A 5 GHz LNA Design Using Neural Smith Chart

Transcription

1 Progress In Electromagnetics Research Symposium, Beijing, China, March 23 27, A 5 GHz LNA Design Using Neural Smith Chart M. Fatih Çaǧlar 1 and Filiz Güneş 2 1 Department of Electronics and Communication Engineering Süleyman Demirel University, Isparta, Turkey 2 Department of Electronics and Communication Engineering Yıldız Technical University, Beşiktaş, Istanbul Abstract This work presents the design of a single-stage, low noise, stable and matched amplifier at 5 GHz. The amplifier is designed around the Agilent ATF-551M4 low noise enhancement mode pseudomorphic HEMT (EpHEMT). An Artificial Neural Network (ANN) model of the Smith Chart is proposed for an alternative solution to impedance matching of this LNA (Low Noise Amplifier) design which has been entitled Neural Smith Chart (NSC) shortly. The input and the output impedance matching networks are performed using NSC outputs and MATLABR RF Toolbox simulation solutions for comparison. 1. INTRODUCTION In wireless communications, receivers need to be able to detect and amplify incoming low-power signals without adding much more noise. Therefore, a LNA is often used as the first stage of these receivers. As the usage of wireless communication in 2.4 GHz band grows, it causes uncontrolled occupancy by users in that band. Since it is an unregulated frequency, the 2.4 GHz band also suffers from enormous interference effects generated by devices like microwave ovens and 2.4 GHz transmitters that will reduce performance especially in wireless local area networks (WLANs). On the other hand, the 5 GHz band provides lots of unlicensed spectrum and it has less interference. Recently, many researchers have been focused on the 5 GHz standard in the design of wireless transceivers which should be used in a, HiperLAN2 and HiSWANa applications. Analysis and design of microwave circuits are generally tedious with their highly nonlinear equations and lack in the insight to their related problems. The Smith Chart provides a very useful graphical tool to these types of the problems with its numerous applications. However, the manual interpretation of the Smith Chart can be error prone. In the literature, works on the computerized Smith Chart took place between by Prasad and her group in [1 3]. In their work, the Smith Chart is represented firstly by a (n n) numerical matrix [1], and then this model has been developed as a massively distributed computing network [3]. Thus, due to this discrete nature of these CAD systems, use of these types of the Smith Chart models remained limited. Neural networks are universal function approximators [9, 10] allowing reuse of the same modeling technology for both linear and nonlinear problems at both device and circuit levels [8]. Yet neural network models are simple and model evaluation is very fast. Recent works have let to their use for modeling of both active and passive components such as transistors [4, 5], planar transmission line microstrip, coplanar wave (CPW) guides [6], vias, CPW discontinuities, spiral inductors [4]. Furthermore ANNs have found modeling in Smith Chart representation and automatic impedance matching [7]. To design a sample LNA, in this work the available gain design technique is used, which involves selecting a single-stub matching network that provides a suitable compromise between gain and noise. After designing the input and output matching networks using lossless transmission lines, it is verified that the design by analyzing the matched LNA and plotting its gain, noise and return loss. The simulated results of theoretical calculations by MATLABR RF Toolbox are compared with impedance matching response of NSC. 2. ANN MODEL OF THE SMITH CHART: NEURAL SMITH CHART (NSC) The black-box model of the Smith Chart for analysis and design of the fundamental transmission line circuit is given in Fig. 1, where the termination Z S = R S + jx S ; the transmission line with l, Z 0 ; operation bandwidth B between f min, f max and the dielectric are the inputs, the corresponding outputs are the standing waves, impedance matching and impedance transformation properties of the transmission line. For this purpose, the two fairly simple, similar ANN modules are generated: One is for the standing waves and impedance matching properties of the transmission line and the other is for the modeling of impedance transformation. As given in Figs. 2(a) and 2(b), NSC is

2 466 PIERS Proceedings, Beijing, China, March 23 27, 2009 generated by the two ANN modules, each of which is a multilayer perceptron (MLP) with the three inputs of the same termination (R S, X S ) and the electrical length (βl) [11]. Impedance Matching Standing Waves Impedance Transformation Figure 1: Black-Box Model of the Smith Chart with the variable definitions. There are four steps designing this model as a view of programmer. Firstly, the input-output data space is mined from the Smith Chart and the analytical equations (formulas) to train and test selected ANN structure. In this session it has obeyed universal data mining rules. The data space is divided into two parts of 50% training and 50% testing data. ANN training and testing are the second and third step, respectively. Unless the testing results satisfy, different types of ANN structures with varied hidden sizes and training algorithms will be tried. These trying operations are being a loop for best test results. At the last step, the fourth step, the targets are compared in the verified error interval. Three key rules are applied in the data generation from the Smith Chart: The whole Smith Chart is divided into the N transmission circles (ideally N ); Each transmission circle is divided into the n(r) arcs with adaptive radius r sampling algorithm [11]; Resistive, capacitive, inductive regions of the Smith Chart can be determined by a rule which may be named as the fl product [11] depending on the ratio of Z S /Z 0 which may be either greater or smaller than the unity. The Levenberg-Marquardt (LM) back-propagation algorithm for the smallest testing error and four layered network with the minimum number of neuron for faster training are performed with the MLP type of network. The performance function of MLP is the Mean Squared Error (MSE). 3. LNA DESIGN AND WORKED EXAMPLE The LNA design initial specifications are as follows: Bandwidth: 4 6 GHz; Noise Figure 1 db; Transducer Gain > 11 db; Operating between 50 Ω load and source terminations. Before proceeding with this design, it is determined the calculated frequencies at which the amplifier is unconditionally stable. µ and µ defines the distance from the center of the Smith Chart to the nearest output (load) and input (source) stability circle, respectively. Having µ > 1 (or µ > 1) is necessary and sufficient for the 2-port linear network to be unconditionally stable. This stability factor is given by where = s 11 s 22 s 21 s 12 : µ = 1 s 11 2 s 22 s 11 + s 21 s 12 ( or µ = ) 1 s 22 2 s 11 s 22 + s 21 s 12 One way to stabilize an amplifier is to add a shunt resistor at the output of the amplifier. However, this approach will also reduce gain and add noise. The maximum shunt resistor value makes µ = 1 that makes the amplifier unconditionally stable. Fig. 3 shows the stable LNA structure with 50 Ω (1)

3 Progress In Electromagnetics Research Symposium, Beijing, China, March 23 27, terminals, input-output matching networks and shunt resistor. In the Fig. 4, input and output stability, available gain and NF circles at 5 GHz are drawn. A star ( ) and a circle-in-dashed-line will also appear on the Smith Chart. The star represents the matching load reflection coefficient (Γ L ) that is the complex conjugate of Γ out. The gain is maximized when Γ L is the complex conjugate of Γ out. The data cursor (black square point) represents the matching values of Γ S and Γ out with high available gain and less NF. (a) Neural Smith Chart Module-I (b) Neural Smith Chart Module-II Figure 2: Neural Smith Chart modules. TL 2 TL 3 R TL 1 TL 4 Z S =50Ω Z L =50Ω Input Matching Γ in Network Γ S Γ out Γ L Output Matching Network Figure 3: Desired LNA schematic with matching networks. Table 1: NSC and simulation results of designed LNA. G T [db] S 11 [db] S 22 [db] N F [db] NSC RF Toolbox The s-parameters of ATF-551M4 transistor which biased at 2 V and 20 ma are collected from the data sheet and converted to s2p format for LNA analyzing. Then, single-stub lossless transmission line matching network stub positions and lengths are calculated for both input and output by using the data in Fig. 4(b). After finding Z s and Z L using Γ S and Γ L (conjugate of Γ out ), these impedances are inputted to the NSC for achieving short-circuit terminated parallel single-stub matching network positions and lengths for both input and output. In Table 1, performance of NSC matched LNA is compared. Transducer and available gain, noise figure, input and output return losses of both simulated matched LNA and NSC matched LNA are figured in Figs. 5(a), 5(b), 5(c) and 5(d).

4 468 PIERS Proceedings, Beijing, China, March 23 27, j1.0 +j1.0 +j0.5 +j2.0 +j0.5 +j2.0 +j0.2 +j5.0 +j0.2 +j j0.2 -j5.0 -j0.2 -j5.0 -j0.5 (a) -j1.0 -j2.0 Input Stability(Freq=5[GHz]) Output Stability(Freq=5[GHz]) Available Gain(Freq=5[GHz]) Noise Figure(Freq=5[GHz]) -j0.5 -j1.0 -j2.0 Available Gain(Freq=5[GHz]) Noise Figure(Freq=5[GHz]) (b) Figure 4: Stability, gain and NF circles at 5 GHz. (a) Without a shunt resistor at the output. (b) With a R = 150 Ω shunt resistor at the output NF [LNA] NF [ANN-LNA] G a [LNA] G T [LNA] G a [ANN-LNA] G T [ANN-LNA] (a) (b) 0-1 s 11 [LNA] s 11 [ANN-LNA] s 22 [LNA] s 22 [ANN-LNA] (c) -80 (d) Figure 5: Gain, NF and return loss at 4 6 GHz.

5 Progress In Electromagnetics Research Symposium, Beijing, China, March 23 27, CONCLUSIONS A Neural Smith Chart is formed by using the ANNs in the simple MLP structures as the nonlinear learning machines from the input space to the output space [11]. An application of LNA design for above specifications is achieved. Especially it is stressed on matching performance of NSC. The graphics in Fig. 5 show that the NSC matching results of a LNA design procedures ensure similarity and availability when initial specifications reviewed. REFERENCES 1. Vai, M., S. Prasad, and H. Wang, A Smith Chart represented by a neural network and its applications, IEEE MTT-S International Microwave Symposium Digest, , Vai, M. and S. Prasad, Automatic impedance matching with a neural network, IEEE Microwave and Guided Wave Letters, Vol. 3, No. 10, , Vai, M. and S. Prasad, Microwave circuit analysis and design by a massively distributed computer network, IEEE Microwave Theory and Techniques, Vol. 43, No. 5, , Günes, F., F. Gürgen, and H. Torpi, Signal-noise neural network model for active microwave device, IEE Proc. Circuits Devices and Systems, Vol. 143, 1 8, Günes, F., F. Gürgen, and H. Torpi, A multidimensional signal-noise naural model for microwave transistor, IEE Proc. Circuits Devices and Systems, Vol. 145, No. 2, , Günes, F. and N. Türker, Artificial neural networks in their simplest forms for analysis and synthesis of RF/microwave planar transmission lines, The International Journal of RF and Microwave Computer-Aided Engineering, Vol. 15, No. 6, , Zhang, Q. J. and K. C. Gupta, Models for RF and microwave components, Neural Networks for RF and Microwave Design, Artech House, Norwood, MA, Çaglar, M. F. and F. Günes, Neural networks as a nonlinear equation set solver in analysis and synthesis of a microwave circuits, INISTA 2005, , Istanbul, Turkey, June Hornik, K., M. Stinchcombe, and H. White, Multilayer feedforward networks are universal approximators, Neural Networks, Vol. 2, , Cybenko, G., Approximation by superpositions of a sigmoidal function, Math. Control Signals Systems, Vol. 2, , Günes, F. and M. F. Çaglar, A novel neural smith chart for use in microwave circuitry, The International Journal of RF and Microwave Computer-Aided Engineering, Vol. 9999, No. 9999, 2008.