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Simulation and Measurement-based
X-parameter Models for Power Amplifiers
with Envelope Tracking




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Published in USA, August 3, 2014
5991-2733EN
Simulation and Measurement-based X-parameter Models
for Power Amplifiers with Envelope Tracking

Haedong Jang1, Andrew Zai2, Tibault Reveyrand3, Patrick Roblin1, Zoya Popovic2, and David E. Root4
1The Ohio State University, Columbus, OH
2
University of Colorado, Boulder, CO
3
XLIM-UMR CNRS, Limoges Cedex, France
4Keysight Technologies, Inc., Santa Rosa, CA

Abstract --Static X-parameter (XP) models for RF power
amplifiers (PAs), derived from both simulations and nonlinear Envelope Envelope Envelope
Detection Shaping Tracker
vector network analyzer (NVNA) measurements, are investigated
for the prediction of PA performance under dynamic signal
conditions such as in envelope tracking (ET). The instantaneous I2 + Q 2
AM-AM, AM-PM and PAE predictions of XP models extracted
from simulation are compared under ET dynamic signal
I Q
conditions to two types of circuit models using envelope 3
I
simulation. An XP PA model is extracted for a peak 8W GaN 1 2
A RF
class-F-1 ET PA from NVNA measurements with automated bias Delay Driver RF PA
align up-convert
control. By applying a constant gain shaping table derived from Q
the XP model to the drain supply voltage, the average PAE is
improved from 40% to 57% for 3.84 MHz WCDMA signals at
Fig. 1. Simplified ET-PA system block diagram with a
2.14 GHz compared to fixed drain bias operation.
nonlinear three-port RF PA.
Index Terms -- X-parameters, envelope tracking, loadpull, characterization at multiple supply voltages. The goal of this
power amplifiers, supply modulation.
work is to develop a model for this application that is easy to
extract from simulations and standard measurements for the
I. INTRODUCTION shaping table design, and validate that it gives good estimates
of the PA performance under dynamic bias operation.
High data rate communication requires spectrally efficient
In this work, bias dependent static X-parameter (XP)
complex modulation schemes such as WCDMA and LTE,
behavioral models [3][4] are developed from simulations and
resulting in signals with high peak to average power ratios
from nonlinear vector network analyzer (NVNA)
(PAPR). These dynamic signals significantly degrade the
measurements to model the nonlinear RF PA for use under
average PA efficiency when operated at a fixed bias condition.
dynamic signal operation with supply modulators. Properties
The envelope tracking (ET) architecture has shown significant
of the bias dependent static X-parameter models are
improvement of the average efficiency by dynamically
summarized in section II. In section III, the FOMs of the static
adjusting PA supply voltages according to look-up tables
model are compared to those of circuit models using dynamic
(LUT), or shaping tables, that specify mappings from input RF
input signals. In section IV, a static XP model is extracted
time-varying envelopes to drain control signals on the PA [1].
from an S-band class-F-1 GaN PA. A shaping table is designed
Nonlinear characterization and modeling of the transistor
from the model and used to define dynamic drain control
that can predict PA performance under varying bias and load
signals to improve efficiency. The intended FOMs based on
is needed for more complex transmitters, such as those that
the static model are measured under the dynamic ET condition
employ envelope tracking [2]. A simplified ET block diagram
using the supply modulator from [1].
is shown in Fig. 1 with a nonlinear RF PA that can be viewed
Furthermore, the performance prediction of a model with
as a three-port device, with the third port being the supply
varying loads is critical for LUT designs and PA performance
input. Most transistor and PA models are not designed with
optimizations under antenna mismatch condition [5]. The load
dynamic bias taken into account. Assuming the device under
dependency prediction of the XP models including harmonic
test (DUT) is quasi-static to the varying supply voltages and
loads [6] is validated by comparing the XP model, extracted
the envelope tracker is ideal, the common PA performance
from NVNA measurements in 50, to time-domain loadpull
figure of merits (FOMs) such as AM-AM, AM-PM and PAE,
data from an independent measurement system. Then the
can be determined using the conventional static