LINEARIZATION OF SALEH, GHORBANI AND RAPP AMPLIFIERS WITH DOHERTY TECHNIQUE

Transcription

1 LINEARIZATION OF SALEH, GHORBANI AND RAPP AMPLIFIERS WITH DOHERTY TECHNIQUE Abhinay Yadav 1, *Dipayan Mazumdar B. R. Karthikeyan 3, Govind R. Kadambi 4 1 Student, M. Sc. [Engg.], Senior Lecturer, 3 Asstiant Professor, 4 Professor and Head, Department of Electronics and Computer Engineering, M.S. Ramaiah School of Advanced Studies, Bangalore *Contact Author timm@msrsas.org Abstract An ideal amplifier operates from DC to infinite frequencies. Its output is a perfectly amplified version of its input and its does not produce any harmonic frequencies. A practical RF power amplifier is composed of RF transistors which are non-linear devices.it is the nonlinear behaviour of transistors that gives rise to harmoncis at the output. In a RF transmitter or receiver there are two phenomena that we observe which make the RF amplifier non-linear. The amplifier transfer function is highly dependent on frequency of operation in both magnitude and phase. The amplifier gain is a non- linear function of the input voltage. Due to non-linear behviour of amplifiers, the input information in two input frequencies is output as the sum and difference of the two input frequencies. Hence, if two frequencies are applied at the amplifier input the amplifier output contains other unwanted frequencies which are linear combinations of the original input frequencies Linearization refers to a multiplicity of techniques, which mitigate the extent of non-linearity exhibited by a power amplifier. Linearization techniques reduce Intermodulation Distortion, Total Harmonic Distortion (THD) and increase the usable linear range of an amplifier. In this research we describe the Doherty technique. The Doherty techqniue requires spiltting of an incoming signal and processing through a main amplifier and a peaking amplifier. The Doherty technique has been demonstrated for 3 separate classes of amplifier models- Saleh, Ghorbani and Rapp. The aim of this work is to achieve reduction in THD for each of the 3 classes of RF power amplifiers. The 3 classes of power amplifiers were modeled in the 9 MHz to 13 MHz range. Physical effects of nonlinear amplifiers like AM/AM distortion and AM/PM distortion are taken into account in the models. The THD is measured with and without the application of Doherty technique. The Doherty technqiue results in an improvement of THD of upto 3 db. Keywords: Power Amplifiers, Linear/ Non- Linear, Saleh, Ghorbani and Rapp Amplifiers, Doherty Technique Abbreviations AM Amplitude Modulation BW Bandwidth IIP3 Third Order Intercept Point IMD Intermodulation Distortion PA Power Amplifier PAE Power Added Efficiency PM Phase Modulation SNR Signal to Noise Ratio THD Total Harmonic Distortion Definitions Gain- The gain of an amplifier is the ratio of output power to input power. It measured in decibels (db). Bandwidth- The bandwidth of an amplifier is the range of frequencies for which the magnitude of amplifier transfer function is flat. Efficiency- Efficiency is a measure of how much of the input power is usefully applied to the amplifier's output. Equation 1 gives an expression for the efficiency of an RF power amplifier. = P RFout η (1) PDC + PRFin Linearity- An ideal amplifier would be a totally linear device, but real amplifiers are only linear within certain practical limits. PAE- It is defined as the ratio of difference between power delivered to the load, power needed to drive the amplifier and total power taken from the DC supply. Equation shows the expressions for the power added efficiency of an RF amplifier. PAE P P RFout RFin = () PDC Intermodulation Distortion- IMD occurs as two or more signals pass through a two-port network with a nonlinear transfer function. The spectrum at the output of the amplifier comprises the original signals and additional spurious signals. The additional spurious signals can cause interference within the original system or in other systems. The spurious signals can overpower the signal of interest, resulting in interference. The undesirable effects of IMD can be mitigated by improving the linearity of the system components which cause IMD. THD- THD is a measure of the additional distortion introduced by a non-linear amplifier. The THD is given by Eq. 3, where A 1 is the amplitude of the fundamental frequency, A is the amplitude of the second harmonic, A 3 is the amplitude of the third harmonic, A 4 is the amplitude of the fourth harmonic, and so on. The THD is a measure of power in the higher harmonics vs power in the fundamental. THD = A + A + 3 A A 1 (3) SASTECH Journal 79 Volume 9, Issue, September 1

2 1. INTRODUCTION 1.1 RF Front ends An RF front end system refers to the analog front end of the wireless communication system. The digital base band signals cannot be transmitted directly through wireless channels due to the properties of the electromagnetic waves. Therefore, these signals must be converted to analog, up-converted to higher frequencies, and transmitted through the channel. The received signals are down-converted to the baseband frequency then converted to digital again. A wireless transmitter is shown in Fig. 1, comprising of an up-converter, a local oscillator and an RF power amplifier. The processing performed on the analog signal in the RF transmitter includes filtering, amplification, and mixing with a different carrier frequency. These processes are imperfect and add various harmonics to the received signal. In this paper the modeling of major harmonics added by each RF component is investigated. An overall PA model, which captured these non linearities together with the linearization techniques are implemented in Simulink software[5]. Fig. 1 Block diagram of typical RF power output Fig. 1 shows the block diagram for a typical RF transmitter. Only the power amplifier and the mixer are included in the modeling, because these components add greater level of harmonics to the transmitter. Other components that do not add harmonics, like filters, are ignored. The mixer being a purely non-linear device introduces phase noise, spurious frequencies and nonlinearity. The power amplifier introduces additional nonlinearity. Fig. 3 Interference due to nonlinear amplifier in adjoining channel Fig. 4 Linear and Non- linear amplifier and their outputs The output of the nonlinear amplifier exhibits significant distortion. This leads to the phenomenon known as spectral regrowth that occurs as a range of frequencies that develop on each side of the carrier (similar to sidebands) and extend into the adjacent frequency bands (Fig. 5). Spectral regrowth is a major problem in OFDM multicarrier amplifiers as it affects the guard bands. It can be mitigated by reducing amplifier nonlinearity and gain. Fig. In- band interference Non-linearity in PA amplifier causes in-band interference as shown in Fig. due to emanation from adjoining channels. This is especially prevalent with low channel spacing. Fig. 3 shows the effect of out of band interference generated due to non-linear amplifier characteristics. The out of band transmission will affect operation of the neighboring channel. Fig. 4 shows the effect of non linearity in creating distortion at the output of a nonlinear amplifier. The waveform at the output of the nonlinear amplifier shows significant distortion and there will be a measurable difference in THD between the linear and nonlinear amplifiers. Fig. 5 Spectral regrowth due to PA non linearity and its effect on adjoining channel 1. Key consequences of nonlinearity of amplifiers When two frequencies ω 1, ω are input into an amplifier, the following effects occur 1. Non-linearity can cause changes in the bias point of the circuit.. Non-linearity can create additional new harmonic frequencies that are linear combinations of the original input frequencies.these inter-modulation frequencies are ω 1 ±ω, ω ±ω 1 and ω ±ω 1 and can be represented by the general form (mω 1 ±n ω ). SASTECH Journal 8 Volume 9, Issue, September 1

3 Fig. 6 Amplitude- phase nonlinear model structure for a complex base band input and output signals in Simulink Linearization techniques can be split into two groups. The first group of linearization techniques is aimed at reducing distortion. First the nonlinear effects appear at the output of the PA and then, by taking some measurement of the present distortion, the objective is to reduce the effects of nonlinearity. The linearizer techniques based on this principle of operation are: Feedback (and its variants: envelope, radiofrequency, Cartesian, polar) Feed forward Doherty amplifier architecture The second group of linearization techniques are aimed at avoiding distortion. These techniques are aimed to prevent the PA from the nonlinear effects at its output and include: Pre-distortion (analogue or digital) LINC EE&R (Envelope Elimination and Restoratio The AM/AM conversion for a nonlinear system is the relationship between the amplitude at the system s input and the amplitude at the system s output. The AM/PM conversion for a nonlinear system is the relationship between the phase change of the system s input and output, and the amplitude of the input signal [4]. This is shown in the Simulink block diagram in Fig. 6. Assuming the passband input signal, the output of the AM/AM and AM/PM Model y PB ( can be written as y PB ( = g( ).cos( wn + ϕ( + f ( )) (4) where g( is the amplitude nonlinearity or AM/AM conversions and f( is the phase nonlinearity or AM/PM conversions. This paper is subdivided into 5 sections. The first section introduces the relevant terminology and discusses the general problem of linearization of amplifiers. It also discusses the effects of non-linearity on communication channels. The second section introduces the 3 nonlinear models due to Saleh, Ghorbani and Rapp. It also explains the concepts behind Quasi- memoryless and memoryless models. The third section explores the structure and regions of operations of the Doherty amplifier which is the specific amplifier architecture explored in this paper. The fourth section contains a discussions about the results of our simulations and the fifth section contains the conclusions.. AMPLIFIER LINEARITY MODELS In memory-less (static) power amplifier models the output signal is a nonlinear function of the current input signal only and previous values of the signal have no effect on the output of the model. Memory-less models only consider AM/AM conversions and assume no phase change. On the other hand, quasi-memory-less models take into account both amplitude and phase distortions. Therefore, they are represented by the amplifier AM/AM as well as AM/PM transfer functions [7]. The models considered here, Saleh, Ghorbani and Rapp, are quasi-memoryless having the form. y y1 f ( ) + y4 y y.1 The Saleh model 3 = (5) The Saleh model [8] is a quasi-memoryless model. It uses four parameters to fit the model to measurement data. The Saleh model captures phase and amplitude distortions. Its AM/AM and AM/PM conversion functions are described by the equations 6 & 7. α a g( ) = (6) β a αϕ f ( ) = (7) β ϕ where [ α a α φ β a βφ ] are the model s parameters and is the complex input signal.. The Ghorbani model The Ghorbani model [8] uses eight parameters to fit the model to the measurement data. This model is quasi-memory less, and it s AM/AM and AM/PM conversions functions are described by the following Eq. (8a) and (8b). x x1 g( ) + x4 x x 3 = (8a) SASTECH Journal 81 Volume 9, Issue, September 1

4 f y y1 ) = + y (8b) y y ( 4 3 x, y 1 x, x, x, y, y, y, where are the model parameters, which are calculated from measured data by means of curve fitting; g(.) and f(.) are the AM/AM and AM/PM relationships respectively..3the Rapp Model The Rapp model [8] uses three parameters, and models amplitude distortion but no phase distortion. Hence, the Rapp model does not have an AM/PM relationship equation. The general expression of the AM/AM conversions is given by Eq. (9). g( ) = 1 + O sat S 1 S (9) Where Osat is a parameter that sets the output saturation level. S is a parameter that sets the smoothness of the transition from linear to saturation states; the smaller the value of S the smoother the transition. The mechanics behind this model is quite simple. It assumes linear performance until the saturation point is approached and then a transition towards a constant saturated output is applied. 3. THE DOHERTY AMPLIFIER The Doherty technique has been around in the domain of UHF power amplifiers since 193s [6]. Only recently it has been bought into the ISM band (.4 GHz) and GSM band (9 MHz). by the carrier amplifier and the remaining part of the signal is amplified by a second amplifier called the Peaking amplifier. In the lower power regime, the peaking amplifier is essentially turned off. The amplified output signals from each branch are essentially recombined. The Doherty amplifier circuit is more complex than a two stage parallel amplifier. However, the increased complexity is offset by more flexible amplifier architecture. The Doherty circuit operation can be tailored by adjusting the transition point to trade off efficiency, gain and linearity. The Doherty configuration employs two separate amplifiers in a quadrature like configuration, as shown in Fig.7. In a two stage Doherty amplifier, as shown in Fig. 7, the basic operation is as follows: At low power output levels, A (Peaking amplifier) is shut down, either by removal of its drive signal or by a suitable alteration of its bias level. A1 (Carrier amplifier) receives the entire input signal and operates in a conventional linear mode. The impedance present at output, due to an impendence transformation performed by the λ/4 transmission-line, ensures that A1 saturates at a level well below the desired system PEP known as the transition point. The λ/4 impedance transformer transforms the output impedance of A1 to a value that is better matched to the load. The output impedance of A1 forces its operation at a level well below the PEP. In standard two stages Doherty amplifier, the transition point occurs at half the maximum output voltage. At this transition point, the carrier amplifier (A1) operates at maximum efficiency, with the Peaking amplifier (A) shut off. The overall system is therefore operating at maximum efficiency. Fig. 7 Diagram of Doherty amplifier with transmission lines 3.1 Structure of a Doherty Amplifier The Doherty amplifier or the Doherty technique works in two transfer function regimes. The lower power regime has a linear input/output relationship. The amplifier comprises two branches the Carrier branch and the Peaking branch. The signal is split into two and fed separately to the Carrier amplifier branch and the Peaking amplifier branch. Bulk of the signal is carried by one branch called the Carrier amplifier which operates in the linear range. The upper power regime is more nonlinear. Some part of the signal is still amplified Fig. 8 Efficiency of a Doherty amplifier vs its input showing clearly the two regions of operation At all output levels above the transition point, A commences activity performing as a controlled current source. A1 remains saturated and therefore operates as a controlled voltage source, the action of the λ/4 transmission line converting this to appear as a current source at the point where the outputs from A1 and A combine. The saturation effects in the Carrier amplifier are compensated by the turn on effects of the peaking amplifier. The overall effect is that the range of linear operation of the composite amplifier is enhanced. SASTECH Journal 8 Volume 9, Issue, September 1

5 Fig. 9 Block diagram showing distortion due to Saleh amplifier without Doherty technique Fig. 1 Block diagram of Saleh amplifier developed in Simulink Fig.11 Simulink model of Saleh power amplifier with Doherty technique SASTECH Journal 83 Volume 9, Issue, September 1

6 Fig.1 Simulink Model of Ghorbani power amplifier with Doherty technique Fig. 13 Simulink Model of Rapp power amplifier with Doherty technique The Doherty amplifier has two parallel paths each with a λ/4 transformer. In the first path the linear Carrier amplifier is followed by a λ/4 transformer. In the second path the non-linear peaking amplifier is preceded by a λ/4 transformer. As given in Fig. 7, the peaking amplifier starts turning on as the Carrier amplifier attains saturation. The Doherty amplifier can provide a wider linear range of operation simply because the Peaking amplifier transfer function compensates for the saturating behaviour of the carrier amplifier. The Doherty amplifier has two efficiency regimes one where the efficiency is a linear function of Power level (linear regio and the other where the efficiency is a nonlinear function of power level, when the peaking amplifier is operating. These two regimes are clearly seen in Fig. 8. The Saleh Power Amplifier model in Fig. 9 shows that there is a significant flattering at the top. Figure 11 shows the block diagram of the Saleh power amplifier and the waveforms at its input and output with Doherty technique. Figure 1 Shows the Ghorbani power amplifier with Doherty Technique. Figure 13 Shows the Rapp power amplifier with Doherty Technique. Figure 1 has perspective distortion level using the Ghorbani model. In Fig. 13 the Rapp amplifier shows the lowest level of distortion. SASTECH Journal 84 Volume 9, Issue, September 1

7 5 X: 1.6 Y: Y: X: 1.3 Y: X: 1.31 Y: X: 1. Y: X: 1.35 Y: Y: X: 1.39 Y: X:.7344 Y: X:.65 Y: -.3 X:.8594 Y: -15 X: Y: X: Y: X: 1.4 Y: THD for SALEH PA with Doherty Technique=9.714 X: 1.6 Y: 6.6 X: 1.3 Y: X: 1.31 Y: X: 1. Y: X: 1.35 Y: THD for SALEH PA without Doherty Technique= X:.7344 Y: X:.65 Y: -.13 Y: 1.44 X:.8594 Y: X: Y: X: Y: X: 1.4 Y: Y: X: 1.39 Y: THD for Ghorbani with Doherty Technique= X: 1.3 Y: -3.3 X: 1. Y: X: 1.6 Y: X: 1.31 Y: X: 1.35 Y: THD for Ghorbani without Doherty Technique= X:.75 Y: X: 1.31 Y: X:.65 Y: -4.6 X:.8594 Y: -17. X: Y: X: Y: X: 1.4 Y: Y: X: 1.39 Y: THD for Rapp with Doherty Technique= THD for Rapp without Doherty Technique= Fig. 14 Power spectrum at the output of three amplifiers with Doherty technique SASTECH Journal 85 Volume 9, Issue, September 1

8 4. RESULTS AND DISCUSSIONS Of the three amplifier structures the Rapp amplifier model gives the lowest THD. Even before distortion, the Rapp model gives the least amount of flattening. In Fig. 9 the Saleh amplifier shows the greatest degree of flattening at the top without Doherty technique. The Ghorbani amplifier also shows significant flattening at the output. The Doherty technique has been discussed in [6], [7] and [8] but no additional information is given about the suitability of the Doherty technique to the Saleh, Ghorbani and Rapp amplifier models. Figure 14 shows the peridogram at the output for Saleh, Ghorbani and Rapp power amplifiers with Doherty technique. By application of the Doherty technique, the THD for the Saleh amplifier model is reduced by 7 db, for the Ghorbani Power amplifier model by 6.5 db and for the Rapp Power amplifier model the THD is reduced by 5.5 db. These results are for a nominal frequency of 1GHz. Doherty technique consistently reduces nonlinearity effects in Power amplifiers. Figure 14 shows that the Rapp PA exhibits lowest distortion. 5. CONCLUSIONS The outputs of Saleh, Ghorbani and Rapp amplifier models are analyzed for the same input waveform. Comparison is performed for the output waveshape and Total Harmonic Distortion with and without application of Doherty technique. The linearization technique (Doherty) described herein affords an improvement of THD by about db for Saleh amplifier model, db for Ghorbani amplifier model and 3 db for Rapp amplifier model. The best case SFDR with Doherty technique is for the Rapp model at about 4dB. This is a massive improvement in SFDR and the flattening of the output voltage waveform due to Saleh and Ghorbani are very much reduced. Future research should focus on combining the Doherty technique with digital precompensation, or LINC method for amplifier control. 6. REFERENCES [1] Behzad Razavi, RF microelectronics, 1 st Edition, Prentice Hall, [] D. C. Cox, Linear amplification with nonlinear components, IEEE Transactions on Microwave Theory and Techniques, Vol., Issue 1, pp , [3] Aldo N. D. Andrea, RF power amplifier linearization through amplitude and phase predistortion IEEE Transactions on Communication, Vol. 44, No. 11, pp , [4] Peter B. Kenington, High linearity RF amplifier design, 1 st Edition, Artech House Inc,. [5] Eyad Arabi and Sadiq Ali, Behavioural modeling of RF front end devices in Simulink, Master s Thesis, Chalmers University of Technology, Sweden, 8. [6] Simon M. Wood and Raymond S. Pengelly,,A high frequency high power UMTS amplifier using a novel Doherty configuration, IEEE Wireless and Microwave Conference Proceedings, RAWCON- 3 Proceeedings, pp 39-33, 3. [7] Jangheon Kim, Jeonghyeon Cha and Ildu Kim, Advanced design methods of Doherty amplifier for wide bandwidth, high efficiency base station Power amplifiers, 35 th European Microwave Conference, 5. [8] Steve Cripps Advanced techniques in RF power amplifier design, nd Edition, Artech House, 6. SASTECH Journal 86 Volume 9, Issue, September 1