3–20-GHz GaN MMIC Power Amplifier Design Through a COUT Compensation Strategy

This letter presents the design approach for a compact, single-stage, wideband MMIC power amplifier. A method is proposed to compensate for the output capacitance of the active device over a frequency range as wide as possible, with minimum impact on the achievable output power, which leads to a two-element compensating network. A three-section transformer is then adopted for a real-to-real transformation. The CW characterization shows the output power higher than 32 dBm and the drain efficiency between 35% and 45%, over a fractional bandwidth of 148%, from 3 to 20 GHz.

In this work, we propose a novel design strategy to compensate for the output capacitance C OUT of the HEMT for any Manuscript  device size, as long as C OUT is an accurate representation of the output reactive effects of the device. A 3-20-GHz singleended MMIC amplifier fabricated on a 100-nm GaN-on-Si process is presented to demonstrate the validity of the approach. The results compare well with the state of the art (see Table I) while relying on a simpler design approach and using a single transistor and small MMIC area.

A. Optimal Load Identification
The optimal intrinsic load of an FET can be considered real and frequency-independent. However, the dispersion effects, which can be modeled with an equivalent output capacitance, make the extrinsic load strongly dependent on the frequency. The proposed PA design method shows a specific, simple way of compensating C OUT , and then relies on a real-to-real transformation from the system impedance to the intrinsic optimum load.
In the estimation of the optimal extrinsic load, the device output capacitance C OUT can be considered constant for the sake of simplicity [7], and it is estimated using Cold-FET simulations [8]. For the adopted device, a GaN-on-Si 100-nm gate-length 8 × 100 μm device supplied by OMMIC, the obtained value for C OUT is 0.37 pF.
As a reference, an idealized output network is shown in Fig. 1(b). The negative capacitance would compensate for the effect of C OUT at each frequency, and the resistor R opt represents the optimal intrinsic load of the device. For this device, R opt ≈ 20 , taking into account a drain-to-source bias voltage: V DD = 12 V, knee voltage: V k = 2 V, and maximum current: From Fig. 1(b), the optimal reflection coefficient opt is found to describe a constant conductance circle as a function of frequency, with the center in −g opt /(1 + g opt ) and the radius 1/(1 + g opt ), given by where Z 0 is the reference impedance (50 in this case), f is the frequency, and g opt = Z 0 /R opt . Fig. 1(a) illustrates the arc that represents opt over a set of frequencies from dc to 25 GHz, which is obtained using (1). The resistance R opt = 20 , as shown in Fig. 1(b), can be synthesized from the reference system impedance Z 0 = 50 , and with an arbitrary bandwidth, using a multisection transformer. In other words, the required bandwidth can be guaranteed for this transformation by using enough sections for the transformer. It is important, however, to balance the number of sections between transformation accuracy and inserted losses and size. If this can be achieved reasonably in the technology adopted, then the problem reduces to designing a network that synthesizes, as precisely as possible, the negative capacitance effect shown in Fig. 1(b).

B. Idealized Solution
In practice, the arc shown in Fig. 1(a) cannot be synthesized by a single passive element. However, using a twoelement network, an approximated solution can be found. In order to estimate the limitations of a practical solution, an idealized solution, which follows perfectly opt in (1), is studied. As illustrated in Fig. 1(c), it is composed of a shunt susceptance B and a series transmission line of electrical length θ and characteristic impedance Z 0 , where and with ω = 2π f , Y 0 = 1/Z 0 and G opt = 1/R opt . Equation (2) suggests that the most trivial implementation of the shunt susceptance is adopting a capacitor (C OUT ). However, if B is linearly dependent on frequency, from (3), it follows that the electrical length θ is not linear with frequency. This is a significant practical limitation, given the linear frequency dependence of the electrical length of transmission lines.
However, as a tradeoff, an open stub can be used to synthesize B instead of a capacitor. Thus, B has a tangent-like dependence on frequency, which makes θ almost linear with frequency, as shown in the example of Fig. 2 and, therefore, better approximated by a common transmission line. Fig. 2 shows the frequency dependence of θ obtained using (3) for two cases, namely, using the ideal capacitor solution for B (2) and using an open stub.

C. OMN Design
Thus, assuming that R opt is realized using a multisection transformer, the proposed OMN is shown in Fig. 3(a).  The reflection coefficient L , p , obtained at the reference plane right after the stub, can then be expressed as Equation (4) represents an arc similar to (1) but mirrored with respect to the real axis of the Smith Chart [see Fig. 3(b)]. Adding a series transmission line in front of the stub, as illustrated in Fig. 3(b), the group of points represented by L , p turns clockwise on the Smith Chart, with an angle proportional to the frequency. Thus, assuming that Z 02 = Z 0 , the expression for L in Fig. 3(a) is given as follows: Using (5), a solution for θ 2 and θ 1 can be found, aiming to keep L close to opt . In general, the value of Z 01 can be used as an optimization parameter to be selected before solving (5). In this case, for simplicity, Z 01 = Z 02 = Z 0 = 50 .
Since the condition L (0GHz) = opt (0GHz) is guaranteed according to our assumptions, and the susceptance is expected to decrease with frequency in both cases, a convenient solution for θ 2 and θ 1 can be obtained solving In order to select the value of f h , the magnitude of the intrinsic load impedance Z int = 1/(Y L + j ωC OUT ) can be observed over frequency. Thus, based on the bandwidth estimation method proposed in [9], the output power can be estimated as follows: The difference between the estimated saturated power P OUT and the maximum expected power from the device assumed as P MAX = 0.125I 2 M R opt = 2.5 W, for different choices of f h , is shown in Fig 4. In this case, targeting for a maximum power reduction over the band lower than 0.7 dB, f h is selected to be 20 GHz, obtaining θ 2 = 23.6 • and θ 1 = 66.8 • at 20 GHz. Fig. 3(b) shows how the series transmission line   Fig. 5(b). The 20-resistance is obtained through a three-section Chebyshev transformer centered at 15.5 GHz. The open-circuited stub is finely tuned to compensate for the reactive effect of the high impedance bias-tee included in parallel. The series transmission line is implemented including a taper that fits with the device drain pin width. The load L ,syn synthesized by the OMN is compared to the theoretical one in Fig. 6, highlighting the good agreement between 5 and 20 GHz. As expected, the differences at the lowest frequencies are due to the inclusion of the bias-tee and dc blocking capacitors.
The IMN has been designed to optimize the transducer gain over the band. A resistor has also been included for out-and in-band stabilizations.
The scattering and CW characterization results over the band of interest are shown in Fig. 7. The on-wafer calibration at the probe tips has been used, while an extended coaxial port calibration has been adopted to enable the power calibration using a power meter. The achieved bandwidth is in line with  the expected one, apart from a slight shift, which affects the upper band edge. A saturated drain efficiency between 35% and 45% has been obtained over 17 GHz of bandwidth, from 3 to 20 GHz. The corresponding PAE ranges from 27% to 38%, while the obtained saturated output power is higher than 32 dBm over the band, and the power gain is between 9 and 16 dB. Table I shows that the results are comparable to the state of the art while using a simple design approach and a small-size MMIC. The measured results are in rather good agreement with the simulations, except for the discrepancy in the saturated efficiency, which can be justified both by the CW measurements being carried out on wafer directly on a room temperature chuck, without dedicated die attachment, and by the fact that load-pull measurements on the same device have shown the large-signal model to overestimate both saturated power and efficiency [10].

IV. CONCLUSION
A compact multioctave MMIC PA has been designed through a simple output capacitance compensation strategy. The obtained drain efficiency is shown to be between 35% and 45% over a 148% fractional bandwidth and with 32 dBm of the output power, in line with state-of-the-art broadband PAs for RF and microwave front-end systems.