Self-heating and memory effects in RF power amplifiers explained through electrothermal

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1 Aalbor Universitet Self-heatin and memory effects in RF power amplifiers explained throuh electrothermal Wei, Wei; Jensen, Ole Kiel; Mikkelsen, Jan Hvolaard Published in: IEEE Press DOI (link to publication from Publisher):.9/NORCHIP Publication date: 23 Document Version Early version, also known as pre-print Link to publication from Aalbor University Citation for published version (APA): Wei, W., Jensen, O. K., & Mikkelsen, J. H. (23). Self-heatin and memory effects in RF power amplifiers explained throuh electro-thermal. In IEEE Press (pp. -4). IEEE. DOI:.9/NORCHIP General rihts Copyriht and moral rihts for the publications made accessible in the public portal are retained by the authors and/or other copyriht owners and it is a condition of accessin publications that users reconise and abide by the leal requirements associated with these rihts.? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.? You may not further distribute the material or use it for any profit-makin activity or commercial ain? You may freely distribute the URL identifyin the publication in the public portal? Take down policy If you believe that this document breaches copyriht please contact us at vbn@aub.aau.dk providin details, and we will remove access to the work immediately and investiate your claim. Downloaded from vbn.aau.dk on: januar 27, 28

2 Self-heatin and Memory Effects in RF Power Amplifiers Explained Throuh Electro-Thermal Modelin Wei Wei, Ole Kiel Jensen, Jan H. Mikkelsen Abstract Self-heatin has already been proven to be one of the key sources to memory effects in RF power amplifiers (PAs). However, mechanisms behind the eneration of memory effects, as caused by self-heatin have not been well documented. On basis of transistor physical properties this paper proposes a simple electro-thermal model and shows how self-heatin can enerate different types of memory effects, such as bandwidth dependent intermodulation components and hysteresis loops. In addition, it is shown that self-heatin can result in eneration of new spectral components even in an otherwise linear PA. A time domain modelin framework is implemented to investiate memory effects enerated by self-heatin and simulation results are shown to aree with theoretical analysis. Index Terms Memory effect, self-heatin, power amplifier, intermodulation, hysteresis, I. INTRODUCTION Memory effects observed in typical RF PAs normally oriinate from 3 sources: self-heatin [], electron trappin [2] and baseband effects [], [3]. Usually, these sources affect the performance of PAs simultaneously, which makes an understandin of the impact of each source difficult. Consequently, PAs with memory effects are normally analyzed and modeled behaviorally on the basis of measured data. For instance, Volterra series [4] represents a typical behavioral modelin approach. However, a behavioral modelin approach does not offer any physical explanation and understandin of the mechanism behind the memory effects. As a memory source self-heatin has been observed to affect intermodulation distortion [], [5]. In a system with memory, the intermodulation depends not only on sinal manitudes but also on sinal bandwidth [6]. This paper shows that bandwidth-dependent intermodulation can be caused by selfheatin and clearly explains the physical mechanism behind. The occurrence of AM/AM hysteresis loops is another typical result of memory effects [7]. So far no link between selfheatin and AM/AM hysteresis loops has been established in the literature. By addin a simple electro-thermal model this paper forms the link and shows how self-heatin can result in AM/AM hysteresis. Thorouh understandin of the eneration of memory effects can improve characterization and modelin of PAs. To achieve this, physical properties of transistors need to be investiated. On the basis of these physical properties, this Wei Wei, Ole Kiel Jensen and Jan H. Mikkelsen are with the Department of Electronic Systems, Aalbor University, Denmark. Manuscript submitted Auust 23, 23 paper explains the mechanism by which self-heatin enerates bandwidth-dependent output spectral components, AM/AM hysteresis loop openin and dynamic AM/AM and AM/PM behavior. Especially, for the first time, it is detailed how self-heatin can be a source to enerate AM/AM hysteresis loops and why the loop openin is bandwidth-dependent. The underlyin physical reason for these memory effects is the interaction between RF sinals and slow thermal responses. This paper is oranized as follows. The electro-thermal response of a class-a PA is discussed in section II, and how an electro-thermal response can enerate memory effects is discussed in section III. Conclusions are finally iven in section VI. II. ELECTRO-THERMAL RESPONSE IN PAS The electro-thermal response observed in PAs can be described by means of a feedback loop [8], as illustrated in Fi. where the transistor is simply modelled as a linear but temperature dependent transconductance.. Fi.. Interaction between RF sinals and thermal response in a FET based PA. v (t) denotes the ate voltae, G m the transconductance, and v d denote the RF components of the drain current and voltae, I DQ and V DQ represent the drain bias current and voltae, C th and θ th terms denote thermal capacitance and resistance. T a, P ds and ΔT denotes the ambient temperature, power dissipation and the temperature chane respectively. Durin operation, both bias and RF sinals result in thermal power dissipation. As a consequence, both bias and RF sinals affect the FET temperature (T FET ). A chanin T FET affects G m, that is, hiher T FET normally results in lower G m followin a rouhly linear relation between G m and T FET [9]. By affectin G m, T FET indirectly interacts with RF sinals, /3/$3. 23 IEEE

3 which ives rise to the electro-thermal response in a PA. In the followin discussion, a simplified linear relation between G m and T FET is assumed: G m = G ma γδt, where G ma is the ate transconductance at the ambient temperature and γ is a positive coefficient. Since P ds is time-varyin, the same will be the case for T FET. If a PA is excited by an RF sinal with a periodic envelope, T FET can be expressed as T FET (t) =T a + T + N T n cos(nω th t + φ n ), () n= where T is the DC component of ΔT (t), ω th = 2π T e and T e is the period of the sinal envelope. The thermal time constant is normally in the rane of μs. Therefore the temperature chane within an RF-period is neliible. Under two-tone excitation, the drain current can thus be expressed as = {G ma γ[t + N T n cos(n(ω th )t + φ n )]} (2) n= V (cos ω t +cosω 2 t), where V is the input amplitude of each tone. The power dissipation has spectral components from DC to RF frequencies. Due to the low-pass property of thermal circuits, only DC and baseband components can contribute to T FET variations. Therefore, under two-tone excitation ω th = ω 2 ω. In the simplified case of N=, based on Eq. (2) the drain current is found to be =(G ma γt )V cos ω t 2 γt V cos(ω φ ) (G ma γt )V cos ω 2 t 2 γt V cos(ω 2 + φ ) 2 γt V cos(n(2ω ω 2 )t φ ) (3) 2 γt V cos(n(2ω 2 ω )t + φ ). From Eq. (3) it is shown that the mixin of the two tones and the thermal response causes amplitude and phase distortion of the two tones (first two lines) and also enerates 3rd order intermodulation products (last two lines). Both manitudes and phases of the enerated intermodulation products are bandwidth dependent since T n terms are bandwidth dependent. Secondly, Eq. (2) shows the appearance of AM/AM hysteresis loops. For simplicity, if only T is considered and harmonic terms of T n are nelected, the input envelope and G m under this simplified condition are shown in Fi. 2. At the risin and fallin edes of the input envelope, all G m curves are symmetrical while φ n =(2n+)π/2, but asymmetrical while φ n = (2n +)π/2. Obviously, asymmetry of G m results in asymmetry of output envelopes. The T term makes G m chane periodically at ω th. Similarly, a T n term makes G m chane periodically at nω th if nω th is below the cut-off frequency of the thermal circuit. Variation of G m causes distortions to sinals. v 2V.5 V G m + T = = /6 = /2 =3 /2.5 Gm -.5 G m - T Fi. 2. Claculated input envelope and periodically chanin transconductance of a class-a PA under two-tone excitation. The moment at which the envelope is zero is assined to be zero on the time axis, and the time is normalized to 2π ω 2 ω. III. MEMORY EFFECTS DUE TO ELECTRO-THERMAL RESPONSE To investiate memory effects, a class-a PA model is implemented in Matlab Simulink with the modelin framework in Fi.. This model is implemented on the basis of a 2-finer FET. The ate width of each finer is 5μm and the parameters of each finer are described by [9]. For this FET, the parameters at T a = 325 K and V GQ = 4.5 V are G ma.2 S and γ.2 S/K. With this FET the simulation is based on the followin parameters: G ma =.2 S, γ =.2 S/K, V DQ I DQ =6W, load impedance = 5 Ω, θ th =4K/W, C th =.25 6 J/K. Two-tone sinals and stepped sinals are introduced to excite the PA. The centre frequency of the RF sinal durin the simulation is GHz. A. T FET under Two Tone Excitation Fi. 3 shows that under two tone excitation, ΔT chanes periodically at the period oπ/(ω 2 ω ), and T n harmonics appear. However, under sinle tone excitation, ΔT is a constant value. It is interestin to see that both the manitude and phase of ΔT depend on the difference frequency, ω 2 ω. This is due to the low-pass properties of the thermal circuit. Fi. 4 shows the frequency response of the thermal impedance, where Z th = θ th /(jω th C th +) denotes the thermal impedance. B. Intermodulation Generated by Self-heatin Intermodulation products under two tone test appear in output sinals, which is shown to aree with Eq. (2). Manitudes of these components depend on the difference frequency of the two tones, as is shown in Fi. 5. Demonstrated in Fi. 4 and 5, both manitudes of IMD3 and Z th decrease as the difference frequency increases. The underlyin physical reason is that a hiher manitude of Z th cause hiher manitudes of T n terms, and hence hiher manitudes of intermodulation components, as illustrated by Eq. (2).

4 Tone 2 Tone 2 5 Phase Shift (De) - 5 Sinle tone khz Tone Spacin 2 khz Tone Spacin 5 khz Tone Spacin khz Tone Spacin Difference Frequency of Two Tones (Hz) Time (ms) Fi. 3. Simulation results of ΔT due to self-heatin in a Class-A PA at V =2V. Manitude of Z th (K/W) 4 2 Manitude Anle Frequency (Hz) Fi. 4. Calculated thermal impedance of the FET with θ th =4K/W and C th =.25 6 J/K. Normalized IMD3 Amplitude (db) Difference Frequency of Two Tones (Hz) Fi. 5. Simulated IMD3 manitude vs. difference frequency at V =2V. IMD3 manitudes are normalized to the manitude of the fundamental tones Anle of Z th ( o ) Fi. 6. Simulated phase shift due to self-heatin vs. difference frequency of two tones at V =2V. C. Phase Variation The phase shift of the two output tones is also bandwidthdependent, as shown in Fi. 6. When the difference frequency is outside the pass band of the thermal circuit, self-heatin cannot cause phase variation to the two output tones. D. AM/AM Characteristic Fi. 7 shows output envelopes and ΔT. The asymmetry of the output envelopes is due to the asymmetry of T FET. Fi. 8 shows AM/AM hysteresis loops. In these 2 fiures, the v envelope is normalized to 2V, and envelopes are normalized to their maximum values, that is,.4 A,.38 A,.34 A,.33 A. The difference frequencies of the two tones are khz, 2kHz, khz, 5 khz, respectively. The size of an AM/AM hysteresis loop depends on both manitude and anle of Z th, and then the loop-openin is also bandwidth-dependent, as is shown in Fi khz khz 2 5 khz khz Fi. 7. Simulation results of output envelopes and ΔT in a half of the envelope period at V =2V. For each tone spacin, time starts at a zero point of the envelope and normalized to 2π ω 2 ω.

5 -f = khz Risin ede Fallin ede.5 V -f = khz Risin ede Fallin ede.5 V -f =2 khz Risin ede Fallin ede.5 V -f =5 khz Risin ede Fallin ede.5 V PA. Thermal properties of FETs have low pass characteristics. Under two-tone excitation, while the difference frequency is lower than the cut-off frequency of the low-pass thermal circuit, the FET temperature and hence the transconductance chanes periodically at the difference frequency. This periodically chanin transconductance enerates new spectral components, causes AM/AM hysteresis loop openin, and introduces manitude and phase variation to output sinals. All these effects are bandwidth dependent and disappear while the difference frequency is outside the pass band of the thermal circuit. Under stepped sinle-tone excitation, the thermal response causes an exponential increase and decrease of the output envelope. Simple mathematics is formulated to describe the mechanism by which self-heatin enerates memory effects. As an outcome of the theoretical analysis, a time domain modelin framework is proposed and implemented. Simulation results are shown to aree with the theoretical analysis. Fi. 8. Simulation results of AM/AM hysteresis loop openin caused by self-heatin at V =2V. Input and output envelopes are normalized to their maximum values respectively. E. Response to Stepped RF sinal Fi. 9 shows that under step sinle-tone excitation, at the risin edes of the input envelope, the output envelope rises exponentially while T FET drops exponentially. In addition, at the fallin edes of the input envelope, the output envelope drops exponentially while T FET rises exponentially. The step response of the output envelope is due to the thermal response of the FET. Due to this step response, the output sinal manitude depends not only on the present input but also on the previous input. (A) T REFERENCES [] N. Le Gallou, J. Nebus, E. Noya, and H. Buret, Analysis of low frequency memory and influence on solid state HPA intermodulation characteristics, in Microwave Symposium Diest, 2 IEEE MTT-S International, vol. 2, 2, pp vol.2. [2] G. Menehesso, G. Verzellesi, R. Pierobon, F. Rampazzo, A. Chini, U. Mishra, C. Canali, and E. Zanoni, Surface-related drain current dispersion effects in AlGaN-GaN HEMTs, Electron Devices, IEEE Transactions on, vol. 5, no., pp , oct. 24. [3] N. Bores de Carvalho and J. Pedro, A comprehensive explanation of distortion sideband asymmetries, Microwave Theory and Techniques, IEEE Transactions on, vol. 5, no. 9, pp. 29 2, sep 22. [4] A. Zhu and T. Brazil, Behavioral modelin of RF power amplifiers based on pruned volterra series, Microwave and Wireless Components Letters, IEEE, vol. 4, no. 2, pp , dec. 24. [5] J. Vuolevi and T. Rahkonen, Analysis of third-order intermodulation distortion in common-emitter BJT and HBT amplifiers, Circuits and Systems II: Analo and Diital Sinal Processin, IEEE Transactions on, vol. 5, no. 2, pp. 994, dec. 23. [6] J. Vuolevi, T. Rahkonen, and J. Manninen, Measurement technique for characterizin memory effects in RF power amplifiers, Microwave Theory and Techniques, IEEE Transactions on, vol. 49, no. 8, pp , au 2. [7] N. Wolf, J.-E. Mueller, and H. Klar, Identification of frequency dependent memory effects and the linearization of a cmos pa for multiple standards, in Radio and Wireless Symposium, 29. RWS 9. IEEE, jan. 29, pp [8] A. Parker and J. Rathmell, Broad-band characterization of FET selfheatin, Microwave Theory and Techniques, IEEE Transactions on, vol. 53, no. 7, pp , july 25. [9] R. Gaska, Q. Chen, J. Yan, A. Osinsky, M. Asif Khan, and M. Shur, Hih-temperature performance of AlGaN/GaN HFETs on SiC substrates, Electron Device Letters, IEEE, vol. 8, no., pp , oct x -3 Time (ms) Fi. 9. Simulation results of output envelope and ΔT under step sinle-tone excitation. V starts at V, steps to Vatms,to2Vat.5ms,to3Vat ms,to2vat.5msandtovat2ms. IV. CONCLUSION On the basis of physical properties of FETs, this paper explains how self-heatin can cause memory effects in an RF