# Analytical Design of an Inverse Class F Power Amplifier for Linear Amplification

#### In this article, a 2.5 to 2.6 GHz highly efficient inverse Class F power amplifier (PA), based on Cree’s CGH40010 GaN HEMT, is presented for linear amplification. The second and third harmonic load impedances are found by harmonic load pull simulation,...

Recently, in order to achieve highly efficient amplification, switch mode power amplifiers (SMPA) with theoretical 100 percent efficiency have been introduced. However, in practice, the efficiency of SMPA cannot achieve as high as 100 percent because of the parasitic parameters of the transistor, the losses of matching networks, etc. Among the subclasses of SMPA, inverse Class F has the highest drain efficiency, due to shaping the drain voltage waveform as half-sinusoidal and the drain current waveform as a square-wave.^{1-2} Many successful design instances of inverse Class F PA have been reported.^{3-6}

Modern and next generation wireless communication systems require high data rate and high spectrum utilization. In this case, the orthogonal frequency division multiplexing (OFDM) signal with high peak-to-average power ratio (PAPR) are being used. Although the inverse Class F PA obtains high efficiency at peak power level, the high PAPR causes low efficiency at the average output power. And the higher the PAPR is, the lower the efficiency will be. Therefore, a crest factor reduction (CFR) technique^{7-8} is employed to reduce the PAPR so as to enhance the efficiency of the PA.

In this article, a 2.5 to 2.6 GHz inverse Class F PA is implemented using Cree’s CGH40010 GaN HEMT for linear amplification in OFDM systems. The input and output harmonic matching networks (HMN) are analytically designed to make the harmonic impedances approximate the values obtained by harmonic source/load pull simulations. CW measurement shows a greater than 75 percent drain efficiency at 2.55 GHz. For a 20 MHz four-carrier OFDM signal with PAPR of 10.39 dB, after employing CFR and digital predistortion (DPD) techniques, the inverse Class F PA achieves good linearity and 31.9 percent efficiency at an average output power of 34.3 dBm.

### Inverse Class F Design Procedure

**Inverse Class F Operation and GaN HEMT**

Ideally, an infinite number of even-harmonic resonators results in an inverse Class F mode with a half-sinusoidal voltage waveform and a square current waveform at the device output terminal.^{9} However, it is impractical to control an infinite number of harmonics using microstrip transmission lines. In this design, only the second and third harmonics are considered. The maximally flat drain voltage and current expressions of inverse Class F PA with the second harmonic open loaded and the third harmonic short loaded are shown below:^{10}

where V_{dd} and I_{dc} are the drain DC supply voltage and current, R_{on} is the switching on-resistance of the transistor.

According to Equations 1 and 2, setting V_{dd} = 28 V, I_{dc} = 0.6 A and R_{on} = 0.5 , the peak drain voltage value for inverse Class F equals to 73.7 V, which is much greater than the peak drain voltage value 55.2 V for Class F operation under the same condition. This results in a higher efficiency of inverse Class F than its Class F counterpart.

GaN HEMT’s large material band gap permits it to operate at high drain voltage and high power density.11 For Cree’s CGH40010, the maximum drain to source voltage is 84 V,^{12} which is large enough for inverse Class F operation with a peak drain voltage of 73.7 V. While for Freescale’s LDMOS FET (such as MRF7S35015), the maximum drain to source voltage is 65 V,^{13} which could not meet the requirement of inverse Class F operation. In this case, a GaN HEMT becomes a promising candidate for inverse Class F PA design.

**Load Pull/Source Pull Simulation Steps**

- With the large signal transistor model of CGH40010 provided by Cree, load pull and source pull simulations are carried out in Agilent’s Advanced Design System (ADS). The center frequency is set at 2.55 GHz, and the transistor is biased at V
_{gs}= -3.6 V and V_{ds}= 28 V with an input power level of 26 dBm. The objective of the simulation is to find out the optimum load and source impedances at both the fundamental frequency and harmonics, when the power-added efficiency (PAE) is maximum, with a high output power. The simulation is performed through the following steps: Set the fundamental source impedance at a default value to perform fundamental load pull simulation, the optimum fundamental load impedance Z_{L_fund}is obtained. Perform fundamental source pull simulation with Z_{L_fund}to get the optimum fundamental source impedance Z_{S_fund}. Several iterations are needed before the optimum fundamental impedances converge. After convergence, Z_{S_fund}= (6.4-j4) Ω and Z_{L_fund}= (13.21+j16.906) Ω are obtained. - Perform inverse Class F harmonic load pull simulation with Z
_{S_fund}and Z_{L_fund}. In this simulation, only the second and third harmonics are considered and the values of the harmonic impedances are restricted to be purely reactive for the successive design. After simulation, the optimum second harmonic load impedance Z_{L_2nd}= j844.097Ω and the optimum third harmonic load impedance Z_{L_3rd}= -j5.987 Ω are obtained. - Perform harmonic source pull simulation. From simulation results, the third harmonic source impedance has little effect on the PAE, while the second harmonic source impedance affects it a lot. The optimum second harmonic source impedance is obtained as Z
_{S_2nd}= -j27.968 Ω. The PAE simulation results obtained by varying the second harmonic source impedance are shown in**Figure 1**. Without any losses, the maximum possible PAE could be 83 percent, when Z_{S_2nd}= -j27.968 Ω. If the second harmonic source impedance is not well controlled in the design, the PAE would drop to 67 percent, a considerable decrease of 16 percent. The input HMN helps to provide a second harmonic source impedance as close as possible to Z_{S_2nd}.

**Figure 1** Harmonic source pull simulation.

**Figure 2** Schematic of the designed inverse Class F PA.

**HMN Analytical Design and Schematic Simulation**

**Figure 2** shows the circuit schematic of the proposed inverse Class F PA. The input/output HMN controls the harmonic source/load impedances for the values obtained by harmonic source/load pull simulation. The input/output fundamental matching network (FMN) then transforms the fundamental impedances Z*’_{S}/Z*’_{L} to 50 Ω. The analytical design procedure for both HMNs is described as follows.

In the output HMN, the electrical length θ_{4} and θ_{6} of the two open stubs are set at π/4 and π/6, which provide a short-circuit at the two junctions for the second and third harmonics, respectively. For the second harmonic load impedance, Equations 3 and 4 can be obtained:

By solving the equation Z_{L}(2f_{0}) = Z_{L_2nd} = j844.097 Ω, when Z_{3} = 50 Ω, one gets θ_{3} = 43.3°. The value of Z_{3} can be altered according to the width of the transistor’s drain pad.

For the third harmonic load impedance, one gets:

By solving the equation Z_{L}(3f_{0}) = Z_{L_3rd} = -j5.987 Ω, when Z_{4} = 50 Ω and Z_{5} = 50 Ω, one gets θ_{5} = 28.9°. The parameters of the output HMN are now determined. According to the same principle, the parameters of the input HMN can be determined.

**Figure 3** Simulated drain voltage and current waveforms.

**Figure 3** shows the simulated drain voltage and current waveforms of the proposed inverse Class F PA. It can be observed that the two waveforms are distorted, when compared with the ideal waveforms of inverse Class F operation. This is because the effects of the nonlinear parasitic parameters that exist in the transistor package. If the package is de-embedded and the waveforms are simulated at the intrinsic drain, the results would be closer to the ideal condition.

From the schematic harmonic balance (HB) simulation in ADS, the maximum in-band PAE of 84.2 percent is obtained at 2.55 GHz, with an output power of 39.54 dBm and a transducer power gain of 13.54 dB.

**Figure 4** Measured amplifier performance.

### Measurement and Linearization

A 2.5 to 2.6 GHz inverse Class F PA has been fabricated to validate the design approach. The selected substrate is RF-35 from Taconic Co. with a dielectric constant of 3.5 and a thickness of 30 mil.

**CW Signal Measurement**

By setting V_{gs} = -3.6 V and V_{ds} = 28 V with a 26 dBm input power, the measured PAE, drain efficiency (DE), output power and power gain are plotted in **Figure 4** within the frequency band from 2.5 to 2.6 GHz. DE is greater than 52 percent, PAE is greater than 47.7 percent and the output power is greater than 36.9 dBm within the 100 MHz bandwidth. The peak DE of 75.2 percent and peak PAE of 73 percent are observed at 2.55 GHz with a maximum output power and power gain of 41.43 and 15.43 dB, respectively.

**Figure 5** Measured results vs. input power.

Driven by a 2.55 GHz CW input signal with the power swept from 13 to 27 dBm, the measurement results of the inverse Class F PA are plotted in **Figure 5** with V_{gs} = -3.6 V, V_{ds} = 28 V. When the input power reaches 27 dBm, the DE and PAE are 76 and 73.5 percent, respectively. However, the power gain has been compressed to 14.6 dB, a 2.2 dB compression, compared with the maximum power gain observed at a 20 dBm input power.

In **Figure 6**, the drain to source voltage is varied from 20 to 29 V, with the input power fixed at 26 dBm and V_{gs} = -3.6 V. DE and PAE achieve a maximum of 79 and 75.4 percent, respectively, at V_{ds} = 21 V.

**Figure 6** Measured results vs. drain to source voltage.

**Linearization with Digital Predistortion**

The PA DPD linearization system consists of a vector signal generator (Rohde & Schwarz SMBV100A), a vector signal analyzer (Agilent VSA-E4445A), a PC with Matlab and Agilent’s 89600 and the proposed inverse Class F GaN PA. The SMBV100A, E4445A and PC are connected via a local area network (LAN). The configuration of the system is shown in **Figure 7**.

**Figure 7** The PA DPD linearization system configuration.

The baseband I/Q signals are modulated and up-converted to an RF signal in SMBV100A, the RF signal is then amplified and distorted by the PA. After attenuation, the RF output signal of the PA is down-converted and demodulated by E4445A. Finally, the output I/Q samples are collected in VSA 89600 for modeling. Using the Hammerstein architecture,^{14} the inverse PA model (digital predistorter) can be established with the input and output I/Q samples of the PA. With the digital predistorter, the distortion of the PA can be compensated.

The input signal of the PA is chosen as a four-carrier OFDM QPSK signal with a 20 MHz bandwidth and 10.39 dB PAPR at the 0.01 percent level of the complementary cumulative distribution function (CCDF). After CFR with a soft clipping technique,^{8} the PAPR is decreased to 8.05 dB.

**Figure 8** Measured PSD before and after linearization.

**Figure 8** shows the measured four-carrier OFDM PSD of the PA before and after linearization. The black trace indicates the original output of the PA. The adjacent channel leakage ratio (ACLR) is -37.48 dBc (lower) and -36.94 dBc (upper) at an average output power of 34.3 dBm. After DPD with Hammerstein, the output PSD of the PA is shown by the red trace, the ACLR of which is suppressed to -41 dBc (lower) and -39.38 dBc (upper). A slight improvement is achieved at this power level of the inverse Class F PA. When the baseband I/Q signal is processed by CFR, distorted by the digital predistorter, and then downloaded to SMBV100A as the input signal of the PA, the output PSD of the PA is shown by the blue trace, the ACLR of which is equal to -48.22 dBc (lower) and -45.8 dBc (upper). The efficiency of the PA is 31.9 percent at a 34.3 dBm average output power.

### Conclusion

This article presented an analytical design approach of inverse Class F PA. The input and output HMNs controlled the source and load harmonic impedances appropriately. The fabricated 2.5 to 2.6 GHz GaN inverse Class F PA achieved a maximum in band drain efficiency greater than 75 percent, with an output power of 41.4 dBm at 2.55 GHz. For linearization, the PAPR of the 20 MHz four-carrier OFDM signal was reduced from 10.39 dB to 8.05 dB through a CFR technique. Then, by using DPD, based on Hammerstein, the ACLR was improved to less than -45 dBc at an average output power of 34.3 dBm with 31.9 percent efficiency. According to the experimental results, the proposed inverse Class F PA is suitable for linear amplification with high efficiency.

### Acknowledgment

This work was supported by the National Key Technologies R&D Program of China under Grant 2010ZX03007-003-02 and in part by the National High-Tech Project under Grant 2009AA011801.

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