ANALYSIS OF MEMORY EFFECTS AND NONLINEAR CHARACTERISTICS IN RADIO FREQUENCY POWER AMPLIFIER

Transcription

1 ANALYSIS OF MEMORY EFFECTS AND NONLINEAR CHARACTERISTICS IN RADIO FREQUENCY POWER AMPLIFIER Rajbir Kaur 1, Manjeet Sgh Patterh 2 1 Student, 2 Professor, Punjabi University (India) ABSTRACT Radio Frequency (RF) power amplifiers (PAs) have large memory effects and high nonlearity.it is very important to analyze the system level performance of PAsaccurately usg a simple behavioral or mathematical model.this paper proposes a system-level behavioral model for RF PA that exhibit memory effects.this model gives quite accurate results predictg the behavior of PAs with memory effects.the proposed model is implemented Agilent software. Description of memory effects and an accurate presentation of highly nonlear characteristics based on the sgle-tone transfer characteristics for PA are presented. Ga for circuit level model and behavioral model is calculated. Keywords: Cross Modulation, Ga Compression, Harmonic Balance, Inter Modulation Distortion, Power Amplifier. I. INTRODUCTION Most of the electronic devices are herently non-lear. Nonlearity is not desirable devices lie PAs.PA of radio communication system boost up the communication signal to adequate power levels before feedg it to the antenna. When PA operates at saturation, three ds of nonlear distortion are produced [1]. First one is harmonics, second one is cross-modulation (CM) and third one is ter modulation distortion (IMD).Harmonics occur at multiples of the carrier frequency f c. Nonlear multichannel PAs cause cross-modulation where the modulation of one carrier is transferred to another carrier. IMD produces harmonics close to the carrier frequency. So this paper, to predict the behavior of PA, a system-level behavioral model for RF PA that exhibit memory effects has been presented. The analysis of memory effects and nonlear characteristics based on the sgle-tone transfer characteristics for PA are presented. The paper les is as: section 1 is troduction, section 2 presents ter-modulation distortion and the effects of ter-modulation components, section 3 discusses non-learity analysis of PA usg Sgle-tone stimulus, results and discussions are section 4 and section 5 is the conclusion. II. INTERMODULATION DISTORTION When a sgle frequency f 1 is fed through a PA,whose put is not a lear function of its put, harmonics of frequency f 1 are generated, i.e. 2f 1, 3f 1, 4f 1, 5f 1, etc. Now, if two separate frequencies exist together a nonlear device, sum and difference frequencies are produced addition to these harmonics. This means if the two 413 P a g e

2 origal frequencies are f 1, f 2 and the higher frequency is f 2, and then we can expect two other components i.e.(f 1 +f 2 ) and (f 2 -f 1 ). These are the IMD, which are frequency components distct from the harmonic components [1-2].To defe the order, we add the harmonic multiplyg constants of the two frequencies producg the termodulationproduct. A typical spectrum produced could be shown as Fig.1. A M P L I T U D E Frequency KHz Figure 1: Spectrum of Inter-Modulation Components The third order components are the closest and also usually the highest amplitude. From Fig.1, the odd order components spread either side of the fundamental components progression gradually decreasg amplitude. These odd order, termodulation components are of considerable concern the first Mixer stage of a receiver. The function of the mixer stage is to produce some form of non-learity so that an termediate lower frequency is formed from the sum or difference between the comg RF signal frequency and a local oscillator frequency. The mixer stage is, therefore, a prime spot for other undesired termodulationproducts [3]. The transfer characteristic for an ideal lear PA are as shown Fig. 2where V t GV. t (1) Where, V t is put, V t is put power and G is the ga of the amplifier.the transfer characteristic is not lear up to the saturation pot. The amplification decreases as the put power creases. 414 P a g e

3 Figure 2: Characteristics of an Ideal and Practical PA A lear curve is plotted for comparison. The saturatg and nonlear behavior is easily seen as the amplification decreases at higher put levels [4]. There are many methods to express the nonlear effects PA mathematically. Polynomial method is one of the important methods to show non-learity of PA.. In this method, a power series will describe the relationship, i.e. V ( t) av ( t) a V ( t) a V ( t) (2) The transfer characteristic now cludes not only the lear term but also the higherorder terms. In the equation 2, a third order polynomial represents the nonlear transfer function. The second-order coefficient is positive and the third-order coefficient negative, which result a compressive characteristic of the curve [5]. The more the put signal grows, the larger the fluence of the higher-order powers. Feedg an amplifier with a signal of some frequency, the put signal will clude unwanted frequency components. This is referred as AM/AM distortion, sce the put amplitude will be distorted relation to the put amplitude.the conversion of put power to put phase is called AM/PM response. The amplitudeof the put signal affects the put signal phase. Increasg amplitude levels willtroduce an creasg phase distortion on the put signal. III. NONLINEARITY ANALYSIS OF PA USING SINGLE-TONE STIMULUS For a lear amplifier put can be described as Z ( t) G. Z ( t) (3) o L Here G L is a time dependent lear amplifier ga.practically due to non-learity the put of amplifier saturates at some value as the put signal amplitude is creased.due to non-learity amplifier has a nonconstant ga and non-lear phase.these amplifiers are called quasi-memoryless amplifiers and described by the polynomial as 415 P a g e

4 K Z ( t) a. Z ( t) (4) o 0 Z t a a Z t a Z t 2 o( ) 0 1. ( ) 2. ( )... a. Z ( t) In equation (5), is the maximum polynomial order which shows the non-learityof the amplifier. a, a, a, a are complex polynomial coefficients,which determe the exact shape of the put-put characteristics[6-7].for memory-less case,these polynomials have only real values. By usg trigonometric formulas, the quasi-memory-less PA will produce new frequency components which are located at the harmonics 2,3, K of the put signal. Z ( t) V( t). Cos t ( t) By substitutg this value equation 4, we get K c (7) Z ( t) a. V ( t). Cos( t ( t)) o c 0 When time constant of the PA is very small compared to the amplitude () (6) Vt and phase () t (5),then for narrow band application i.e <1.2 MHz,these amplitude and phase variations can be neglected and we assume it to be constant. But for high PAs, it comes the form of memory effects[8-9]. Memory effects can be described as changes the amplitude and phase of the put signal as function of the put signal amplitude and can be expressed as: o 0 c Z ( t) V ( V ).cos t ( V ) (8) Whose complex envelop will be j ( V ) (9) A ( t) V ( V ). e Here V ( V ) and ( V ) represent the AM/AM and AM/PM conversions of the put signal at fundamental frequency. Both AM/AM and AM/PM conversions depend upon the amplitude signal. VI. REULTS AND DISCUSSIONS V of the put For simulation setup, parameters for PA are set as SP 12=0,SP 22=0.234+j0.005,SP 11=0.365-j0.419.Tone P1 is selected, which provides a sgle frequency susoid at a specified power. The available source power is set to 30 dbm, Signal Frequency is taen as 2.4GHz and the non- lear order is set to 7.The put voltages and current waveforms are observed by the harmonic balance simulation. Output waveform contas various frequency components as shown Fig. 5. At 0 GHz, only DC term is present. There are three solutions to solve this scenario, one is auto select which is a lear solver, second one is direct solver when problem is too small i.e. few non-lear components are present and third one is Krylov solver, which is used for large number of non-lear components. 416 P a g e

5 Fig.3 illustrates the results of the simulation, showg the fundamental and higher order harmonics, amplitude decreasg with creasg frequency. Fig. 4 shows the load voltage with time. The put response to RF power put has been shown Fig. 5.The results for different harmonic components have been shown Fig.6, 7, 8, and 9. The blue color represents circuit level behavior whereas red color shows behavioral response. Thus overall memory effects and nonlear characteristics are represented with the help of sgle-tone transfer characteristics for PA to predict the PA behavior. From measurements Fundamental frequency is computed as 2.4 GHz, available source power is 10dBm, put power is dBm, transducer power ga is dBm, second harmonic is computed as dbc, third harmonic is computed as dBc, fourth harmonic is computed as dBm. Low signal power at fifth, sixth and seventh harmonics have very less significance. Figure3: Harmonics at PA Output Figure 4: Output power of Power Amplifier Figure 5: First Harmonic Component of Behavioral Model and Circuit Model Figure 6: Second Harmonic Component of Behavioral Model and Circuit Model 417 P a g e

6 Figure 7: Third Harmonic Component of Behavioral Model and Circuit Modal Figure8: Fourth Harmonic Component of Behavioral Model and Circuit Model Figure9: Tangents for Fundamental, Second and Third Harmonics of Behavioral Model and Circuit Model V. CONCLUSION A new, accurate method for measurg and modelg sgle-tone transfer characteristics has been presented to tae to account the memory effect of high power amplifiers. The dependence of the ter-modulation 418 P a g e

7 distortion components on sgle tone signal is presented to discover memory effects PA.In this paper memory is predicted terms of first and second harmonics accurately i.e modal constructed match first and second harmonics accurately.the third and fourth harmonics are predicted less accurately.these measured sgle-tone amplitudes have been modeled. The model accurately represents high nonlearities of a high power amplifier. A LTE signal measurement and simulation have been conducted for verification. This nonlear behavioral model of a high power amplifier is very useful for the design of various predistortion learizers. REFERENCES [1] Z. El. Khatib et al., Distributed CMOS bidirectional amplifiers: broadbandgand learization Techniques, Analog Circuits and Signal Processg (Sprger Science Busess Media New Yor 2012) [2] X. Li, B.S. Chen, C.M. Liu, X.R. Wang, K.R. Cho, and F. Li, Spectrum modelgand re-growthfor 4G wireless signals, Electronics Letters, 48, (4), [3] N. Borges De Carvalho and J. C. Pedro, Two-tone IMD asymmetry microwave power amplifiers, IEEE MTT-S Int. Microwave Symposium Digest, 2000, [4] H. Ku, M. D. McKley and J. S. Kenney, Extraction of accurate behavioral models for power amplifiers with memory effects usg two-tone measurements,ieee MTT-S Int. Microwave Symposium Digest.,1,2002, [5] H. Ku,M. D.McKley, and J. S. Kenney, Quantifyg memory effects RF power amplifiers, IEEE Trans. Microwave Theory Tech., 50 (12),2002, [6] Ghannouchi F.M., Hammi O., Behavioral Modelg and Predistortion, Microwave Magaze, IEEE, 10(7), Dec. 2009, [7] D. Wisell, B. Rudlund, and D. Rönnow, Characterization of memory effects RF power amplifiers usg digital two-tone measurements, IEEE Trans. Instruments Meas., 56 (6),2007, [8] D. Schreurs, M. O. Broma, A. A. Goacher and M. Gadrger, RF power amplifier behavioral modelg(cambridge University Press, 2009). [9] Hyunchul Ku, J.Stevenson Kenney, Behavioral modelgof nonlear RF power amplifiers considerg memory effects, IEEE transactions on microwave theory andtechniques., 51(12),2003, P a g e