexers are the same in the proposed design, both diplexers can be placed the same in Fig. 3, but to describe the design procedures, two design examples are presented named diplexer1 and diplexer2.

Fig. 3
figure 3

Final output matching network structure of HPA

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3.1 Design of Filter1 in the Diplexer1

The proposed filter1 is depicted in Fig. 4(a). To design filter1, two rectangular-shaped resonators are used to create the main resonator, then T and L-shaped resonators are used. Also, the equivalent circuit and the transfer function are extracted to compute transmission zeros of the designed filter1 [35]. By using the transfer function, pass band and stopband frequencies can be located. The LC circuit of the designed filter1 is shown in Fig. 4(b). The frequency response for the filter1 and the LC circuit response are compared in Fig. 4(c).

Fig. 4
figure 4

The filter1 (a) structure (b), the LC circuit and (c) frequency responses comparison between EM simulation and LC circuit

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The calculated values of the parameters in the filter1 LC circuit (Fig. 4(b)) are summarized in Table 1.

Table 1 The calculated parameter values of the LC circuit for filter1
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The LC circuit is extracted by using Eqs. 1 and 2. To control transmission zero points, the transfer function is suggested. The transfer function of the designed filter1 is written in Eq. 3 based on [35]. In Eqs. (3, 4, 5, and 6), the value of R is assumed equal to 50 ohms.

$$L_{{\text{s}}} = \frac{1}{\omega } \times z_{{\text{s}}} \times \sin \left( {\frac{2\pi }{{\lambda_{{\text{g}}} }}l_{{\text{s}}} } \right)$$
(1)
$$C_{{\text{s}}} = \frac{1}{\omega } \times \frac{1}{{z_{{\text{s}}} }} \times \tan \left( {\frac{\pi }{{\lambda_{{\text{g}}} }}l_{{\text{s}}} } \right)$$
(2)
$$TF = R + \frac{1}{{c10s + \frac{1}{{\frac{1}{c9s} + L10s}} + \frac{1}{{L9s + \frac{1}{{c8s + \frac{1}{{\frac{1}{{\left( {\frac{c6}{{1 + c6L7s^{2} }} + c7} \right)s}} + L8s}} + \frac{1}{{L6s + \frac{1}{{c5s + \frac{1}{{L5s + \frac{1}{{\frac{1}{{s\left( {c4 + \frac{c3}{{1 + c3L3s^{2} }}} \right)}} + \frac{1}{{L2s + \frac{1}{{\frac{1}{R} + c1s + \frac{1}{{\frac{1}{c2s} + L1s}}}}}}}}}}}}}}}}}}}}$$
(3)

3.2 Design of filter2 in the diplexer1

The proposed filter2 is depicted in Fig. 5(a). The design procedure of filter2 is similar to filter1. In filter2 structure, two rectangular resonators are used. The LC circuit of the designed filter2 is extracted and shown in Fig. 5(b). The frequency response for the filter2 and the LC circuit are compared as shown in Fig. 5(c).

Fig. 5
figure 5

The filter2 (a) structure (b), the LC circuit and (c) frequency responses comparison between EM simulation and LC circuit

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The calculated values of the parameters in the filter2 LC circuit (Fig. 5(b)) are summarized in Table 2.

Table 2 The calculated parameter values of the LC circuit for filter2
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To control transmission zero points, the transfer function of filter2 is extracted, which is written in Eq. 4.

$$TF = R + L5s + \frac{1}{{c3s + \frac{1}{{L6s + \frac{1}{{c5s + \frac{c6}{{s + c6L7s}}}}}} + \frac{1}{{L4s + \frac{1}{{c4s + \frac{1}{{R + L1s + L2s + \frac{1}{{C1s + \frac{c2}{{s + c2L3s}}}}}}}}}}}}$$
(4)

3.3 Diplexer1 structure

The structure of diplexer1, which designed in Sects. 3.1 and 3.2, is depicted in Fig. 6(a). The diplexer1 frequency response is depicted in Fig. 6(b). The size of the diplexer1 is about 25 mm × 30 mm about (0.165λg × 0.198λg).

Fig. 6
figure 6

The a layout and b simulated frequency response of the diplexer1

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3.4 Design of filter3 in the diplexer2

The structure of the proposed filter3 is depicted in Fig. 7(a). For designing of filter3 high impedance transmission lines are used. The L-shaped resonator is used as the main resonator to obtain the desired bandpass frequency. Then, by adding two rectangular-shaped resonators and a short transmission line as a suppressor, wide stopband is obtained. The LC equivalent circuit of the designed filter3 is extracted, which is depicted in Fig. 7(b). The frequency response for the filter3 and the LC circuit response are compared in Fig. 7(c).

Fig. 7
figure 7

The filter3 a structure, b The LC circuit and c frequency responses comparison between EM simulation and LC circuit

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The calculated values of the parameters in the filter3 LC circuit (Fig. 7(b)) are summarized in Table 3.

Table 3 The calculated parameter values of the LC circuit for filter3
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To control transmission zero points, the transfer function is suggested. The transfer function of the designed filter3 is written in Eq. 5.

$$TF = R + L5s + \frac{{\left( {A + \frac{1}{c7s}} \right)\left( {\frac{1}{c9s} + L6s} \right)}}{{c8s\left( {\frac{1}{c8s} + \frac{1}{c9s} + L6s} \right)\left( {A + \frac{1}{c7s} + \frac{{\frac{1}{c9s} + L6s}}{{c8s\left( {\frac{1}{c8s} + \frac{1}{c9s} + L6s} \right)}}} \right)}}$$
(5)

where: Eq. 6

$$A = \frac{1}{c7s} + \frac{{L4s + \frac{{\left( {\frac{{\frac{2}{{c1s\left( {R_{1} + L_{1} s} \right)}} + \frac{1}{c2s}}}{{c3\left( {\frac{2}{{c1s(R_{1} + L_{1} s)}} + \frac{1}{c2s} + \frac{1}{c3s}} \right)s}} + L2s} \right)\left( {\frac{1}{c5s} + L3s} \right)}}{{c4s\left( {\frac{1}{c4s} + \frac{1}{c5s} + L3s} \right)\left( {\frac{{\frac{2}{{c1s\left( {R_{1} + L_{1} s} \right)}} + \frac{1}{c2s}}}{{c3\left( {\frac{2}{{c1s(R_{1} + L_{1} s)}} + \frac{1}{c2s} + \frac{1}{c3s}} \right)s}} + L2s + \frac{{\frac{1}{c5s} + L3s}}{{c4s\left( {\frac{1}{c4s} + \frac{1}{c5s} + L3s} \right)}}} \right)}}}}{{c6s\left( {\frac{1}{c6s} + L4s + \frac{{\left( {\frac{{\frac{2}{{c1s\left( {R_{1} + L_{1} s} \right)}} + \frac{1}{c2s}}}{{c3\left( {\frac{2}{{c1s(R_{1} + L_{1} s)}} + \frac{1}{c2s} + \frac{1}{c3s}} \right)s}} + L2s} \right)\left( {\frac{1}{c5s} + L3s} \right)}}{{c4s\left( {\frac{1}{c4s} + \frac{1}{c5s} + L3s} \right)\left( {\frac{{\frac{2}{{c1s(R_{1} + L_{1} s)}} + \frac{1}{c2s}}}{{c3\left( {\frac{2}{{c1s(R_{1} + L_{1} s)}} + \frac{1}{c2s} + \frac{1}{c3s}} \right)s}} + L2s + \frac{{\frac{1}{c5s} + L3s}}{{c4s\left( {\frac{1}{c4s} + \frac{1}{c5s} + L3s} \right)}}} \right)}}} \right)}}$$
(6)

3.5 Design of filter4 in the diplexer2

The structure of the proposed filter4 is depicted in Fig. 8(a). The design procedure of filter4 is similar to filter3.High impedance transmission lines are used in filter4 structure similar to filter3.TheLC circuit of the designed filter4 is illustrated in Fig. 8(b). The frequency response for the filter4 and the LC circuit response are compared in Fig. 8(c).

Fig. 8
figure 8

The filter4 a structure, b The LC circuit and c frequency responses comparison between EM Simulation and LC circuit

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The calculated values of the parameters in the filter4 LC circuit (Fig. 8(b)) are summarized in Table 4.

Table 4 The calculated parameter values of the LC circuit for filter4
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To control transmission zero points, the transfer function is suggested. The transfer function of the designed filter4 is written in Eq. 7.

$$TF = R + L5s + \frac{1}{{C8s + \frac{1}{{\frac{1}{C7s} + \frac{1}{{C6s + \frac{1}{{L4s + \frac{1}{{C9s + \frac{C5s}{{1 + C5L6s^{2} }} + \frac{1}{{L2s + \frac{1}{{c3s + \frac{1}{{\frac{1}{c2s} + \frac{1}{{c1s + \frac{1}{R + L1s} + \frac{c4}{{s + c4L3s}}}}}}}}}}}}}}}}}}}}$$
(7)

3.6 Diplexer2 structure

The structure of diplexer2, which designed in Sects. 3.4 and 3.5, is depicted in Fig. 9(a), while its frequency response is depicted in Fig. 9(b). The size of diplexer2 is about 114.9 mm × 11.6 mm (0.75λg × 0.07λg).

Fig. 9
figure 9

The a layout and b simulated frequency response of the diplexer2

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4 Measurement results of the fabricated diplexer

To verify the simulated result, the diplexer2 is fabricated. The fabricated image of the diplexer2 is shown in Fig. 10. The RT/duroid 5880 substrates with a relative dielectric constant of 2.2 thickness of 31mil, and loss tangent of 0.0009 were applied for the designed diplexers.

Fig. 10
figure 10

The fabricated image of the proposed diplexer2

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The frequency response comparison between EM simulation and experimental measurements for the diplexer2 is shown in Fig. 11(a) and (b). In the first (1.5 GHz) and second (2.1 GHz) frequency channels, measured insertion losses are about 0.3 dB and 0.7 dB, respectively, while the measured return losses are 32.4 dB and 17.4 dB, respectively. The isolation of the proposed diplexer is depicted in Fig. 11(b). The obtained isolation is better than 21 dB in the entire bandwidth, while the measured isolations are 27 dB and 30 dB at the main frequencies. Table 5 shows the comparison between performances of the designed diplexers and other diplexers. According to the table, the insertion loss, return loss and isolation of the proposed diplexer is better than other works while the size of the proposed diplexer is acceptable.

Fig. 11
figure 11

The experimental and simulated results of the proposed diplexer2 a S11 and S21 parameters, b S23 and S31parameters

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Table 5 Comparison between performances of the designed diplexers and other diplexers
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5 Design of hybrid power amplifier

A novel HPA is designed in this section, according to presented hybrid power amplifier idea and the proposed diplexers. The structure of the proposed HPA created by using the designed diplexers is illustrated in Fig. 12. The output structure of the amplifier contains the designed diplexers 1 and 2 to provide two paths in different frequencies. The designed HPA operates at 1.5 GHz in class F mode and operates at 2.1 GHz in class F −1 mode. A low voltage transistor pHEMT ATF-34143 is used in the proposed HPA as a switch. The designed HPA is simulated with the advanced design system (ADS) simulator, based on the RT/Duroid 5880 substrate with 2.2 dielectric constant, 0.0009 loss tangent, and thickness of 31mil. The transmission lines and output matching networks are designed to form class F and class F−1 in the desired operating frequencies. Table 6, shows the dimensions of the applied microstrip transmission lines in the proposed HPA.

Fig. 12
figure 12

The structure of the proposed HPA using designed diplexers

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Table 6 Dimensions of the applied transmission lines in proposed HPA
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The simulated drain efficiency (DE), power added efficiency (PAE), and gain parameters of the proposed HPA versus input power at operating frequencies of 1.5 GHz are illustrated in Fig. 13. According to the results, the maximum values for DE, PAE and gain at 1.5 GHz are 60%, 53% and 17.4 dB. Also, the simulated DE, PAE and gain parameters of the designed HPA versus input power at operating frequencies of 2.1 GHz are shown in Fig. 14. As can be seen in the results, the maximum values for DE, PAE and gain at 2.1 GHz are 65%, 51.5% and 12.5 dB. However, according to the data sheet of the applied transistor the higher values of input power are not considered in the results of the proposed HPA.

Fig. 13
figure 13

The simulated results of a DE, b PAE, and c gain parameters for the proposed HPA versus input power at 1.5 GHz

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Fig. 14
figure 14

The simulated results of a DE, b PAE, and c gain parameters for the proposed HPA versus input power at 2.1 GHz

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The obtained results of the proposed HPA by using the designed diplexers are compared with other similar approaches in Table 7. As can be seen from Table 7, the proposed HPA has achieved desirable efficiency with pHEMT ATF34143 transistor. The proposed HPA along with the designed diplexers have resulted in the class and frequency selectivity, which are desirable abilities in the modern microwave and communications systems.

Table 7 Comparison between designed HPA and similar works
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6 Conclusion

In this paper, two diplexers are designed, which are used in novel hybrid power amplifier (HPA). By using the proposed diplexers, two separate paths can be provided for the HPA to operate at two desired classes of operation in arbitrary frequencies. The proposed diplexers are designed using rectangular, L and T shaped resonators. The equivalent circuits and transfer functions are extracted to control transmission zero points for the proposed diplexer blocks. The designed HPA and diplexers can operate at two desired frequencies of 1.5 GHz and 2.1 GHz, with good specifications. The obtained measured and simulated results show that the designed diplexers and HPA have excellent specifications.