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% NIWeek 2014 Poster by T. Reveyrand
% www.microwave.fr
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% TITLE AND AUTHOR NAME
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{ \bf \huge {Large Signal Network Analyzer} \\ \Large \it An affordable PXI-based microwave non-linear characterization platform} % Poster title
{\vspace{0.3em} \smaller Tibault Reveyrand$^1$, Scott Schafer$^1$, John Boudreaux$^1$, Takao Inoue$^2$, Zoya Popovi\'c$^1$ \\ % Author names
\smaller $^1$\it {University of Colorado at Boulder} \\ $^2$\it{National Instruments} } % Author email addresses
{\includegraphics[scale=0.45]{NI.jpg}} % University/lab logo
%----------------------------------------------------------------------------------------
% INTRODUCTION
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\headerbox{Introduction}{name=introduction,column=0,row=0, span=3}{
\begin{itemize}
\item The goal of this research is to integrate microwave-frequency Large Signal Network Analysis capabilities with commercially available National Instruments' PXI modular instrumentation and LabVIEW environment.
\vspace{-0.2cm}
\item The Microwave Research Group at the University of Colorado has decades of experience in UHF through millimeter-wave transmitters, including recent X-band (10-GHz) MMIC implementations in GaN. Our aim is to extend the frequency range and capabilities of available commercial instrumentation provided by NI.
\vspace{-0.2cm}
\item The proposed instrumentation development will enable new types of measurements such as those required for harmonically-terminated PAs, various transmitter architectures (Doherty, outphasing and supply modulated PAs), as well as microwave transistor rectifiers. The time-domain characterization is expected to provide dramatic improvement in RF circuit design capabilities.
\end{itemize}
}
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% CALIBRATION
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\headerbox{Calibration}{name=calibration,column=0,below=introduction}{
LSNA calibration algorithm consists of \textbf{3 steps} at each RF frequency: % \cite{verspecht2005large}
\begin{enumerate}
\item A relative VNA calibration creates an error-term matrix related to ports 1 and 2:
\begin{equation*}
\begin{pmatrix} a_ 1 \\ b_1 \\ a_2 \\ b_2 \end{pmatrix}=K\begin{bmatrix} 1 & \beta_1 & 0 & 0\\ \gamma_1 & \delta_1 & 0 & 0 \\ 0 & 0 & \alpha_2 & \beta_2 \\ 0 & 0 & \gamma_2 & \delta_2 \end{bmatrix}.\begin{pmatrix} r_ 1 \\ r_2 \\ r_3 \\ r_4 \end{pmatrix}
\label{eq:cal_2_ports}
\end{equation*}
\item The power calibration gives $|K|$
\item The phase calibration yields $\arg\{K\}$
\end{enumerate}
Power and phase calibration are performed at an auxiliary reference plane ($P_{aux}$) after its own 1-port SOL coaxial calibration:
\begin{equation*}
\begin{pmatrix} a_{aux} \\ b_{aux} \end{pmatrix}=K_{aux}\begin{bmatrix} 1 & \beta_{aux} \\ \gamma_{aux} & \delta_{aux} \end{bmatrix}.\begin{pmatrix} r_1 \\ r_2 \end{pmatrix}
\label{eq:cal_port_aux}
\end{equation*}
\begin{center}
\includegraphics[width=0.7\linewidth]{CALIBRATION.pdf}
\end{center}
\textbf{$\Rightarrow$ Power} calibration at $P_{aux}$ reference plane requires the connection of a power sensor. According to the measured value, in $dBm$, we can calculate $|K_{aux}|$ such as:
\begin{equation*}
|K_{aux}|=\left|{\frac{10^{(Power-10)/20}}{ r_1 + \beta_{aux} . r_2}}\right|
\label{eq:cal_power}
\end{equation*}
\textbf{$\Rightarrow$ Phase} calibration at $P_{aux}$ is performed by connecting a direct receiver (e.g. $r_3$) at $P_{aux}$:
\begin{equation*}
\arg\{K_{aux}\}=\arg\left\{{\frac{r_3}{ r_1 + \beta_{aux} . r_2}}\right\}
\label{eq:cal_phase}
\end{equation*}
\textbf{$\Rightarrow$ Reciprocity} transfers the absolute calibration from $P_{aux}$ to ports 1 and 2 ($P1$ and $P2$):
\begin{equation*}
K=\pm\sqrt{1/Det\{[M]\}}
\label{eq:reciprocity_1}
\end{equation*}
with
\begin{equation*}
M=\begin{bmatrix} 1 & \beta_1 \\ \gamma_1 & \delta_1 \end{bmatrix}. {\left [ K_{aux}.\begin{bmatrix} 1 & \beta_{aux} \\ \gamma_{aux} & \delta_{aux} \end{bmatrix} \right]}^{-1}
\label{eq:reciprocity_2}
\end{equation*}
}
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% OTHER INSTRUMENTATION
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\headerbox{Time-domain instrumentation for non-linear devices}{name=instruments,span=2,column=1,row=1, below=introduction}{ % To reduce this block to 1 column width, remove 'span=2'
\begin{center}
\resizebox{0.9\textwidth}{!}{\begin{minipage}{\textwidth}
\begin{tabular}{l l l l}
\toprule
\textbf{Name} & \textbf{Manufacturer} & \textbf{Receivers} & \textbf{Availability}\\
\midrule
MTA (requires two synchronized) & HP & Sampler & Discontinued \\
LSNA & Agilent & Sampler & Discontinued \\
PNA-X + Nonlinear option & Agilent & Mixer & \$\$ \\
ZVA + Nonlinear option & Rohde and Schwarz & Mixer & \$\$ \\
SWAP X-402 & VTD & Sampler & Discontinued \\
\bottomrule
\end{tabular}
\end{minipage}}
\end{center}
}
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% MIXER vs. SAMPLERS
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\headerbox{Receiver: Mixer vs. Sampler}{name=receiver,span=2,column=1,row=1, below=instruments}{
\begin{center}
\includegraphics[width=1\linewidth]{RECEIVER.pdf}
\end{center}
}
%----------------------------------------------------------------------------------------
% MEASUREMENT SETUP
%----------------------------------------------------------------------------------------
\headerbox{Measurement Setup for Envelope Tracking Application}{name=application,span=2,column=1,below=receiver}{
The setup includes \textbf{two LSNAs simultaneously}. One is dedicated to RF (sampler based downconversion), the other one samples directly the LF stimulus. The purpose is to investigate \textbf{low-frequencies $S_{22}$} of the DUT under RF large signal conditions.
\begin{center}
\includegraphics[width=\linewidth]{BENCH.pdf}
\small \textit{Low-frequency measurement of drain supply envelope-bandwidth impedance for supply-modulated PAs}
\end{center}
}
%----------------------------------------------------------------------------------------
% CONCLUSION
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\headerbox{Conclusion}{name=conclusion,column=1,below=application,span=2}{
This new project will enable a new RF measurement capability by enabling an instrument that currently does not exist on the market. Some additional benefits include:
\vspace{-0.2cm}
\begin{itemize}
\item frequency range extension of NI RF instrument products currently available;
\vspace{-0.2cm}
\item sampler architecture offers a unique multi-scale time analysis possibility (e.g. signal and carrier domains);
\vspace{-0.2cm}
\item can be implemented with various ADCs and downconverters (e.g. THAs);
\vspace{-0.2cm}
\item 100\% LabVIEW environment;
\vspace{-0.2cm}
\item goal is to offer open-source LabVIEW software for user measurement flexibility.
\end{itemize}
}
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% REFERENCES
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% ACKNOWLEDGEMENTS
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\headerbox{Acknowledgements}{name=acknowledgements,column=0,below=conclusion, above=bottom,span=3}{
\smaller
This work is funded by National Instruments (Dr. Truchard) through a charitable donation. We would like to acknowledge DARPA (Dr. Greene) and ONR (Dr. Maki) for funding the initial part of this work under grant N00014-11-1-0931. \hfill \tiny \textit{Poster downloaded from} \textbf{www.microwave.fr}
}
\end{poster}
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