An extraction technique for small signal intrinsic parameters of HEMTs based on artificial neural networks

Int. J. Electron. Commun. (AEÜ) 67 (2013) 123–129

Contents lists available at SciVerse ScienceDirect

International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue

An extraction technique for small signal intrinsic parameters of HEMTs based on artificial neural networks M. Hayati a,b,∗ , B. Akhlaghi a a b

Electrical Engineering Department, Faculty of Engineering, Razi University, Tagh-E-Bostan, Kermanshah 67149, Iran Computational Intelligence Research Centre, Razi University, Tagh-E-Bostan, Kermanshah 67149, Iran

a r t i c l e

i n f o

Article history: Received 21 September 2011 Accepted 8 July 2012 Keywords: HEMT Equivalent circuit parameters Parameter extraction Artificial neural networks Radial basis function Multi layer perceptron

a b s t r a c t This paper presents a fast and accurate procedure for extraction of small signal intrinsic parameters of AlGaAs/GaAs high electron mobility transistors (HEMTs) using artificial neural network (ANN) techniques. The extraction procedure has been done in a wide range of frequencies and biases at various temperatures. Intrinsic parameters of HEMT are acquired using its values of common-source S-parameters. Two different ANN structures have been constructed in this work to extract the parameters, multi layer perceptron (MLP) and radial basis function (RBF) neural networks. These two kinds of ANNs are compared to each other in terms of accuracy, speed and memory usage. To validate the capability of the proposed method in small signal modeling of GaAs HEMTs, data and modeled values of S-parameters of a 200 ␮m gate width 0.25 ␮m GaAs HEMT are compared to each other and very good agreement between them is achieved up to 30 GHz. The effect of bias, temperature and frequency conditions on the extracted parameters of HEMT has been investigated, and the obtained results match the theoretical expectations. The proposed model can be inserted to computer-aided design (CAD) tools in order to have an accurate and fast design, simulation and optimization of microwave circuits including GaAs HEMTs. © 2012 Elsevier GmbH. All rights reserved.

1. Introduction Compared with bipolar transistor devices, field effect transistor (FET) devices have a better noise performance. Specially, GaAs metal extended semiconductor FETs (MESFETs) are widely used at microwave frequencies, due to their low noise and high gain characteristics. Their performance can be enhanced if a heterojunction is used between GaAs and AlGaAs, such as in high electron mobility transistors (HEMTs). GaAs HEMTs are rapidly replacing conventional MESFET technology in military and commercial applications. They are promising devices for millimeter-wave applications and optical communication systems due to their excellent high frequency and low noise performance [1–3]. Currently low noise HEMTs are used in front end of satellite communications, radio astronomy and satellite direct broadcasting receiver systems [3,4]. An accurate extraction method for a proper small signal equivalent circuit of HEMTs is necessary for designing a circuit and evaluating the process technology. It also allows the development of accurate and yield-effective computer-aided design (CAD) of

∗ Corresponding author at: Electrical Engineering Department, Faculty of Engineering, Razi University, Tagh-E-Bostan, Kermanshah 67149, Iran. E-mail address: mohsen [email protected] (M. Hayati). 1434-8411/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.aeue.2012.07.012

monolithic microwave integrated circuits (MMICs) and optoelectronic integrated circuits (OEICs) [5,6]. Several approaches are used to model small signal active devices. Some of these techniques include table-based models, temperature-dependent nonlinear models, and artificial neural networks (ANNs). These models are then utilized for computeraided design and optimization of microwave circuits [7]. ANN computational models have gained recognition as an unconventional and useful tool for microwave modeling and design (including component or circuit level) [8,9]. Fast, accurate and reliable neural network models can be developed from measured or simulated microwave data through a process called training. Neural network transistor models for a new semiconductor device can be developed even if the device theory/equations are unavailable [8]. That is to say, ANN technique is useful in modeling microwave devices because it can generalize, that means the model can respond to new data that have not been used during training process. ANN techniques are time saving comparing to temperature-dependent and table-based nonlinear models since require only a few algebraic operations. In some previous literatures, ANN techniques have been applied to extract equivalent circuit parameters (ECPs) of some microwave components and circuits including heterojunction bipolar transistors (HBTs) [10] and MESFETs [7,11]. Some large signal modeling of HEMTs has been reported in previous literatures [12–14]. Some

124

M. Hayati, B. Akhlaghi / Int. J. Electron. Commun. (AEÜ) 67 (2013) 123–129

literatures [15,16] have presented a small signal model for HEMT using ANN. Advantages of the present work in contrast with previous literatures are that in the proposed method, two kinds of neural networks, i.e. multi layer perceptron (MLP) and radial basis function (RBF) networks, are constructed for extraction of intrinsic parameters of HEMT. Then these networks are compared to each other in order to determine the best neural model in terms of accuracy, speed and memory usage. Moreover, because parameters of temperature and frequency could alter the overall performance of the circuit, the device model must take into account these parameters [7,17,18]. Therefore, in this work temperature and frequency in addition to bias points are considered as inputs of the proposed neural models while in previous publications only bias points are applied to the input of the network. The rest of the paper is organized as follows: Section 2 deals with the modeling methodology, which consists of two subsections: in Section 2.1 intrinsic and extrinsic elements of small signal equivalent circuit of GaAs HEMT at microwave frequencies are introduced. In Section 2.2 neural network modeling methodology is given as follows: Sections 2.2.1 and 2.2.2 describe the MLP and RBF network structures respectively, and the learning algorithm for each networks’ parameters. In Section 3, we present structures of the implemented neural networks. Error analysis and comparison of two neural networks are presented in Section 4. Section 5 presents small signal modeling validation of the proposed ANN models. Finally, in Section 6 the main conclusions are summarized.

extraction (analytical) techniques [5,19,20]. The optimization procedures [21–23] may cause element values with no physical sense, and the results depend on the initial guess values or the optimization method itself. The analytical procedures [1,3,5,20,24–29] overcome these drawbacks and allow extracting ECPs straightforwardly. In direct extraction method, the intrinsic elements are extracted according to the following steps [5]: Step 1. The extrinsic elements are extracted from two sets of S-parameter measurements under ‘cold’ bias condition (Vds = 0 V, i.e. passive device), which include of ‘unbiased cold’ (Vds = 0 V and Vgs = 0 V) and ‘pinched cold’ (Vds = 0 V and Vgs < Vp ), where Vgs is gate-source voltage, Vds is drainsource voltage, and Vp is pinch off voltage. Step 2. S-parameter measurements are done under ‘hot’ bias condition (Vgs < 0 V and Vds > 0 V, i.e. active device). Step 3. Contribution of the extrinsic elements is removed from this set of S-parameters (i.e. obtained from 2nd step). Step 4. The intrinsic parameters are analytically obtained from this new set of S-parameters (i.e. obtained from 3rd step). The direct extraction technique for obtaining extrinsic and intrinsic elements of HEMT is described in details in [26]. The aim of this paper is to use the data obtained from the stages 1–4 to create an accurate ANN model for parameter extraction of HEMT.

2. Modeling methodology

2.2. Neural network model

2.1. Extraction of intrinsic elements from measured S-parameter values

For extraction of small signal intrinsic parameters of HEMT addressed in this paper, we consider implementation with two neural network structures. The first of these was a feed forward MLP neural network with training according to scaled conjugate gradient algorithm (trainscg) optimization. The second was a RBF network. The MLP and RBF networks have four inputs, i.e. Vgs , Vds , freq (frequency) and T (operating temperature) and eight outputs, i.e. Cds , Cgd , Cgs , Rgs , gds , gm ,  and fT (cut off frequency). We start with a review of basic concepts of the MLP approach, and then we will describe the RBF network. All simulations and tests for the MLP and RBF networks are done using MATLAB’s neural network toolbox.

Fig. 1 shows small signal equivalent circuit of AlGaAs/GaAs HEMT in its common-source format. It can be partitioned into two basic parts: extrinsic elements consist of parasitic capacitances, inductances and resistances. These elements account for nondesired effects or represent the connections of the intrinsic part to another device in a complete circuit and are bias-independent, and intrinsic elements, which consist of Rgs (channel resistance), gds (drain conductance), gm (transconductance),  (time delay associated with transconductance), Cgs , Cgd , Cds (gate to source, gate to drain and drain to source capacitances, respectively) and are bias-dependent. The basic cell for linear, nonlinear and noise model is intrinsic transistor [3], so this work focuses in taking out the intrinsic elements. The small signal ECP extraction methodologies can be classified into two categories: optimization-based and direct

Fig. 1. Small signal equivalent circuit of GaAs HEMT.

Fig. 2. Schematic of the proposed MLP neural network model.

M. Hayati, B. Akhlaghi / Int. J. Electron. Commun. (AEÜ) 67 (2013) 123–129

2.2.1. Multi layer perceptron Multi layer perceptron is a popular type of neural networks used for microwave device modeling. The MLP architecture usually consists of an input layer, an output layer and one or more hidden layers of computing nodes termed neurons. Neurons of adjacent layers are connected each other through adaptive weights [30]. The hidden layers have a number of neurons, which has to be optimized to gain the best model accuracy. In a MLP neural network with one hidden layer, the input to the node p in the hidden layer is given by: np =

q 

(xm wmp ) + bp

p = 1, 2, . . . , k

(1)

m=1

where w is the weighting factor, b is the bias term, q is the number of neurons in the input layer and k is the number of neurons in the hidden layer [31]. The output of pth neuron of the hidden layer is given by: op = f (np )

(2)

where f is activation function of the hidden layer. The activation function can be found in different forms, either linear or non-linear. Some of the commonly used activation functions are linear, threshold, tangent hyperbolic, Gaussian and sigmoid transfer functions. MLP neural networks often use the sigmoid transfer function in their hidden layers and linear activation function in their output layer. In this work, a smooth logarithm-sigmoid (logsig) activation function has been used for each hidden layer, so the output of pth neuron of the hidden layer is defined by: op = logsig(np ) =

1 1 + enp

(3)

The output of the ith neuron in the output layer is given by:

yi =

k 

(om wmi ) + bi

i = 1, 2, . . . , l

(4)

m=1

where w is the weighting factor, b is the bias term and l is the number of neurons in the output layer [31]. In training process of a neural network the set of adjustable parameters, i.e. weights and biases are optimized to reach to the best prediction of the target variables based on background variables. MLP networks are trained with the standard backpropagation algorithm, which is explained in detail in [32]. Fig. 2 shows schematic of the proposed MLP neural network structure.

125

2.2.2. Radial basis function neural network Radial basis function networks are a relatively new class of ANNs. They use transfer functions of radial shape, often Gaussian, applied to each hidden neuron. Fig. 3 shows a schematic of this network. It has r inputs, u neurons with Gaussian activation functions, and s neurons with linear activation function. Radial basis networks usually require more neurons than MLP networks, but often they can be trained and designed much faster [33]. They are constructed in two methods using MATLAB neural network toolbox: ‘newrbe’, which is an exact-fit design and ‘newrb’, which is a more efficient design. The newrbe very quickly designs a radial basis network with zero error on training vectors. The drawback to newrbe is that it creates as many neurons as there are input patterns but newrb adds neurons to the hidden layer of a radial basis network until it meets the specified mean squared error goal making it capable to use less neuron at the hidden layer [33]. The designer must choose an appropriate spread constant, which is the width of the RBF neurons [7]. The spread constant must be chosen so that enough radial neurons respond to an input, but not so large that all of the radial neurons respond equally. More details on the spread constant for RBF networks are explained in [34]. 3. Structures of implemented neural networks As an example to verify the method proposed above, in order to obtain dataset for creating our ANN models, S-parameters of a 200 ␮m gate width 0.25 ␮m GaAs HEMT (FHR02X, supplied by Fujitsu Manufacturing Corporation), over frequency range extending from 100 MHz to 30 GHz, bias ranges of Vgs (−3 V to 0 V) and Vds (0 V to 3.5 V) and at the temperatures of 10 ◦ C, 25 ◦ C, 50 ◦ C and 80 ◦ C, were obtained using Agilent’s Advanced Design System (ADS) simulation environment. Subsequently, intrinsic parameters of the device were calculated according to the stages 1–4 explained in Section 2.1. Both MLP and RBF models were constructed using 1200 data values, and then the networks were trained and tested with 70% and 30% of the data set, respectively. Many structures of MLP network with the different number of hidden layers have been implemented in order to achieve the best performance based on good accuracy, memory usage and convergence speed. Network parameters such as learning algorithms, transfer functions of hidden layer and different numbers of hidden neurons were varied for each of these structures. Among them, three types of structures with one, two and three hidden layers that are tabulated in Table 1 showed the best performance. Fig. 4 illustrates network performance for the structures listed in Table 1. From this figure, we can see network B with one hidden layer

Fig. 3. RBF neural network architecture.

126

M. Hayati, B. Akhlaghi / Int. J. Electron. Commun. (AEÜ) 67 (2013) 123–129

Table 1 The best characteristics of three types of MLP networks. Characteristics

Network A

Network B

Network C

Number of hidden layers Number of hidden neurons in each hidden layer Learning algorithm Type of activation function of hidden layers MRE%

2 28–32 trainscg logsig 0.17603

1 84 trainlm logsig 0.68008

3 18–20–20 trainscg logsig 0.39971

Table 2 Characteristics of four structures of RBF networks with 60, 200, 500 and 880 training patterns. Characteristics

Structure A

Structure B

Structure C

Structure D

Number of training patterns Number of hidden neurons MRE% Convergence speed (Sec)

60 50 15.85521 0.09954

200 200 7.93775 1.44759

500 500 2.75501 21.92543

880 875 0.20705 43.14650

Table 3 Prediction accuracy of intrinsic elements in MLP and RBF models. MLP model

Intrinsic parameters Cds Cgd Cgs Rgs gds gm fT 

Fig. 4. Network performance for MLP networks A (with two hidden layers), B (with one hidden layer) and C (with three hidden layers).

RBF model

MRE%

MSE%

MRE%

MSE%

0.00503 0.00953 0.02222 0.01250 0.08163 0.69049 0.40435 0.18245

3.984E−07 3.142E−07 2.613E−07 7.356E−07 1.405E−05 0.06660 1.789E−06 6.901E−04

0.11939 0.01327 0.05359 0.15349 0.13924 0.27351 0.20811 0.69580

0.00132 2.405E−06 1.283E−05 8.487E−04 2.148E−04 0.03455 0.00167 0.01432

are trained with less number of training patterns have less number of hidden neurons, but their accuracy is unacceptable. Even though factors such as the convergence speed and the memory usage can be important in efficient network design, neither can be as important as the accuracy. 4. Error analysis and comparison

converges faster than the other networks, but from Table 1, its prediction accuracy is less than networks A and C. Network C, has the worst convergence speed and its prediction accuracy is more than network B and less than network C. Network A has the best accuracy, and its convergence speed is acceptable. So the best structure for the MLP model was chosen with the 4–28–32–8 neurons in the input, hidden and output layers respectively, training algorithm according to trainscg optimization and the logsig activation function in hidden layers. To compare the accuracy of the three different structures, we used percentage of mean relative error (MRE%) criterion, which will be introduced in the following section. In order to design RBF model, we used newrb function. With applying the same number of training patterns applied to MLP network (880 patterns, i.e. about 70% of whole data) for training the RBF network, 875 neurons in hidden layer will be required in order to reach to sum-squared error equal to 0 and consequently achieve the accurateest results for the RBF model. In order to reduce the number of hidden neurons, we can use less number of training patterns. Several structures of RBF network with the different number of training patterns have been implemented. For instant, four of these RBF structures with 60, 200, 500 and 880 training patterns have been listed in Table 2. In all of these structures, spread constant and goal error have adjusted equal to 1 and 0, respectively. Results show although by reducing the number of training patterns, number of hidden neurons will be decreased, but the prediction accuracy will be dropped significantly. From Table 2, it can be concluded that network D is the most efficient RBF network in case of modeling GaAs HEMT, because although RBF networks, which

The prediction accuracy of the proposed models was measured by the percentage of mean relative error (MRE%) and mean square error (MSE%) defined as: 1  yi − di N yi

(5)

1 2 (yi − di ) N

(6)

N

MRE% = 100

i=1 N

MSE% = 100

i=1

where yi and di represent measured values (exact values) and our ANN model predicted values for the ith experiment, respectively. N indicates the total number of test data. The corresponding MREs and MSEs for eight parameters of HEMT in the optimal MLP and RBF models, i.e. networks A and D respectively, are tabulated in Table 3. As seen from this table, both models estimate the intrinsic parameters with good accuracy. All of the MREs are under 0.7%. MSEs are under 0.067% and most of them are about 0. In Table 4, the accuracy, memory usage and convergence speed of the optimal MLP and the RBF network structures, i.e. networks A and D respectively, are compared. Memory usage was measured in terms of the number of hidden neurons used. From this table, we can conclude that the MLP network is more accurate than the RBF (MLP’s MRE is about 0.03% less than the RBF’s) and also the RBF network requires much more neurons than the MLP network. Therefore, the MLP model is more efficient in case of modeling GaAs

M. Hayati, B. Akhlaghi / Int. J. Electron. Commun. (AEÜ) 67 (2013) 123–129 Table 4 Accuracy, memory usage and convergence speed comparison of the MLP and RBF models. Type of the network

MLP model

RBF model

MRE% for test data MSE% for test data Number of hidden neurons Convergence speed (Sec)

0.176030 0.006618 60 173.48743

0.207054 0.008412 875 43.14650

HEMTs comparing to RBF, even though the RBF network is much faster. 5. Small signal modeling validation As it was explained in previous sections, the values of intrinsic parameters were obtained at various bias points, i.e. Vgs from −3 V to 0 V and Vds from 0 V to 3.5 V, frequency range extending from 100 MHz to 30 GHz and temperatures of 10 ◦ C, 25 ◦ C, 50 ◦ C and 80 ◦ C. Applying four parameters of Vgs , Vds , freq and T as input data and eight small signal intrinsic parameters of GaAs HEMT, i.e. Rgs , gds , gm , , Cgs , Cgd , Cds and fT , as output data of the networks, the MLP and RBF models were constructed. In this section, reliability of the proposed procedure is investigated. To validate the ability of the proposed ANN models in small signal modeling of GaAs HEMTs, the data (obtained from the datasheet of the device) and modeled S-parameters of FHR02X have been compared. Fig. 5 shows such comparison under the bias condition of Vgs = −2.3 V and Vds = 0.5 V and T = 25 ◦ C. In order to extract the modeled results, we replaced the FHR02X with the intrinsic part of the equivalent circuit shown in Fig. 1, which its intrinsic element values were obtained from the accurateest ANN model, i.e. the MLP network A. The intrinsic elements values are listed in Table 5. As it can be observed, there is an excellent agreement between data and modeled S-parameters in a wide frequency range (100 MHz to 30 GHz). The validity of this procedure was also verified by checking the frequency, bias and temperature dependence of the intrinsic elements, as shown in Figs. 6 and 7 and Table 6, respectively. Each time, one of the input parameters of the model, i.e. frequency, bias point or temperature, was varied and the other input parameters were

Fig. 5. Comparison between data and modeled values of S-parameters of FHR02X at Vds = 0.5 V, Vgs = −2.3 V, T = 25 ◦ C and frequency range of 100 MHz to 30 GHz.

127

Table 5 Intrinsic elements used to obtain simulation results for FHR02X. Intrinsic elements

Values

Cds (fF) Cgd (fF) Cgs (fF) Rgs () gds (mS) gm (mS)  (pSec)

82.7209110941614 56.3661113216370 132.758723216549 6.33263167110036 3.61933379452174 0.96441732758025 4.78881737792100

kept constant. Again, the intrinsic parameter values are obtained from the MLP network A. Fig. 6 confirms the intrinsic elements were extracted accurately, because it shows that changes in operation frequency affect in the values of the small signal intrinsic parameters slightly as this object is mentioned in [5]. However, this factor is applied as an input of the ANN models in order to obtain more accurate results. Fig. 7 shows a three-dimensional plot of Cds , Cgs , gds , and gm vs. gate-source and drain-source bias voltages. The intrinsic elements were extracted at 121 different bias points at the frequency of 3 GHz and temperature of 25 ◦ C. The behavior of these parameters matched the theoretical expectations. Table 6 compares values of the intrinsic elements in temperatures of 10 ◦ C, 25 ◦ C, 50 ◦ C and 80 ◦ C. The bias point and frequency were kept fixed at Vgs = −0.5 V, Vds = 2 V and freq = 3 GHz. In this table x = x(T2 ) − x(T1 ), where x is the intrinsic element and T is the temperature in which the intrinsic element is extracted. As it can be

Fig. 6. Performance of gm , gds , Cds , Cgd , and Cgs parameters of a 200 ␮m gate width GaAs HEMT vs. frequency at Vgs = −0.5 V, Vds = 2 V and T = 25 ◦ C.

128

M. Hayati, B. Akhlaghi / Int. J. Electron. Commun. (AEÜ) 67 (2013) 123–129 Table 6 Investigation of the effect of temperature variations in intrinsic parameters’ values. Intrinsic parameters

T1 = 25 ◦ C T2 = 10 ◦ C

T1 = 25 ◦ C T2 = 50 ◦ C

T1 = 25 ◦ C T2 = 80 ◦ C

Cds (fF) Cgd (fF) Cgs (fF) Rgs () gds (mS) gm (mS)  (pSec)

−1.409852E−01 1.359996E−01 −3.689849 −6.679989E−02 1.100248E−02 −9.100793E−03 −3.202094E−02

1.833060 −1.775000 4.804024E+01 7.702017E−01 −1.352000E−01 1.192991E−01 4.059970E−01

2.420503E+01 −2.344198E+01 9.344600E+01 9.120704 −1.783300 1.574299 5.171979

observed from this table, except in case of Cgd and gds , increasing in temperature will increase the values of the parameters. As [18] demonstrated, knowledge of the temperature dependence of a circuit model valid for a specific transistor type could be useful to define a starting small signal model for devices of another technological family. 6. Conclusion In this paper, two very accurate small signal models for an AlGaAs/GaAs HEMT (FHR02X) were developed under various bias, frequency and temperature conditions using MLP and RBF neural networks. In terms of accuracy and memory usage, MLP network showed better performance than RBF network, but in terms of convergence speed, RBF proved to be much better than MLP network when extracting intrinsic elements of AlGaAs/GaAs HEMTs. Depending on the specific needs, the designer makes the decision whether the device should be modeled using a MLP network or an RBF network. In addition, the influence of frequency, temperature and bias on the values of the intrinsic elements was investigated. We showed that changes in intrinsic parameters’ values with respect to changes in frequency are slight, but to reach to the accurateest results, we considered this factor as an input of the proposed ANN models. Optimal values for the number of hidden neurons and the best training algorithm in the MLP network were found by trial-anderror. The results show that the proposed ANN models can be used as an efficient tool for parameter extraction of GaAs HEMTs with good accuracy. The proposed models can be inserted to different circuit simulators like HSPICE for accurate and fast design and analysis of microwave circuits including GaAs HEMTs. References

Fig. 7. Behavior of Cds , Cgs , gds , and gm values of a 200 ␮m gate width GaAs HEMT vs. gate and drain bias at freq = 3 GHz and T = 25 ◦ C.

[1] Caddemi A, Crupi G, Donato N. Microwave characterization and modeling of packaged HEMTs by a direct extraction procedure down to 30 K. IEEE Trans Instrum Meas 2006;55:465–70. [2] Nguyen LD, Brown AS, Thompson MA, Jelloian LM. 50-nm selfalignedgate pseudomorphic AlInAs/GaInAs high electron mobility transistors. IEEE Trans Electron Dev 1992;39:2007–14. [3] Tayel M, Elgendy A. Extraction of HEMT intrinsic elements from S-parameter measured values. In: AIML 06 international conference. 2006. p. 95–100. [4] Comparini MC, Feudale M, Suriani A. Applications of HEMT devices in space communication systems and equipment: a European perspective. Solid-State Electron 1999;43:1577–89. [5] Caddemi A, Crupi G, Donato N. A robust and fast procedure for the determination of the small signal equivalent circuit of HEMTs. Microelectron J 2004;35:431–6. [6] Feng M, Shen SC, Caruth DC, Huang JJ. Device technologies for RF front-end circuits in next-generation wireless communications. Proc IEEE 2004;2:354–75. [7] Langoni D, Weatherspoon MH, Foo SY, Martinez HA. A speed and accuracy test of backpropagation and RBF neural networks for small-signal models of active devices. Eng Appl Artif Intell 2006;19:883–90. [8] Devabhaktuni VK, Yagoub MCE, Fang Y, Xu J, Zhang QJ. Neural networks for microwave modelling: model development issues and nonlinear modelling techniques. Int J RF Microw Comput Aided Eng 2001;11:4–21. [9] Zhang Q, Gupta KC, Devabhaktuni VK. Artificial neural networks for RF and microwave design – from theory to practice. IEEE Trans Microw Theory Tech 2003;51:1339–50.

M. Hayati, B. Akhlaghi / Int. J. Electron. Commun. (AEÜ) 67 (2013) 123–129 [10] Taher H, Schreurs D, Nauwelaers B. Extraction of small signal equivalent circuit model parameters for statistical modelling of HBT using artificial neural. In: 13th GaAs symposium. 2005. p. 213–6. [11] Ahmed MK, Ibrahem SMM. Small signal GaAs MESFET model parameters extracted from measured S-parameters. In: National radio science conference. 1996. p. 507–15. [12] Xu J, Yagoub MCE, Ding R, Zhan Q-J. Exact adjoint sensitivity analysis for neural based microwave modelling and design. In: IEEE MTT-S International microwave symposium digest. 2001. p. 1015–8. [13] Schreurs DMM-P, Verspecht J, Vandenberghe S, Vandamme E. Straightforward and accurate nonlinear device model parameter-estimation method based on vectorial large-signal measurements. IEEE Trans Microw Theory Tech 2002;50:2315–9. [14] Shirakawa K, Shimizu M, Okubo N, Daido Y. Structural determination of multilayered large-signal neural-network HEMT model. IEEE Trans Microw Theory Tech 1997;46:1367–75. [15] Gao J, Zhang L, Xu J, Zhang Q-j. Nonlinear HEMT modeling using artificial neural network technique. IEEE Trans Microw Theory Tech 2005:469–72. [16] Lazaro M, Santamaria I, Pantaleon C. Neural networks for large and smallsignal modelling of MESFET/HEMT transistors. IEEE Trans Instrum Meas 2001;50(6):1587–93. [17] Tan JPH. Thermal and small-signal characterisation of AlGaAs/InGaAs pHEMTs in 3D multilayer CPW MMIC, PhD thesis. University of Manchester; 2010. [18] Caddemi A, Crupi G, Donato N. Temperature effects on DC and small signal RF performance of AlGaAs/GaAs HEMTs. Microelectron Reliab 2006;46: 169–73. [19] Oudir A, Mahdouani M, Bourguiga R, Pardo F, Pelouard JL. An analytic procedure for extraction of metallic collector-up InP/InGaAsP/InGaAs HBT small signal equivalent circuit parameters. Solid-State Electron 2008;52:1742–50. [20] Lu J, Wang Y, Ma L, Yu Z. A new small-signal modelling and extraction method in AlGaN/GaN HEMTs. Solid-State Electron 2008;52:115–20. [21] Chibante R, Araujo A, Carvalho A. Finite element power diode model optimised through experiment-based parameter extraction. Int J Numer Modell Electron Netw Dev Fields 2008;22:351–61.

129

[22] Harscher P, Olfi E, Vahldieck R. EM-simulator based parameter extraction and optimization technique for microwave and millimetre wave filters. In: IEEE MTT-S international microwave symposium digest. 2002. p. 1113–6. [23] Lin F, Kompa G. FET model parameter extraction based on optimization with multiplane data-fitting and bidirectional search – a new concept. IEEE Trans Microw Theory Tech 1994;42:1114–21. [24] Bousnina S, Mandeville P, Kouki AB, Surridge R, Ghannouchi F. Direct parameter extraction method for HBT small-signal model. IEEE Trans Microw Theory Tech 2002;50:529–36. [25] Caddemi A, Donato N, Crupi G. A robust approach for the direct extraction of HEMT circuit elements vs. bias and temperature. In: Proceedings of the sixth IEEE international conference on telecommunications in modern satellite, cable and broadcasting systems. 2003. p. 557–60. [26] Grebennikov A. RF and microwave power amplifier design. New York: McGrawHill Professional Engineering; 2004. [27] Jeon MY, Kim BG, Jeon YJ, Jeong YH. A technique for extracting small signal equivalent circuit elements of HEMTs. IEICE Trans Electron 1999;E82C:1968–76. [28] Karlsson PR, Jeppson Ko. Direct extraction of MOS transistor model parameters. Analog Integr Circ Signal Process 1994;5:199–212. [29] Teo TH, Xiong YZ, Fu JS, Liao H, Shi J, Yu M, et al. Systematic direct parameter extraction with substrate network of SiGe HBT. In: IEEE digest of papers, radio frequency integrated circuits (RFIC) symposium. 2004. p. 603–6. [30] Giannini F, Leuzzi G, Orengo G, Albertini M. Artificial neural network approach for MMIC passive and active devices. In: Gallium arsenide applications symposium. 2000. [31] Taylor JG. Neural networks and their applications. West Sussex, UK: John Wiley & Sons Ltd.; 1996. [32] Gallant AR, White H. On learning the derivatives of an unknown mapping with multilayer feed forward networks. Neural Netw 1992;5:129–38. [33] Demuth H, Beale M. Neural network toolbox for use with MATLAB. MathWorks Inc.; 2002. [34] Hagan MT, Demuth HB, Beale MH. Neural network design. Boston, Massachusetts: PWS Publishing Company; 1996.