J Comput Electron (2014) 13:943–949 DOI 10.1007/s10825-014-0612-x
Linearization design method in class-F power amplifier using artificial neural network Mohsen Hayati · Farzin Shama · Sobhan Roshani · Abdolali Abdipour
Published online: 27 August 2014 © Springer Science+Business Media New York 2014
Abstract This paper represents the design of a class-F power amplifier (PA), its artificial neural network (ANN) model and a PA linearization method. The designed PA operates at 1.8 GHz with gain of 12 dB and 1dB output compression point (P1dB) of 36 dBm. The proposed ANN model is used to predict the output power of designed class-F PA as a function of input and DC power. This model utilizes the designed class-F PA as a block, which could be used in a desired linearization circuit. In addition, the power added efficiency (PAE) and the other specifications of a PA, related to power can be predicted using the proposed model. A simple feedforward technique is used to improve the linearity of designed PA. For verification, this linearization method is compared with presented neural network model simulations. The results show the improvement of P1dB from 36 to 41 dBm, which is predicted using the proposed model. Also, the PAE of the final linearized circuit PA is predicted.
M. Hayati (B) · F. Shama · S. Roshani Faculty of Engineering, Razi University, Tagh-E-Bostan, 67149 Kermanshah, Iran e-mail:
[email protected];
[email protected] F. Shama e-mail:
[email protected] S. Roshani e-mail:
[email protected] M. Hayati Computational Research Center, Razi University, Tagh-E-Bostan, 67149 Kermanshah, Iran A. Abdipour Department of Electrical Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran, Iran e-mail:
[email protected]
Keywords Artificial neural network · Class-F power amplifier · Modeling · Linearization
1 Introduction Power amplifiers are high power-consuming in any communication system and therefore, their efficiency is a very important factor in the design process. High efficiency PAs have become one of the most significant components in the modern communication. RF power amplifiers are divided into several classes such as, A, B, AB, C, D, E, F, etc. [1,2]. They differ in the method of operation, linearity, efficiency and output power. Class-F PA has become very popular recently among of mentioned classes. This is because of its high efficiency and output capability [3]. So far, several types of models have been introduced for PAs modeling, such as Volterra series [4], Wiener [5] and physical based models [6]. However, these models suffer from several disadvantages, such as large number of complicated coefficients extraction and approximation based approach for obtaining the specifications of the device. Neural models have a lot of advantages compared to the other models. For instance, they are faster and more accurate [7–14]. Using ANN to model power amplifiers [15–18] has become the subject of interest, in the recent years. The model proposed in [15] is a static ANFIS model without consideration of the memory effects of the power amplifier, and it is not easy to determine the structure of ANFIS. In [16] a three layer neural network is used to model an FET device at circuit level. The proposed model is physically oriented and takes a long time to simulate. In [17] a neural network suitable for dynamic modeling of the baseband nonlinear behaviors of third generation (3G)
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Fig. 1 The schematic of the designed class-F PA
V DD VGG
TL5 Input
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Cin
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TL 3 = 2.9 mm TL 4 = 2.7 mm TL 5 = 28 mm
base-station PA is presented, which used a large numbers of neurons making the model complex. The power spectral density (PSD) is investigated in this work, while the other specifications of PA are not considered. In a Similar approach [18], a radial basis function neural network (RBFNN) is used to model an RF power amplifier for 3G, which investigated the adjacent channel power ratio (ACPR). Neural network methods have also been used to model the other microwave components, such as low noise amplifiers (LNA), microstrip filters etc. [19–30]. For example in [29] a low voltage RF CMOS LNA is modeled using MLP, RBF and ANFIS. In this approach, the scattering parameters (S-parameters) are considered as the inputs and transistors channels length (l) and width (w) considered as the outputs of the model. In [30], a microstrip lowpass filter is modeled, using ANN. In this work a multilayer perceptron (MLP) neural network with 12 neurons and two hidden layers is used to predict the S-parameters of the lowpass filter. Several linearization techniques have been presented to improve the linearity of the power amplifier such as: Feedforward [31], Doherty [32], Envelope Elimination and Restoration (EER) [33], Balanced amplifiers [34], Predistortion [5], etc. The mentioned conventional modeling approaches cannot model the PA as a block or sub circuit for circuit design. The presented method can overcome this problem, for example, this model could be used in an analog linearization technique. In this paper, a class-F power amplifier is designed using a low voltage pHEMT with input and output matching circuits. The designed class-F PA operates at 1.8 GHz and has maximum power added efficiency (PAE) of 76 % and maximum gain of 16dB at input power of 26 and 10 dBm, respectively. An artificial neural network model is proposed for designed PA to model the nonlinearity of the power amplifier with input, output and DC power as the effective parameters.
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TL4
pHEMT ATF - 34143
TL 1 = 1 mm TL 2 = 8.1 mm
TL6 TL7
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TL6 = 28 mm TL7 = 6.5 mm TL8 = 7 mm TL9 = 7 mm TL10= 1 mm
2 Class-F design The output impedance in class F amplifier is zero at even harmonics and is infinite at odd harmonics. Therefore, the voltage becomes square wave, while the current waveform becomes half sine [35–37]. According to this fact, harmonic control circuit plays an important role in the design of class-F PA. The designed PA with circuit used for input and output impedance matching, and harmonic control is shown Fig. 1. In this figure microstrip transmission lines (TL) and applied transistor, are shown. The Transmission Lines TL2–TL5 are used for input matching, while TL6–TL9 are used for output matching network. Also transmission lines work as harmonic control circuits to shape the class-F power amplifier voltage and current. The voltage and current of the class-F power amplifiers can be written as follows [38]: V D (θ ) = VDC +Vm sin (θ )+V3m sin (3θ ) + V5m sin (5θ ) . . . (1) i D (θ ) = I DC − Im sin (θ ) − I2m sin (2θ )− I4m sin (4θ ) . . . (2) where VD is drain voltage, i D is drain current and Vm is amplitude of drain voltage at the fundamental frequency. As mentioned, drain voltage contains odd harmonics and drain current contains even harmonics. The power and PAE equations in class-F PA can be written as: Vm2 2R PDC = VDC I DC Po − Pi P AE = PDC Po =
(3) (4) (5)
In above equations Po and PDC are output power and DC power, respectively. Power amplifiers convert the DC power into AC power.
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Fig. 3 Simulated transistor drain voltage and current waveforms of the designed class-F PA
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Fig. 4 Architecture for the proposed MLP model
Fig. 2 a Output power, b gain and efficiency of designed class-F PA
The class-F PA is designed and simulated using a low voltage pHEMT ATF-34143. The simulation is performed using advanced design system (ADS) software. The root model of the applied transistor is available in the software and can be downloaded from the vendor’s website. The DC bias voltages for the transistor in the designed circuit are as Vd = 7.3V and Vg = 0.2V. The output power, gain and efficiency of the designed class-F PA is shown in Fig. 2. According to this figure, P1dB is 36 dBm, while the gain and maximum PAE are 76 % and 12 dBm under the input power of 26 dBm, respectively. Simulated drain voltage and current waveforms of the designed class-F power amplifier, are shown in Fig. 3. As seen, the drain voltage and current waveforms are similar to square and half sine shapes, respectively.
3 ANN model of the proposed class-F PA An information processing system that is a mathematical abstraction of human cognition, and neural biology is called artificial neural network (ANN). Recently, ANNs have played an important role in estimation and prediction problems. ANNs can be considered as a mathematical system consisting of simple processing elements named neuron, running in parallel, which can be generated as one or multiple layers. The multi-layer perceptron (MLP) networks are the most widely used architectures in ANNs, which have feed forward topology with minimum three layers: input layer,
hidden layer and output layer. Each layer consists of a number of neurons with an activation function, and each neuron is fully interconnected with weighted connections to neurons in the subsequent layer. The ANN weights are trained using a form of error feedback, which can be viewed as a generalization of LMS. Specifically, the networks are trained using an error backpropagation algorithm (BPA), which modifies the weights of the various layers of the MLP. Adding more neurons to each layer and also adding more layers to network can improve the ability of network, but the complexity is the cost of this performance. Several structures and topologies of neural networks with different numbers of hidden layers, number of neurons, activation functions, biases, etc. have been tested, in order to propose best structure and topology for the designed class-F PA. To implement the proposed class-F PA, the proposed MLP model is shown in Fig. 4. The input variables used in this model are input power and DC power, while, the output variable is the output power (all in dBm). Used data set for training of the MLP is obtained using the performed simulations by ADS software in baseband frequency (1.8 GHz). The used rule for training of the network is performed by the Levenberg–Marquardt (LM) algorithm. In order to develop the ANN model, the total existent data are divided into two parts: 70 % for training and 30 % for testing the trained model. Training of the ANN model was done by MATLAB 7.6.0 software. Table 1 illustrates the specifications of the proposed ANN model in this study.
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Table 1 The specifications of proposed ANN model MLP
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1
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400
Activation function
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Table 2 The obtained errors for training and testing results of the proposed ANN model Error
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Test
MRE %
0.0001
0.0024
RMSE
0.0275
0.0293
MAE %
1.9882
2.4652
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Table 2 shows the obtained results for the proposed ANN model, where the mean relative error percentage (MRE %), the root means square error (RMSE) and the mean absolute error percentage (MAE %) of the network, are defined by below equations: N 1 X i (E x p) − X i (Pr ed) (6) MRE % = 100 × N X i (E x p) i=1 ⎡ N ⎤0.5 2 (X (E x p) − X (Pr ed)) i i ⎢ ⎥ ⎢ i=1 ⎥ RMSE = ⎢ (7) ⎥ ⎣ ⎦ N
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(8)
Fig. 5 Comparison of real and predicted results of a training data for output power b testing data for output power
i=1
where, N is the number of data and ‘X (Exp)’ and ‘X (Pred)’ stand for real and predicted (ANN) values, respectively. The training and testing results of the proposed ANN model are shown in Fig. 5a, b respectively. As seen from Table 2 and Fig. 5, the predicted output power by ANN model is close to the real results, clearly. These results validate the accurate applicability of ANN as a reliable model to predict the proposed PAs output power from the input power and DC power. Most important advantage of the proposed MLP architecture is its simplicity. In addition, a simple relationship can be determined from the ANN model to calculate the output power as a function of input and DC power of the PA: Pout ≈ −22.6325 Tansig (−0.1132 Pin + 0.2346PDC − 2.5667) + 8.4140 Tansig (−0.1911Pin + 0.4056 PDC − 10.5271) + 16.8992 Tansig (0.1374 Pin − 0.1988 PDC + 4.5622) + 51.5169
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(9)
where: Tansig (x) =
2 −1 1 + exp −2 (x)
(10)
The predicted and simulated output power as a function of input power and DC power, are shown in Fig. 6a, b respectively. As seen, the linearity status is suitable until about 25 dBm input power, but for larger input power, the nonlinear region occurs.
4 Linearization using feedforward method As mentioned, there are several ways to enhance the linearity in power amplifiers. A simple feedforward technique using designed class-F amplifier is presented, shown in Fig. 7. As seen in the figure, the input power is divided within two ways
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Fig. 7 A simple feedforward topology for linearization of design classF amplifier
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Fig. 8 The simulated and predicted output power of proposed feedforward technique
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Fig. 6 Predicted and simulated output power (dBm) as a function of: a input power b DC power
Feedforward simulated PAE Feedforward predicted PAE
80 70%
PAE
leading to two class-F PAs. The divided power, reaching to input of each PA, is lower than previous applied power for single class-F PA. Hence, each PA sees a lower power at input and operates more linear. The proposed ANN model was applied to implement the feedforward topology as shown in Fig. 7. The simulated and predicted output power of proposed feedforward technique is shown in Fig. 8. According to this figure, P1dB is 41 dBm, which shows a better linearity compared with designed conventional class-F PA. As mentioned before, proposed ANN model for designed Class-F PA can be used to predict the output power or PAE of designed PA as a sub circuit. For instance, the output power and PAE of proposed feedforward scheme as shown in Fig. 7, are predicted using proposed ANN model for single Class-F PA.
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Fig. 9 The simulated and predicted PAE of proposed feedforward technique
This predicted output power is compared with simulated output power and PAE using advanced design system (ADS), which is illustrated in Figs. 8 and 9.
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5 Conclusions A new simple feedforward method was presented for improving the linearity of class-F PA. For verification, the output power was predicted using proposed ANN model for the designed power amplifier. The proposed linearization method is extremely straightforward and easy to construct to improve the linearity of a power amplifier. The P1dB of the PA improves from 36 to 41 dBm. The proposed linearization method has been validated by ANN model. With above discussion, the presented ANN model can be applied instead of a class-F power amplifier, for other implementations.
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