Design principles of the broadband DPA input network

As outlined above, we consider two devices interconnected at their gate terminals to a passive input network, with the purpose of obtaining a three-port sub-circuit suitable for the subsequent development of the entire DPA. In accordance with the general requirements of broadband operation, the input network should have broadband capabilities in terms of both power splitting and impedance matching. For this purpose, we developed the microstrip technology network shown in Fig. 2, which is composed of the following parts: an uneven broadband two-stage unequal power divider, a reference line with electrical length of π (cascaded to the upper output port) and a broadband Schiffman phase shifter (cascaded to the lower output port) [Reference Lucarelli, Maddio, Collodi and Cidronali12–Reference Ahn14]. Given the output power splitter ratio k ², and a real positive number A to be used as a degree of freedom, the output impedances to the first stage of the power splitter are Z _A = k ² · A and Z _B = A. The impedance of the four branches composing the splitter are $Z_2 =\sqrt {AZ_0k^2(1+k^2)}$, $Z_3 =\sqrt {AZ_0({1+k^2}/{k^2})}$, $Z_4 =k\sqrt {AZ_L}$, and $Z_5 =\sqrt {AZ_L}$. The resistance connecting the first stage of the splitter is R = A(1 + k ²) [Reference Ahn14]. The splitting ratio adopted in this design is $k=\sqrt {2}$, which corresponds to a − 2 and − 5 dB splitting between the two ports; with respect to schematic diagram in Fig. 2, the impedances resulting from the design optimization are Z _A = 66.8, Z _B = 33.4, Z ₂ = 100, Z ₃ = 50, Z ₄ = 40.8, Z ₅ = 28.9, while R = 100OhmΩ. The transmission lines with impedance characteristics Z ₂, Z ₃, Z ₄, and Z ₅ are impedance transformers, thus their electrical length is π/4.

Fig. 2.

Two-stage uneven splitter and broadband 90 degree phase delay.

The asymmetric splitter is cascaded with a broadband 90-degree Shiffman phase shifter using a stepped impedance open stub and a coupled-line with a weak coupling to relax the constraints on the implementation. The phase shifter is implemented with the characteristic impedance of 25OhmΩ, by using the design principles described in [Reference Liu, Liu, Shen, Li, Yu and Lu15]. The 90-degree power splitter described above has been designed and optimized in the frequency band of 600 MHz to 1 GHz, with an expected power transmission of − 1.2 and − 6 dB respectively at ports 3 and 2. The network at its input port shows an impedance of 50OhmΩ, while at both the output ports the impedance is 25OhmΩ. The inclusion of the reference line is optimized to track the phase shift of the output impedance inverter over the frequency band. The results of the prototype characterization, fabricated on a 10 mil plastic substrate ε_r = 3.5, are reported in Fig. 3, for both the simulated and measured phase difference between output port, Fig. 3(b), and the magnitude of the transmission coefficient at the two ports, Fig. 3(a). The comparison reveals a good accuracy of the simulation across the entire range of analysis, from 500 MHz to 1.2 GHz, while the useful range for its use in a DPA architecture could be considered in principle about 850 MHz with a total bandwidth of 300 MHz.

Fig. 3.

Uneven quadrature power splitter characterization, cf Fig. 2. (a) Amplitude of the transmission coefficients. (b) Phase between transmission coefficients.

The input network is completed cascading the above described splitter, with a lumped element π-type matching network for each branch, which transform the 25 OhmΩ output impedance to respectively the main and peak devices input impedance.

Design principles of the output network

The key point of this paper is the large-signal vector characterization of the main and peak devices of the DPA as a three-port device, by the test fixture of Fig. 1. As far as the drain terminations are of concern, the test fixture should terminate the two devices at their optimum device impedance. There are two main reasons why this is required. The first is related to the design purpose, that requires the power devices to be terminated with the optimum impedance value to maximize the power delivered to the load, possibly by implementing a trade off between efficiency and linearity constraints. Secondly, the accuracy of the model to be extracted from the measurements depends on the non-linear state of the device, and hence its terminations used during the characterization stage. Thus, a non-linear characterization should be carried out by embedding the device with terminations very similar to those that will be used in operation: this guarantees the proper use of the model and minimizes the need for extrapolation. For this purpose, a preliminary phase of load–pull simulations were carried out in order to identify the best load terminations for both the main and peak devices. The results are reported in Fig. 4(a) and 4(b), for the main and peak devices respectively, at a carrier frequency of 750 MHz. At this stage, the bias point of Vd = 50 V is supplied to both the devices, with the main device biased at 800 mA, and the peak at its threshold. The data shown in Fig. 4 assume a de-embedding of a parasitic capacitor of about 24 pF for both devices, while the optimum terminations are about 5.5 and 7.8 OhmΩ for the main and peak devices respectively. The next step of the design of the test fixture consists of the design of an output network capable of transforming the 50 OhmΩ load to the optimum impedance, over the specified bandwidth. In this work, we adopted a tapered transmission line capable of providing the impedance transformation across the specified bandwidth of 700–960 MHz. A limitation of this approach consists in the maximum width of the taper, which is dictated by the device drain terminal spacing. In this case, a reduction of the width can be implemented by using artificial line synthesis [Reference Cidronali, Giovannelli, Maddio, Del Chiaro, Schuberth, Magesacher and Singerl16]. By considering that during the operation of the DPA, the load modulation changes the impedance seen by both the peak and the main devices, we used 10 OhmΩ as a trade off between the feasibility of the taper and the actual value for the terminations. In Fig. 5(a) we show the output network of the test fixture, which is composed of two tapered transmission lines, shaped by the Klopfenstein rule [Reference Klopfenstein17], and arranged in a pair consistent with mechanical constraints. The numerical electromagnetic simulated response is reported in Fig. 5(b) in terms of the reflection coefficient at the drain termination port between 0 and 10 GHz. The broadband behavior is required to maintain the approximation of the value of the termination over the design bandwidth and at the harmonics. A picture of the final assembly of the test fixture for the large-signal vector characterization is presented in Fig. 6. In the picture are visible also the input networks between the broadband splitter and the devices gate, as well as the gate bias networks. The assembly uses a thermal sink, which turns out to be particularly important for maintaining the temperature of the device below a critical level.

Fig. 4.

Main and peak device load pull analysis at 750 MHz, Z ₀ = 5OhmΩ. (a) Main device. (b) Peak device.

Fig. 5.

Output network of DPA test fixture. (a) Layout of the test fixture. (b)Reflection coefficients at the termination port between 0 and 10 GHz, Z ₀ = 25OhmΩ.

Fig. 6.

Picture of the test fixture prototype assembled for large-signal vectorial characterization.

Non-linear-VNA setup

The purpose of the test fixture is to provide a connection between the calibrated ports of the three-port large-signal vector measurement setup [Reference Cidronali, Giovannelli, Maddio, Del Chiaro, Schuberth, Magesacher and Singerl16] and the DPA sub-circuit. The measurement setup is based on a three ports nonlinear-VNA (NVNA), where two sources are actuated at operating frequencies and levels capable of stimulating the RF device pair with a large signal from the input network, and simultaneously injecting tick signals [Reference Cidronali, Gupta, Jargon, Remley, DeGroot and Manes18] for the extraction of the X-parameters. The schematic block diagram of the characterization setup is shown in Fig. 7, where an external generator is aimed at providing the large-signal stimulus for the characterization.

Fig. 7.

Schematic block diagram of the non-linear-VNA-based characterization setup.

A driver amplifier is included in the path to the input port of the DPA sub-circuit, and it is capable of driving the device under test (DUT) up to 40 dBm over the design bandwidth. Two additional amplifiers are also included at the output ports with the aim of amplifying the extraction tone applied to ports 2 and 3 of the DUT, for the purpose of the X-parameters extraction. According to a general rule, the extraction tone should be on the order of − 20 to − 30 dBc in magnitude with respect to the carrier and the harmonics at the output of the DUT. Thus the driver amplifiers involved need a sufficient gain and dynamics. A pair of high-power attenuators complete the setup and ensure the proper signal levels.

In this setup, the main limitation is imposed by the extraction tone amplifiers, which should provide a sufficient tick signal level over a bandwidth defined at its lowest end by the lowest frequency of a ₁₁, and at its highest by the highest a ₁₁ harmonics, considered in the characterization. For instance, with reference to Fig. 8, for an output power of 50 dBm, at least 20 dB of attenuation is needed at ports 2 and 3: this makes the tick signal tone generated at ports 2 and 3, about 50 dBm − 30 dBc + 20 dB = 40 dBm at the fundamental frequency and capable of providing comparable levels also at the harmonics. In addition, the driver amplifier must drive the DUT and provide the extraction tone with levels which are − 20 to − 30 dBc lower than the fundamental tone across the measurement bandwidth.

Fig. 8.

Picture of the non-linear-VNA setup arrangement for the test fixture prototype characterization.

This arrangement actually makes the NVNA suitable for the extraction of three-port X-parameters, with the independent incident wave applied at port 1, namely a ₁₁, where the second index indicates the fundamental of the excitation. In the setup, ports 2 and 3 are those connected to the output of the main, respectively, peak device.

A picture of the laboratory setup of the three-port non-linear-VNA is shown in Fig. 8. There can be recognized a four-port vector network analyzer properly modified with external high-power bidirectional couplers connected to the DUT and to the internal receivers of the analyzer. The output port of each coupler defines the calibrated section of the measurement setup. In addition, the picture shows the high-power attenuators, while the extraction tone amplifiers are behind them and not visible in the picture. The phase reference of the system is connected at port 2 of the test-set, and it is adopted for both the calibration phase as well as run-time during the measurement test. In accordance with the use of high-power devices, the characterization is actuated by pulsed measurements with 10% duty cycle.

Three-port X-parameters model of the DPA subcircuit

The model adopted in this study is based on the definition of the non-linear scattering functions, F _ik, that relate the input spectral components a _jl with the output spectral components b _ik [Reference Peyton Jones and Billings19]

(1)$$ b_{ik}=F_{ik} (a_{11}, a_{12}, \ldots, a_{11}, \ldots ), $$

where i,j are respectively the ith and jth input and output ports and k,l the corresponding harmonic indexes. Introducing the term P = a ₁₁/|a ₁₁|, which corresponds to the phase of a ₁₁, and assuming a single-tone excitation at port 1, we can linearize (1) about |a ₁₁| with respect to a _jl · P ^−l; this permits of introducing the parameters

(2)$$ \eqalign{ XB_{ik} ( \vert a_{11} \vert ) &= F_{ik} ( \vert a_{11} \vert , 0, 0, \ldots), \cr XS_{ik,jl} ( \vert a_{1,1} \vert ) &= \left. {{\delta F_{ik}} \over {\delta (a_{\,jl}\cdot P^{-l})}} \right\vert _{ \vert a_{11}\vert }, \cr XT_{ik,jl} ( \vert a_{1,1} \vert ) &= \left. {{\delta F_{ik}} \over {\delta (a_{\,jl}\cdot P^{-l})^\ast}} \right\vert _{\vert a_{11}\vert }, } $$

and in turn applying the harmonic superposition principle [Reference Root, Verspecht, Sharrit, Wood and Cognata1] which leads to

(3)$$ b_{ik}=XB_{ik}+ \sum_{i,j \neq 1,1} {XS_{ik,jl} P^{k-l}a_{\,jl}}+ XT_{ik,jl} P^{k+l}a^\ast_{\,jl} $$

where i;j=1,2,3 and k;l = 1, …, max{harmonic}; a ₁₁ is the incident wave at the input port, while b _ik is the scattered wave at the i-th port and k-th harmonic.

From (2) we recognize that the term XB _ik corresponds to a non-linear mapping of a ₁₁ to b _ik, while from (2) and (3), that XS _ik,jl and XT _ik,jl correspond to the terms of a non-analytic harmonic superposition, by which is included the dependence of the b _ik phase upon the a _jl phase. In particular, the terms XT _ik,jl take into account the fact that F _ik can not be analyticFootnote ¹.

Moving on the measurement setup discussed in section “Design principles of the broadband DPA input network”, the acquired raw data were properly de-embedded [Reference Lee, Lin, Lin and Lee20] from the magnitude and delay inserted by the output tapered transmission line: this procedure permits extracting the incident and reflected waves at the drain terminals of the two devices, starting from those measured at ports 2 and 3 of the test fixture. Based on these data, the characterization permits achieving a three-port behavioral model suitable for the large-signal analysis of the DPA, as well as its optimization.

The experiments discussed herein below are limited to 3 harmonics; this means that the non-linear mapping parameters XB _ik are in total 9 (that is 3 port times 3 harmonics); according with the number of DUT ports, that is 3, and the number of higher order of harmonics, that is 3, the XS _ij,kl and XT _ij,kl parameters are respectively 3⁴ = 81. Thus in total we have 9+81+81=171 X-parameters, which are complex numbers, function of |a ₁₁|, and frequency.

In the following, we will discuss the behavior of the DPA sub-circuit on the basis of the main X-parameters as derived by the characterization technique described in the previous section.

The first set of parameters under consideration consists on the non-linear mapping parameters XB ₂₁ and XB ₃₁, which relate the fundamental of the incident wave at port 1 to the fundamental of the scattered waves at the output ports of the sub-circuit, namely the main, port 2, and the peak, port 3, devices respectively. Their behavior at the carrier frequency of 850 MHz is shown in Fig. 9 as a function of |a _jl|. In the figure we compare the X-parameters extracted by the large-signal characterization of the sub-circuit and the corresponding X-parameters extracted by CAD simulations using the vendor's model. We see that for XB ₂₁, which corresponds to the main device operating in AB class, we obtain a significant coherence between the two models; while the measured XB ₃₁ differs significantly from the corresponding parameter obtained from simulated data. This can be attributed to the better accuracy of the CAD model in the class-AB region rather than in the class-C region. A similar comparison of the phase terms of XB ₂₁ and XB ₃₁ is shown in Fig. 10, where the phase response of the CAD model is approximately constant over the entire range of amplitude of the stimulus, while the corresponding parameters extracted from measurements exhibit a non-constant behavior, in particular XB ₃₁, which corresponds to the peak device. It is worth noting that only for the lowest amplitude is the phase difference between the non-linear response consistent with the 90 degree delay induced by the input network. For higher powers, the phase difference for the CAD model remains approximately constant, while the X-parameters extracted by the measurement deviate from this expected response.

Fig. 9.

Comparison between measured (symbols) and simulated (continuous) XB ₂₁ and XB ₃₁ magnitudes at 850 MHz.

Fig. 10.

Comparison between measured (symbols) and simulated (continuous) XB ₂₁ and XB ₃₁ phases at 850 MHz.

The discrepancy between the modeled and measured X-parameters is to be mainly attributed to the fact that the power devices are contained in the same package very close to each other, whereas the CAD model is provided as a pair of identical device models, with an elementary description of the mutual interaction between the two intrinsic devices. This latter, associated to the inherently low accuracy of class-C operating mode, makes the CAD model incapable of capturing the higher order of interaction between devices, as described in particular below.

An insight into the interaction between the devices in the DPA sub-circuit is provided by the parameters XS ₃₁₂₁ and XS ₂₁₃₁, shown in Fig. 11(a), which relate the linearized response at the fundamental frequency between the peak and the main devices, and vice-versa, for XS ₃₁₂₁, respectively, XS ₂₁₃₁; Fig. 11(b) shows schematically the setup concerning the parameter characterization. The graph in Fig. 11(a) shows quantitatively that the behavior of the X-parameters extracted from CAD simulations differs greatly from that from the large-signal characterization, in particular, those measured are significantly higher than those obtained from the CAD model. Also in this case the behaviors reflect an incorrect characterization of the interaction between the devices, that can be attributed to both an incorrect modeling of the intrinsic device interaction within the package, as well as the path that arises through the input network that connects the gates of the two devices.

Fig. 11.

X-parameters related to the output devices cross talks. (a) Comparison of simulated (continuos) and measured (symbols) XS _31,21 and XS _21,31 parameters at 850 MHz. (b) Schematic setup for the definition of XS _31,21; similarly for XS _21,31.

To complete the overview of the X-parameters, Fig. 12 presents a comparison of some XS and XT parameters obtained from the measurements and from the circuit model. Recall that XS _ik,jl and XT _ik,jl consist respectively on the linearization of the non-linear mapping associated to the non-linear scattering function, about |a ₁₁|, with respect to a _jl · P ^−l and $(a_{jl}\cdot P^{-l})^\ast$; this helps with the considerations that follow. From Fig. 12(a) we observe a behavior that resembles those already shown for the non-linear mapping of Fig. 9. In particular we can clearly observe that the parameters exhibit a behavior qualitatively similar to the derivative of the corresponding non-linear mapping functions. Fig. 12(b) reports a comparison of the measured and modeled XT _31,11 and XT _21,11, which are the terms that include the non-analyticity of the describing function F _ik. From the comparison it is evident that the model suffers from low accuracy with respect to this feature of the behavior of the device. Consequently, a comparison in terms of phase is reported only for the terms XS _31,11 and XS _21,11, and is provided in Fig. 12(c) over the entire range of power levels at the frequency of 850 MHz. From the curve we can observe that the peak device exhibits a power-dependent phase response, much more evident than that exhibited by the main device; this behavior is not reproduced by the X-parameters extracted from the model simulations.

Fig. 12.

Comparison of XS and XT parameters at 850 MHz; simulation: continuous curves, symbols: experiments. (a) Magnitude of XS _31,11 and XS _21,11. (b)Magnitude of XT _31,11 and XT _21,11. (c) Phase of XS _31,11 and XS _21,11.

Lastly, Fig. 13 compares the parameters XB ₂₁ and XB ₃₁ at a carrier power of 31 dBm, over the 600–960 MHz frequency band. The two models exhibit qualitatively the same behavior, confirming that the non-linear mapping function is well represented by the two models. In terms of the bandwidth response of the subcircuit, we can observe that while the phase response, cf. Fig. 13(b), associated to the model is within ± 9 degree over more than 200 MHz of the bandwidth, the experimental results show a much narrower band response, namely 80 MHz about 700 MHz for the same phase deviation. The limitation of the bandwidth response is also exhibited by the magnitudes of the parameters in Fig. 13(a), which reports qualitatively equal responses with amplitude significantly decreasing above 800 MHz. The band pass behavior exhibited by the magnitude of the parameters XB ₂₁ and XB ₃₁ is revealed in b ₂₁ and b ₃₁ as the latter are the main contributions to the output waves; an optimized DPA output network can equalize the final DPA response over the bandwidth.

Fig. 13.

Comparison of measured (symbols) and simulated (continuos) XB ₂₁ and XB ₃₁ parameters at 31 dBm input power across the frequency band. (a)Magnitude of XB ₃₁ and XB ₂₁. (b) Phase difference between XB ₃₁ and XB ₂₁.