We describe the CAD identification and software implementation of a Volterra-like integral series expansion for the behavioral-level simulation of communication amplifiers. The model represents an improvement with respect to the classical AM-AM AM-PM memoryless approach. The performance of the model is compared with both the AM-AM AM-PM approach and circuit-level CAD simulatio

Brazil, T.

Filicori, F.

Florian, C.

Mirri, D.

Wren, M.

AMS Acta

IFTH-22 CAD Identification and Validation of a Non-Linear Dynamic Model for Performance Analysis of Large-Signal Amplifiers Corrado Florian*, Fabio Filicori*, Domenico Mid", Thomas Brazilt, Michael Wren' *Dipartimento di Elettronica, Informatica e Sistemistica, Universita di Bologna, Viale Risorgimento 2, Bologna, 40136, Italy 'Dipartimento di Ingegneria Elettrica, Univ. di Bologna, Viale Risorgimento 2, Bologna, 40136 Italy $Department of Electronic and Electrical Engineering, University College Dublin, Dublin 4 , Ireland I Abmocf - We describe the CAD identification and software implementation of a Volterra-like integral series expansion for the behavioral-level simulation of communication amplifiers. The model represents an improvement with respect to the classical AM-AM AM-PM memoryless approach. The performance of the model is compared with both the AM-AM AM-PM approach and circuit-level CAD simulation. 1. INTRODUCTION The simulation of the performance of communication power amplifiers and nonlinear circuits is in general dependent on the availability of models capable of describing their behavior with a high level of accuracy. In the environment of a CAD package, it is possible to choose between two different approaches, namely, circuit- level simulation or system-level simulation. The first approach is the most accurate, hut needs a detailed description of all the circuit components by means of physical or electrical models: the solution is then carried out by solving the circuit equations for all these models and this is obviously quite complex and time-consuming. On the contrary, system-level simulation utilizes models based on terminal measurements that are, by their nature, much more computationally efficient. This kind of mathematical black-box, or look-up table model, gives a description of the behavior of the nonlinear system from the point of view of its external pdrts. When simulating the performance of a power amplifier in a communication link, we are particularly interested in the effects of the circuit nonlinearities on the spectrum of the transmitted signal. Being driven near its maximum output power and with broadband signals, -the amplifier gain is usually affected by nonlinear distortion and nonlinear memory effects. Depending on the amplifier topology and technology (bias networks, RF matching, thermal effects) and on the nature of the input signal (bandwidth), the circuit behavior could vary from nonlinear quasi-memoryless to nonlinear with memory. The classical behavioral description known as the AM- AM AM-PM model is well suited to describing a quasi- memoryless amplifier, that is to say a system with memory time constants (r) significantly less than the period of the carrier T=I& In this case, the amplitude and phase distortion of the output signal at a certain time instant depends only on the input signal level close to the same instant, and this relationship is well described by the Pin/Pout amplifier characteristic (AM-AM conversion) and the amplitude-dependent phase shift characteristic (AM-PM conversion), computed by means of a power sweep of the carrier (fo frequency). This is true for every kind of modulated input signal applied to such a system regardless of bow large is its bandwidth. In fact denoting by fmux the maximum frequency of the envelope bandwidth of the input signal, the memory time constants r will he always negligible with respect the modulation bandwidth ( r < < l / f " )  since they are already less than the period of the camer. This simple description is no longer appropriate when dealing with amplifiers that present longer memory time constants T and when dealing with broadband signals. Indeed, when the memory effects are on the order of the period of the envelope signal ( I / f m n t ) ,  the system response depends not only on the input envelope amplitude but also on its frequency. The classical demonstration of these phenomena is the situation where the two-tone intermodulation distortion (IMD) depends on the tone spacing, as can he made evident by varying the offset frequency between the tones in the envelope modulation bandwidth [l]. It is important to notice that the AM-AM AM-PM quasi-memoryless model can still be useful to describe I: -. 0-7803-7695-1/03/$17.00 0 2003 E E E  2125 2003 IEEE ? K I T S  Digest this kind of system, but only in the presence of very narrowband signals for which the inequality r<<l/@nax is satisfied. However in many cases the modulated signals involved in modem communication systems have bandwidths that are not at all negligible with respect to the memory characteristics of the amplifier, and so a memoryless assumption fails to give the correct response. This has been observed to be particularly true for systems containing internal devices for distortion reduction through compensation of the nonlinear characteristics [11[21. To address this type of application, a new dynamic non- linear amplifier model that takes account of distortions due to both the large amplitude and the large bandwidth of the input signal, has been formulated. The model, the full mathematical basis for which is described in [3] ,  is based on a modified Volterra-like integral series, previously used for the modeling of PHEMT devices [4] and VCO circuits [5],  and is especially oriented to the analysis of non-linear systems operating with modulated signals. The main aim of this paper is the verification of the capabilities of this kind of model. To this end, we will briefly present the model formulation (Section U), and then we will describe a new frequencyariented version of the model formula and the model identification process within the Agilent ADS2002 environment (Section 111). Section 1V is focused on the implementation of the model in MATLAB 5.3 code, while in Section V the model performance will he discussed. 11. NON-LINEAR DYNAMIC MODEL A more complete description of the mathematical development that leads to the present model formulation is contained in [3].  The basic idea of this approach is to develop an integral series expansion (Volterra series) around a well-behaved signal trajectory that should be chosen depending on the particular application [6].  In this way, and with quite general hypothesis, it is possible to reduce the Volterra formulation to a simplified and compact form, that consists of an instantaneous static non- linearity plus one or more convolution integrals nonlinearly dependent on the instantaneous amplitude and frequency of the input signal. The important property of this approach is the separation of purely static nonlinear effects from memory effects, which are mixed in the classical Volterra approach. The model formulation starts from a general description of the relationship between the input and output signals of the amplifier: (1) + T, u ( f ) = F [ s ( f - r ) ]  Where it has been assumed that the output u(tj of a large signal amplifier can be expressed as a generic functional of the input signal s(tj. This means that the output signal depends non-linearly on the values of the input signal over a sufficiently large "memory interval" (O_Cr_n,) around the instant f at which the output is evaluated. ' Starting form this general assumption, eventually the model formulation becomes [3]: b(t) = a(Offh,la(Ol)+ + p h(r,) .[a@ - r , )  - a( f ) ]e" '~~"dr ,  + ( 2 )  + F g,(rI,h,la(+. [a(t -rl)  - a(t)]e-j*"O"drl + + d ( f )  6" g;(r,, fo, la(f)l). [U*(, - r l )  - ~ ' ( / ) ] . e ' ~ ~ " ' d r ,  Where b(tj is the complex modulation envelope of the first zonal output component around the carrier and a(t) is the complex modulation envelope of the input signal. An examination of Eq. ( 2 )  is very useful in identifying the different terms that contribute to the output in-band signal: the first term represents the non-linear memory- less contribution, the second term is the purely dynamic linear contribution, while the last two terms are the purely dynamic nonlinear contributions. The function H simply corresponds to the AM-AM AM-PM amplifier characteristic. That characteristic is determined by driving the amplifier with a non-modulated carrier and sweeping the power level. This means that in practice, the AM-AM AM-FM plots represent just a zero- order approximation of the system behavior. Thus, in the presence of a modulated signal, the AM- AM AM-PM characterization of the amplifier is sufficiently accurate only when the bandwidth of the complex modulation envelope of the input signal (fmax) is so small as to make the amplitude of the dynamic deviations e(t-rJ= a(f-rJ-a(t) for each rj almost negligible in practice. The latter is true only for quasi-memoryless systems or systems where the memory time constants are negligible with respect to the reciprocal of the envelope modulation bandwidth r <<l/fmax. These constraints c q o t  be met in many practical cases, when dealing with large-handwidth modulated signals. In such cases the model of Equation 2 gives superior accuracy by taking into account more terms of the series expansion of the functional in Equation 1. In fact, even if the series is truncated to the fust-order term @=I), a considerable improvement in accuracy can be achieved compared to the coarser zero-order approximation of the conventional AM-AM AM-PM characteristic alone. 2126 It is important to notice the hypothesis involved in performing a first order truncation @=I): the bandwidth of the modulation envelope fmar must be small enough to make the product of the amplitude of the dynamic deviations e(l,rJ for each i, almost negligible in practice (3). We have developed an efficient model identification procedure based on this frequency-domain formulation using the Agilent ADS2002 Envelope simulator [7]. This simulator allows us to drive the amplifier with any generic modulated signal with complex envelope a(0 and computes the corresponding in-band output modulation (3) envelope b(t), implementing the complex envelope modulator/demodulator system described in [3 1. It should be clear [3] that this hypothesis is far less restrictive than the hypothesis 6 < l l f , ,  and can he satisfied in many applications of interest. Furthermore, even if this approach remains inadequate for an accurate description of systems with particularly long memory phenomena such as those arising from thermal effects, it represents an improvement for such cases compared to the memoryless approach. Indeed when the duration of memory effects is sufficiently long to invalidate the hypothesis made in truncating the series to first-order, the model will take account of nonlinear memory phenomena as well, but in this case the truncation error introduced will he larger. 111. THE MODEL IDENTIFICATION We can rewrite the model formulation of Eq. (2) in a frequency-oriented version, as follows: The final formulation for discrete spectrum signals becomes: IV. MODEL IMPLEMENTATION The model has been implemented in Matlab 5.3 environment. The Matlab code implements Eq. (6) ,  reading from look-up tables that store the model functions. Instantaneous interpolations in the envelope amplitude and frequency domains are performed with Matlab interpolation functions. For comparison purposes, an AM-AM AM-PM model has also been developed. The benchmark for OUT simulation results is the circuit level simulation performed with Agilent ADS2002 Envelope simulator. Even if, as we said before, there are some kind of linearised amplifiers that might be the best choice to make evident the deficiencies of the traditional compressiodphase distortion model in modeling their dynamic behavior, as a first approach we choose a single- ended PHEMT amplifier (designed and realized at UCD in microstrip technology) for the validation of the proposed non-linear dynamic model. V. SIMULATION RESULTS As a first analysis of the model’s broadband capabilities we chose a test signal that consists of two tones deliberately widely-spaced to IOOMHz around the frequency fe2GHz. The output signal complex envelope is amplitude and frequency modulated. In Fig. 1 and Fig.2 we can appreciate how the nonlinear dynamic model gives a prediction closer to the circuit-level simulation solution, -both for the amplitude and phase modulation. In particular the AM-AM AM-PM gives only a rough estimation of the phase modulation. The output spectrum data in Table 1 shows that the Nonlinear Dynamic Model predicts with very good accuracy the asymmetric response of the amplifier to the two tones, while obviously the narrowband AM-AM AM- PM model is not able to model the frequency dependence of the amplifier gain (the two output tones are predicted to he identical). Other tests of the model with a W-CDMA signal (data rate 32KbiUsec) generated within the ADS2002 DSP environment have been carried out with good results, which are omitted here due to space restrictions. 2127 .- ., . .” . . . VI. CONCLUSION AND FUTURE ACTIVITY The implementation and the performance evaluation of a new kind of nonlinear dynamic model previously described by the authors have been presented. It has been j shown that this modeling approach leads to an improvement in broadband behavioral modeling for a power amplifier compared to the classical memolyless AM-AM AM-PM approach. Further investigations of the model’s capabilities using different amplifier designs as well as an experimental implementation of the identification and.validation set-up are planned for the near future. For this purpose, new instrumentation has recently been acquired at UCD allowing an experimental implementation of the identification bench described in [3]. The instrumentation .. ~ consists of the Agilent E4438C Vector Signal Generator and the E4406A Vector Signal Analyzer Series the validation of the model can be carried out. I Fig.. 1. complex Envelope Amplitude Modulation of the Output Signal: a Comparison Between the Three Approaches. Transmitter Tester, with which both the identification and Simulator Fig. 2. Signal: a Comparison Between the Three Approaches Complex Envelope Phase Modulation of the Output PI  Tones Two Tone Test Output Spectrum I-AMAM-PMM~~~~ i 1 0 . 8 d ~ m  i 1 0 . 8 d ~ m  II I ADS2002 Envelone 1 .  12.4dBm I 8.9 dBm I I n l i n e a r  Dynamic Model 1 12.4 dSm i 9.2 dBm 1 r-7 1 I 1‘1 Table 1. Output Spectrum Resulting from the Two-Tone Test REFERENCES W. Bosch and G. Gatti, “Measurement and Simulation of Memory Effects in Predistortion Linearkers”, IEEE Trans. Microwave Theory and Tech., vol. 37, no. 12, pp. 1885- 1890, December 1989. J. S. Kenney, W. Woo, L. Ding, R. Raich, H. Ku and G. T. Zhou, “The impact of memory effects on predistortion linearization of RF power amplifiers”, in Proc. of the 6‘h Inr. A)“. On Microwave and Optical Techn., Montreal, Canada, June 19-23 2001,pp. 189.193. D. Mim, F. Filicori, G. luculano, G. Pasini, “A Nan-Linear Dynamic Model for Performance Analysis of Large-Signal Amplifiers in Communication Systems”, 1999 IEEE Inshumenlalion and Measuremenl Technologv Conference Proc., vol. 1,pp. 193-197,May 1999. A. Costantini, R.P. Paganelli, P.A. Traverso, D. Argento, G. Fame, M. Pagani, A. Santarelli, G. Vannini, F. Filicori, ‘“Accurate prediction of PHEMT intermodulation distortion using the nonlinear discrete convolution model”, 2002 IEEE M77’lnt. Microwave Symp. Dig., vol. 2, pp. 857-860. A. Costantini, C. Florian, G. Vannini “VCO Behavioral Modeling based on the Non Linear Integral Approach”, 2002 IEEE ISCAS Inl. Symp. on Circuit and Systems Dig., vol. 2 ,  pp. 137-140, May 2002. D. Mirri, G. luculano, F. Filicori, G. Pasini, G. Vannini and G. Pellegrini Gualtieri, “A Modified Volterra Series Approach for Nonlinear Dynamic Systems Modeling”, IEEE Trans. Circuits and Systems-I: Fundamental 7kory  and Applications, vol. 49, no. 8, pp. 1118-1128, August 2002. How-Siang Yap, “Designing to digital wireless soecifications usine Circuit Envelooe simulation”. in Proc. o j  the Asia-Pac& Microwave don/erence, Hong Kong 1997, vol. 1, pp. 173-176. 2128 

CAD identification and validation of a non-linear dynamic model for performance analysis of large-signal amplifiers

AMS Acta - Alm@DL - Università di Bologna

IFTH-22 
CAD Identification and Validation of a Non-Linear Dynamic Model 
for Performance Analysis of Large-Signal Amplifiers 
Corrado Florian*, Fabio Filicori*, Domenico Mid", Thomas Brazilt, Michael Wren' 
*Dipartimento di Elettronica, Informatica e Sistemistica, Universita di Bologna, Viale Risorgimento 2, 
Bologna, 40136, Italy 
'Dipartimento di Ingegneria Elettrica, Univ. di Bologna, Viale Risorgimento 2, Bologna, 40136 Italy 
$Department of Electronic and Electrical Engineering, University College Dublin, Dublin 4 , Ireland 
I 
Abmocf - We describe the CAD identification and 
software implementation of a Volterra-like integral series 
expansion for the behavioral-level simulation of 
communication amplifiers. The model represents an 
improvement with respect to the classical AM-AM AM-PM 
memoryless approach. The performance of the model is 
compared with both the AM-AM AM-PM approach and 
circuit-level CAD simulation. 
1. INTRODUCTION 
The simulation of the performance of communication 
power amplifiers and nonlinear circuits is in general 
dependent on the availability of models capable of 
describing their behavior with a high level of accuracy. 
In the environment of a CAD package, it is possible to 
choose between two different approaches, namely, circuit- 
level simulation or system-level simulation. The first 
approach is the most accurate, hut needs a detailed 
description of all the circuit components by means of 
physical or electrical models: the solution is then carried 
out by solving the circuit equations for all these models 
and this is obviously quite complex and time-consuming. 
On the contrary, system-level simulation utilizes models 
based on terminal measurements that are, by their nature, 
much more computationally efficient. This kind of 
mathematical black-box, or look-up table model, gives a 
description of the behavior of the nonlinear system from 
the point of view of its external pdrts. 
When simulating the performance of a power amplifier 
in a communication link, we are particularly interested in 
the effects of the circuit nonlinearities on the spectrum of 
the transmitted signal. Being driven near its maximum 
output power and with broadband signals, -the amplifier 
gain is usually affected by nonlinear distortion and 
nonlinear memory effects. Depending on the amplifier 
topology and technology (bias networks, RF matching, 
thermal effects) and on the nature of the input signal 
(bandwidth), the circuit behavior could vary from 
nonlinear quasi-memoryless to nonlinear with memory. 
The classical behavioral description known as the AM- 
AM AM-PM model is well suited to describing a quasi- 
memoryless amplifier, that is to say a system with 
memory time constants (r) significantly less than the 
period of the carrier T=I& In this case, the amplitude and 
phase distortion of the output signal at a certain time 
instant depends only on the input signal level close to the 
same instant, and this relationship is well described by the 
Pin/Pout amplifier characteristic (AM-AM conversion) 
and the amplitude-dependent phase shift characteristic 
(AM-PM conversion), computed by means of a power 
sweep of the carrier (fo frequency). 
This is true for every kind of modulated input signal 
applied to such a system regardless of bow large is its 
bandwidth. In fact denoting by fmux the maximum 
frequency of the envelope bandwidth of the input signal, 
the memory time constants r will he always negligible 
with respect the modulation bandwidth ( r < < l / f " )  since 
they are already less than the period of the camer. 
This simple description is no longer appropriate when 
dealing with amplifiers that present longer memory time 
constants T and when dealing with broadband signals. 
Indeed, when the memory effects are on the order of the 
period of the envelope signal ( I / f m n t ) ,  the system 
response depends not only on the input envelope 
amplitude but also on its frequency. 
The classical demonstration of these phenomena is the 
situation where the two-tone intermodulation distortion 
(IMD) depends on the tone spacing, as can he made 
evident by varying the offset frequency between the tones 
in the envelope modulation bandwidth [l]. 
It is important to notice that the AM-AM AM-PM 
quasi-memoryless model can still be useful to describe 
I: -. 
0-7803-7695-1/03/$17.00 0 2003 E E E  
2125 
2003 IEEE ? K I T S  Digest 
this kind of system, but only in the presence of very 
narrowband signals for which the inequality r<<l/@nax is 
satisfied. 
However in many cases the modulated signals involved 
in modem communication systems have bandwidths that 
are not at all negligible with respect to the memory 
characteristics of the amplifier, and so a memoryless 
assumption fails to give the correct response. This has 
been observed to be particularly true for systems 
containing internal devices for distortion reduction 
through compensation of the nonlinear characteristics 
[11[21. 
To address this type of application, a new dynamic non- 
linear amplifier model that takes account of distortions 
due to both the large amplitude and the large bandwidth of 
the input signal, has been formulated. The model, the full 
mathematical basis for which is described in [3] ,  is based 
on a modified Volterra-like integral series, previously 
used for the modeling of PHEMT devices [4] and VCO 
circuits [5],  and is especially oriented to the analysis of 
non-linear systems operating with modulated signals. 
The main aim of this paper is the verification of the 
capabilities of this kind of model. To this end, we will 
briefly present the model formulation (Section U), and 
then we will describe a new frequencyariented version of 
the model formula and the model identification process 
within the Agilent ADS2002 environment (Section 111). 
Section 1V is focused on the implementation of the 
model in MATLAB 5.3 code, while in Section V the 
model performance will he discussed. 
11. NON-LINEAR DYNAMIC MODEL 
A more complete description of the mathematical 
development that leads to the present model formulation is 
contained in [3].  The basic idea of this approach is to 
develop an integral series expansion (Volterra series) 
around a well-behaved signal trajectory that should be 
chosen depending on the particular application [6].  In this 
way, and with quite general hypothesis, it is possible to 
reduce the Volterra formulation to a simplified and 
compact form, that consists of an instantaneous static non- 
linearity plus one or more convolution integrals 
nonlinearly dependent on the instantaneous amplitude and 
frequency of the input signal. 
The important property of this approach is the 
separation of purely static nonlinear effects from memory 
effects, which are mixed in the classical Volterra 
approach. The model formulation starts from a general 
description of the relationship between the input and 
output signals of the amplifier: 
(1) + T, u ( f ) = F [ s ( f - r ) ]  
Where it has been assumed that the output u(tj of a large 
signal amplifier can be expressed as a generic functional 
of the input signal s(tj. 
This means that the output signal depends non-linearly 
on the values of the input signal over a sufficiently large 
"memory interval" (O_Cr_n,) around the instant f at which 
the output is evaluated. ' 
Starting form this general assumption, eventually the 
model formulation becomes [3]: 
b(t) = a(Offh,la(Ol)+ 
+ p h(r,) .[a@ - r , )  - a( f ) ]e" '~~"dr ,  + ( 2 )  
+ F g,(rI,h,la(+. [a(t -rl)  - a(t)]e-j*"O"drl + 
+ d ( f )  6" g;(r,, fo, la(f)l). [U*(, - r l )  - ~ ' ( / ) ] . e ' ~ ~ " ' d r ,  
Where b(tj is the complex modulation envelope of the 
first zonal output component around the carrier and a(t) is 
the complex modulation envelope of the input signal. 
An examination of Eq. ( 2 )  is very useful in identifying 
the different terms that contribute to the output in-band 
signal: the first term represents the non-linear memory- 
less contribution, the second term is the purely dynamic 
linear contribution, while the last two terms are the purely 
dynamic nonlinear contributions. 
The function H simply corresponds to the AM-AM 
AM-PM amplifier characteristic. That characteristic is 
determined by driving the amplifier with a non-modulated 
carrier and sweeping the power level. This means that in 
practice, the AM-AM AM-FM plots represent just a zero- 
order approximation of the system behavior. 
Thus, in the presence of a modulated signal, the AM- 
AM AM-PM characterization of the amplifier is 
sufficiently accurate only when the bandwidth of the 
complex modulation envelope of the input signal (fmax) is 
so small as to make the amplitude of the dynamic 
deviations e(t-rJ= a(f-rJ-a(t) for each rj almost negligible 
in practice. The latter is true only for quasi-memoryless 
systems or systems where the memory time constants are 
negligible with respect to the reciprocal of the envelope 
modulation bandwidth r <<l/fmax. 
These constraints c q o t  be met in many practical cases, 
when dealing with large-handwidth modulated signals. 
In such cases the model of Equation 2 gives superior 
accuracy by taking into account more terms of the series 
expansion of the functional in Equation 1. In fact, even if 
the series is truncated to the fust-order term @=I), a 
considerable improvement in accuracy can be achieved 
compared to the coarser zero-order approximation of the 
conventional AM-AM AM-PM characteristic alone. 
2126 
It is important to notice the hypothesis involved in 
performing a first order truncation @=I): the bandwidth 
of the modulation envelope fmar must be small enough to 
make the product of the amplitude of the dynamic 
deviations e(l,rJ for each i, almost negligible in practice 
(3). 
We have developed an efficient model identification 
procedure based on this frequency-domain formulation 
using the Agilent ADS2002 Envelope simulator [7]. 
This simulator allows us to drive the amplifier with any 
generic modulated signal with complex envelope a(0 and 
computes the corresponding in-band output modulation 
(3) envelope b(t), implementing the complex envelope 
modulator/demodulator system described in [3 1. 
It should be clear [3] that this hypothesis is far less 
restrictive than the hypothesis 6 < l l f , ,  and can he 
satisfied in many applications of interest. 
Furthermore, even if this approach remains inadequate 
for an accurate description of systems with particularly 
long memory phenomena such as those arising from 
thermal effects, it represents an improvement for such 
cases compared to the memoryless approach. Indeed 
when the duration of memory effects is sufficiently long 
to invalidate the hypothesis made in truncating the series 
to first-order, the model will take account of nonlinear 
memory phenomena as well, but in this case the truncation 
error introduced will he larger. 
111. THE MODEL IDENTIFICATION 
We can rewrite the model formulation of Eq. (2) in a 
frequency-oriented version, as follows: 
The final formulation for discrete spectrum signals 
becomes: 
IV. MODEL IMPLEMENTATION 
The model has been implemented in Matlab 5.3 
environment. The Matlab code implements Eq. (6) ,  
reading from look-up tables that store the model 
functions. Instantaneous interpolations in the envelope 
amplitude and frequency domains are performed with 
Matlab interpolation functions. For comparison purposes, 
an AM-AM AM-PM model has also been developed. 
The benchmark for OUT simulation results is the circuit 
level simulation performed with Agilent ADS2002 
Envelope simulator. Even if, as we said before, there are 
some kind of linearised amplifiers that might be the best 
choice to make evident the deficiencies of the traditional 
compressiodphase distortion model in modeling their 
dynamic behavior, as a first approach we choose a single- 
ended PHEMT amplifier (designed and realized at UCD 
in microstrip technology) for the validation of the 
proposed non-linear dynamic model. 
V. SIMULATION RESULTS 
As a first analysis of the model’s broadband capabilities 
we chose a test signal that consists of two tones 
deliberately widely-spaced to IOOMHz around the 
frequency fe2GHz. The output signal complex envelope 
is amplitude and frequency modulated. In Fig. 1 and Fig.2 
we can appreciate how the nonlinear dynamic model gives 
a prediction closer to the circuit-level simulation solution, 
-both for the amplitude and phase modulation. In particular 
the AM-AM AM-PM gives only a rough estimation of the 
phase modulation. 
The output spectrum data in Table 1 shows that the 
Nonlinear Dynamic Model predicts with very good 
accuracy the asymmetric response of the amplifier to the 
two tones, while obviously the narrowband AM-AM AM- 
PM model is not able to model the frequency dependence 
of the amplifier gain (the two output tones are predicted to 
he identical). 
Other tests of the model with a W-CDMA signal (data 
rate 32KbiUsec) generated within the ADS2002 DSP 
environment have been carried out with good results, 
which are omitted here due to space restrictions. 
2127 
.- ., . .” . . . VI. CONCLUSION AND FUTURE ACTIVITY 
The implementation and the performance evaluation of 
a new kind of nonlinear dynamic model previously 
described by the authors have been presented. It has been 
j shown that this modeling approach leads to an 
improvement in broadband behavioral modeling for a 
power amplifier compared to the classical memolyless 
AM-AM AM-PM approach. 
Further investigations of the model’s capabilities using 
different amplifier designs as well as an experimental 
implementation of the identification and.validation set-up 
are planned for the near future. For this purpose, new 
instrumentation has recently been acquired at UCD 
allowing an experimental implementation of the 
identification bench described in [3]. The instrumentation 
.. ~ consists of the Agilent E4438C Vector Signal Generator 
and the E4406A Vector Signal Analyzer Series 
the validation of the model can be carried out. 
I 
Fig.. 1. complex Envelope Amplitude Modulation of the Output 
Signal: a Comparison Between the Three Approaches. 
Transmitter Tester, with which both the identification and 
Simulator 
Fig. 2. 
Signal: a Comparison Between the Three Approaches 
Complex Envelope Phase Modulation of the Output 
PI  
Tones 
Two Tone Test Output Spectrum 
I-AMAM-PMM~~~~ i 1 0 . 8 d ~ m  i 1 0 . 8 d ~ m  I
I I 
ADS2002 Envelone 1 .  12.4dBm I 8.9 dBm I 
I n l i n e a r  Dynamic Model 1 12.4 dSm i 9.2 dBm 1 r-7 
1 I 1‘1 
Table 1. Output Spectrum Resulting from the Two-Tone Test 
REFERENCES 
W. Bosch and G. Gatti, “Measurement and Simulation of 
Memory Effects in Predistortion Linearkers”, IEEE Trans. 
Microwave Theory and Tech., vol. 37, no. 12, pp. 1885- 
1890, December 1989. 
J. S. Kenney, W. Woo, L. Ding, R. Raich, H. Ku and G. T. 
Zhou, “The impact of memory effects on predistortion 
linearization of RF power amplifiers”, in Proc. of the 6‘h 
Inr. A)“. On Microwave and Optical Techn., Montreal, 
Canada, June 19-23 2001,pp. 189.193. 
D. Mim, F. Filicori, G. luculano, G. Pasini, “A Nan-Linear 
Dynamic Model for Performance Analysis of Large-Signal 
Amplifiers in Communication Systems”, 1999 IEEE 
Inshumenlalion and Measuremenl Technologv Conference 
Proc., vol. 1,pp. 193-197,May 1999. 
A. Costantini, R.P. Paganelli, P.A. Traverso, D. Argento, 
G. Fame, M. Pagani, A. Santarelli, G. Vannini, F. Filicori, 
‘“Accurate prediction of PHEMT intermodulation distortion 
using the nonlinear discrete convolution model”, 2002 
IEEE M77’lnt. Microwave Symp. Dig., vol. 2, pp. 857-860. 
A. Costantini, C. Florian, G. Vannini “VCO Behavioral 
Modeling based on the Non Linear Integral Approach”, 
2002 IEEE ISCAS Inl. Symp. on Circuit and Systems Dig., 
vol. 2 ,  pp. 137-140, May 2002. 
D. Mirri, G. luculano, F. Filicori, G. Pasini, G. Vannini and 
G. Pellegrini Gualtieri, “A Modified Volterra Series 
Approach for Nonlinear Dynamic Systems Modeling”, 
IEEE Trans. Circuits and Systems-I: Fundamental 7kory  
and Applications, vol. 49, no. 8, pp. 1118-1128, August 
2002. 
How-Siang Yap, “Designing to digital wireless 
soecifications usine Circuit Envelooe simulation”. in Proc. 
o j  the Asia-Pac& Microwave don/erence, Hong Kong 
1997, vol. 1, pp. 173-176. 
2128 


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CAD identification and validation of a non-linear dynamic model for performance analysis of large-signal amplifiers

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