Real-time amplifier optimization algorithm for adaptive radio using a tunable-varactor matching network

Reconfigurable matching circuitry is needed in cognitive and adaptive wireless transmitters for real-time changes in operating frequency and system performance requirements. We designed a 1.3 GHz matching network using the approach of Fu [1] and used this to perform fast tuning of a field-effect transistor (FET), optimizing gain using a fast steepest-ascent algorithm. Nemati has demonstrated design of varactor-based tunable matching networks for dynamic load modulation [2]. Qiao [3] and du Plessis [4] have reported real-time impedance matching using genetic algorithms, which tend to be inherently slow for many impedance matching problems. We have previously demonstrated optimization of load impedance to maximize output power [5]. This previous application of algorithms, however, is idealized in many ways. In this paper, we implement the fast load-pull search to maximize transducer gain $G_{T}$ using a prototype tunable-varactor circuit for use in real-time reconfigurable transmission.

We designed a tunable-varactor matching network based on the method of Fu [1] at 1.3 GHz (Fig. 1(a)). The circuit was fabricated on a 59-mil FR4 substrate (Fig. 1(b)) and characterized at 0 dBm input power using S-parameter measurements (Fig. 2). The characterized range of the tuner covers much of the Smith Chart.

Fig. 1.

(a) Design of 1.3 GHz tunable matching network, based on Fu [1], (b) Implemented tunable-varactor matching network

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Fig. 2.

Characterized load reflection coefficient states for the tunable varactor matching network

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Fig. 3.

Measured $\vert S_{21}\vert$ versus input power for the varactor matching network at $\Gamma_{L}=0.7/\underline{90^{\circ}}$.

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The tuner was also tested for nonlinear behavior. Significant variations in the S-parameters with increasing input power are observed. Figure 3 shows that at $\Gamma_{L}=0.7/\underline{90^{\circ}}$, the matching network $\vert S_{21}\vert$ varies approximately 2.5 dB over input power variation from −5 dBm to +23 dBm. Additional testing over different varactor bias conditions for $C_{1}, C_{2}$, and $C_{3}$ shows that variations are most significant for large values of the varactor bias voltages. As such, accurate characterization of $\Gamma_{L}$ is needed near the value of power expected to be input to the matching network. Because the purpose of the present paper is to demonstrate the feasibility of fast tuning using a tunable-varactor matching network, a low power value is used to avoid these nonlinearities.

Our previous gradient search optimization [5] was modified and implemented with the tunable-varactor network to maximize $G_{T}$. A plane can be fit to the $G_{T}$ surface near the candidate $\Gamma_{L}$ representing the change in $G_{T}$ from the candidate as a function of $\Delta \Gamma_{L}=\Delta\Gamma_{r}+j\Delta\Gamma_{i}$:

View Source\begin{equation*} \Delta G_{T}=a\Delta\Gamma_{r}+b\Delta\Gamma_{i},\tag{1}\end{equation*}

$$\begin{align*} &\Delta G_{T1}=a\Delta\Gamma_{r1}+b\Delta\Gamma_{i1}\\ &\Delta G_{T2}=a\Delta\Gamma_{r2}+b\Delta\Gamma_{i2} \end{align*}$$ View Source\begin{align*} &\Delta G_{T1}=a\Delta\Gamma_{r1}+b\Delta\Gamma_{i1}\\ &\Delta G_{T2}=a\Delta\Gamma_{r2}+b\Delta\Gamma_{i2} \end{align*}

$$\begin{equation*} \nabla(\Delta G_{T})=\hat{\Gamma}_{r}a+\hat{\Gamma}_{i}b, \tag{2} \end{equation*}$$ View Source\begin{equation*} \nabla(\Delta G_{T})=\hat{\Gamma}_{r}a+\hat{\Gamma}_{i}b, \tag{2} \end{equation*}

$$\begin{equation*} \overline{v}=\frac{D_{s}\nabla(\Delta G_{T})}{\vert \nabla(\Delta G_{T})\vert}, \tag{3} \end{equation*}$$ View Source\begin{equation*} \overline{v}=\frac{D_{s}\nabla(\Delta G_{T})}{\vert \nabla(\Delta G_{T})\vert}, \tag{3} \end{equation*}

Fig. 4.

(a) Estimation of gradient by $\Gamma_{L}$ measurements of nearby points separated by neighboring-point distance $D_{n}$. (b) Jump to the next candidate point in the direction of steepest ascent by search distance $D_{s}$ (reprinted from [5] for convenience).

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The algorithm was measurement tested using a Microwave Technologies MWT-173 FET, with single-tone input power of −20 dBm at 1.3 GHz. The small input power value was used to ensure the varactor network is operated in its linear region. Custom load-pull software was implemented for matching and fixture network characterization and correction, as well as communication with instrumentation. Figure 5 shows the −20 dBm loadpull characteristics as measured by the varactor tuner, compared with contours measured by a standard Maury Microwave tuner. The optimum $\Gamma_{L}$ and $G_{T}$ values are nearly identical for the varactor and Maury tuners.

Fig. 5.

1.3 GHz single-tone MWT-173 FET load-pull transducer gain $(G_{T})$ contours measured using the tunable-varactor matching network (dashed curves, optimum $G_{T}=10.88\ \text{dB}$ at $\Gamma_{L}\ =\ 0.36/\underline{124^{\circ}}$) and Maury load-pull tuner (solid curves, optimum $G_{T}=10.80\ \text{dB}$ at $\Gamma_{L}=0.29/\underline{118^{\circ}}$) for −20 dBm input power.

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Figures 6 and 7 show two algorithm searches taken from different starting values of $\Gamma_{L}$ within the operating region of the matching network. Table I shows excellent agreement of the search end $\Gamma_{L}$ and maximum $G_{T}$ values for algorithm search results from 16 different starting $\Gamma_{L}$ values. The results also correspond well with traditional load-pull from varactor and Maury tuners.

Even for bench-top testing with significant equipment overhead, searching with the varactor tuner is much faster than with the Maury tuner. An algorithm run from $\Gamma_{L}=0$ required 1 minute, 15 seconds using the varactor tuner, compared to 5 minutes, 38 seconds using the Maury tuner.

Fig. 6.

Fast load-impedance optimization for output power fromstarting location $\Gamma_{L}=0.50/\underline{-90.0^{\circ}}$. A maximum $G_{T}=10.92\ \text{dB}$ was obtained at $\Gamma_{1}=0.38/122^{\circ}$ with 16 experimental queries.

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Fig. 7.

Fast load-impedance optimization for output power from starting location $\Gamma_{L}=0.50/\underline{0^{\circ}}$. A maximum $G_{T}=10.87\ \text{dB}$ was obtained at $\Gamma_{L}=0.34/\underline{134^{\circ}}$ with 33 experimental queries.

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A fast real-time load-impedance search algorithm has been demonstrated on a tunable-varactor matching network. The tunable-varactor network provides repeatable results from multiple starting reflection coefficients with a small number of measurements, comparing well with traditional load-pull measurements, but allowing fast, real-time reconfiguration. Results show excellent correspondence for different starting load reflection coefficient values, and compare well with traditionally measured load-pull results. This algorithm is expected to be useful for implementation in cognitive communication and radar systems, allowing the matching network to quickly adapt for changing frequency bands and performance requirements. Future work will investigate advanced power-dependent characterization to counteract the effects of matching-network nonlinearities.

Table I: Tunable-varactor matching network algorithm results from multiple starting reflection coefficients