Design of a ring-resonant filtering network for PAs

The traditional ring-resonant structure, as shown in Fig. 1(a), is composed of two microstrip lines with lengths θ ₁ and θ ₂, with their transmission zeros (TZs) appearing at ${\theta _1} + {\theta _2}\, = \,2{{n\pi }}$ or ${\theta _1} - {\theta _2}\, = \,{{\pi }}\left( {2{\text{n}} - 1} \right)$, where n is a positive integer [Reference Luo, Zhu and Sun17, Reference Luo, Zhu and Sun18]. Considering the circuit size of the ring-resonant filter network, θ ₁ and θ ₂ will be further limited, but this does not impact outputs of this research, where θ ₁ and θ ₂ have a variation range of 0−2π and satisfy ${\theta _1}\, + \,{\theta _2}\, = \,2{{\pi }}$.

Figure 1.

(a) Conventional ring-resonant filter structure. (b) Improved ring-resonant filter with compensation structure.

The TZ of the ring-resonant filtering network depends on the distribution of θ ₁ and θ ₂ and the process of the TZ varying with θ ₁ has been investigated in papers [Reference Luo, Zhu and Sun17, Reference Luo, Zhu and Sun18] as demonstrated in Fig. 2. As shown in Fig. 2, it is shown that as the electrical length θ ₁ increases, the TZ will gradually move toward the high-frequency direction, indicating that a wider frequency response can be obtained. Specifically, when θ ₁ reaches 150°, the passband response has exceeded 3.0 GHz, but it is evident that the roll-off characteristics of the transition band and the out-of-band attenuation are not ideal enough.

Figure 2.

The frequency response of conventional ring-resonant filtering networks under different θ _1.

Therefore, in order to further enhance the roll-off characteristics of the transition band and the attenuation of the stop-band, the traditional ring-resonant filtering network has been improved by adding compensation structure with parallel stub, as shown in Fig. 1(b). The stub will exhibit capacitance characteristics, which can greatly improve the performance of the ring-resonant filtering network [Reference Luo, Zhu and Sun17, Reference Luo, Zhu and Sun18], thereby improving the out of band attenuation and roll-off characteristics of the transition region.

Figure 3 shows the frequency response of the improved and conventional ring-resonant filter network at θ ₁ = 150°, in terms of forward transfer functions S₂₁. It can be observed that the frequency response of the improved ring-resonant filtering network attenuates more significantly in the stopband and provides a sharp roll-off, indicating stronger harmonic suppression ability outside the band.

Figure 3.

Simulated frequency response comparison between improved and conventional ring-resonant filter network at θ ₁ = 150°.

After the above analysis, it has been proven that the improved ring-resonant network can significantly promote the performance of the filter in terms of out-of-band attenuation and roll-off characteristics in the transition region. In order to apply this proposed architecture in PA design, the relationship between the impedances Z _in and Z _L of the two ports of the ring-resonant filter network needs to be further determined, as shown in Fig. 1(b). This calculation process starts with obtaining the A-matrix for each part. Based on this, according to transmission line theory [Reference Pozar19], the A-matrix of Parts 1, 5, and 6 can be expressed as follows:

(1)\begin{equation}{{\mathbf{A}}_1} = \left[ {\begin{array}{*{20}{c}} {\cos ({\theta _2})}&{j{Z_2}\sin \left( {{\theta _2}} \right)} \\ {\frac{{j\sin \left( {{\theta _2}} \right)}}{{{Z_2}}}}&{\cos ({\theta _2})} \end{array}} \right]\end{equation}

(2)\begin{equation}{{\mathbf{A}}_5} = \left[ {\begin{array}{*{20}{c}} {\cos ({\theta _6})}&{j{Z_6}\sin \left( {{\theta _6}} \right)} \\ {\frac{{j\sin \left( {{\theta _6}} \right)}}{{{Z_6}}}}&{\cos ({\theta _6})} \end{array}} \right]\end{equation}

(3)\begin{equation}{{\mathbf{A}}_6} = \left[ {\begin{array}{*{20}{c}} {\cos ({\theta _7})}&{j{Z_7}\sin \left( {{\theta _7}} \right)} \\ {\frac{{j\sin \left( {{\theta _7}} \right)}}{{{Z_7}}}}&{\cos ({\theta _7})} \end{array}} \right]\end{equation}

Parts 3 and 4 have the same expression and can be obtained as follows:

(4)\begin{equation}{{\mathbf{A}}_3} = \left[ {\begin{array}{*{20}{c}} 1&0 \\ {\frac{{j{\text{tan}}\left( {{\theta _3}} \right)}}{{{Z_3}}}}&1 \end{array}} \right]\end{equation}

(5)\begin{equation}{{\mathbf{A}}_4} = \left[ {\begin{array}{*{20}{c}} 1&0 \\ {\frac{{j{\text{tan}}\left( {{\theta _5}} \right)}}{{{Z_5}}}}&1 \end{array}} \right]\end{equation}

Specifically, for Part 2, the port cascade theory of the A-matrix can be adopted and expressed as follows (6):

(6)\begin{align}{{\mathbf{A}}_2} = \left[ {\begin{array}{*{20}{c}} {\cos ({\theta _1} * 0.5)}&{j{Z_2}\sin \left( {{\theta _1} * 0.5} \right)} \\ {\frac{{j\sin \left( {{\theta _1} * 0.5} \right)}}{{{Z_1}}}}&{\cos ({\theta _1} * 0.5)} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 1&0 \\ {\frac{{j{\text{tan}}\left( {{\theta _4}} \right)}}{{{Z_4}}}}&1 \end{array}} \right] \nonumber\\ \left[ {\begin{array}{*{20}{c}} {\cos ({\theta _1} * 0.5)}&{j{Z_2}\sin \left( {{\theta _1} * 0.5} \right)} \\ {\frac{{j\sin \left( {{\theta _1} * 0.5} \right)}}{{{Z_1}}}}&{\cos ({\theta _1} * 0.5)} \end{array}} \right]\end{align}

Next, in order to acquire the A-matrix of Parts 1 and 2 parallel structures, which we named A_1-2-matrix, the A-matrix of Parts 1 and 2 obtained separately needs to be first transformed into a Y-matrix. Given the A-matrix, the transformation rules for the Y-matrix can be summarized as follows [Reference Pozar19]:

(7)\begin{equation}{\mathbf{Y}} = \left[ {\begin{array}{*{20}{c}} {\frac{D}{B}}&{\frac{{BC - AD}}{B}} \\ { - \frac{1}{B}}&{\frac{A}{B}} \end{array}} \right]\end{equation}

The Y-matrix converted for Parts 1 and 2 are Y₁-matrix and Y₂-matrix, respectively. So, the total Y-matrix of Parts 1 and 2 in parallel is the sum of the two, which we call the Y_1-2-matrix. In this case, to obtain the total A-matrix of the improved ring-resonant filtering network, the Y_1-2-matrix needs to be transformed into the A-matrix again so that the A_1-2-matrix can be determined. At this point, the matrix of the entire network can be expressed through cascading rules as follows:

(8)\begin{equation}{\mathbf{A}} = {{\mathbf{A}}_3} * {{\mathbf{A}}_{1{\text{ - }}2}} * {{\mathbf{A}}_4} * {{\mathbf{A}}_5} * {{\mathbf{A}}_6}\end{equation}

Then, the A-matrix parameters can be easily transformed into scattering parameters [Reference Pozar19]. Considering the improved ring-resonant filtering network is a two-port network, the scattering matrix can be expressed as the following four parameters: S₁₁( f), S₁₂( f), S₂₁( f), and S₂₂( f). It should be noted that if the characteristic impedance Z ₆ and load impedance Z _L of the transmission line in Part 5 are equal, the reflection coefficient Г_in ( f) of the input port of the improved ring-resonant filter will be equal to S₁₁( f). So the input impedance Z _in can be expressed as follows:

(9)\begin{equation}{Z_{{\text{in}}}}\left( f \right) = {Z_7}\frac{{1 + {\Gamma _{in}}\left( f \right)}}{{1 - {\Gamma _{in}}\left( f \right)}}\end{equation}

So far, the relationship between the load impedance Z _L and input impedance Z _in of the improved ring-resonant filtering network has been established. Although the establishment of this relationship is complex, it is easy to calculate in mathematical software (e.g., MATLAB).

Realization of broadband PA with ring-resonant filter architecture

In this section, the design of a PA based on an improved ring-resonant filter architecture and SCMs is presented from the operating frequency band of 0.55−3.3 GHz. Considering the design goals to be achieved, a commercially available 10-W GaN device from Wolfspeed is picked, and the gate and drain bias voltages are set at −2.7 and 28 V, respectively.

Theory of SCMs

Through the improved ring-resonant filtering network proposed in the “Design of a ring-resonant filtering network for PAs” section, it can be found that the out-of-band attenuation and roll-off characteristics of the transition region have been significantly improved, indicating that the proposed structure has excellent performance in out-of-band harmonic suppression. Based on this, harmonic-tuning theory can be combined to achieve broadband and high-efficiency performance in PAs. Conventional harmonic-tuning theory, which requires second harmonic resonance in open- or short-circuit states, has advantages in improving the efficiency of PAs. However, it is greatly limited in bandwidth expansion and cannot meet the application needs of current mobile communication systems. In this case, SCMs [Reference Chen, He, You, Tong and Peng10] are proposed by extending the second-harmonic impedance to pure reactance while extending the design space of the fundamental impedance. This mode also includes continuous Class-B/J and continuous Class-F modes, which have excellent performance in balancing bandwidth expansion and efficiency improvement.

The normalized drain current can be described as

(10)\begin{equation}{i_{DS}}\left( \theta \right) = \frac{1}{\pi } + \frac{1}{2}{\text{cos}}\theta + \frac{2}{{3\pi }}\cos 2\theta + \cdot \cdot \cdot \cdot \end{equation}

The normalized drain voltage waveform is

(11)\begin{equation}{v_{DS}}\left( \theta \right) = \left( {1 - \alpha \cos \theta + \beta \cos 3\theta } \right)\left( {1 - \gamma \sin \theta } \right)\end{equation}

where γ is swept between −1 and 1. The different operating modes depend on the values of α and β, such as α = 2√3, β = 1/(3√3) corresponding to the continuous Class-F mode, and α = 1, β = 0 corresponding to the continuous Class-B/J mode. It should be noted that to prevent the voltage from clipping to zero, the following conditions should be satisfied:

(12)\begin{equation}\left\{ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\alpha {\text{ - }}\beta = 1}&{1 \leqslant \alpha \leqslant \frac{9}{8}} \end{array}} \\ {\begin{array}{*{20}{c}} {\alpha \left( {\frac{2}{3} + \frac{{2\beta }}{\alpha }} \right)\sqrt {\frac{1}{4} + \frac{\alpha }{{12\beta }}} = 1}&{\alpha \geqslant \frac{9}{8}} \end{array}} \end{array}} \right.\end{equation}

As a consequence, it can be seen that α and β affect each other. As long as one of the values is determined, the other will be acquired. Then, the fundamental, second-, and third-harmonic impedances at the current generate plane (I-gen plane) can be acquired by integrating (10) and (11), as follows:

(13)\begin{equation}{Z_1} = \alpha + {\text{j}} \cdot \gamma \end{equation}

(14)\begin{equation}{Z_2} = - \frac{{3\pi }}{8} \cdot j \cdot \gamma \cdot \left( {\alpha + \beta } \right)\end{equation}

(15)\begin{equation}{Z_3} = \infty \end{equation}

From (13) and (14), it can be seen that the second-harmonic impedance of SCMs is not required to resonate in an open- or short-circuit state, and the real and imaginary parts of the fundamental impedance solution are no longer constant but vary with α and γ, respectively, meaning further expansion of the impedance solution space. To visually display the spatial distribution of impedance for SCMs, the calculated fundamental and harmonic impedance solutions are drawn in Fig. 4, where the fundamental impedance solution changes around a series of resistance circles in the Smith chart, the second-harmonic impedance solution varies around the edges of the Smith chart, and the third-harmonic impedance resonance is in open-circuit. It should be noted that due to the inherent nonlinearity C _DS of the device, efficiency is not very sensitive to the third-harmonic impedance [Reference Xia, Zhu and Zhang20], and the fundamental impedance and second-harmonic impedance are mainly considered in this article.

Figure 4.

The fundamental and harmonic impedances of the SCMs on Smith chart. (The characteristic impedance Z ₀ of the Smith chart is 50 Ω).

Design of broadband PA based on improved ring-resonant filter network and SCMs

As SCMs impedance solution spaces are presented, the design of wideband PAs based on the improved ring-resonant filter architecture can be implemented by using the CGH40010F transistor provided by Wolfspeed. However, it should be emphasized in advance is that since the impedance solution space provided by SCMs is located on the I-gen plane, and a transistor with a flange package, meaning that the plane for impedance matching needs to be determined. There are two options to choose from here. One is to first transform the impedance solution space located at the I-gen plane to the package plane using the package parasitic network [Reference Tasker and Benedikt21], and then implement the impedance matching at the package plane. The second is to conduct impedance matching directly at the I-gen plane based on the package parasitic network of the selected transistor [Reference Tasker and Benedikt21]. Considering that the conversion of the impedance solution space from the I-gen plane to the package plane can easily cause the loss of the impedance solution, the second option is given priority. Based on this, by combining the impedance conversion relationship between the two ports of the improved ring-resonant network obtained in (9) and the package parasitic network provided in paper [Reference Tasker and Benedikt21], the load impedance of the PA can be matched to the target impedance space shown in Fig. 4. It should be further noted that the optimal second-harmonic impedance is located at the edge of the Smith chart. Therefore, on the one hand, (9) needs to be used to manipulate the second-harmonic impedance within the design frequency band to gradually approach the edge of the Smith chart, which is to reduce the real part of the second-harmonic impedance. On the other hand, simulation software needs to be combined to assist in optimizing circuit parameters, moving the second-harmonic impedance within the target frequency band as much as possible towards the edge of the Smith chart. As a result, the topology structure of the entire PA can be determined by using a substrate of Rogers 4350B with a thickness H of 0.762 mm, as demonstrated in Fig. 5, where the input matching network employs the conventional impedance gradient architecture.

Figure 5.

Circuit schematic overview of the designed PA.

Figure 6 exhibits the simulated voltage and current waveforms located in the I-gen plane at three frequency points of 1.0, 2.0, and 3.0 GHz, respectively. As shown in Fig. 6, it can be clearly observed that the voltage and current waveforms present a staggered distribution in the time domain, indicating that the energy loss between the drain and source stages is within an acceptable range and high efficiency can be achieved.

Figure 6.

Simulated voltage and current waveforms at I-gen plane. (a) 1.0 GHz, (b) 2.0 GHz, (c) 3.0 GHz.

In addition, to further evaluate the performance of the proposed improved ring-resonant filtering network in achieving impedance matching, the simulated impedance trajectory of the output matching network at the I-gen plane is plotted in Fig. 7. It can be clearly seen that the completed impedance is basically located within the target region in the fundamental frequency band, and the second-harmonic impedance gradually approaches the edge of the Smith chart under the out-of-band suppression effect of the proposed matching network. Consequently, the simulated results further reveal the rationality of the design theory.

Figure 7.

The simulated impedances trajectory of the output matching network at the I-gen plane.

The simulated frequency response of the designed ring-resonant filter matching network is displayed in Fig. 8, which shows the passband response and out-of-band attenuation characteristics of the target frequency band, further demonstrating the rationality of the output matching network design.

Figure 8.

Simulated frequency responses of the designed ring-resonant filtering matching networks for broadband PA.

Implementation and measurements of PA

After conducting a rationality evaluation, the designed broadband PA is fabricated on a Rogers 4350B substrate and mounted on an aluminum fixture, as demonstrated in Fig. 9. In order to further verify the frequency response of the PA, small signal testing was first implemented. The measurement and simulation results of the S-parameter are shown in Fig. 10. As shown in the figure, from the target frequency band, the measured S₂₁ remains above 10 dB, S₁₁ is below −5 dB, and S₂₂ is basically below −10 dB, indicating the rationality of the matching network design.

Figure 9.

Fabricated PA circuit.

Figure 10.

Measured and simulated S-parameters across the entire operating bandwidth.

Furthermore, large signal testing was performed under the stimulus of a single-tone continuous wave signal in the frequency sweep range of 0.5–3.3 GHz. The final test results are plotted in Fig. 11, and it can be seen that within the target frequency band range of 0.55–3.3 GHz with a relative bandwidth of 142.9%, a DE of 58.2–70.3%, a power-added efficiency (PAE) of 53.2v64.3%, and a gain of 8.5–12 dB can be achieved while maintaining a saturated output power of 38.5–42 dBm. In addition, the performance comparison between this work and the latest PA is displayed in Table 1. To comprehensively and fairly measure the performance of the proposed PA, we defined two operating bandwidths for the test results based on the range of output power variation. One is the range of output power variation from 0.7 to 3.3 GHz, which is 3 dBm. The second is that the range of output power variation from 0.55 to 3.3 GHz is 3.5 dBm. It can be seen that regardless of the bandwidth partitioning scheme, the performance presented in this paper is prominent when the operating bandwidth is considered.

Figure 11.

Measured and simulated DE, PAE, output power, and gain across the entire operating bandwidth.

Table 1.

Comparisons with state-of-the-art broadband PAs

BW: bandwidth, RBW: relative bandwidth, SCMs: a series of continuous modes, CCGF: continuous Class-GF, CB/J: waveform engineered Class B/J.

To measure the dynamic characteristics of the PA, the measured DE, gain versus output power at five design frequencies of 1.0, 1.5, 2.0, 2.5, and 3 GHz, is plotted, as shown in Fig. 12. It can be seen that the gain compresses with the increase in output power while the efficiency improves, indicating that the trade-off between efficiency and gain needs to be balanced. Therefore, when we use the output corresponding to 3 dB gain compression as the saturated output power, the efficiency is also within an acceptable range.

Figure 12.

Measured DE, gain versus output power at different operating frequencies.

The measured second harmonic power level relative to the fundamental output power is plotted in Fig. 13. From the graph, it can be seen that when the operating frequency is below 1.7 GHz, the relative power of the second harmonic remains at −15.34 to −12.75 dBc, while when the operating frequency exceeds 1.7 GHz, under the out-of-band signal suppression of the ring-resonant filtering network, the relative power of the second harmonic remains at −36.4 to −20.07 dBc from 1.7 to 3.3 GHz. The reason for this phenomenon is that below 1.7 GHz, the second harmonic in the low-frequency range falls into the fundamental wave in the high-frequency range, resulting in a better relative suppression level of the second harmonic after exceeding 1.7 GHz.

Figure 13.

The results of the measured second relative harmonics level over the entire bandwidth.