Power Compression and Phase Analysis of GaN HEMT for Microwave Receiver Protection

: This paper reports a high-performance microwave receiver protector (RP) based on a single gallium nitride (GaN) high electron mobility transistor (HEMT) at an operation frequency of 30 to 3000 MHz. The HEMT-based RP exhibits multi features: high power compression, constant output power, tunable threshold power level, and insensitivity to frequency variation. With a low drain voltage (V ds ) of 3 V, constant output power of 9.9 dBm was acquired for input power over its threshold power of 3.2 dBm. Power compression of 13.3 dB was achieved at the input power of P in = 20 dBm. In addition, adjustable threshold power level P th could be obtained by merely tuning drain voltage. Transducer gain measurement results were employed to explain the occurrence of output power saturation. Relatively higher P th was linked to wider gate voltage swing which extended the linear region of the P out -P in characteristic. In addition, the GaN HEMT’s power compression capability shows great immunity to frequency variation, which is promising for protecting sensitive receiver components at both low and high frequencies. Finally, the phase shift of the GaN HEMT RP at high input power was measured and analyzed by the nonlinear behaviors of input capacitance C gs .


Introduction
Receiver protectors (RPs) are widely used to provide protection to radio frequency (RF) and microwave receivers and components, such as low noise amplifiers (LNAs) [1,2] and analog-to-digital converters (ADCs) [3,4].An RP allows input power below a certain value to pass through ideally without loss, and attenuating input signal strength when it exceeds the threshold.A number of device technologies have been developed to achieve RF and microwave RPs, including Schottky barrier diodes (SBDs) [5][6][7], p-i-n diodes [3,8,9], and transistors [10][11][12].Employing a steep-mesa technology, a gallium nitride (GaN) SBD based RP demonstrated a low on-resistance (R ON ) and a power compression of 3.3 dB with a corresponding input power of 20 dBm at 2 GHz [7].A low insertion loss of 0.3 dB has also been reported for a diamond diode based RP at an operation frequency of 1 GHz [9].However, for a diode-based RP, typically a tradeoff often has to be made between C off and R on [7][8][9].Although diode-based RPs have made steady progress, they still face some important challenges, such as insufficient power compression, inadequacy in tuning their threshold power level (the input power with 1-dB gain compression), and sensitivity to frequency change.Some attempts, including reverse-biased configurations, stacked antiparallel configurations, etc. have been enacted to mitigate the issues [3,13]; however, most of the efforts required complex circuits to work with.Transistors have been regarded as another viable option for RF RPs.The basic principle of transistor-based RPs is to operate the transistors in their saturation region to limit the output power [10,14,15].Owing to their saturated output power, RPs formed by transistors possess the advantages of constant output power and outstanding power compression capability.
In this paper, we demonstrated a microwave RP based on a single GaN HEMT on Silicon carbide (SiC) substrate.The HEMT receiver protector offers a certain gain for the small input signal and attenuates input signal strength beyond the threshold power into a constant output power.The threshold power could be well adjusted by varying the bias.It is also demonstrated that the power reduction capability was hardly sensitive to working frequency.Moreover, the phase shift-a critical issue when an RP was applied in high performance phased-array receiver front end [25]-was investigated and analyzed by the small RF signal measurements.The results paved a solid path for a single GaN HEMT to form an RP with high power compression, threshold power adjustability, and frequency stability.

Materials and Methods
The GaN-based HEMT used in this study was grown and fabricated on a SiC substrate as shown in Figure 1a.The epitaxial structure includes an Al 0.25 Ga 0.75 N barrier layer, a GaN layer buffer layer, and an AlN nucleation layer.The fabrication process of the HEMT started with mesa isolation, which was completed in Inductive Coupled Plasma Reactive Ion Etching (ICP-RIE) and wet etching in 5% TMMA at 50 • C.Then, the ohmic contact was formed by depositing Ti/Al/Ni/Au (20/150/50/80 nm), followed by annealing at 850 • C for 45 s.Finally, a Ni/Au (50/150 nm) Schottky metal was evaporated as the gate and interconnection.The gate terminal was fabricated into a rectangular shape with its length and width of 1.2 µm and 100 µm, respectively, and the distances between gate to source and to drain were 1.5 µm and 2 µm (L g = 1.2 µm, L gs = 1.5 µm, L gd = 2 µm, W g = 100 µm).
Electronics 2022, 11, x FOR PEER REVIEW 2 of 10 in tuning their threshold power level (the input power with 1-dB gain compression), and sensitivity to frequency change.Some attempts, including reverse-biased configurations, stacked antiparallel configurations, etc. have been enacted to mitigate the issues [3,13]; however, most of the efforts required complex circuits to work with.Transistors have been regarded as another viable option for RF RPs.The basic principle of transistor-based RPs is to operate the transistors in their saturation region to limit the output power [10,14,15].Owing to their saturated output power, RPs formed by transistors possess the advantages of constant output power and outstanding power compression capability.AlGaN/GaN-based high electron mobility transistors (HEMTs) with embedded 2-dimension electron gas (2DEG) have been widely used in power amplifiers (PAs) [16,17], RF switches [18,19] and LNAs with extremely short recovery time [20,21], due to superior properties such as high power density at high frequencies, high breakdown voltages and large carrier density and mobility [22][23][24].
In this paper, we demonstrated a microwave RP based on a single GaN HEMT on Silicon carbide (SiC) substrate.The HEMT receiver protector offers a certain gain for the small input signal and attenuates input signal strength beyond the threshold power into a constant output power.The threshold power could be well adjusted by varying the bias.It is also demonstrated that the power reduction capability was hardly sensitive to working frequency.Moreover, the phase shift-a critical issue when an RP was applied in high performance phased-array receiver front end [25]-was investigated and analyzed by the small RF signal measurements.The results paved a solid path for a single GaN HEMT to form an RP with high power compression, threshold power adjustability, and frequency stability.

Materials and Methods
The GaN-based HEMT used in this study was grown and fabricated on a SiC substrate as shown in Figure 1a.The epitaxial structure includes an Al0.25Ga0.75Nbarrier layer, a GaN layer buffer layer, and an AlN nucleation layer.The fabrication process of the HEMT started with mesa isolation, which was completed in Inductive Coupled Plasma Reactive Ion Etching (ICP-RIE) and wet etching in 5% TMMA at 50 °C.Then, the ohmic contact was formed by depositing Ti/Al/Ni/Au (20/150/50/80 nm), followed by annealing at 850 °C for 45 s.Finally, a Ni/Au (50/150 nm) Schottky metal was evaporated as the gate and interconnection.The gate terminal was fabricated into a rectangular shape with its length and width of 1.2 µm and 100 µm, respectively, and the distances between gate to source and to drain were 1.5 µm and 2 µm (Lg = 1.2 µm, Lgs = 1.5 µm, Lgd = 2 µm, Wg = 100 µm).The setup shown in Figure 1b was used for power compression measurements of the GaN HEMT RP.To investigate the power limiting performance of the GaN HEMT at various frequencies, an on-wafer GaN HEMT measurement was conducted without being constrained by the matching network.The input RF signal which was generated by the signal generator (Rohde & Schwarz SMA100B) was injected into the gate using a bias-tee.The output RF signal was extracted from the drain terminal using a spectrum analyzer.To protect the spectrum analyzer from being overdriven, a 30 dB attenuator was used.Power-dependent measurements at various DC bias voltages and different frequencies were carried out with the aid of a computer based controller.The phase shift derived from the reference value at P in = −20 dBm was measured by a Vector Network Analyzer (VNA) (Keysight ENA5080A).

DC Characteristic
Figure 2a shows the transfer characteristics of the GaN HEMT, with a peak DC transconductance (g m ) of 197 mS/mm obtained at V gs /V ds = −1/3 V.The threshold voltage V th was determined to be −1.8V, extracted from the linear extrapolation of the I ds -V gs curve.Figure 2b depicts the output characteristics of the GaN HEMT, showing saturated drain current density (I dsat ) of 667 mA/mm at V gs = 4 V.The slight drop of the drain current during relatively high drain voltage with V gs >1 V is due to the self-heating effect (SHE) [26].Under the field strength of 0.5 MV/cm, the gate leakage current density of this GaN HEMT was measured to be 1.95 × 10 −3 mA/mm, which is much smaller than the typical gate breakdown standard of 1 mA/mm [27,28], indicating a V gd breakdown voltage higher than 100 V.
Electronics 2022, 11, x FOR PEER REVIEW 3 of 10 The setup shown in Figure 1b was used for power compression measurements of the GaN HEMT RP.To investigate the power limiting performance of the GaN HEMT at various frequencies, an on-wafer GaN HEMT measurement was conducted without being constrained by the matching network.The input RF signal which was generated by the signal generator (Rohde & Schwarz SMA100B) was injected into the gate using a bias-tee.The output RF signal was extracted from the drain terminal using a spectrum analyzer.To protect the spectrum analyzer from being overdriven, a 30 dB attenuator was used.Power-dependent measurements at various DC bias voltages and different frequencies were carried out with the aid of a computer based controller.The phase shift derived from the reference value at Pin = −20 dBm was measured by a Vector Network Analyzer (VNA) (Keysight ENA5080A).

DC Characteristic
Figure 2a shows the transfer characteristics of the GaN HEMT, with a peak DC transconductance (gm) of 197 mS/mm obtained at Vgs/Vds = −1/3 V.The threshold voltage Vth was determined to be −1.8V, extracted from the linear extrapolation of the Ids-Vgs curve.Figure 2b depicts the output characteristics of the GaN HEMT, showing saturated drain current density (Idsat) of 667 mA/mm at Vgs = 4 V.The slight drop of the drain current during relatively high drain voltage with Vgs >1 V is due to the self-heating effect (SHE) [26].Under the field strength of 0.5 MV/cm, the gate leakage current density of this GaN HEMT was measured to be 1.95 × 10 −3 mA/mm, which is much smaller than the typical gate breakdown standard of 1 mA/mm [27,28], indicating a Vgd breakdown voltage higher than 100 V.

High Power Compression of the GaN HEMT RP
Figure 3a presents representative output power (Pout) as a function of input power.When the input power was low, the receiver protector offered a fixed gain of 2.9 dB.The results show that Pout increased linearly as injected power was enhanced from −20 dBm to 3.2 dBm, with a fixed gain of 2.9 dB rather than insertion loss typically observed in a diodebased RP.With an input power of 3.2 dBm, a gain reduction of 1 dB was observed.When the input power was further enhanced, the output power began to saturate and was clamped at 9.9 dBm as shown in Figure 3a.The input power level could only reach 21 dBm due to the short length of the Lgd (2 microns), and it could be further improved by

High Power Compression of the GaN HEMT RP
Figure 3a presents representative output power (P out ) as a function of input power.When the input power was low, the receiver protector offered a fixed gain of 2.9 dB.The results show that P out increased linearly as injected power was enhanced from −20 dBm to 3.2 dBm, with a fixed gain of 2.9 dB rather than insertion loss typically observed in a diode-based RP.With an input power of 3.2 dBm, a gain reduction of 1 dB was observed.When the input power was further enhanced, the output power began to saturate and was clamped at 9.9 dBm as shown in Figure 3a.The input power level could only reach 21 dBm due to the short length of the L gd (2 microns), and it could be further improved by some advanced processing technologies, such as a metal-insulator-semiconductor (MIS) HEMT with a gate dielectric [29] or structures with surface passivation [30].some advanced processing technologies, such as a metal-insulator-semiconductor (MIS) HEMT with a gate dielectric [29] or structures with surface passivation [30].
In the shaded area of Figure 3b, the power compression as a function of input power could be well fitted by a linear relationship with a slope of 1 dB per 1dB, which indicated a constant output power.The improvement of the power compression of this GaN HEMT RP was at the expense of DC power consumption.The GaN HEMT RP in this work presented a better power limiting capability than diode-based RPs reported in the literature [7,31,32].As shown in Figure 3c, when the injection power was 17 dB higher than individual threshold power levels, the GaN HEMT RP had 2~4 dB more power compression than those diode-base RPs.It was attributed to the saturated output power of the GaN HEMT, while the diode-based RP cannot sufficiently attenuate the input power due to its non-zero on-resistance (Ron) at high input power [33].Moreover, there was a tradeoff between high power compression and circuit complexity for a diode based RP [34].The high power compression, as shown in Figure 3b, was challenging to realize for a single-stage diode based RP [3,33].Therefore, increasing the number of stages was often used to achieve a constant output power at a large input signal, which would increase the size and complexity of the diode based RP circuit.Whereas, for the GaN HEMT-based RP, the circuit complexity only came from the bias circuit.

Tunable Threshold of the GaN HEMT RP
Figure 4a shows the relationship between the output power and the input power of the GaN HEMT RP at Vgs = −1 V (working frequency of 3 GHz), with three different drain voltages (3/5/10 V).When the Pin was below 3.5 dBm, uniform output power Pout was acquired for all the bias conditions.However, when the Pin was beyond 7 dBm, apparent divergence was spotted as Vds increased from 3 V to 5 V and 10 V.In addition to enhanced output power with increasing Vds, the threshold power level Pth was also enhanced.Threshold power levels Pth of 3.97/6.97/7.97dBm were extracted from Vds = 3/5/10 V, respectively, indicating that a higher drain bias may extend the linear region of an RP and postpone the occurrence of power saturation.In the shaded area of Figure 3b, the power compression as a function of input power could be well fitted by a linear relationship with a slope of 1 dB per 1dB, which indicated a constant output power.The improvement of the power compression of this GaN HEMT RP was at the expense of DC power consumption.
The GaN HEMT RP in this work presented a better power limiting capability than diode-based RPs reported in the literature [7,31,32].As shown in Figure 3c, when the injection power was 17 dB higher than individual threshold power levels, the GaN HEMT RP had 2~4 dB more power compression than those diode-base RPs.It was attributed to the saturated output power of the GaN HEMT, while the diode-based RP cannot sufficiently attenuate the input power due to its non-zero on-resistance (R on ) at high input power [33].Moreover, there was a tradeoff between high power compression and circuit complexity for a diode based RP [34].The high power compression, as shown in Figure 3b, was challenging to realize for a single-stage diode based RP [3,33].Therefore, increasing the number of stages was often used to achieve a constant output power at a large input signal, which would increase the size and complexity of the diode based RP circuit.Whereas, for the GaN HEMT-based RP, the circuit complexity only came from the bias circuit.

Tunable Threshold of the GaN HEMT RP
Figure 4a shows the relationship between the output power and the input power of the GaN HEMT RP at V gs = −1 V (working frequency of 3 GHz), with three different drain voltages (3/5/10 V).When the P in was below 3.5 dBm, uniform output power P out was acquired for all the bias conditions.However, when the P in was beyond 7 dBm, apparent divergence was spotted as V ds increased from 3 V to 5 V and 10 V.In addition to enhanced output power with increasing V ds , the threshold power level P th was also enhanced.Threshold power levels P th of 3.97/6.97/7.97dBm were extracted from V ds = 3/5/10 V, respectively, indicating that a higher drain bias may extend the linear region of an RP and postpone the occurrence of power saturation.To investigate the dependence of the threshold power level Pth on the drain voltage Vds, the transducer gain, which was measured at a low input power of −20 dBm, was utilized.Figure 4b depicts transducer gain as a function of Vgs at the frequency of 3 GHz.The gate voltage swing (GVS) [35] for a 9 dB transducer gain drop was determined to be 2.9 V, 4.4 V, and 5.2 V, for Vds = 3/5/10 V, respectively.
A relative wider GVS means the transistor could keep the transducer gain high for an ample range of input power, as the input power was applied at the gate-source terminals.Thus, with a wide GVS, the transistor could allow a broad range of input power through without causing output power to be compressed, as shown in an extended linear region of the Pout-Pin graph [Figure 4a].As a result, a larger threshold power level Pth could be obtained by merely increasing drain-source bias, and Pth can be easily electronicallytuned by Vds, which contributes to the application of the HEMT based RP in a dynamic environment and the precise protection of sensitive devices [13,36].It should also be noted that reducing the Lg of a GaN HEMT would enhance the non-uniformity of gm, which could enable the lowering of Pth to protect more power-sensitive devices [37,38].However, for a p-i-n diode RP, the threshold power level was typically governed by the thickness of the i-layer, and can hardly be adjusted once the device was manufactured [39].

Frequency Independent HEMT RP
Figure 5a reports the input and output power characteristics of the GaN HEMT based RP at various working frequencies.The measured data show that at a given Vds, the GaN HEMT based RP exhibited typically the same power compression capability and threshold power level over a wide frequency range from 30 MHz to 3 GHz.For example, at a Vds of 3 V, the maximum output power and Pth were extracted to be 9.86 ± 0.3 dBm and 2.81 ± 0.4 dBm, respectively, showing little divergence among various operation frequencies from 30 MHz to 3 GHz.Whereas, Pth of a p-i-n based RP dropped rapidly as shifting to low operation frequencies due to the transit time of carriers across the i-region is shorter than the signal period time at a low frequency, e.g., Pth was reduced from 20 dBm at 3 GHz to 9 dBm at 30 MHz for a silicon p-i-n diode [31].To investigate the dependence of the threshold power level P th on the drain voltage V ds , the transducer gain, which was measured at a low input power of −20 dBm, was utilized.Figure 4b depicts transducer gain as a function of V gs at the frequency of 3 GHz.The gate voltage swing (GVS) [35] for a 9 dB transducer gain drop was determined to be 2.9 V, 4.4 V, and 5.2 V, for V ds = 3/5/10 V, respectively.
A relative wider GVS means the transistor could keep the transducer gain high for an ample range of input power, as the input power was applied at the gate-source terminals.Thus, with a wide GVS, the transistor could allow a broad range of input power through without causing output power to be compressed, as shown in an extended linear region of the P out -P in graph [Figure 4a].As a result, a larger threshold power level P th could be obtained by merely increasing drain-source bias, and P th can be easily electronicallytuned by V ds , which contributes to the application of the HEMT based RP in a dynamic environment and the precise protection of sensitive devices [13,36].It should also be noted that reducing the L g of a GaN HEMT would enhance the non-uniformity of g m , which could enable the lowering of P th to protect more power-sensitive devices [37,38].However, for a p-i-n diode RP, the threshold power level was typically governed by the thickness of the i-layer, and can hardly be adjusted once the device was manufactured [39].

Frequency Independent HEMT RP
Figure 5a reports the input and output power characteristics of the GaN HEMT based RP at various working frequencies.The measured data show that at a given V ds , the GaN HEMT based RP exhibited typically the same power compression capability and threshold power level over a wide frequency range from 30 MHz to 3 GHz.For example, at a V ds of 3 V, the maximum output power and P th were extracted to be 9.86 ± 0.3 dBm and 2.81 ± 0.4 dBm, respectively, showing little divergence among various operation frequencies from 30 MHz to 3 GHz.Whereas, P th of a p-i-n based RP dropped rapidly as shifting to low operation frequencies due to the transit time of carriers across the i-region is shorter than the signal period time at a low frequency, e.g., P th was reduced from 20 dBm at 3 GHz to 9 dBm at 30 MHz for a silicon p-i-n diode [31].Unlike p-i-n based RPs, this GaN HEMT based RP can maintain a good frequency response within its cut-off frequency (ft) of 11.28 GHz.The frequency-insensitive property could be attributed to the uniform transducer gain of the device over a wide operation frequency, as shown in Figure 5b, which shows the transducer gain as a function of frequency for this GaN HEMT.In the range of 30-3000 MHz, an almost steady transducer gain was obtained for either a small RF signal (Pin = −20 dBm) or relatively large RF power (Pin = 5 dBm).As a result, almost identical output power could be expected in the linear region and saturation region of the device.Therefore, constant output power could be achieved at both small and large input power, resulting in a good broadband property without matching circuits.It should be noted that adding a matching network in a real application will not affect the characteristics of the GaN HEMT RP, such as high power compression and tunable threshold power.
The frequency response of this HEMT RP is related to the current cut-off frequency (ft) and maximum oscillation frequency (fmax).It is noted that the device used in this study featured a gate length of 1.2 µm and held an ft of 11.28 GHz and an fmax of 22.35 GHz, respectively.It is expected that the frequency steadiness property could be extended to an even higher frequency on shrinking the gate length dimension [40][41][42].Based on its frequency-insensitive property, GaN HEMT could be used to protect sensitive components such as mixers in transmitters over a large frequency range.In addition, it paved a path to improving the frequency response without using multiple devices or auxiliary circuits [3].

Phase Shift Analysis of the HEMT RP
Figure 6a illustrates the phase shift of GaN HEMT based RP with different Vds.The output phase was typically unchanged when the device was fed with a small input power lower than 0 dBm.However, as Pin increased, the phase dropped dramatically.Phase shift over 1 degree occurred at the Pin of 6.2/10.7/12.7 dBm for Vds = 3/5/10 V respectively.Unlike p-i-n based RPs, this GaN HEMT based RP can maintain a good frequency response within its cut-off frequency (f t ) of 11.28 GHz.The frequency-insensitive property could be attributed to the uniform transducer gain of the device over a wide operation frequency, as shown in Figure 5b, which shows the transducer gain as a function of frequency for this GaN HEMT.In the range of 30-3000 MHz, an almost steady transducer gain was obtained for either a small RF signal (P in = −20 dBm) or relatively large RF power (P in = 5 dBm).As a result, almost identical output power could be expected in the linear region and saturation region of the device.Therefore, constant output power could be achieved at both small and large input power, resulting in a good broadband property without matching circuits.It should be noted that adding a matching network in a real application will not affect the characteristics of the GaN HEMT RP, such as high power compression and tunable threshold power.
The frequency response of this HEMT RP is related to the current cut-off frequency (f t ) and maximum oscillation frequency (f max ).It is noted that the device used in this study featured a gate length of 1.2 µm and held an f t of 11.28 GHz and an f max of 22.35 GHz, respectively.It is expected that the frequency steadiness property could be extended to an even higher frequency on shrinking the gate length dimension [40][41][42].Based on its frequency-insensitive property, GaN HEMT could be used to protect sensitive components such as mixers in transmitters over a large frequency range.In addition, it paved a path to improving the frequency response without using multiple devices or auxiliary circuits [3].

Phase Shift Analysis of the HEMT RP
Figure 6a illustrates the phase shift of GaN HEMT based RP with different V ds .The output phase was typically unchanged when the device was fed with a small input power lower than 0 dBm.However, as P in increased, the phase dropped dramatically.Phase shift over 1 degree occurred at the P in of 6.2/10.7/12.7 dBm for V ds = 3/5/10 V respectively.A small RF signal equivalent circuit model of this GaN HEMT is shown in Figure 6b [43,44].This model consisted of an input resistance (Ri), an input (Cgs), output (Cds) and feedback (Cgd) capacitors, and a voltage controlled current source (gm•Vgsiexp(-jωτ)) where τ was transconductance delay.The RF power source is modeled by a voltage source and an internal impedance Zs = Rs.The output load is modeled by an admittance YL = GL.
The feedback capacitor Cgd could be ignored due to the fact that it had small value.Therefore, the phase of output voltage could be computed as Equation ( 1): Since Cds (at fF level) is much smaller than the input capacitor Cgs, the phase of output voltage could be further simplified as Equation ( 2): ∠V out = arctan ( − ωC gs R s +R i ) − ωτ. (2) Thus, the phase of output voltage could be regarded to be merely determined by the Cgs.Cgs could be extracted by the small RF signal equivalent circuit model shown in the dashed box in Figure 6b [44].
Figure 6c shows Cgs as a function of Vgs.For a given Vds, Cgs was unchanged around Vgs = −1 V, which corresponds to a relatively low input power.However, on increasing the input power, which could be interpreted as increasing the Vgs, a dramatically enhanced Cgs was observed.The increase of Cgs would cause a decrease in the phase of output voltage according to Equation (2), resulting in a significant drop in the phase shift at large inputs as shown in Figure 6a.
When Vds was increased from 3 V to 5 V and 10 V, the corresponding transition voltages extracted from the linear extrapolation of Cgs-Vgs curve were also increased from 1.2 V to 2.6 V and 6.2 V, respectively.The lower transition voltage at a relatively smaller drain voltage leads to the early onset of Cgs increasing, which causes the early significant output phase drop at a relatively small Vds when a large power is injected into the gate of the device.

Conclusions
High performance microwave RP based on a single GaN HEMT is demonstrated, with features of high power compression, tunable threshold power level, and a frequencyinsensitive property.Although additional power was dissipated, constant output power was achieved at large input power owing to the saturated output power of the HEMT RP, indicating a competitive advantage over diode-based RPs.In addition, adjustable Pth was presented and Pth could be easily tuned by adjusting drain voltage.The tunable Pth was well modeled and explained by transducer gain measurement results.The higher Pth was attributed to the wider gate voltage swing, which extended the linear region of the Pout-Pin A small RF signal equivalent circuit model of this GaN HEMT is shown in Figure 6b [43,44].This model consisted of an input resistance (R i ), an input (C gs ), output (C ds ) and feedback (C gd ) capacitors, and a voltage controlled current source (g m •V gsi exp(-jωτ)) where τ was transconductance delay.The RF power source is modeled by a voltage source and an internal impedance Z s = R s .The output load is modeled by an admittance Y L = G L .
The feedback capacitor C gd could be ignored due to the fact that it had small value.Therefore, the phase of output voltage could be computed as Equation ( 1): ∠V out = arctan( − ωC gs (R s +R i )) + arctan − ωC ds g ds +G L − ωτ.
Since C ds (at fF level) is much smaller than the input capacitor C gs , the phase of output voltage could be further simplified as Equation (2): ∠V out = arctan( − ωC gs (R s +R i ) − ωτ. (2) Thus, the phase of output voltage could be regarded to be merely determined by the C gs .C gs could be extracted by the small RF signal equivalent circuit model shown in the dashed box in Figure 6b [44].
Figure 6c shows C gs as a function of V gs .For a given V ds , C gs was unchanged around V gs = −1 V, which corresponds to a relatively low input power.However, on increasing the input power, which could be interpreted as increasing the V gs , a dramatically enhanced C gs was observed.The increase of C gs would cause a decrease in the phase of output voltage according to Equation (2), resulting in a significant drop in the phase shift at large inputs as shown in Figure 6a.
When V ds was increased from 3 V to 5 V and 10 V, the corresponding transition voltages extracted from the linear extrapolation of C gs -V gs curve were also increased from 1.2 V to 2.6 V and 6.2 V, respectively.The lower transition voltage at a relatively smaller drain voltage leads to the early onset of C gs increasing, which causes the early significant output phase drop at a relatively small V ds when a large power is injected into the gate of the device.

Conclusions
High performance microwave RP based on a single GaN HEMT is demonstrated, with features of high power compression, tunable threshold power level, and a frequencyinsensitive property.Although additional power was dissipated, constant output power was achieved at large input power owing to the saturated output power of the HEMT RP, indicating a competitive advantage over diode-based RPs.In addition, adjustable P th was presented and P th could be easily tuned by adjusting drain voltage.The tunable P th was well modeled and explained by transducer gain measurement results.The higher P th was attributed to the wider gate voltage swing, which extended the linear region of the

Figure 1 .
Figure 1.(a) Micrographs of GaN HEMT grown and fabricated on SiC with GSG test module; (b) the test setup of this HEMT RP experiment diagram.Figure 1.(a) Micrographs of GaN HEMT grown and fabricated on SiC with GSG test module; (b) the test setup of this HEMT RP experiment diagram.

Figure 1 .
Figure 1.(a) Micrographs of GaN HEMT grown and fabricated on SiC with GSG test module; (b) the test setup of this HEMT RP experiment diagram.Figure 1.(a) Micrographs of GaN HEMT grown and fabricated on SiC with GSG test module; (b) the test setup of this HEMT RP experiment diagram.

Figure 2 .
Figure 2. (a) Transfer characteristics at Vds = 3 V; (b) output characteristics as Vgs increases from −3 V to 4 V with a step of 1 V.

Figure 2 .
Figure 2. (a) Transfer characteristics at V ds = 3 V; (b) output characteristics as V gs increases from −3 V to 4 V with a step of 1 V.

Figure 3 .
Figure 3. (a) Output power (Pout) versus input power (Pin) for the single GaN HEMT RP at 3 GHz; (b) power compression as a function of Pin; (c) comparison of the power compression between this single GaN HEMT and diode-based RPs in the literatures.

Figure 3 .
Figure 3. (a) Output power (P out ) versus input power (P in ) for the single GaN HEMT RP at 3 GHz; (b) power compression as a function of P in ; (c) comparison of the power compression between this single GaN HEMT and diode-based RPs in the literatures.

Figure 4 .
Figure 4. (a) Pout versus Pin at different Vds; (b) transducer gain in small signal mode versus Vgs.

Figure 4 .
Figure 4. (a) P out versus P in at different V ds ; (b) transducer gain in small signal mode versus V gs .

Figure 6 .
Figure 6.(a) Phase shift versus Pin with different Vds; (b) small RF signal equivalent circuit for GaN HEMT; (c) Cgs versus gate voltage.

Figure 6 .
Figure 6.(a) Phase shift versus P in with different V ds ; (b) small RF signal equivalent circuit for GaN HEMT; (c) C gs versus gate voltage.