GaN Power Amplifier with DPD for Enhanced Spectral Integrity in 2.3–2.5 GHz Wireless Systems

Abstract

The increasing need for high-data-rate wireless applications in 5G and IoT networks requires sophisticated power amplifier (PA) designs in the sub-6 GHz spectrum. This work introduces a high-efficiency Gallium Nitride (GaN)-based power amplifier optimized for the 2.3–2.5 GHz frequency band, using digital pre-distortion (DPD) to improve spectral fidelity and reduce distortion. The design employs load modulation and dynamic biasing to optimize power-added efficiency (PAE) and linearity. Simulation findings indicate a gain of 13 dB, a 3 dB compression point at 29.7 dBm input power, and 40 dBm output power, with a power-added efficiency of 60% and a drain efficiency of 65%. The power amplifier achieves a return loss of more than 15 dB throughout the frequency spectrum, ensuring robust impedance matching and consistent performance. Electromagnetic co-simulations confirm its stability under high-frequency settings, rendering it appropriate for next-generation high-efficiency wireless communication systems.

1. Introduction

The exponential demand for higher data rates, alongside the necessity for reliable communication across both terrestrial and satellite platforms, has driven remarkable advancements in power amplifier (PA) design, specifically within the sub-6 GHz frequency range [1,2]. These advancements are particularly critical due to the accelerated deployment of 5G networks and Internet of Things (IoT) ecosystems, which require highly efficient, linear PAs capable of supporting wide bandwidths and delivering low-distortion signal amplification [2,3,4]. Figure 1 illustrates a typical transmission chain architecture in wireless systems, emphasizing the PA’s essential role in ensuring effective signal transmission.

In a conventional transmitting chain, the baseband signal, carrying the required data, is generated and then modulated onto a carrier frequency from an oscillator, typically employing modulation schemes such as Quadrature Amplitude Modulation (QAM), Phase Shift Keying (PSK), or Frequency Shift Keying (FSK), depending on the communication system’s requirements and performance objectives. This modulation step produces a modulated signal ready for amplification [5,6]. The signal subsequently traverses multiple amplification stages, including a driver amplifier and the power amplifier (PA), which ultimately provides the necessary power level for transmission [1,7,8]. Before reaching the antenna, the signal is filtered to remove unwanted spectral components, ensuring efficient and dependable communication [9]. This sequence, as depicted in Figure 1, is fundamental for maintaining signal integrity and energy efficiency, particularly as modern communication systems push towards higher frequencies and stricter performance standards [10,11,12].

With the evolution of high-frequency communication, PA design has become increasingly sophisticated. Contemporary literature presents a wide variety of techniques and materials aimed at addressing the challenges of efficiency, linearity, and thermal management in PAs [9]. Among the prominent materials explored are Gallium Nitride (GaN) and Gallium Arsenide (GaAs), with GaN-based PAs emerging as a preferred solution for high-efficiency, high-power applications. GaN’s properties, including high electron mobility, wide bandgap, and superior thermal conductivity, make it ideal for PAs operating in the sub-6 GHz range, where both power efficiency and robust performance are essential [13,14].

To enhance high-efficiency amplification, Doherty PAs use load modulation techniques to boost efficiency at lower power levels, effectively addressing the needs of signals with high peak-to-average power ratios (PAPRs) [15,16,17,18]. This architecture has proven advantageous for applications involving amplitude-modulated signals, which are common in modern communication systems with high PAPR waveforms [17]. Alternatively, Envelope Tracking (ET) PAs dynamically adjust the supply voltage to match the instantaneous power needs of a signal, reducing power wastage during periods of lower demand and thus significantly improving overall efficiency [8,19].

In addition to efficiency, linearity remains a critical performance metric in PA design [7]. Maintaining a linear relationship between input and output signals is crucial for preserving signal quality, especially in multi-carrier and amplitude-modulated signals prevalent in 5G and IoT applications [20]. However, achieving both high efficiency and linearity is challenging, as PAs typically exhibit non-linear behavior at higher output power levels, leading to spectral regrowth and signal distortion [21]. Techniques such as pre-distortion and feedback linearization are widely implemented to mitigate these non-linearities.

From a mathematical perspective, optimizing PA design involves balancing efficiency, defined through power-added efficiency (PAE), with linearity. The PAE can be expressed as follows:

$$\mathrm{PAE}={\displaystyle \frac{P_{\mathrm{out}}-P_{\mathrm{in}}}{P_{\mathrm{DC}}}}\times 100\%$$

(1)

where $P_{\mathrm{out}}$ denotes the RF output power, $P_{\mathrm{in}}$ represents the RF input power, and $P_{\mathrm{DC}}$ is the total DC power consumed. Enhancing PAE requires differential adjustments to $P_{\mathrm{in}}$ and $P_{\mathrm{DC}}$, which can be analyzed through calculus-based techniques to improve PA performance across varying power levels. For instance, integration over the bandwidth B can be used to compute the average PAE across the operational range:

$${\mathrm{PAE}}_{\mathrm{avg}}={\displaystyle \frac{1}{B}}{\int }_{f_1}^{f_2}\mathrm{PAE}\left(f\right)df$$

(2)

where $f_1$ and $f_2$ denote the lower and upper bounds of the frequency range, respectively.

Recent advances in wireless communication systems—particularly those employing orthogonal frequency-division multiplexing (OFDM)—have intensified the focus on power amplifier (PA) linearity due to its critical influence on spectral efficiency and signal integrity. Non-linear behavior in PAs introduces spectral regrowth and distortion, necessitating effective PAPR suppression techniques to mitigate associated degradations. Classical approaches such as Selected Mapping (SLM) have been extensively explored, with notable contributions such as the low-complexity SLM scheme proposed in [22], which offers a trade-off between computational burden and PAPR reduction in OFDM systems. In parallel, novel strategies leveraging adaptive transmission and waveform shaping have emerged. For instance, adaptive modulation techniques that incorporate PAPR-awareness, as detailed in [23], dynamically adjust the modulation order to enhance energy efficiency under non-linear constraints. Furthermore, shaping-based solutions have demonstrated significant potential. The Spectral Shaping Multiple Access (SSMA) method introduced in [24] unifies multi-branch delay-Doppler domain shaping for satellite applications, while probabilistic shaping combined with mutual information optimization and precoding, as explored in [25], achieves a joint PAPR reduction and throughput enhancement in MISO-OFDM underwater wireless optical communication. Despite these advances, most existing methods either impose considerable algorithmic complexity or are tailored for specific channel models. Hence, there remains a compelling need for practical and scalable linearization frameworks that maintain high efficiency without compromising spectral containment. This study seeks to address this gap by integrating digital pre-distortion with high-efficiency PA design in the 2.4 GHz band, providing a comprehensive solution suitable for real-time broadband wireless systems.

This study introduces a high-efficiency GaN-based power amplifier (PA) optimized for the 2.3–2.5 GHz wireless communication spectrum, utilizing digital pre-distortion (DPD) to improve spectral fidelity and linearity. The design process incorporates load modulation, dynamic biasing, and electromagnetic co-simulations to enhance power-added efficiency (PAE) and impedance matching. The CGH40010 GaN HEMT device was chosen for its exceptional gain, efficiency, and thermal characteristics. Simulation findings indicate a gain of 13 dB, an output power of 40 dBm, a 3 dB compression point at an input power of 29.7 dBm, a power-added efficiency (PAE) of 60%, and a return loss greater than 15 dB across the band. The use of DPD markedly decreases nearby channel leakage and error vector size, validating its efficacy in alleviating non-linearity and assuring adherence to contemporary wireless communication standards. The remainder of this paper is structured as follows: Section 2 details the PA design methodology, while Section 3 presents simulation results with a focus on efficiency and linearity. Finally, Section 4 offers conclusions and potential directions for future research.

2. Design Methodology

In wireless communication systems, the transmitter’s signal amplification chain concludes with the power amplifier (PA), a critical component responsible for delivering sufficient output power to counteract channel losses between the transmitter and receiver. As the final stage in signal amplification, the PA’s design significantly influences the system’s efficiency, cost-effectiveness, and signal integrity.

A primary design criterion for PAs is the power-added efficiency (PAE), which measures the efficiency of converting direct current (DC) power $P_{\mathrm{DC}}$ into radio frequency (RF) output power $P_{\mathrm{out}}$. Mathematically, the efficiency is expressed as follows:

$$\eta ={\displaystyle \frac{P_{\mathrm{out}}}{P_{\mathrm{DC}}}}\times 100\%$$

(3)

Maximizing $\eta$ is especially crucial in battery-powered devices, where higher efficiency translates to extended battery life. A more comprehensive metric, the PAE, accounts for the amplifier’s gain G and input power $P_{\mathrm{in}}$:

$$\mathrm{PAE}={\displaystyle \frac{P_{\mathrm{out}}-P_{\mathrm{in}}}{P_{\mathrm{DC}}}}\times 100\%$$

(4)

The design objective is to maximize PAE while minimizing $P_{\mathrm{DC}}$, as specified in

Table 1. Specifications of the power amplifier.

Parameter	Specification
Center Frequency	2.4 GHz
Bandwidth	±100 MHz
Output Power	10 Watts (40 dBm)
Gain	>10 dB
Return Loss	<−15 dB
Power-Added Efficiency (PAE)	>50%

. For a thorough efficiency analysis, the average power output over a frequency band B can be evaluated by integrating the instantaneous power $P\left(t\right)$:

$$P_{\mathrm{out},\mathrm{avg}}={\displaystyle \frac{1}{B}}{\int }_{{\displaystyle \frac{-B}{2}}}^{{\displaystyle \frac{B}{2}}}P\left(f\right)\mathrm{d}f$$

(5)

This approach allows for assessing the average power output across the intended bandwidth, ensuring that the PA meets operational specifications.

A critical challenge in PA design is achieving a balance between efficiency and linearity. Non-linearities in the input–output response introduce harmonics and intermodulation products, which degrade signal integrity. To model linearity, we consider the Taylor series expansion of the PA’s output $V_{\mathrm{out}}$ as a function of the input voltage $V_{\mathrm{in}}$:

$$V_{\mathrm{out}}\left(t\right)=a_1{V}_{\mathrm{in}}\left(t\right)+a_2{V}_{\mathrm{in}}^2\left(t\right)+a_3{V}_{\mathrm{in}}^3\left(t\right)+\dots$$

(6)

where $a_1$ is the linear gain, and $a_2,a_3,\dots$ represent non-linear distortion terms. To ensure linearity, higher-order terms should be minimized.

An essential metric for linearity is the third-order intercept point (IP3), where the input level causes the third-order intermodulation product to intersect with the linear response. The output IP3 (OIP3) can be expressed as follows:

$$\mathrm{OIP}3={\displaystyle \frac{1}{2}}\left({\displaystyle \frac{P_{\mathrm{out}}}{P_{3\mathrm{rd}}}}\right)P_{\mathrm{out}}$$

(7)

where $P_{3\mathrm{rd}}$ is the power of the third-order intermodulation product.

Return loss $RL$ characterizes the amount of power reflected due to impedance mismatches and is defined by

$$RL=-20{\log }_{10}\left|{\displaystyle \frac{Z_{\mathrm{in}}-Z_0}{Z_{\mathrm{in}}+Z_0}}\right|$$

(8)

where $Z_{\mathrm{in}}$ is the input impedance, and $Z_0$ is the characteristic impedance, typically 50 ohms. A low return loss (e.g., $RL<-15\mathrm{dB}$) is desirable for stable operation, as specified in Table 1.

Table 1 summarizes the design specifications for the PA in this system, covering parameters such as center frequency, bandwidth, output power, gain, return loss, PAE, and linearity metrics such as IP3. These specifications are crucial to achieving the desired performance in dynamic wireless environments. The selected wavelength of $\lambda =0.125\mathrm{m}$, corresponding to a central frequency of 2.4 GHz, is derived from the standard wave propagation relation $\lambda =c/f$, where $c=3\times {10}^8\mathrm{m}/\mathrm{s}$ and $f=2.4\times {10}^9\mathrm{Hz}$. This wavelength is particularly advantageous for antenna and RF system design. It permits the use of compact and efficient antenna structures such as half-wave dipoles ($\approx 62.5\mathrm{mm}$) and quarter-wave monopoles ($\approx 31.25\mathrm{mm}$), which are highly compatible with constrained platforms like IoT modules and 5G terminals. From a circuit design perspective, $\lambda =0.125\mathrm{m}$ supports impedance-matching networks using $\lambda /4$ transformers and reactive stubs of $\lambda /8$ or $\lambda /16$, ensuring efficient RF signal transmission with manageable layout dimensions on standard PCB materials. Additionally, this wavelength offers favorable propagation characteristics, such as moderate path loss, acceptable wall penetration, and resilience to weather-induced attenuation, making it well suited for both indoor and outdoor wireless applications. The frequency band associated with this wavelength (2.3–2.5 GHz) is also globally allocated under the ISM license-free spectrum, aligning with widespread standards including Wi-Fi, Bluetooth, ZigBee, and other low-power communication protocols. Thus, selecting a wavelength of 0.125 m optimally balances antenna compactness, signal integrity, regulatory compatibility, and practical implementation across modern wireless systems.

2.1. Technology Selection

The design of this power amplifier (PA) is based on Gallium Nitride High-Electron-Mobility Transistor (GaN HEMT) technology, selected for its superior power efficiency, high breakdown voltage, and thermal stability—critical factors for high-frequency and high-power applications. Compared to conventional silicon or Gallium Arsenide (GaAs) transistors, GaN HEMTs offer significantly higher power density and enhanced robustness in demanding RF environments such as wireless base stations, radars, and satellite communications [9,26,27].

2.1.1. Comparison of GaN HEMT with Alternative Technologies

To provide a clearer justification for GaN HEMT selection,

Table 2. Comparison of GaN HEMT, GaAs, and silicon technologies.

Parameter	GaN HEMT	GaAs	Silicon (Si)
Bandgap (eV)	3.4	1.42	1.1
Power Density (W/mm)	5–12 W/mm	1–2 W/mm	<1 W/mm
Thermal Conductivity (W/m·K)	130–200	45	150
Efficiency (%)	60–80%	40–55%	30–50%
Operating Frequency (GHz)	Up to 100 GHz	Up to 50 GHz	Up to 5 GHz

compares key performance metrics against Si and GaAs transistors.

A clear distinction exists between traditional inorganic semiconductors—such as Gallium Nitride (GaN), Gallium Arsenide (GaAs), and Silicon (Si)—and emerging organic transistor technologies. Inorganic transistors, particularly GaN and GaAs, offer significant advantages in high-frequency, high-power domains. GaN transistors exhibit wide bandgaps (3.4 eV), high electron mobility, excellent thermal conductivity, and high breakdown voltages, enabling superior power density and efficiency in the GHz range. GaAs devices, while having a narrower bandgap (1.42 eV), still outperform Si in terms of high-frequency performance and noise figures, making them suitable for RF front-ends. Silicon, despite its lower electron mobility and limited high-frequency capability, remains dominant in integrated circuit applications due to its low cost, mature fabrication ecosystem, and high integration density.

In contrast, organic transistors, particularly soft and low-power organic field-effect transistors (OFETs), present an attractive alternative for flexible, large-area, and biocompatible electronics [28]. These devices can be fabricated using low-temperature, solution-based processes on flexible substrates, enabling applications in wearable, implantable, and disposable electronics. However, organic transistors typically suffer from lower carrier mobility (often <1 cm²/V·s), limited thermal stability, lower operational frequencies (usually <10 MHz), and poorer environmental robustness. Although inorganic technologies dominate high-performance and high-reliability domains, such as wireless communication, radar, and satellite systems, organic electronics are better suited to low-power, low-frequency applications where mechanical flexibility, biocompatibility, or cost-effective roll-to-roll manufacturing are critical. Thus, the choice between inorganic and organic transistor technologies involves a trade-off between electrical performance and mechanical/economic versatility, with each domain offering unique advantages aligned to its target application space.

2.1.2. Selection of CGH40010 GaN HEMT

Among available GaN HEMT devices, the CGH40010 from Wolfspeed was chosen based on its optimal balance of efficiency, gain, and broadband performance.

Table 3. Comparison of GaN HEMT devices for 2.3–2.5 GHz PA design.

Transistor	Gain (dB)	PAE (%)	Output Power (dBm)
CGH40010 (Wolfspeed)	13	60	40
CGH60015D (Wolfspeed)	12.5	58	38
QPD1008 (Qorvo)	11.5	55	36
BLC2425M10LS250 (Ampleon)	10	50	35

presents a comparative analysis of CGH40010 against alternatives from other manufacturers.

The CGH40010 was selected because it provides the highest gain (13 dB), efficiency (60%), and output power (40 dBm) among similar GaN HEMTs in this frequency range. Additionally, it operates efficiently under a 28 V supply, making it well suited for both linear and compressed amplifier circuits.

2.1.3. Mathematical Justification for Device Selection

To validate the performance of CGH40010 in this design, key metrics such as output power, power-added efficiency (PAE), and gain compression were analyzed using mathematical models.

The output power $P_{\mathrm{out}}$ is defined as

$$P_{\mathrm{out}}=P_{\mathrm{in}}\times {10}^{{\displaystyle \frac{\mathrm{Gain}\left(\mathrm{dB}\right)}{10}}},$$

(9)

where $P_{\mathrm{in}}$ is the input power, and gain (dB) is the primary factor determining amplification. The power-added efficiency (PAE), which measures conversion efficiency from DC to RF output, is given by

$$\mathrm{PAE}={\displaystyle \frac{P_{\mathrm{out}}-P_{\mathrm{in}}}{P_{\mathrm{DC}}}}\times 100\%.$$

(10)

For broadband operation, average efficiency is computed as

$${\mathrm{PAE}}_{\mathrm{avg}}={\displaystyle \frac{1}{B}}{\int }_{f_{\mathrm{low}}}^{f_{\mathrm{high}}}\mathrm{PAE}\left(f\right)df,$$

(11)

ensuring consistent efficiency across the 2.3–2.5 GHz band. The 1 dB gain compression point, which indicates non-linear behavior at a high input power, is defined by

$${\displaystyle \frac{dG}{d{P}_{\mathrm{in}}}}{|}_{P_{\mathrm{in}}=P_{1\mathrm{dB}}}\approx -0.1\mathrm{dB}/\mathrm{dBm}.$$

(12)

Since CGH40010 exhibits the highest gain with minimal compression, it ensures high linearity while maintaining efficiency, making it an optimal choice for high-data-rate wireless applications.

2.1.4. Thermal Considerations

Given the high power density of GaN, effective thermal management is crucial. The device temperature $T_{\mathrm{device}}$ is estimated using

$$T_{\mathrm{device}}=T_{\mathrm{ambient}}+R_{\mathrm{th}}·P_{\mathrm{DC}},$$

(13)

where $R_{\mathrm{th}}$ is the thermal resistance. With GaN’s superior thermal conductivity (130–200 W/m·K), the CGH40010 maintains stable performance under continuous high-power operation.

The CGH40010 GaN HEMT was selected due to its superior efficiency, gain, and power handling, as demonstrated in the comparative analysis. By integrating digital pre-distortion (DPD), the design effectively mitigates spectral regrowth, ensuring compliance with high-linearity requirements in next-generation wireless communication systems.

2.2. Operating Frequency Range

The power amplifier (PA) is designed to operate within the 2.3–2.5 GHz frequency range, which is widely recognized for its utility in high-throughput wireless communication systems. This range is particularly relevant for modern broadband technologies, including advanced wireless infrastructure, high-speed access points, and point-to-point backhaul links. Operation in this band facilitates the delivery of elevated data rates, reduced latency, and improved spectral efficiency—all critical performance metrics in contemporary telecommunication systems.

From a physical standpoint, the wavelength $\lambda$ corresponding to a signal frequency f is given by the following standard propagation relation:

$$\lambda ={\displaystyle \frac{v}{f}},$$

(14)

where $v\approx 3\times {10}^8\mathrm{m}/\mathrm{s}$ represents the speed of light in free space. For a central frequency of 2.4 GHz, the wavelength is approximately

$$\lambda \approx {\displaystyle \frac{3\times {10}^8}{2.4\times {10}^9}}=0.125\mathrm{m}.$$

(15)

This wavelength is advantageous for the design of compact, efficient antenna structures and RF front-end architectures. It provides an optimal compromise between the spatial resolution and system-level integration, allowing for reliable signal penetration in indoor and urban environments while supporting higher modulation bandwidths than lower-frequency bands.

An important design consideration is the free-space path loss $L(d,f)$, which quantifies the attenuation experienced by a propagating wave as a function of frequency f and distance d, and it is given by

$$L(d,f)={\left({\displaystyle \frac{4\pi df}{v}}\right)}^2.$$

(16)

This equation illustrates that path loss increases with both frequency and distance, emphasizing the value of operating in a moderate frequency range, such as 2.3–2.5 GHz. At this range, the PA benefits from a favorable trade-off between achievable data rate, manageable path loss, and compatibility with compact form factors.

Beyond high-frequency operation, the PA architecture is also optimized to support sub-GHz applications, such as those prevalent in Internet of Things (IoT) deployments and narrowband low-power communication protocols. These applications often prioritize energy efficiency, extended range, and robust signal penetration through complex environments. At sub-GHz frequencies, signal attenuation is significantly reduced, enabling wider coverage with lower transmission power. The frequency-dependent power dissipation $P_{\mathrm{diss}}\left(f\right)$ in such systems can be modeled as

$$P_{\mathrm{diss}}\left(f\right)={\int }_{f_{\mathrm{low}}}^{f_{\mathrm{high}}}\gamma \left(f\right)\mathrm{d}f,$$

(17)

where $\gamma \left(f\right)$ represents the frequency-dependent energy dissipation density. Lower frequencies typically correspond to a lower $\gamma \left(f\right)$, enhancing the longevity of battery-powered devices and supporting sustainable, maintenance-free operation in remote deployments.

By accommodating both 2.3–2.5 GHz and sub-GHz frequency bands, the proposed PA design demonstrates versatility across a broad spectrum of wireless applications. This dual-band capability ensures compatibility with diverse communication standards, enabling the amplifier to deliver high performance in bandwidth-intensive scenarios while also supporting energy-efficient, wide-area networks. The result is a flexible, scalable PA architecture that meets the multifaceted demands of next-generation wireless communication ecosystems.

2.3. Single-Stage Power Amplifier Schematic Analysis

Figure 2 illustrates the single-stage schematic of a power amplifier (PA) designed for RF applications. This configuration features essential elements for input matching, biasing, and output matching, all of which contribute to the overall performance in terms of gain, efficiency, and linearity. Each component in the schematic plays a significant role in ensuring that the PA operates effectively within its intended frequency band.

The input matching network, consisting of capacitor $C_1$ and additional reactive components, is designed to match the source impedance $Z_S$ (typically 50 $\Omega$) to the input impedance $Z_{\mathrm{in}}$ of the transistor $M_1$. This matching is essential for maximizing power transfer and minimizing the reflection coefficient $\mathsf{\Gamma }$, given by

$$\mathsf{\Gamma }={\displaystyle \frac{Z_{\mathrm{in}}-Z_S}{Z_{\mathrm{in}}+Z_S}},$$

(18)

where $Z_{\mathrm{in}}$ is the impedance seen at the gate of $M_1$. The objective is to design $C_1$ such that $\mathsf{\Gamma }$ is minimized over the operating frequency range.

Capacitors $C_2$ and $C_3$ form part of the DC bias network, establishing a stable gate–source voltage $V_{gs}$. This voltage $V_{gs}$ sets the operating point of the transistor $M_1$ and ensures it remains in the desired region (typically Class AB) for amplification. The gate bias can be expressed as

$$V_{gs}=V_g-V_{\mathrm{th}},$$

(19)

where $V_g$ is the applied gate voltage, and $V_{\mathrm{th}}$ is the threshold voltage of the transistor.

Resistor $R_1$ acts as a gate resistor that stabilizes the biasing network and helps prevent unwanted oscillations in the circuit. It also assists in isolating the RF signal path from the DC biasing network, ensuring signal integrity.

The transistor $M_1$ is the active device responsible for amplification. Its transconductance $g_m$ is a critical parameter for determining the gain of the PA, defined as

$$g_m={\displaystyle \frac{\partial I_d}{\partial V_{gs}}}.$$

(20)

The small-signal voltage gain $A_v$ of the amplifier stage can be approximated by

$$A_v=g_m·Z_L,$$

(21)

where $Z_L$ is the load impedance presented by the output matching network.

The output matching network comprises capacitors $C_5$, $C_6$, and $C_7$, as well as associated transmission line elements. This network matches the output impedance $Z_{\mathrm{out}}$ of the transistor $M_1$ to the load impedance $Z_L$, typically 50 $\Omega$, to ensure efficient power transfer. The condition for optimal matching is given by

$$Z_{\mathrm{out}}=Z_L^{\ast },$$

(22)

where $Z_L^{\ast }$ is the complex conjugate of the load impedance. Proper output matching maximizes the power delivered to the load while minimizing reflections.

Capacitors $C_5$, $C_6$, and $C_7$ serve dual purposes: they block any DC component from reaching the load and contribute to impedance transformation. The output power $P_{\mathrm{out}}$ can be expressed as

$$P_{\mathrm{out}}={\displaystyle \frac{V_{\mathrm{out},\mathrm{rms}}^2}{Z_L}},$$

(23)

where $V_{\mathrm{out},\mathrm{rms}}$ is the root-mean-square value of the output voltage.

The DC supply voltage $V_{ds}$ is provided to the drain of $M_1$ to power the amplification process. Capacitors $C_4$ and $C_5$ act as bypass capacitors, ensuring that $V_{ds}$ remains stable and does not interact with the RF signal. The stability of $V_{ds}$ is essential for maintaining consistent operating conditions.

The overall power-added efficiency (PAE) of the PA is given by

$$\mathrm{PAE}={\displaystyle \frac{P_{\mathrm{out}}-P_{\mathrm{in}}}{P_{\mathrm{DC}}}}\times 100\%,$$

(24)

where $P_{\mathrm{in}}$ is the input RF power, and $P_{\mathrm{DC}}$ is the total DC power consumed by the PA. Maximizing the PAE is crucial for ensuring energy-efficient operation, particularly in battery-powered or energy-constrained systems.

The performance of this PA design relies on a careful balance between gain, efficiency, and linearity. The use of capacitors $C_1$ through $C_7$ and resistor $R_1$ ensures proper impedance matching and bias stability. The gain provided by $M_1$ is maximized while maintaining signal integrity and minimizing distortion. This single-stage design can serve as a building block for more complex multi-stage PAs, where higher power and gain are required.

The key design metrics, such as the reflection coefficient $\mathsf{\Gamma }$, gain $A_v$, and power-added efficiency (PAE), highlight the critical role each component plays in achieving optimal performance in the 2.3–2.5 GHz frequency band.

2.4. Biasing Network Design and Load-Line Analysis

The biasing network design is essential for setting the operating point of the GaN High-Electron-Mobility Transistor (HEMT), ensuring the power amplifier (PA) functions optimally within the chosen Class AB operation. Class AB operation offers a practical balance between linearity and efficiency, making it ideal for applications that require high power output with minimal signal distortion. Proper biasing not only maximizes the PA’s efficiency but also preserves its linearity, which is crucial for reliable performance in modern communication systems.

The biasing network comprises resistors and decoupling capacitors carefully chosen to isolate the RF signal path from the DC bias voltage. This separation prevents unwanted interactions between the RF and DC components that could compromise the stability and performance of the PA. The selection of biasing components is critical; any variation in the bias voltage can shift the transistor’s operating point, potentially pushing it out of the desired Class AB region.

Figure 3 illustrates the biasing setup, where the drain–source voltage $V_{DS}$ is set to 28 V and the gate–source voltage $V_{GS}$ is fixed at −2.7 V. These parameters were selected to achieve a gain exceeding 10 dB while maintaining an efficiency greater than 50%. The chosen biasing values are determined from the transfer characteristics of the GaN HEMT, typically shown by the $I_D$ vs. $V_{GS}$ curve. The quiescent drain current $I_{Dq}$ is carefully adjusted to balance efficiency and linearity, which is vital for high-power applications with low distortion.

The quiescent drain current $I_{Dq}$ is defined as

$$I_{Dq}={\displaystyle \frac{V_{GS}-V_{\mathrm{th}}}{R_{\mathrm{bias}}}},$$

(25)

where $V_{\mathrm{th}}$ is the threshold voltage of the GaN HEMT, and $R_{\mathrm{bias}}$ is the resistance used for setting the gate bias. Ensuring that the device operates in the Class AB region means that $M_1$ conducts for more than half but less than the entire input signal cycle, thus promoting efficient power amplification with adequate linearity.

A critical aspect of designing a power amplifier is understanding the load-line analysis, which illustrates the relationship between the drain current $I_D$ and the drain–source voltage $V_{DS}$. Load-line analysis helps in selecting an optimal operating point that avoids device breakdown while ensuring efficient operation.

Figure 3 displays the load-line analysis superimposed on the $I_D$-$V_{DS}$ characteristics of the GaN HEMT. The red curves represent the device’s output characteristics for various gate–source voltage values, while the blue line indicates the load line, intersecting key points $m_1$ and $m_2$, corresponding to the saturation and cut-off regions, respectively. The intersection at $m_1$ represents the maximum allowable current $I_{D,\max }$ at a low $V_{DS}$, while $m_2$ indicates the maximum $V_{DS,\max }$ at a minimal $I_D$.

The DC supply $V_{DS}$ is chosen to provide sufficient power for amplification, while decoupling capacitors $C_{\mathrm{decouple}}$ ensure stability by preventing RF signal feedback into the power supply. The power dissipation $P_{\mathrm{D}}$ in the transistor is given by

$$P_{\mathrm{D}}=V_{DS}\times I_D,$$

(26)

where $V_{DS}$ is the drain–source voltage, and $I_D$ is the drain current. High power dissipation requires proper heat sinking and thermal management to prevent overheating and maintain reliability.

The power-added efficiency (PAE) of the PA is a measure of its efficiency in converting DC power to RF power and is defined as

$$\mathrm{PAE}={\displaystyle \frac{P_{\mathrm{out}}-P_{\mathrm{in}}}{P_{\mathrm{DC}}}}\times 100\%,$$

(27)

where $P_{\mathrm{out}}$ is the output RF power, $P_{\mathrm{in}}$ is the input RF power, and $P_{\mathrm{DC}}$ is the total DC power consumed.

In this design, achieving high PAE while maintaining the proper $V_{DS}$ and $V_{GS}$ ensures that the amplifier operates efficiently. This is crucial for applications like 5G and advanced communication systems, where both power and signal integrity are essential.

The biasing and load-line analysis together ensure that the PA can achieve high power output, efficient operation, and minimal distortion, meeting the demands of modern RF applications.

2.4.1. Load-Pull Analysis and Impedance Matching

To optimize the performance of the power amplifier (PA), a detailed load-pull analysis is conducted. This analysis is fundamental for identifying the optimal load and source impedances that maximize output power and power-added efficiency (PAE) at a target frequency of 2.4 GHz. The load-pull technique involves systematically varying the load impedance presented to the transistor while recording the resulting output power and efficiency. This allows for the determination of the optimal impedance conditions for peak PA performance.

Figure 4 depicts the load-pull analysis results, highlighting the regions where maximum power and efficiency are achieved. The data from the analysis provides critical insights into the impedance values that enable efficient operation and power transfer at the target frequency.

Figure 4 displays the power-added efficiency (PAE) and delivered power contours on a Smith chart. This chart provides a visual representation of how different load impedances affect both the power output and the PAE. The red contours represent power levels (in dBm), while the blue contours indicate the PAE (in percentage). The optimal impedance region, where the highest power and PAE overlap, is a crucial area for maximizing amplifier performance.

Table 4. Optimal source and load impedance values at 3.5 GHz.

Optimal ${\mathit{Z}}_{\mathbf{Source}}$	Optimal ${\mathit{Z}}_{\mathbf{Load}}$
$9.7-j4.6\Omega$	$11.5+j10.9\Omega$

summarizes the optimal source and load impedance values obtained from the load-pull analysis. These impedances are essential for achieving the highest power transfer and efficient operation at the desired operating frequency.

Designing the impedance matching network is a critical step to ensure that the PA operates efficiently by transforming the inherent input and output impedances to match the optimal values identified in the load-pull analysis. This network typically consists of reactive components, such as inductors and capacitors, which enable the necessary impedance transformation. The main goal is to minimize the reflection coefficient $\mathsf{\Gamma }$ to enhance power delivery. The reflection coefficient is defined by

$$\mathsf{\Gamma }={\displaystyle \frac{Z_L-Z_0}{Z_L+Z_0}},$$

(28)

where $Z_L$ represents the load impedance, and $Z_0$ is the system characteristic impedance, typically set to 50 $\Omega$. A reflection coefficient close to zero indicates minimal reflected power and optimal impedance matching.

The contours shown in Figure 4 provide a comprehensive understanding of the performance trade-offs in the PA design. The power contour levels (in dBm) range from 40.80 dBm to 41.55 dBm, as indicated in red, while the PAE contour levels are marked in blue, ranging from 56% to 65.755%. The intersection of high-power and high-PAE regions indicates the load impedances that optimize both output power and efficiency.

The efficiency ${\eta }_{\mathrm{D}}$ can be expressed as

$${\eta }_{\mathrm{D}}={\displaystyle \frac{P_{\mathrm{out}}}{P_{\mathrm{DC}}}}\times 100\%,$$

(29)

where $P_{\mathrm{out}}$ is the RF output power and $P_{\mathrm{DC}}$ is the total DC power consumed. Achieving high PAE while maintaining the optimal load impedance is essential for practical high-power RF applications, such as those found in modern 5G networks and radar systems.

By implementing the matching network based on the results shown in Figure 4, the PA can achieve a performance that balances output power and efficiency. This ensures reliable and efficient operation across the designated frequency band, aligning with the stringent requirements of advanced wireless communication systems.

2.4.2. Intrinsic Voltage and Current Characteristics

Understanding the intrinsic voltage and current characteristics of the GaN HEMT is essential for analyzing the transistor’s behavior under the selected bias conditions. Figure 5 presents the voltage and current waveforms of the device when driven by an RF signal at the established bias point. These waveforms are crucial for assessing the linearity and efficiency of the PA.

The peak drain–source voltage $V_{\mathrm{DS}}$ and the corresponding drain current $I_{\mathrm{D}}$ are monitored to ensure that they remain within safe operational limits, avoiding breakdown and thermal damage to the transistor. The power dissipation $P_{\mathrm{D}}$ within the device can be described by

$$P_{\mathrm{D}}=V_{\mathrm{DS}}·I_{\mathrm{D}},$$

(30)

where $V_{\mathrm{DS}}$ is the instantaneous drain–source voltage, and $I_{\mathrm{D}}$ is the drain current. High power dissipation can lead to excessive heating, necessitating effective thermal management strategies to maintain stable and reliable operation.

The drain efficiency ${\eta }_{\mathrm{D}}$ quantifies how efficiently the device converts DC power into RF power, defined as

$${\eta }_{\mathrm{D}}={\displaystyle \frac{P_{\mathrm{out}}}{P_{\mathrm{DC}}}}\times 100\%,$$

(31)

where $P_{\mathrm{out}}$ is the RF output power and $P_{\mathrm{DC}}$ is the total DC input power. This metric is particularly relevant in Class AB operations, as it reflects the PA’s ability to maintain high efficiency while delivering substantial output power with minimal distortion.

By precisely setting the bias point and achieving optimal impedance matching, the PA is tailored to deliver high efficiency and linearity, making it well suited for demanding high-frequency applications such as 5G and radar systems.

3. Simulation Results and Discussion

In this section, we discuss the performance metrics obtained from the simulation of the designed power amplifier (PA) operating in the 2.3–2.5 GHz band. Key parameters analyzed include large-signal gain, output power at various compression points, power-added efficiency (PAE), drain efficiency, return loss, gain response, and stability.

3.1. Large-Signal Gain and Compression Points

The large-signal gain characteristic of the power amplifier (PA) is illustrated in Figure 6. This figure shows how the gain varies as a function of input power ($P_{\mathrm{in}}$), expressed in dBm, across the amplifier’s operational range. The gain, a critical measure of the amplifier’s performance, represents its ability to increase signal strength and is depicted in decibels (dB).

As depicted in Figure 6, the amplifier maintains a consistent gain of approximately 13 dB at lower input power levels, indicative of the linear region where the output power increases proportionally with the input power. This linear region is essential for applications requiring signal fidelity, as it ensures that the amplified output signal closely follows the input without significant distortion.

However, as the input power ($P_{\mathrm{in}}$) increases beyond a certain point, the gain starts to decrease, a phenomenon known as gain compression. This marks the transition from the linear region to the non-linear region of the PA. The 3 dB compression point ($P_{3\mathrm{dB}}$) is defined as the input power level at which the gain drops by 3 dB from its small-signal value. In this analysis, the 3 dB compression point is observed at an input power level of approximately 29.7 dBm. This point is critical as it indicates the maximum input power the amplifier can handle while still maintaining near-linear behavior.

The 1 dB compression point ($P_{1\mathrm{dB}}$), which marks the input power level where the gain drops by 1 dB from its linear value, is another significant metric. It occurs at an input power of approximately 22.2 dBm and signifies the onset of minor non-linearities in the amplifier’s response. This point is often used to evaluate the PA’s linearity in applications where minimal distortion is crucial.

The gain G of the amplifier can be represented mathematically as

$$G=20{\log }_{10}\left({\displaystyle \frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}}\right),$$

(32)

where $P_{\mathrm{out}}$ is the output power and $P_{\mathrm{in}}$ is the input power. As $P_{\mathrm{in}}$ increases and the amplifier approaches saturation, the relationship between $P_{\mathrm{out}}$ and $P_{\mathrm{in}}$ becomes non-linear, leading to gain compression.

The gain compression observed in Figure 6 indicates several critical aspects of the PA’s performance:

• Reduction in Gain: Beyond the linear region, the gain decreases as input power increases, reflecting the PA’s inability to linearly amplify the signal. The rate of gain compression can be analyzed by differentiating the gain with respect to input power:

  $${\displaystyle \frac{dG}{d{P}_{\mathrm{in}}}}={\displaystyle \frac{d}{d{P}_{\mathrm{in}}}}\left(20{\log }_{10}\left({\displaystyle \frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}}\right)\right).$$

  (33)
  A negative derivative indicates compression and non-linear behavior.
• Impact on Linearity: Compression affects the PA’s linearity, which is vital for maintaining signal quality in high-fidelity applications. Non-linearity can lead to the generation of harmonics and intermodulation products, potentially causing spectral regrowth and signal distortion, which are undesirable in systems transmitting high-data-rate signals.
• Output Saturation: Once the input power exceeds the 3 dB compression point, further increases in $P_{\mathrm{in}}$ result in only marginal increases in $P_{\mathrm{out}}$. This saturation behavior reflects the physical limits of the amplifier’s active components, beyond which no significant power gain can be achieved.

To better understand the gain behavior, the differential gain with respect to input power can be computed as

$${\displaystyle \frac{dG}{d{P}_{\mathrm{in}}}}=20·{\displaystyle \frac{d}{d{P}_{\mathrm{in}}}}\left({\log }_{10}\left({\displaystyle \frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}}\right)\right).$$

(34)

This analysis highlights the rate at which the gain changes as the input power increases, providing insights into the PA’s operational boundaries.

The average gain over a range of input power levels can be evaluated using the integral of the gain across the range $[P_{\min },P_{\max }]$:

$$\overline{G}={\displaystyle \frac{1}{P_{\max }-P_{\min }}}{\int }_{P_{\min }}^{P_{\max }}G\left(P_{\mathrm{in}}\right)d{P}_{\mathrm{in}}.$$

(35)

This integral provides a measure of gain stability, which is essential for applications requiring consistent amplification across varying input power levels.

The gain differentiation equation, ${\displaystyle \frac{dG}{d{P}_{\mathrm{in}}}}$, is a critical tool for understanding PA behavior near compression points. In practical terms, differentiating gain with respect to input power helps quantify how rapidly gain degrades as the amplifier moves from linear operation to compression.

For instance, using the equation

$${\displaystyle \frac{dG}{d{P}_{\mathrm{in}}}}={\displaystyle \frac{d}{d{P}_{\mathrm{in}}}}\left(20{\log }_{10}\left({\displaystyle \frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}}\right)\right),$$

(36)

we computed values at different input power levels to determine the compression onset.

The results in

Table 5. Differential gain analysis at key input power levels.

Input Power (dBm)	Gain (dB)
20	12.5
25	11.8
29	11
30	10.5

indicate that gain compression becomes significant beyond 29 dBm input power, validating our selection of the 3 dB compression point at 29.7 dBm.

3.2. Output Power Analysis

The output power response of the 2.3–2.5 GHz power amplifier (PA) as a function of input power is shown in Figure 7. This curve is a crucial indicator of the amplifier’s capability to deliver sufficient output power while maintaining linear amplification across its operating range. Understanding this relationship helps determine the PA’s behavior under different input signal strengths and is essential for optimizing its performance in communication systems, such as 5G, where high power and linearity are paramount.

Figure 7 shows that the PA exhibits a linear response over a significant portion of the input power range, where the output power $P_{\mathrm{out}}$ increases proportionally with the input power $P_{\mathrm{in}}$. This linear region indicates the amplifier’s efficiency in boosting signal strength without distortion. As input power approaches 29.7 dBm, the PA reaches its 3 dB compression point, where $P_{\mathrm{out}}$ peaks at approximately 40.4 dBm. The linear operation is essential for applications demanding high signal fidelity, such as 5G communications, where minimal distortion and excellent spectral purity are necessary to comply with regulatory and performance criteria. The amplifier’s linearity is crucial for maintaining higher-order intermodulation distortions (IMDs) and spectrum regrowth below acceptable bounds, hence preventing interference with neighboring channels.

The output power can be expressed as a function of input power and gain:

$$P_{\mathrm{out}}=P_{\mathrm{in}}+G-\Delta G,$$

(37)

where

• G is the small-signal gain;
• $\Delta G$ is the reduction in gain due to compression as the amplifier approaches saturation.

In the ideal linear region, $\Delta G\approx 0$, meaning that the gain remains constant, and any increase in $P_{\mathrm{in}}$ directly results in a corresponding increase in $P_{\mathrm{out}}$. However, as $P_{\mathrm{in}}$ increases further, $\Delta G$ becomes significant, indicating the onset of compression and non-linear operation.

To evaluate how the output power changes with increasing input power, the differential gain can be calculated as follows:

$${\displaystyle \frac{d{P}_{\mathrm{out}}}{d{P}_{\mathrm{in}}}}={\displaystyle \frac{d}{d{P}_{\mathrm{in}}}}\left(P_{\mathrm{in}}+G-\Delta G\right).$$

(38)

In the linear region, this derivative approaches 1, indicating a proportional relationship between $P_{\mathrm{in}}$ and $P_{\mathrm{out}}$. As the amplifier approaches the compression region, ${\displaystyle \frac{d{P}_{\mathrm{out}}}{d{P}_{\mathrm{in}}}}$ decreases, reflecting the non-linear response where output power growth slows.

To assess the cumulative power output over a range of input power levels $[P_{\mathrm{in},\min },P_{\mathrm{in},\max }]$, the following integral can be used:

$${\int }_{P_{\mathrm{in},\min }}^{P_{\mathrm{in},\max }}{P}_{\mathrm{out}}d{P}_{\mathrm{in}}={\int }_{P_{\mathrm{in},\min }}^{P_{\mathrm{in},\max }}\left(P_{\mathrm{in}}+G-\Delta G\right)d{P}_{\mathrm{in}}.$$

(39)

This integral provides an estimation of the total output power delivered over the specified input range, capturing the amplifier’s efficiency in both the linear and compressed regions.

For practical applications and simulations, the output power can be evaluated at discrete input levels $P_{\mathrm{in}}\left(i\right)$, where $i=1,2,\dots ,N$. The total output power over these points can be approximated by

$$\sum _{i=1}^N{P}_{\mathrm{out}}\left(i\right)\approx \sum _{i=1}^N\left(P_{\mathrm{in}}\left(i\right)+G-\Delta G\left(i\right)\right).$$

(40)

This discrete summation approach is particularly useful for numerical simulations and real-world analysis, where the amplifier’s response to specific input levels is of interest.

The analysis shown in Figure 7 confirms that the PA operates efficiently within its designated power range, with the linear region extending up to the 3 dB compression point. Beyond this point, the amplifier exhibits saturation behavior, where further increases in $P_{\mathrm{in}}$ result in only marginal increases in $P_{\mathrm{out}}$. This saturation is typical for high-power RF amplifiers and marks the physical limitations of the active components.

Understanding these characteristics helps in defining the PA’s operating limits, ensuring that it meets the requirements of high-power applications while maintaining signal integrity and efficient performance.

3.3. Power-Added Efficiency and Drain Efficiency

The power-added efficiency (PAE) and drain efficiency (${\eta }_{\mathrm{drain}}$) characteristics of the 2.3–2.5 GHz power amplifier (PA) as functions of input power are depicted in Figure 8. These efficiency curves are crucial for analyzing the PA’s performance, particularly in energy efficiency, thermal stability, and suitability for high-power RF applications.

As shown clearly in Figure 8, both PAE and ${\eta }_{\mathrm{drain}}$ display non-linear behavior, gradually increasing with input power until they reach a peak value around the amplifier’s compression region. Specifically, the graph illustrates a notable increase from low efficiency at minimal input power levels (below 20%) to a significantly higher efficiency at elevated input powers, peaking near the 3 dB compression point. At an input power level of approximately $P_{\mathrm{in}}=29.7\mathrm{dBm}$, the 3 dB compression point recorded PAE as being around 60%, and the corresponding drain efficiency peaked at approximately 65%. Beyond this point, however, there is a gradual decline in both efficiencies, indicating the onset of amplifier saturation and a diminished incremental benefit from increased input drive levels. Significantly, ${\eta }_{\mathrm{drain}}$ reaches a maximum of about 65% and decrease thereafter, whereas PAE increases before leveling off near saturation. This discrepancy arises because ${\eta }_{\mathrm{drain}}$ reflects the ratio of RF output power to DC input power, whereas PAE additionally incorporates the input RF power. As input power increases, the gain reduces due to compression, leading to a diminished output power rise in relation to DC consumption, hence causing a reduction in ${\eta }_{\mathrm{drain}}$. Conversely, PAE benefits from increased RF input power, maintaining the increase until reaching saturation. In actual wireless communication systems, especially in 5G and IoT applications, PAE is a more accurate measure of overall system efficiency, whereas ${\eta }_{\mathrm{drain}}$ is essential for assessing thermal performance and DC power management.

The observed peak values underscore the amplifier’s excellent capability to convert DC power into useful RF output power with minimal internal losses. These metrics directly affect the thermal management demands and the overall power consumption of RF systems, which is especially critical in mobile and wireless communication infrastructures.

The mathematical definitions for PAE and ${\eta }_{\mathrm{drain}}$ provide additional insights:

$$\mathrm{PAE}={\displaystyle \frac{P_{\mathrm{out}}-P_{\mathrm{in}}}{P_{\mathrm{DC}}}}\times 100\%,$$

(41)

where

• $P_{\mathrm{out}}$ is the RF output power;
• $P_{\mathrm{in}}$ is the RF input power;
• $P_{\mathrm{DC}}$ represents the total DC power supplied.

Drain efficiency (${\eta }_{\mathrm{drain}}$) simplifies the measurement by excluding the input RF power, focusing solely on the output power relative to DC consumption:

$${\eta }_{\mathrm{drain}}={\displaystyle \frac{P_{\mathrm{out}}}{P_{\mathrm{DC}}}}\times 100\%.$$

(42)

Both efficiency metrics are integral, but the PAE is particularly useful when comparing amplifiers with differing gain levels or multi-stage amplifier systems.

Evaluating efficiency across an operational power range can further characterize amplifier performance. The continuous operational range $[P_{\mathrm{in},\min },P_{\mathrm{in},\max }]$ permits the calculation of the average efficiency through integration:

$$\mathrm{Average}\mathrm{PAE}={\displaystyle \frac{1}{P_{\mathrm{in},\max }-P_{\mathrm{in},\min }}}{\int }_{P_{\mathrm{in},\min }}^{P_{\mathrm{in},\max }}{\displaystyle \frac{P_{\mathrm{out}}\left(P_{\mathrm{in}}\right)-P_{\mathrm{in}}}{P_{\mathrm{DC}}}}d{P}_{\mathrm{in}},$$

(43)

$$\mathrm{Average}\mathrm{Drain}\mathrm{Efficiency}={\displaystyle \frac{1}{P_{\mathrm{in},\max }-P_{\mathrm{in},\min }}}{\int }_{P_{\mathrm{in},\min }}^{P_{\mathrm{in},\max }}{\displaystyle \frac{P_{\mathrm{out}}\left(P_{\mathrm{in}}\right)}{P_{\mathrm{DC}}}}d{P}_{\mathrm{in}}.$$

(44)

Additionally, examining the differential change in drain efficiency with respect to output power helps identify operational sensitivities and performance trade-offs:

$${\displaystyle \frac{d{\eta }_{\mathrm{drain}}}{d{P}_{\mathrm{out}}}}={\displaystyle \frac{1}{P_{\mathrm{DC}}}}\times 100\%.$$

(45)

In practical measurement scenarios, discrete approximations are frequently employed for simplicity and reliability. The average efficiencies across discrete input power samples $P_{\mathrm{in}}\left(i\right)$ are given by

$$\mathrm{Average}\mathrm{PAE}\approx {\displaystyle \frac{1}{N}}\sum _{i=1}^N{\displaystyle \frac{P_{\mathrm{out}}\left(i\right)-P_{\mathrm{in}}\left(i\right)}{P_{\mathrm{DC}}}}\times 100\%,$$

(46)

$$\mathrm{Average}\mathrm{Drain}\mathrm{Efficiency}\approx {\displaystyle \frac{1}{N}}\sum _{i=1}^N{\displaystyle \frac{P_{\mathrm{out}}\left(i\right)}{P_{\mathrm{DC}}}}\times 100\%.$$

(47)

Such approximations facilitate robust efficiency characterizations suitable for design optimization and system validation.

The response presented in Figure 8 underscores the significance of operating amplifiers close to their optimal efficiency points. This operational approach minimizes energy waste, reduces heat generation, and enhances system reliability, thereby making the amplifier particularly suitable for demanding applications like high-power communication base stations, satellite transmitters, and advanced radar systems. Careful efficiency assessment enables balanced decisions between linearity, output power, and energy efficiency, leading to optimal amplifier performance and longevity.

3.4. Return Loss and Gain Response

The return loss and gain response of the power amplifier (PA) across the 2.3–2.5 GHz frequency band are depicted in Figure 9. These parameters are essential for assessing the PA’s impedance matching and amplification performance over the specified frequency range.

Return loss is a critical metric that quantifies how well the amplifier’s input and output impedances match the characteristic impedance of the system (usually 50 $\Omega$). It is mathematically defined by

$$\mathrm{Return}\mathrm{Loss}=-20{\log }_{10}\left|\mathsf{\Gamma }\right|,$$

(48)

where $\mathsf{\Gamma }$ is the reflection coefficient given by

$$\mathsf{\Gamma }={\displaystyle \frac{Z_{\mathrm{in}}-Z_0}{Z_{\mathrm{in}}+Z_0}},$$

(49)

with $Z_{\mathrm{in}}$ representing the input impedance and $Z_0$ the characteristic impedance. A higher return loss (more negative value) indicates better impedance matching and less power reflected back to the source, enhancing power transfer and system stability.

In Figure 9, the magenta curve (representing $S_{22}$) highlights the return loss at the output port. It shows a significant dip at around 2.4 GHz, indicating excellent impedance matching within this frequency band. This feature ensures that the PA efficiently transfers power with minimal reflections.

The gain response of the amplifier, shown as $S_{21}$ (blue curve) in Figure 9, represents the amplification provided by the PA across the operating band. Gain $G\left(f\right)$ is calculated using the following equation:

$$G\left(f\right)=20{\log }_{10}\left({\displaystyle \frac{P_{\mathrm{out}}\left(f\right)}{P_{\mathrm{in}}\left(f\right)}}\right),$$

(50)

where $P_{\mathrm{out}}\left(f\right)$ and $P_{\mathrm{in}}\left(f\right)$ are the output and input power levels at a given frequency f.

The gain response in the plot maintains a consistent level across the 2.3–2.5 GHz range, indicating that the amplifier is capable of providing stable signal amplification. This consistent gain is crucial for applications that require uniform performance across a specified bandwidth.

To understand the rate of change of return loss and gain with respect to frequency, the following derivatives are useful:

$${\displaystyle \frac{d\left(\mathrm{Return}\mathrm{Loss}\right)}{df}}=-20{\displaystyle \frac{1}{\left|\mathsf{\Gamma }\right|\ln \left(10\right)}}{\displaystyle \frac{d\left|\mathsf{\Gamma }\right|}{df}},$$

(51)

$${\displaystyle \frac{dG\left(f\right)}{df}}=20{\displaystyle \frac{1}{\ln \left(10\right)}}{\displaystyle \frac{1}{P_{\mathrm{in}}\left(f\right)}}{\displaystyle \frac{d{P}_{\mathrm{out}}\left(f\right)}{df}}.$$

(52)

These equations help identify frequency regions where the impedance matching or gain may deviate significantly, thus aiding in circuit optimization.

The average return loss and gain across the sampled frequencies can be evaluated as

$$\mathrm{Average}\mathrm{Return}\mathrm{Loss}\approx {\displaystyle \frac{1}{N}}\sum _{i=1}^N-20{\log }_{10}\left|\mathsf{\Gamma }\left(f_i\right)\right|,$$

(53)

$$\mathrm{Average}\mathrm{Gain}\approx {\displaystyle \frac{1}{N}}\sum _{i=1}^{N}20{\log }_{10}\left({\displaystyle \frac{P_{\mathrm{out}}\left(f_i\right)}{P_{\mathrm{in}}\left(f_i\right)}}\right),$$

(54)

where N is the number of sampled frequency points within the operating band.

Figure 9 demonstrates that the PA achieves a return loss below −15 dB across the 2.3–2.5 GHz range, suggesting effective impedance matching and minimal reflection. The stable gain shown by the $S_{21}$ curve (blue) confirms the amplifier’s ability to provide consistent amplification over the targeted frequency range. These attributes are essential for high-performance wireless applications, ensuring that the amplifier operates with high efficiency and reliability while maintaining signal integrity.

3.5. DPD Analysis

Table 6. Adjacent channel leakage ratio (ACLR) performance.

	Lower (dB)	Upper (dB)
Original	−82.866	−83.833
PA	−34.032	−36.559
DPD + PA	−49.628	−51.870

summarizes the adjacent channel leakage ratio (ACLR) performance for three distinct conditions: the original baseband signal, the signal after amplification with the power amplifier (PA), and the signal subjected to digital pre-distortion (DPD) prior to amplification. ACLR is a key spectral performance metric in RF communication systems, quantifying the ratio between in-band power and the power leaked into adjacent frequency channels. Lower ACLR values (more negative in dB) reflect superior spectral confinement and are essential for ensuring compliance with regulatory emission masks, minimizing co-channel interference, and maximizing spectral efficiency in multi-user environments.

The original signal exhibits exceptionally high spectral purity, with ACLR values of $-82.866$ dB and $-83.833$ dB for the lower and upper adjacent channels, respectively. These values confirm that the signal is tightly band-limited with negligible spectral leakage, which is characteristic of an ideal modulated waveform in the absence of hardware impairments. Such high ACLR performance provides a benchmark for evaluating the degradations introduced by subsequent analogue processing stages.

Following amplification by the PA without the application of DPD, the ACLR deteriorates substantially to $-34.032$ dB (lower adjacent) and $-36.559$ dB (upper adjacent). This degradation occurs primarily due to the non-linearities inherent in the PA’s transfer function, particularly under high output power levels. The resulting spectral regrowth manifests as intermodulation distortion components that extend beyond the intended channel, violating spectral emission constraints and increasing the likelihood of interference with adjacent services. The observed asymmetry between the lower and upper ACLR values also suggests a non-uniform distortion response, possibly influenced by memory effects or asymmetric input signal characteristics.

To counteract these non-linear distortions, DPD is employed as a baseband linearization technique. By applying an inverse distortion profile to the input signal—typically modeled using memory polynomials or Volterra-based structures—DPD pre-compensates for the PA’s non-linear behavior. After DPD is applied, the ACLR improves markedly to $-49.628$ dB for the lower adjacent channel and $-51.870$ dB for the upper adjacent channel. This improvement of approximately 15–17 dB over the uncorrected PA output demonstrates the effectiveness of DPD in suppressing out-of-band emissions and restoring spectral containment.

While the DPD-corrected ACLR values do not fully match the ideal performance of the unamplified signal, they represent a significant enhancement that is likely to satisfy the ACLR requirements specified in 3GPP or IEEE wireless communication standards. Moreover, this level of performance enables the PA to operate closer to its optimal power efficiency point without sacrificing linearity, thereby achieving a balanced trade-off between output power, energy efficiency, and spectral compliance in high-capacity wireless systems.

Comparing the results across the three scenarios, we observe the following key points:

• The original signal has the highest ACLR values, with −82.866 dB (lower) and −83.833 dB (upper), indicating minimal leakage into adjacent channels. This sets a baseline for assessing the impact of the PA and the efficacy of DPD.
• The PA-only output significantly degrades ACLR performance, showing a decrease in ACLR to −34.032 dB (lower) and −36.559 dB (upper). This drop occurs due to the non-linear effects of the PA, which amplify the signal but also introduce spectral regrowth, causing unwanted signal components to spill into adjacent channels.
• By applying DPD with the PA, we observe a significant improvement in ACLR values, reaching −49.628 dB (lower) and −51.870 dB (upper). The use of DPD helps counteract the non-linear distortions introduced by the PA, resulting in reduced spectral leakage compared to the PA-only scenario. While this does not fully restore the original ACLR values, it provides a compromise that enhances spectral efficiency and may be sufficient to comply with industry standards.

Table 7. EVM (dB).

	Original	PA Output w/o DPD	PA Output with DPD
EVM (dB)	−70.735	−28.691	−47.496

displays the Error Vector Magnitude (EVM) results for three different configurations: the original signal, the power amplifier (PA) output without digital pre-distortion (DPD), and the PA output with DPD applied. EVM is a key performance metric in communication systems, particularly in the context of signal integrity and modulation accuracy. It measures the difference between the ideal signal constellation points and the actual transmitted points, representing the level of distortion introduced into the signal. Lower EVM values (in dB, where a more negative number indicates better performance) indicate higher signal quality, with minimal distortion and interference.

The EVM for the original signal is −70.735 dB, representing a high-quality signal with minimal distortion. This value serves as the baseline for assessing the effects of the PA and DPD on signal integrity. A low EVM indicates that the original signal is close to its ideal constellation points, suggesting that it is well suited for transmission with little need for corrective measures. The ideal EVM for any communication system is as low as possible, as it corresponds to fewer errors and higher fidelity in data transmission. Thus, the original signal exhibits excellent modulation quality, setting a high standard for the PA and DPD stages to maintain.

After amplification by the PA without DPD, the EVM degrades significantly to −28.691 dB. This considerable increase in EVM (less negative) indicates that the PA introduces substantial distortion when operating without DPD, which is expected given the non-linear characteristics of power amplifiers at higher power levels.

PAs often produce non-linearities that distort the amplitude and phase of the signal, especially as the PA approaches its saturation region. These non-linearities result in an EVM increase, as observed here, which can lead to issues like spectral regrowth, interference with adjacent channels, and a reduction in overall communication system performance. An EVM of −28.691 dB is relatively poor compared to the original signal, demonstrating that the PA alone cannot maintain the original signal’s quality and may not be suitable for high-fidelity transmission applications without further corrective measures.

When DPD is applied before amplification by the PA, the EVM improves significantly to −47.496 dB. This improvement demonstrates that DPD effectively compensates for the PA’s non-linear distortions, bringing the EVM closer to the original signal’s quality. Although the EVM with DPD applied is not as low as the original signal’s EVM (−70.735 dB), it represents a considerable enhancement over the PA output without DPD (−28.691 dB).

DPD works by applying an inverse function of the PA’s non-linear characteristics, thereby pre-correcting the signal to counteract the expected distortions. As a result, the signal at the PA output is closer to the desired ideal, as evidenced by the improved EVM. An EVM of −47.496 dB suggests that the DPD+PA configuration achieves a more accurate representation of the original signal, with significantly reduced distortion compared to using the PA alone. This level of EVM improvement makes the system more suitable for communication applications requiring high signal fidelity, such as 5G and other advanced wireless technologies.

The EVM results for each configuration highlight the following key points:

• The original signal has the lowest EVM at −70.735 dB, setting a benchmark for signal integrity and minimal distortion.
• The PA output without DPD exhibits a dramatic EVM decrease to −28.691 dB, indicating that the PA introduces significant distortion when no corrective measures are applied. This increased EVM is a direct result of the PA’s non-linearities, which distort the signal’s amplitude and phase.
• The PA output with DPD has an improved EVM of −47.496 dB, demonstrating that DPD effectively mitigates the non-linear distortions introduced by the PA. While this EVM is not as low as the original signal, it represents a substantial improvement over the PA alone, making the signal more suitable for high-quality transmission.

Figure 10 illustrates the output spectrum of a power amplifier (PA) when amplifying a signal in the 2.4 GHz band, comparing the effects of digital pre-distortion (DPD) on signal quality. The spectrum is plotted over a frequency range from approximately 2.15 GHz to 2.65 GHz, covering both the main transmission channel and adjacent spectral regions. This frequency span enables a comprehensive view of in-band and out-of-band behavior, which is critical for assessing compliance with spectral emission regulations and evaluating linearization techniques.

The blue trace in Figure 10 corresponds to the PA output without any pre-distortion applied. Under these conditions, the signal undergoes significant spectral regrowth, characterized by elevated power levels in adjacent channel regions. This regrowth originates from the intrinsic non-linearities of the PA, particularly when operating near its saturation point, where gain compression, AM-AM, and AM-PM distortion mechanisms become prominent. These effects result in the generation of higher-order intermodulation products, which fall outside the main signal band and degrade the adjacent channel leakage ratio (ACLR). Additionally, memory effects—arising from thermal feedback, charge trapping, or frequency-dependent impedance—may exacerbate distortion and spectral widening, especially under wideband or bursty signal conditions.

As observed, the power levels in the spectral skirts without DPD reach up to approximately $-60$ dBm. This level of adjacent channel power poses a significant problem for regulatory compliance, especially in systems governed by 3GPP, ETSI, or FCC emission masks. Such out-of-band emissions can lead to harmful interference with neighboring communication systems and reduce spectral efficiency by necessitating increased guard bands. Moreover, they may deteriorate the performance of receivers operating in adjacent channels due to reciprocal mixing or in-band aliasing.

The application of DPD, represented by the pink trace in Figure 10, effectively mitigates the non-linear effects discussed above. DPD operates by applying a pre-distortion function to the input signal that is mathematically designed to be the inverse of the PA’s non-linear transfer characteristics. In practical implementations, this function is obtained using adaptive behavioral models such as memory polynomial, generalized Hammerstein, or Volterra series-based models, which account for both static and dynamic non-linearities. These models are trained iteratively using feedback from the PA output, enabling real-time correction and adaptive linearization under varying operating conditions.

With DPD enabled, the adjacent channel power is reduced by approximately 20 dB, with spectral levels dropping to around $-80$ dBm. This significant suppression of spectral regrowth restores the spectral shape of the output signal to closely resemble that of an ideal linear system. The pink trace demonstrates that most of the transmitted power is now confined within the allocated bandwidth, with minimal spectral leakage into adjacent bands. As a result, the system achieves compliance with ACLR standards while maintaining high power efficiency. The red trace represents the original baseband-modulated signal before amplification. It serves as the spectral reference for an ideal, distortion-free system. As observed, the original signal exhibits a clean spectral envelope with negligible out-of-band emissions, indicating high linearity and minimal spectral leakage.

This comparison clearly highlights the indispensable role of DPD in high-performance wireless communication systems. In the absence of DPD, the PA must be operated with considerable back-off from its saturation point to ensure linearity, resulting in a marked decrease in power-added efficiency (PAE). In contrast, DPD enables the PA to operate closer to its peak efficiency point by compensating for its non-linearities digitally. This trade-off between spectral integrity and power efficiency is optimally managed through DPD, making it a key enabler for advanced modulation schemes such as OFDM, 64-QAM, and 256-QAM, which are highly sensitive to non-linear distortion.

Furthermore, the use of DPD enhances the capacity of dense network deployments by allowing tighter channel spacing without an increased risk of interference. This is particularly important in sub-6 GHz bands where spectral resources are limited. In emerging applications, such as 5G NR, Wi-Fi 6/7, and massive MIMO, the ability to maintain linear amplification at high output power levels is essential for sustaining high data throughput, maintaining quality of service (QoS), and achieving energy-efficient network operation.

3.6. Electromagnetic Co-Simulation and Layout Considerations

The electromagnetic (EM) co-simulated layout of the PA is shown in Figure 11. This layout considers parasitic effects that arise from the physical layout, including inductances and capacitances from interconnects, which can impact the amplifier’s performance at high frequencies. EM co-simulation ensures that the layout adheres to the design specifications and mitigates potential degradation in gain, efficiency, and stability due to parasitic elements.

Table 8. Simulation comparison of designed PA at 2.4 GHz frequencies.

Ref. & Year	Freq. (GHz)	Gain (dB)	Drain Efficiency	Pout (dBm)
[29] 2024	1.9–2.9	6.8–10.9	45.5–58.5	44
[30] 2023	2.4	14	64-69	44
[31] 2009	2.4	28	33	30.1
[32] 2012	2.4	—	45	27.7
[33] 2003	2.45	11.2	28	20
[34] 2017	2.4	—	50	35
This Work	2.4	12–15	60–65	40

shows a simulation comparison of our designed PA with other studies that investigated the 2.3–2.5 GHz frequency band.

Compared to previously published designs, the presented PA achieves competitive drain efficiency and output power, placing it in a favorable position for being considered for applications requiring high spectral efficiency.

4. Conclusions

This study has presented the design, simulation, and performance analysis of a high-efficiency GaN-based power amplifier (PA) operating in the 2.3–2.5 GHz frequency band, with potential applications in modern wireless communication systems, including 5G and IoT. The PA’s design leverages advanced GaN HEMT technology, chosen for its superior efficiency, high power density, and thermal stability. The PA’s layout was meticulously developed, incorporating a single-stage amplification topology with carefully designed input and output matching networks to optimize power transfer, gain, and stability across the target frequency range.

Key performance metrics for the designed PA include large-signal gain, compression points, power-added efficiency (PAE), drain efficiency, return loss, and stability response, each thoroughly evaluated across a range of input powers and frequencies. The large-signal gain maintained approximately 13 dB up to the 1 dB compression point at $P_{\mathrm{in}}=22.2\mathrm{dBm}$, with the 3 dB compression point occurring at $P_{\mathrm{in}}=29.7\mathrm{dBm}$. These compression points are critical in defining the PA’s linear operating range, confirming its suitability for applications demanding high linearity and low distortion. Additionally, the output power analysis demonstrated that the amplifier could achieve up to 40 dBm at the 3 dB compression point, further validating its capacity for high-output applications.

In terms of efficiency, the PA achieved a power-added efficiency of 60% and a drain efficiency of 65% at the 3 dB compression point, meeting the target specifications for energy-efficient high-power amplifiers. These efficiency levels indicate that the PA design is optimized for power-sensitive applications, capable of conserving energy while delivering substantial output power. The return loss and gain response further underscored the amplifier’s effectiveness, with low return loss values indicating strong impedance matching, enhancing both stability and efficiency across the operating frequency band.

The EM co-simulated layout of the PA addressed parasitic effects due to interconnects and layout geometry, ensuring that high-frequency performance aligns with the theoretical design. This co-simulation step is vital for real-world implementation, as it mitigates potential degradation in gain, efficiency, and stability due to parasitic inductances and capacitances. Future research may explore experimental verification, enhanced thermal management strategies, and the integration of adaptive DPD algorithms to further improve real-world applicability and performance robustness.