Design of the principle of the output matching network

Considering that the proposed PA needs to expand bandwidth while maintaining high efficiency, the selection of impedance MN is particularly important. By summarizing the existing impedance matching topology, a variable universal output MN is proposed. The topological network formed by this universal structure can almost cover all the existing structures with any number of branches and impedance gradient matching. The proposed output MN topology with the left-rotating T-type structure as the basic unit circuit (BUC) for cascading is shown in Fig. 1, where the number of cascades is determined by optimization. This BUC is composed of a series microstrip line and two shunt stubs connected to the ground through a virtual switch (VS), where the shunt stubs are presented as open or short stubs depending on the state of the VS. It can be clearly seen that the proposed topology contains N BUCs and 2N VS. Each form of composition has different responses, which provides great flexibility for MN design. Therefore, the performance of the designed MN is basically determined by the number of BUC_si (1 ≤ i ≤ N) and the opening or closing of VS_i (1 ≤ i ≤ 2N).

Figure 1. A schematic diagram of the proposed distributed matching network.

The most basic approach to measuring the performance of impedance matching is to evaluate the closeness between the impedance realized by MN and the target impedance at the corresponding design frequency point. In view of this, obtaining the expression of input impedance Z _OMN becomes a key point. The feasible way is to first acquire the transmission matrix A_i suitable for describing each basic left-rotating T-type unit of the cascade network, then conduct cascade multiplication, and finally convert it into a scattering matrix. Based on the above analysis, the ABCD matrix of BUCs in Fig. 1 can be expressed as follow (1):

(1)\begin{align}{{\textbf{A}}_i} & = \left[ \begin{matrix} {\cos \left( {{\theta _i}} \right) + {{j \cdot \left( {{Z_{{\textrm{IN}},U - i}} + {Z_{{\textrm{IN}},D - i}}} \right){Z_i}\sin \left( {{\theta _i}} \right)} \over {{Z_{{\textrm{IN,}}U - i}} \cdot {Z_{{\textrm{IN,}}D - i}}}}} & {j \cdot {Z_i}\sin \left( {{\theta _i}} \right)} \\ {{{j \cdot \sin \left( {{\theta _i}} \right)} \over {{Z_i}}} + {{\left( {{Z_{{\textrm{IN}},U - i}} + {Z_{{\textrm{IN}},D - i}}} \right) \cdot \cos \left( {{\theta _i}} \right)} \over {{Z_{{\textrm{IN}},U - i}} \cdot {Z_{{\textrm{IN,}}D - i}}}}} & {\cos \left( {{\theta _i}} \right)} \end{matrix} \right]\, \nonumber \\ & \qquad \qquad \qquad \qquad 1 \le i \le N,\end{align}

where Z _i and θ_i are the characteristic impedances and electrical length of the series lines, respectively; Z_IN,U-i and Z_IN,D-i are the input impedances of the two shunt stub of the ith BUCs, respectively, and can be calculated as follows:

(2)\begin{equation}\{ \begin{matrix} {{Z_{{\textrm{IN}},D - i}} = \overline {{\textrm{V}}{{\textrm{S}}_i}} \cdot j{Z_{Ui}} \cdot \tan \left( {{\theta _{Ui}}} \right) + {{{\textrm{V}}{{\textrm{S}}_i}} \over {j{Z_{Ui}} \cdot \tan \left( {{\theta _{Ui}}} \right)}}} \\ {{Z_{{\textrm{IN}},U - i}} = \overline {{\textrm{V}}{{\textrm{S}}_{N + i}}} \cdot j{Z_{Di}} \cdot \tan \left( {{\theta _{Di}}} \right) + {{{\textrm{V}}{{\textrm{S}}_{N + i}}} \over {j{Z_{Di}} \cdot \tan \left( {{\theta _{Di}}} \right)}}} \end{matrix} \quad 1 \le i \le N,\end{equation}

where Z_Ui and Z_Di are the characteristic impedances of the two shunt stub lines, respectively; θ_Ui and θ_Di are the electrical lengths of the two shunt stub lines, respectively; VS_i (1 ≤ i ≤ 2N) represents the on and off states of the ith VS, which can be defined as

(3)\begin{equation}{\textrm{V}}{{\textrm{S}}_i} = {\textrm{V}}{{\textrm{S}}_{N + i}} = \begin{cases} 0 & {\textrm{ON}} \\ 1 & {\textrm{OFF}} \qquad 1 \le i \le N. \end{cases}\end{equation}

The output MN can be treated as a cascaded structure of N BUCs interconnected with a load impedance R _L. Considering the electric length θ as a function of frequency, the ABCD matrix of the output MN can be expressed as follow (4):

(4)\begin{align}{\textbf{A}} & = \left[ \prod\limits_N^{i = 1} {A_i}\left(\, f \right) \right] \cdot \left[ \begin{matrix} {\cos \left( {{\theta _e}} \right)} & {j{Z_e}\sin \left( {{\theta _e}} \right)} \\ {{{j{Z_e}\sin \left( {{\theta _e}} \right)} \over {{Z_e}}}} & {\cos ({\theta _e})} \end{matrix} \right] \nonumber \\ & \qquad = {\left[ \begin{matrix} {{A_T}\left(\, f \right)} & {{B_T}\left(\, f \right)} \\ {{C_T}\left(\, f \right)} & {{D_T}\left(\, f \right)} \end{matrix} \right]_{{\textrm{Total}}}}\quad 1 \le i \le N,\end{align}

where Z_e and θ_e represent the characteristic impedances and electrical length of the transmission line TL_e, respectively.

The ABCD parameters of the proposed output MN are acquired and can be easily transformed to scattering parameters [Reference Frickey22]. The output MN can be regarded as a two-port network, so the scattering matrix should include four parameters: S ₁₁(f), S ₁₂(f), S ₂₁(f), and S ₂₂(f). It needs to be noted that if the characteristic impedance Z_e of TL_e is equal to the load impedance R _L, the following equation can be satisfied.

(5)\begin{equation}{\Gamma _{{\textrm{OMN}}}}\left(\, f \right) = {S_{11}}\left(\, f \right),\end{equation}

where Γ_OMN is the reflection coefficient of the output MN, and the input impedance Z _OMN can be expressed as

(6)\begin{equation}{Z_{{\textrm{OMN}}}}\left( f \right) = {Z_1}{{1 + {\Gamma _{{\textrm{OMN}}}}\left( f \right)} \over {1 - {\Gamma _{{\textrm{OMN}}}}\left( f \right)}}.\end{equation}

To achieve wideband high-efficiency performance of PAs, it is necessary to ensure that Z _OMN is close to the target impedance in the desired bandwidth. To this end, the cost function in an optimization procedure [Reference Dai, He, You, Peng, Chen and Dong23] is taken as follows:

(7)\begin{equation}T = \sum\limits_K^{i = 1} {\left| {{{{Z_{{\textrm{OMN}}}}\left(\, {{f_i}} \right) - {Z_{{\textrm{OPT}}}}\left(\, {{f_i}} \right)} \over {{Z_{{\textrm{OPT}}}}\left(\, {{f_i}} \right)}}} \right|^2}.\end{equation}

Hence, the optimization objective can be defined as (7), where Z _OPT is the optimal impedance, which can be acquired by load-pull technology, and f _i (where i = 1, 2, …, k) are frequency points within the desired bandwidth. As a result, the output matching topology can be determined through optimization.

Realization of wideband highly efficient PA

In this brief, the desired specifications are stated as follows: A wideband highly efficient PA is designed in a target operating frequency band of 0.8–3.9 GHz. To achieve the design goals, a 10-W GaN HEMT device CGH40010F is selected and the static bias points are set at V _GS = −2.7 V and V _DS = 28 V.

Acquisition of optimal impedance

Considering that the harmonic component has a great impact on the output power and efficiency, it is necessary to analyze the harmonic component in the design process of PA. For the typical PA design, the conventional load-pull technique is used to obtain the fundamental impedance, while the influence of harmonic impedance is ignored. Therefore, in the design of ultra-wideband PA, there is a deviation in impedance matching, which limits the performance of PA bandwidth and efficiency.

In order to comprehensively analyze the influence of harmonic impedance on the performance of the PA, especially the second harmonic, the multi-harmonic bilateral pull technique [Reference Chen and Zhang24] is used to obtain the optimum fundamental and second harmonic impedance.

Based on the transistor large signal model provided by Cree, optimal fundamental and second harmonic impedance regions of the load for 1.0 to 4.0 GHz demonstrated in Fig. 2(a) are generated by employing the multi-harmonic bilateral pull technique at the output terminals. It is worth noting that the internal region of the impedances of the fundamental and second harmonic contours represents the tolerable region in which high efficiency and high output power can be acquired.

Figure 2. The optimal fundamental impedance distribution of (a) load and (b) source for 1.0–4.0 GHz.

Moreover, it can be observed from Fig. 2(a) that when the second harmonic resistance within the entire desired frequency band is maintained between 0 and 25 Ω, higher than η _max-5% efficiency and P _max-3 dBm output power can be obtained. Meanwhile, when the second harmonic reactance is maintained between 0 and 55 Ω, higher than η _max-3% efficiency and P _max-2 dBm output power can also be achieved. Therefore, based on the above analysis, a conclusion can be drawn that when the second harmonic impedance is extended to a resistive-reactive and partially overlaps with the optimal fundamental impedance region, excellent performance can still be achieved. As a result, especially, the second harmonic in the frequency band can be incorporated into the optimal fundamental impedance region, thus making it possible to realize a multifrequency high-efficiency PA.

Furthermore, it can be clearly seen from Fig. 2(a) that across a wide bandwidth, the optimum fundamental impedances of a transistor at different frequency points are not close to each other. Therefore, the entire operating bandwidth is divided into seven frequency sections depending on the required bandwidth and the variation of the optimal impedances. For each frequency section, the region with high output power and high-efficiency contours can be selected as the optimum fundamental impedance of the frequency section. Similarly, the optimal impedance of the input terminals is also shown in Fig. 2(b).

Realization of input and output matching network

As the optimal impedance region is determined, the design theory presented in the second section can be employed to acquire an appropriate topology. Then, the variable K described in (7) takes the value 7. Figure 3(a) depicts the implemented topology for output matching, which is based on the Rogers 4350B microstrip transmission line with a thickness of 0.762 mm. Similarly, based on the output MN synthesized, the input MN is also proposed by using a similar method, as shown in Fig. 3(b).

Figure 3. The completed output (a) and input (b) matching network. The trajectories of the realized Z _OMN(f) and Z _S(f).

As a consequence, the wideband highly efficient GaN HEMT PA including input and output MN achieved by using transmission lines is demonstrated in Fig. 4. It should be noted that since the designed frequency band exceeds one octave, considering the in-band stability, a stability network comprising of the parallel RC pair of 9 pF and 3 ohms is specially added to the input terminal. Especially, the gate bias resistors perform low frequency stabilization.

Figure 4. The final schematic of the proposed multioctave bandwidth PA.

Moreover, to better evaluate whether Γ_S and Γ_OMN realized by the designed input and output MN are close to the optimal impedance region, the source and load impedance trajectories obtained by using simulation software are plotted in Fig. 3(a) and (b). From Fig. 3(a), it can be clearly observed that the trajectories of load impedance Γ_OMN(f) are represented by a curve composed of cyan solid triangles. Starting from 0.8 GHz, with the increase of frequency, it gradually moves down from the upper right corner of the Smith chart and ends at 3.9 GHz. It is obvious that the impedance trajectories basically fall into the target impedance region, which is the gray-shaded dashed background. In addition, the trajectories of the source impedance Γ_S(f) (purple triangle curve) are depicted in Fig. 3(b). It is evident that the impedance curve from 0.8 to 3.9 GHz is well manipulated in a small area where the target impedance is located. Therefore, the above simulation results reveal the fact that the proposed design theory is superior.

Implementation and measurements

The photograph of the fabricated wideband highly efficient PA with a size of 3.8 × 5.7 cm² is presented in Fig. 5.

Figure 5. The photograph of the fabricated PA.

To verify the proposed design theory and evaluate the performance of the assembled PA, continuous wave is generated by the signal generator from 0.7 to 3.9 GHz with a 0.1 GHz step to implement the PA measurement. Figure 6 demonstrates that from the operating bandwidth of 0.7–3.8 GHz with a relative bandwidth of 137.8%, the drain efficiency (DE) between 59% and 70%, the power added efficiency (PAE) of 53.2%–63.1%, the output power of 39–42.1 dBm, and the gain of 9–12.1 dB are achieved under the condition of maintaining the input power of 30 dBm. From the measured performance of the PA, the measured and simulated results are basically consistent, and the rationality of the proposed theory is proved again. In addition, it is worth noting that there are some deviations between simulation and measurement results in terms of efficiency, output power, and operating bandwidth, which is mainly reflected in the deterioration of the measured results at 3.9 GHz compared with the simulation results, but good performance at 0.7 GHz. The possible causes of this phenomenon are attributed to the assembly tolerance, simulation model error, and electromagnetic coupling of practical circuits.

Figure 6. Measured and simulated DE, PAE, output power, and gain across the entire bandwidth.

The measured DE gain versus the corresponding input power at seven frequency points of 0.8, 1.0, 1.5, 2.0, 2.5, 3.0, and 3.5 GHz is drawn in Fig. 7. It can be seen from the figure that when the gain is compressed by 3 dB in the 0.7–3.8 GHz range, the output power has reached a saturation and the DE can reach 59–70%.

Figure 7. Measured DE and gain versus input power at different operating frequencies.

A summary of some recently reported broadband high-efficiency PAs is presented in Table 1. To facilitate comparison between the proposed PA and the other relevant designs, the proposed PA measurement results are also given in Table 1. It is obvious that the proposed PA has greatly expanded its operating bandwidth and relative bandwidth while maintaining high DE.

Table 1. Comparisons with state-of-the-art broadband PAs

^a PAE.

BW: bandwidth, RBW: relative bandwidth.