sinarads/4410-4412.tex

\input{preamble.tex}
\graphicspath{{images/4410-4412}{images}}

\title{4410/4412 DDS Urukul}
\author{M-Labs Limited}
\date{January 2022}
\revision{Revision 2}
\companylogo{\includegraphics[height=0.73in]{artiq_sinara.pdf}}

\begin{document}
\maketitle

\section{Features}

\begin{itemize}
\item{4-channel 1GS/s DDS}
\item{Output frequency from \textless 1 to \textgreater 400 MHz}
\item{Sub-Hz frequency resolution}
\item{Controlled phase steps}
\item{Accurate output amplitude control}
\end{itemize}

\section{Applications}

\begin{itemize}
\item{Dynamic low-noise RF source}
\item{Driving RF electrodes in ion traps}
\item{Driving acousto-optic modulators}
\item{Form a laser intensity servo with 5108 Sampler}
\end{itemize}

\section{General Description}
The 4410/4412 DDS Urukul card is a 4hp EEM module, part of the ARTIQ/Sinara family. It adds frequency generation capabilities to carrier cards such as 1124 Kasli and 1125 Kasli-SoC.

It provides 4 channels of DDS (direct digital synthesis) at 1GS/s. Output frequencies from \textless 1 to \textgreater 400 MHz are supported. The nominal maximum output power of each channel is 10dBm. Each channel can be attenuated from 0 to -31.5 dB by a digital attenuator. RF switches (1ns temporal resolution) on each channel provide 70 dB isolation.

4410 DDS Urukul features AD9910 chips, while 4412 DDS Urukul features AD9912 chips. AD9912 is capable of higher frequency precision (~8 \textmu Hz) than the AD9910 (~0.25 Hz). The ARTIQ SU-Servo configuration is only available for AD9910.

% Switch to next column
\vfill\break

\begin{figure}[h]
    \centering
    \scalebox{0.88}{
    \begin{circuitikz}[european, scale=0.95, every label/.append style={align=center}]

        \begin{scope}[]

            % Node to pin-point the locations of SMA symbols
            \draw[color=white, text=black] (-0.1, 0) node[twoportshape, circuitikz/bipoles/twoport/width=1.2, scale=0.4 ] (ext_clk) {};
            \draw[color=white, text=black] (-0.1, -0.35) node[twoportshape, circuitikz/bipoles/twoport/width=1.2, scale=0.4 ] (mmcx) {};
            \draw[color=white, text=black] (-0.1, -1.75) node[twoportshape, circuitikz/bipoles/twoport/width=1.2, scale=0.4 ] (rf0) {};
            \draw[color=white, text=black] (-0.1, -2.45) node[twoportshape, circuitikz/bipoles/twoport/width=1.2, scale=0.4 ] (rf1) {};
            \draw[color=white, text=black] (-0.1, -3.15) node[twoportshape, circuitikz/bipoles/twoport/width=1.2, scale=0.4 ] (rf2) {};
            \draw[color=white, text=black] (-0.1, -3.85) node[twoportshape, circuitikz/bipoles/twoport/width=1.2, scale=0.4 ] (rf3) {};

            % Labels for female EXT_CLK, MMCX, RF {0, 1, 2, 3}
            \node [label=left:\tiny{EXT CLK}] at (0.35, 0) {};
            \node [label=left:\tiny{MMCX}] at (0.35, -0.35) {};
            \node [label=left:\tiny{RF 0}] at (0.35, -1.75) {};
            \node [label=left:\tiny{RF 1}] at (0.35, -2.45) {};
            \node [label=left:\tiny{RF 2}] at (0.35, -3.15) {};
            \node [label=left:\tiny{RF 3}] at (0.35, -3.85) {};

            % draw female EXT_CLK, MMCX, RF {0, 1, 2, 3}
            \begin{scope}[scale=0.07 , rotate=-90, xshift=0cm, yshift=2cm]
                \draw (0,0.65) -- (0,3);
                \clip (-1.5,0) rectangle (1.5,1.5);
                \draw (0,0) circle(1.5);
                \clip (-0.8,0) rectangle (0.8,0.8);
                \draw (0,0) circle(0.8);
            \end{scope}
            \begin{scope}[scale=0.07 , rotate=-90, xshift=5cm, yshift=2cm]
                \draw (0,0.65) -- (0,3);
                \clip (-1.5,0) rectangle (1.5,1.5);
                \draw (0,0) circle(1.5);
                \clip (-0.8,0) rectangle (0.8,0.8);
                \draw (0,0) circle(0.8);
            \end{scope}
            \begin{scope}[scale=0.07 , rotate=-90, xshift=25cm, yshift=2cm]
                \draw (0,0.65) -- (0,3);
                \clip (-1.5,0) rectangle (1.5,1.5);
                \draw (0,0) circle(1.5);
                \clip (-0.8,0) rectangle (0.8,0.8);
                \draw (0,0) circle(0.8);
            \end{scope}
            \begin{scope}[scale=0.07 , rotate=-90, xshift=35cm, yshift=2cm]
                \draw (0,0.65) -- (0,3);
                \clip (-1.5,0) rectangle (1.5,1.5);
                \draw (0,0) circle(1.5);
                \clip (-0.8,0) rectangle (0.8,0.8);
                \draw (0,0) circle(0.8);
            \end{scope}
            \begin{scope}[scale=0.07 , rotate=-90, xshift=45cm, yshift=2cm]
                \draw (0,0.65) -- (0,3);
                \clip (-1.5,0) rectangle (1.5,1.5);
                \draw (0,0) circle(1.5);
                \clip (-0.8,0) rectangle (0.8,0.8);
                \draw (0,0) circle(0.8);
            \end{scope}
            \begin{scope}[scale=0.07 , rotate=-90, xshift=55cm, yshift=2cm]
                \draw (0,0.65) -- (0,3);
                \clip (-1.5,0) rectangle (1.5,1.5);
                \draw (0,0) circle(1.5);
                \clip (-0.8,0) rectangle (0.8,0.8);
                \draw (0,0) circle(0.8);
            \end{scope}

            % Draw the internal oscillator
            \draw (0.02, -0.8) node[twoportshape, t={OSC}, circuitikz/bipoles/twoport/width=0.8, scale=0.4] (xo) {};

            % Draw the clock buffers as selector
            % \tikzset{demux/.style={muxdemux, muxdemux def={Lh=6, Rh=6, NL=3, NT=1, NB=0, NR=1, w=2.5}, no input leads, scale=0.4}};
            % \draw (1.55, -0.35) node[demux]{\rotatebox[origin=c]{-90}{CLK BUFFERS}};
            \draw (1.45, -0.35) node[twoportshape, t={CLK Buffers}, circuitikz/bipoles/twoport/width=2.2, scale=0.4, rotate=-90] (clk_buf) {};

            % Connect CLK_IN to DDS clock buffers
            \draw [-latexslim] (ext_clk.east) -- ++(1,0);
            \draw [-latexslim] (mmcx.east) -- ++(1,0);
            \draw [-latexslim] (xo.east) -- ++(1,0);

            % Connect CPLD clk_sel to DDS clock buffers
            \draw [-latexslim] (clk_buf.east) -- ++(0,-0.42);

            % Signal path: From control signals / clock of DDS to output of the RF switches
            \draw (1.35, -1.75) node[twoportshape, t={DDS Signal Path}, circuitikz/bipoles/twoport/width=2, scale=0.4] (sig0) {};
            \draw (1.35, -2.45) node[twoportshape, t={DDS Signal Path}, circuitikz/bipoles/twoport/width=2, scale=0.4] (sig1) {};
            \draw (1.35, -3.15) node[twoportshape, t={DDS Signal Path}, circuitikz/bipoles/twoport/width=2, scale=0.4] (sig2) {};
            \draw (1.35, -3.85) node[twoportshape, t={DDS Signal Path}, circuitikz/bipoles/twoport/width=2, scale=0.4] (sig3) {};

            % Extra node to expand the dotted area eastward
            \draw[color=white, text=black] (2.1, -3.85) node[twoportshape, circuitikz/bipoles/twoport/width=0.4, scale=0.4 ] (sig3_east) {};

            % Connect RF to DDS block
            \draw [latexslim-] (rf0.east) -- (sig0.west);
            \draw [latexslim-] (rf1.east) -- (sig1.west);
            \draw [latexslim-] (rf2.east) -- (sig2.west);
            \draw [latexslim-] (rf3.east) -- (sig3.west);

            % DDS signal path dotted area
            \node[draw, dotted, thick, rounded corners, inner xsep=0.7em, inner ysep=0.4em, fit=(rf3)(sig0)(sig3_east.east)] (abs_dds) {};
            \node[fill=white, rotate=-90, scale=0.7] at (abs_dds.west) {DDS Channels};

            % CPLD
            \draw (3.8, -0.35) node[twoportshape, t={CPLD}, circuitikz/bipoles/twoport/width=1.1, scale=0.8, rotate=-90] (cpld) {};

            % Synthronization clock buffer for DDS block
            \draw (3.5, -2.5) node[twoportshape, t=\fourcm{Sync}{Buffer}, circuitikz/bipoles/twoport/width=1.2, scale=0.5] (sync_buf) {};

            % Connect CPLD to:
            %   DDS clock buffer
            \draw [latexslim-] (clk_buf.north) -- (cpld.south);
            %   DDS signal path
            \draw [latexslim-latexslim] (3.4, -0.7) -- ++ (-1.5, 0) -- ++ (0,-0.72);
            %   Draw to intersection point, then complete the connection to sync buffer
            \draw [-] (4.2, -0.7) -- (4.55, -0.7) -- (4.55, -2.5);
            \draw [-latexslim] (4.55, -2.5) -- (sync_buf.east);

            % Connect sync buffer to DDS block
            \draw [-latexslim] (sig0.east) -- (3.35, -1.75) -- ++ (0, -0.5);
            \draw [-latexslim] (sync_buf.south) -- ++ (0, -0.3) -- ++ (-1.05, 0);

            % LVDS Transceivers
            \draw (6, 0) node[twoportshape, t=\fourcm{LVDS}{Transceiever}, circuitikz/bipoles/twoport/width=1.8, scale=0.5] (lvds0) {};
            \draw (6, -0.7) node[twoportshape, t=\fourcm{LVDS}{Transceiever}, circuitikz/bipoles/twoport/width=1.8, scale=0.5] (lvds1) {};
            \draw (6, -2.5) node[twoportshape, t=\fourcm{LVDS}{Transceiever}, circuitikz/bipoles/twoport/width=1.8, scale=0.5] (lvds2) {};
            \draw (6, -3.2) node[twoportshape, t=\fourcm{LVDS}{Transceiever}, circuitikz/bipoles/twoport/width=1.8, scale=0.5] (lvds3) {};

            % Connect CPLD to transceivers
            \draw [latexslim-latexslim] (lvds0.west) -- ++ (-1.13, 0);
            \draw [latexslim-latexslim] (lvds1.west) -- ++ (-0.35, 0) -- ++ (0, 0.6) -- ++ (-0.78, 0);
            \draw [latexslim-latexslim] (lvds2.west) -- ++ (-0.45, 0) -- ++ (0, 2.3) -- ++ (-0.68, 0);
            \draw [latexslim-latexslim] (lvds3.west) -- ++ (-0.55, 0) -- ++ (0, 2.9) -- ++ (-0.58, 0);

            % EEPROMs
            \draw (6, -1.4) node[twoportshape, t={EEPROM}, circuitikz/bipoles/twoport/width=1.8, scale=0.5] (eeprom0) {};
            \draw (6, -3.9) node[twoportshape, t={EEPROM}, circuitikz/bipoles/twoport/width=1.8, scale=0.5] (eeprom1) {};

            % Repeaters for DDS0 sync clock & DDS sync output from sync buffer
            \draw (3.5, -3.85) node[twoportshape, t={Repeaters}, circuitikz/bipoles/twoport/width=1.2, scale=0.5] (rep) {};

            % Connect DDS0 to repeaters
            \draw [-latexslim] (sig0.east) -- ++ (0.3, 0) -- ++ (0, -1.55) -- (3.35, -3.3) -- ++ (0, -0.3);

            % Connect sync_buf to repeaters
            \draw [-latexslim] (sync_buf.south) -- ++ (0, -0.3) -- ++ (0.15, 0) -- ++ (0, -0.55);

            % EEMs
            \draw (8, -0.9) node[twoportshape, t={EEM Port 0}, circuitikz/bipoles/twoport/width=3.2, scale=0.5, rotate=-90] (eem0) {};
            \draw (8, -3.4) node[twoportshape, t={EEM Port 1}, circuitikz/bipoles/twoport/width=3.2, scale=0.5, rotate=-90] (eem1) {};

            % Connect LVDS and EEM
            \draw [latexslim-latexslim] (lvds0.east) -- (7.75, 0);
            \draw [latexslim-latexslim] (lvds1.east) -- (7.75, -0.7);
            \draw [latexslim-latexslim] (lvds2.east) -- (7.75, -2.5);
            \draw [latexslim-latexslim] (lvds3.east) -- (7.75, -3.2);

            % Connect EEPROM to EEM
            \draw [latexslim-latexslim] (eeprom0.east) -- (7.75, -1.4);
            \draw [latexslim-latexslim] (eeprom1.east) -- (7.75, -3.9);

            % Connect EEM0 to sync_buf
            \draw [latexslim-] (3.65, -2.25) -- (3.65, -1.85) -- (7.75, -1.85);

            % Connect repeaters output to EEM1
            \draw [-latexslim] (rep.south) -- (3.5, -4.35) -- (7.75, -4.35);

            % Synchronization ICs encased in another dotted area
            \node[draw, dotted, thick, rounded corners, inner xsep=0.7em, inner ysep=0.4em, fit=(rep.south west)(sync_buf.north east)] (sync_path) {};
            \node[fill=white, rotate=-90, scale=0.5] at (sync_path.east) {AD9910 Only};

        \end{scope}

    \end{circuitikz}
    }

    \caption{Simplified Block Diagram}
\end{figure}

\begin{figure}[h]
    \centering
    \scalebox{0.88}{
    \begin{circuitikz}[european, scale=0.95, every label/.append style={align=center}]

        \begin{scope}[]
            % RF switches {0, 1, 2, 3} for SMA {0, 1, 2, 3}
            \draw (1.4, 0) node[twoportshape, t={RF Switch}, circuitikz/bipoles/twoport/width=1.5, scale=0.6] (sw) {};

            % Amplifiers {0, 1, 2, 3} for RF switches {0, 1, 2, 3}
            \draw (3, 0) node[buffer, circuitikz/bipoles/twoport/width=1.2, scale=-0.5] (amp) {};

            % Attenuators {0, 1, 2, 3} for amplifiers {0, 1, 2, 3}
            \draw (4.6, 0) node[twoportshape, t=\fourcm{Digital}{Attenuator}, circuitikz/bipoles/twoport/width=2, scale=0.6, rotate=-90] (att) {};

            % DDS {0, 1, 2, 3} for attenuators {0, 1, 2, 3}
            \draw (6.6, 0) node[twoportshape, t={DDS}, circuitikz/bipoles/twoport/width=1.2, scale=0.7] (dds) {};

            % Connect main signal path
            \draw [-latexslim] (dds.west) -- (att.north);
            \draw [-latexslim] (att.south) -- (amp.west);
            \draw [-latexslim] (amp.east) -- (sw.east);

            % Connect abstract DDS clock input
            \node [label=above:\tiny{CLK Buffers}] at (8, -0.2) {};
            \draw [latexslim-] (dds.east) -- (8, 0);

            % Insert CPLD signal to relevant components
            \node [label=above:\tiny{CPLD}] at (8, 1.1) {};
            \draw [-] (1.4, 1.3) -- (8, 1.3);
            \draw [-latexslim] (1.4, 1.3) -- (sw.north);
            \draw [-latexslim] (4.6, 1.3) -- (att.west);
            \draw [-latexslim] (6.6, 1.3) -- (dds.north);

            % Connect sync_buf signal to DDS
            \draw [latexslim-] (6.9, -1.35) -- (6.9, -0.35);
            \draw [-latexslim] (6.3, -1.35) -- (6.3, -0.35);
            \node [label=below:\tiny{Sync Buffer /}] at (6.6, -1.15) {};
            \node [label=below:\tiny{Repeaters}] at (6.6, -1.4) {};
            \node [label={[rotate=-90]above:\tiny{DDS 0}}] at (6.8, -0.9) {};
            \node [label={[rotate=-90]above:\tiny{Only}}] at (6.55, -0.9) {};

        \end{scope}

    \end{circuitikz}
    }

    \caption{Simplified DDS Signal Path}
\end{figure}

\begin{figure}[hbt!]
    \centering
    \includegraphics[height=2.2in]{Urukul_FP.jpg}
    \includegraphics[height=2.2in]{photo4410.jpg}
    \caption{Urukul card and front panel}
\end{figure}

% For wide tables, a single column layout is better. It can be switched
% page-by-page.
\onecolumn

\sourcesection{4410/4412 DDS Urukul}{https://github.com/sinara-hw/Urukul/}

\section{Electrical Specifications}

Specifications of parameters are based on the datasheets of the DDS IC
(AD9910\footnote{\label{ad9910}\url{https://www.analog.com/media/en/technical-documentation/data-sheets/AD9910.pdf}},
AD9912\footnote{\label{ad9912}\url{https://www.analog.com/media/en/technical-documentation/data-sheets/AD9912.pdf}}),
clock buffer IC (Si53312\footnote{\label{clock_buffer}\url{https://www.skyworksinc.com/-/media/SkyWorks/SL/documents/public/data-sheets/Si5331x_datasheet.pdf}}),
digital attenuator IC (HMC542BLP4E\footnote{\label{attenuator}\url{https://www.analog.com/media/en/technical-documentation/data-sheets/hmc542b.pdf}}), Sinara project information\footnote{\label{urukul_wiki}\url{https://github.com/sinara-hw/Urukul/wiki\#details-specification-and-typical-performance-data}}
and corresponding test results\footnote{\label{sinara354}\url{https://github.com/sinara-hw/sinara/issues/354\#issuecomment-352859041}}.
\begin{table}[h]
\centering
\begin{threeparttable}
\caption{Recommended Operating Conditions}
\begin{tabularx}{0.9\textwidth}{l | c c c | c | X}
    \thickhline
    \textbf{Parameter} & \textbf{Min.} & \textbf{Typ.} & \textbf{Max.} &
    \textbf{Unit} & \textbf{Conditions} \\
    \hline
    Clock input & & & & &\\
    \hspace{3mm} Input frequency\repeatfootnote{ad9910}\textsuperscript{,}\repeatfootnote{ad9912} & 10 &  &  1000 & MHz & PLL disabled \\
    & 3.2 &  &  60 & MHz & AD9910, PLL enabled, no clock division \\
    & 12.8 &  &  240 & MHz & AD9910, PLL enabled, 4x clock division \\
    & 11 &  &  200 & MHz & AD9912, PLL enabled, no clock division \\
    & 44 &  &  800 & MHz & AD9912, PLL enabled, 4x clock division \\
    \hspace{3mm} Nominal input power\repeatfootnote{clock_buffer} & & 10 & & dBm & \\
    \thickhline
\end{tabularx}
\end{threeparttable}
\end{table}

\begin{table}[h]
\centering
\begin{threeparttable}
\caption{RF Output Specifications}
\begin{tabularx}{0.9\textwidth}{l | c c c | c | X}
    \thickhline
    \textbf{Parameter} & \textbf{Min.} & \textbf{Typ.} & \textbf{Max.} &
    \textbf{Unit} & \textbf{Conditions} \\
    \hline
    Low frequency power\repeatfootnote{sinara354} & & & -20 & dBm & 100 kHz output \\
    & & & 10 & dBm & 1 MHz output \\
    \hline
    Frequency\repeatfootnote{urukul_wiki} & 1 &  & 400 & MHz & \\
    \hline
    Digital attenuation\repeatfootnote{attenuator} & -31.5 & & 0 & dB & \\
    \hline
    Resolution & & & & & \\
    \hspace{3mm} Frequency\repeatfootnote{ad9910}\textsuperscript{,}\repeatfootnote{urukul_wiki} & & 0.25 & & Hz & AD9910 \\
     & & 8 & & $\mu$Hz & AD9912 \\
    \hspace{3mm} Phase offset\repeatfootnote{ad9910}\textsuperscript{,}\repeatfootnote{ad9912} & & 16/14 & & bits & AD9910/AD9912 respectively \\
    \hspace{3mm} Digital amplitude\repeatfootnote{ad9910} & & 14 & & bits & AD9910 \\
    \hspace{3mm} DAC full scale current\repeatfootnote{ad9910}\textsuperscript{,}\repeatfootnote{ad9912} & & 8/10 & & bits & AD9910/AD9912 respectively \\
    \hspace{3mm} Temporal (I/O Update)\repeatfootnote{urukul_wiki} & & 4 & & ns & \\
    \hspace{3mm} Digital attenuation\repeatfootnote{attenuator} & & 0.5 & & dB & \\
    \thickhline
\end{tabularx}
\end{threeparttable}
\end{table}

The tabulated performance characteristics are produced using the following setup unless otherwise noted:
\begin{itemize}
    \item 100 MHz input clock into SMA, 10 dBm
    \item Input clock divided by 4
    \item PLL with x40 multiplier
    \item Output frequency at 80 MHz or 81 MHz
\end{itemize}

\begin{table}[h]
\begin{threeparttable}
\caption{Electrical Characteristics}
\begin{tabularx}{\textwidth}{l | c | c c c | c | X}
    \thickhline
    \textbf{Parameter} & \textbf{Symbol} & \textbf{Min.} & \textbf{Typ.} & \textbf{Max.} &
    \textbf{Unit} & \textbf{Conditions} \\
    \hline
    Digital attenuator glitch duration\repeatfootnote{sinara354} & $t_s$ & & 100 & & ns & \\
    \hline
    RF switch\repeatfootnote{sinara354} & & & & & &\\
    \hspace{3mm} Rise to 90\% & $t_{on}$ & & 100 & & ns & \\
    \hspace{3mm} Isolation & & & 70 & & dB & \\
    \hspace{3mm} Turn-on chirp & $\gamma$ & & & 0.1 & deg/s & Excluding the first $\mu$s\\
    \hline
    Crosstalk\repeatfootnote{sinara354} & & & -84 & & dB & Victim RF switch opened \\
    & & & -110 & & dB & Victim RF switch closed \\
    \hline
    Cross-channel-intermodulation\repeatfootnote{sinara354} & & & -90 & & dB & \\
    \hline
    Phase noise\repeatfootnote{sinara354} & $\mathcal{L}(f)$ & & -85 & & dBc/Hz & 0.1 Hz \\
    & & & -95 & & dBc/Hz & 1 Hz \\
    & & & -107 & & dBc/Hz & 10 Hz \\
    & & & -116 & & dBc/Hz & 100 Hz \\
    & & & -126 & & dBc/Hz & 1 kHz \\
    & & & -133 & & dBc/Hz & 10 kHz \\
    & & & -135 & & dBc/Hz & 100 kHz \\
    & & & -128 & & dBc/Hz & 1 MHz \\
    & & & -149 & & dBc/Hz & 10 MHz \\
    \hline
    Second-order harmonics\repeatfootnote{sinara354} & & & -40 & & dB & 6 dBm output \\
    & & & -34 & & dB & 10.5 dBm output \\
    \hline
    Third-order harmonics\repeatfootnote{sinara354} & & & -54 & & dB & 6 dBm output \\
    & & & -28 & & dB & 10.5 dBm output \\
    \hline
    Power consumption (AD9910)\repeatfootnote{urukul_wiki} & $P$ & & 7 & & W & 4x 400 MHz, 10.5 dBm, 52\degree C\\
    Power consumption (AD9912)\repeatfootnote{urukul_wiki} & $P$ & & 6.5 & & W & 4x 400 MHz, 10.5 dBm, 52\degree C\\
    \thickhline
\end{tabularx}
\end{threeparttable}
\end{table}

\newpage

Harmonic content of the DDS signals from 4410 DDS Urukul is tabulated below\footnote{\label{urukul29}\url{https://github.com/sinara-hw/Urukul/issues/29}}. An external 125 MHz clock signal was supplied.

\newcommand{\ts}{\textsuperscript}
\newcolumntype{Y}{>{\centering\arraybackslash}X}

\begin{table}[h]
\begin{threeparttable}
\caption{Harmonic content with 0.0 dB digital attenuation}
\begin{tabularx}{\textwidth}{| c | Y | Y | Y | Y | Y | Y | Y | Y | Y |}
    \thickhline
    \multirow{2}{*}{\textbf{Frequency (MHz)}} &
    \multicolumn{9}{c|}{\textbf{Output power (dBm) of the n\ts{th}-order harmonic}}\\
    \cline{2-10} & 1\ts{st} & 2\ts{nd} & 3\ts{rd} & 4\ts{th} & 5\ts{th} & 6\ts{th} &
    7\ts{th} & 8\ts{th} & 9\ts{th} \\
    \hline
    0.1 & -21.14 & -59.03 & -54.93 & -93.07 & -73.38 & -94.07 & -84.78 & -91.77 & -96.61 \\
    \hline
    0.5 & 4.51 & -15.45 & -11.61 & -25.02 & -24.35 & -51.70 & -35.14 & -34.46 & -37.85 \\
    \hline
    1 & 7.67 & -16.80 & -12.32 & -18.27 & -29.25 & -30.87 & -34.51 & -39.28 & -39.84 \\
    \hline
    10 & 10.67 & -12.69 & -13.94 & -26.12 & -27.76 & -36.11 & -55.32 & -43.85 & -42.65 \\
    \hline
    20 & 10.86 & -24.90 & -13.65 & -22.87 & -28.67 & -47.68 & -35.85 & -35.45 & -38.48 \\
    \hline
    50 & 10.74 & -14.18 & -15.01 & -27.57 & -29.01 & -38.05 & -51.52 & -44.53 & -42.71 \\
    \hline
    100 & 9.70 & -33.59 & -16.72 & -34.36 & -26.81 & -40.14 & -41.07 & -43.88 & -56.89 \\
    \hline
    200 & 8.97 & -22.22 & -16.23 & -24.89 & -30.49 & -37.97 & -37.79 & -38.80 & -40.14 \\
    \hline
    300 & 8.27 & -19.17 & -19.51 & -29.80 & -34.75 & -38.90 & -51.92 & -53.38 & -57.95 \\
    \hline
    400 & 7.68 & -17.82 & -21.60 & -33.04 & -37.80 & -50.37 & -57.45 & -59.80 & -64.68 \\
    \hline
    500 & -1.80 & -41.57 & -51.71 & -72.36 & -89.35 & -91.63 & -93.15 & -84.54 & -107.57 \\
    \thickhline
\end{tabularx}
\end{threeparttable}
\end{table}

\begin{table}[hbt!]
\begin{threeparttable}
\caption{Harmonic content with 10.0 dB digital attenuation}
\begin{tabularx}{\textwidth}{| c | Y | Y | Y | Y | Y | Y | Y | Y | Y |}
    \thickhline
    \multirow{2}{*}{\textbf{Frequency (MHz)}} &
    \multicolumn{9}{c|}{\textbf{Output power (dBm) of the n\ts{th}-order harmonic}}\\
    \cline{2-10} & 1\ts{st} & 2\ts{nd} & 3\ts{rd} & 4\ts{th} & 5\ts{th} & 6\ts{th} &
    7\ts{th} & 8\ts{th} & 9\ts{th} \\
    \hline
    0.1 & -27.06 & -81.35 & -62.09 & -97.37 & -84.11 & -103.78 & -91.37 & -100.48 & -104.22 \\
    \hline
    0.5 & -3.2 & -37.82 & -52.21 & -66.76 & -77.86 & -85.92 & -86.37 & -97.59 & -120.76 \\
    \hline
    1 & -0.43 & -34.47 & -47.80 & -75.28 & -86.45 & -101.91 & -93.22 & -96.14 & -106.71 \\
    \hline
    10 & 1.95 & -31.04 & -28.23 & -51.76 & -57.29 & -76.26 & -78.15 & -83.85 & -80.20 \\
    \hline
    20 & 2.10 & -33.05 & -28.30 & -54.50 & -52.31 & -72.39 & -70.96 & -82.98 & -82.58 \\
    \hline
    50 & 1.89 & -33.24 & -28.50 & -52.67 & -48.35 & -74.77 & -77.26 & -79.33 & -73.58 \\
    \hline
    100 & 0.80 & -38.51 & -63.22 & -61.73 & -71.97 & -97.45 & -97.67 & -107.40 & -93.03 \\
    \hline
    200 & 0.05 & -38.25 & -42.16 & -63.01 & -84.55 & -82.66 & -108.85 & -116.62 & -99.45 \\
    \hline
    300 & -0.51 & -35.91 & -48.83 & -82.43 & -100.53 & -111.79 & -118.62 & -120.05 & -97.72 \\
    \hline
    400 & -1.20 & -38.37 & -49.77 & -89.45 & -74.66 & -108.12 & -116.75 & -114.08 & -102.29 \\
    \hline
    500 & -11.20 & -61.47 & -77.59 & -74.73 & -100.23 & -93.12 & -99.83 & -86.71 & -112.63 \\
    \thickhline
\end{tabularx}
\end{threeparttable}
\end{table}

\newpage

\begin{table}[h]
\begin{threeparttable}
\caption{Harmonic content with 20.0 dB digital attenuation}
\begin{tabularx}{\textwidth}{| c | Y | Y | Y | Y | Y | Y | Y | Y | Y |}
    \thickhline
    \multirow{2}{*}{\textbf{Frequency (MHz)}} &
    \multicolumn{9}{c|}{\textbf{Output power (dBm) of the n\ts{th}-order harmonic}}\\
    \cline{2-10} & 1\ts{st} & 2\ts{nd} & 3\ts{rd} & 4\ts{th} & 5\ts{th} & 6\ts{th} &
    7\ts{th} & 8\ts{th} & 9\ts{th} \\
    \hline
    0.1 & -31.06 & -82.29 & -68.34 & -109.04 & -92.48 & -111.23 & -99.94 & -109.85 & -112.36 \\
    \hline
    0.5 & -11.99 & -56.69 & -71.73 & -95.76 & -101.86 & -114.37 & -102.81 & -106.94 & -116.72 \\
    \hline
    1 & -9.94 & -54.54 & -56.49 & -89.12 & -105.94 & -110.93 & -102.79 & -107.01 & -117.29 \\
    \hline
    10 & -7.89 & -50.19 & -57.35 & -91.36 & -97.88 & -107.95 & -103.53 & -96.04 & -108.26 \\
    \hline
    20 & -7.79 & -52.72 & -58.03 & -90.75 & -99.82 & -102.07 & -101.55 & -104.73 & -103.31 \\
    \hline
    50 & -7.96 & -52.36 & -59.26 & -84.44 & -87.55 & -86.88 & -97.76 & -92.61 & -83.19 \\
    \hline
    100 & -9.04 & -57.40 & -61.76 & -78.50 & -91.80 & -117.64 & -107.40 & -112.64 & -102.07 \\
    \hline
    200 & -9.73 & -57.39 & -72.31 & -72.66 & -93.26 & -95.95 & -125.22 & -122.35 & -130.24 \\
    \hline
    300 & -10.27 & -58.65 & -74.60 & -109.24 & -107.74 & -115.75 & -125.36 & -124.54 & -98.86 \\
    \hline
    400 & -10.94 & -59.62 & -79.36 & -98.48 & -74.72 & -111.95 & -119.18 & -114.63 & -104.34 \\
    \hline
    500 & -21.00 & -78.52 & -99.07 & -74.91 & -99.55 & -92.91 & -103.02 & -87.33 & -114.87 \\
    \thickhline
\end{tabularx}
\end{threeparttable}
\end{table}

\begin{table}[hbt!]
\begin{threeparttable}
\caption{Harmonic content with 31.5 dB digital attenuation}
\begin{tabularx}{\textwidth}{| c | Y | Y | Y | Y | Y | Y | Y | Y | Y |}
    \thickhline
    \multirow{2}{*}{\textbf{Frequency (MHz)}} &
    \multicolumn{9}{c|}{\textbf{Output power (dBm) of the n\ts{th}-order harmonic}}\\
    \cline{2-10} & 1\ts{st} & 2\ts{nd} & 3\ts{rd} & 4\ts{th} & 5\ts{th} & 6\ts{th} &
    7\ts{th} & 8\ts{th} & 9\ts{th} \\
    \hline
    0.1 & -37.89 & -85.04 & -77.41 & -122.04 & -114.29 & -115.58 & -110.65 & -120.06 & -123.70 \\
    \hline
    0.5 & -22.38 & -71.24 & -89.84 & -107.81 & -108.76 & -127.83 & -114.12 & -118.34 & -127.07 \\
    \hline
    1 & -21.01 & -72.10 & -90.08 & -111.97 & -111.30 & -127.43 & -114.38 & -118.07 & -128.06 \\
    \hline
    10 & -19.22 & -72.13 & -90.74 & -110.14 & -105.28 & -114.04 & -113.51 & -94.85 & -116.15 \\
    \hline
    20 & -19.28 & -75.95 & -94.72 & -91.71 & -107.55 & -112.85 & -112.24 & -116.33 & -114.02 \\
    \hline
    50 & -19.27 & -74.93 & -92.21 & -95.77 & -101.06 & -97.92 & -108.30 & -103.60 & -93.96 \\
    \hline
    100 & -20.27 & -79.05 & -87.48 & -89.73 & -104.00 & -117.98 & -112.12 & -110.51 & -105.80 \\
    \hline
    200 & -21.19 & -78.33 & -106.81 & -82.70 & -92.31 & -109.93 & -133.86 & -120.94 & -102.95 \\
    \hline
    300 & -21.58 & -80.96 & -112.44 & -110.40 & -108.11 & -115.68 & -122.51 & -125.25 & -99.63 \\
    \hline
    400 & -22.44 & -82.73 & -105.55 & -98.03 & -74.84 & -113.93 & -119.41 & -114.93 & -104.55 \\
    \hline
    500 & -31.73 & -93.37 & -99.74 & -75.03 & -99.27 & -92.84 & -104.14 & -87.46 & -116.22 \\
    \thickhline
\end{tabularx}
\end{threeparttable}
\end{table}

\newpage

The RMS voltage of a 4410 DDS Urukul channel at different amplitude scale factors is measured below. The DDS channel is directly connected to an oscilloscope with a 50\textOmega~termination. The reported values are obtained from the oscilloscope.

\begin{multicols}{2}
\begin{figure}[H]
    \begin{tikzpicture}
        \begin{axis}[
            xlabel={AD9910 Amplitude Scale Factor},
            ylabel={DDS RMS Voltage ($V_{rms}$)},
            xmin=0, xmax=1,
            ymin=0, ymax=1,
            xtick={0, 0.2, 0.4, 0.6, 0.8, 1},
            ytick={0, 0.2, 0.4, 0.6, 0.8, 1},
            legend pos=north west,
            ymajorgrids=true,
            grid style=dashed,
        ]

        \addplot[
            color=black,
            mark=square,
            samples=11
        ] coordinates {
            (0.0, 0) (0.1, 0.087924) (0.2, 0.176157) (0.3, 0.262437) (0.4, 0.345833) (0.5, 0.429203)
            (0.6, 0.512235) (0.7, 0.59130) (0.8, 0.66877) (0.9, 0.73344) (1.0, 0.78761)
        };

        \addplot[
            color=blue,
            mark=square,
            samples=11
        ] coordinates {
            (0.0, 0) (0.1, 0.089807) (0.2, 0.179723) (0.3, 0.268852) (0.4, 0.354310) (0.5, 0.441055)
            (0.6, 0.526386) (0.7, 0.61233) (0.8, 0.69044) (0.9, 0.75856) (1.0, 0.81703)
        };

        \addplot[
            color=green,
            mark=square,
            samples=11
        ] coordinates {
            (0.0, 0) (0.1, 0.093101) (0.2, 0.186762) (0.3, 0.277704) (0.4, 0.369172) (0.5, 0.459391)
            (0.6, 0.548191) (0.7, 0.63607) (0.8, 0.71469) (0.9, 0.78221) (1.0, 0.84139)
        };

        \addplot[
            color=red,
            mark=square,
            samples=11
        ] coordinates {
            (0, 0) (0.1, 0.092502) (0.2, 0.184728) (0.3, 0.276224) (0.4, 0.366914) (0.5, 0.457255)
            (0.6, 0.544924) (0.7, 0.62991) (0.8, 0.70582) (0.9, 0.77104) (1.0, 0.82737)
        };
        \legend{200 MHz, 100 MHz, 50 MHz, 10 MHz}

        \end{axis}
    \end{tikzpicture}
\caption{RMS voltage, 0dB attenuation}
\end{figure}

\columnbreak

\begin{figure}[H]
\begin{tikzpicture}
    \begin{axis}[
        xlabel={AD9910 Amplitude Scale Factor},
        ylabel={DDS RMS Voltage ($mV_{rms}$)},
        xmin=0, xmax=1,
        ymin=0, ymax=200,
        xtick={0, 0.2, 0.4, 0.6, 0.8, 1},
        ytick={0, 40, 80, 120, 160, 200},
        legend pos=north west,
        ymajorgrids=true,
        grid style=dashed,
    ]

    \addplot[
        color=black,
        mark=square,
        samples=11
    ] coordinates {
        (0, 0) (0.1, 16.1805) (0.2, 32.1530) (0.3, 48.2039) (0.4, 64.172) (0.5, 80.452)
        (0.6, 96.405) (0.7, 112.427) (0.8, 128.776) (0.9, 144.967) (1.0, 161.148)
    };

    \addplot[
        color=blue,
        mark=square,
        samples=11
    ] coordinates {
        (0, 0) (0.1, 16.6691) (0.2, 33.3762) (0.3, 49.8844) (0.4, 67.055) (0.5, 83.652)
        (0.6, 99.970) (0.7, 116.906) (0.8, 133.368) (0.9, 150.839) (1.0, 167.033)
    };

    \addplot[
        color=green,
        mark=square,
        samples=11
    ] coordinates {
        (0, 0) (0.1, 17.0562) (0.2, 34.0713) (0.3, 51.0456) (0.4, 68.241) (0.5, 85.241)
        (0.6, 102.328) (0.7, 119.279) (0.8, 136.584) (0.9, 153.737) (1.0, 170.829)
    };

    \addplot[
        color=red,
        mark=square,
        samples=11
    ] coordinates {
        (0, 0) (0.1, 16.8030) (0.2, 33.6407) (0.3, 50.4039) (0.4, 67.348) (0.5, 84.127)
        (0.6, 100.852) (0.7, 117.618) (0.8, 134.415) (0.9, 151.267) (1.0, 168.160)
    };
    \legend{200 MHz, 100 MHz, 50 MHz, 10 MHz}

    \end{axis}
\end{tikzpicture}
\caption{RMS voltage, 15dB attenuation}
\end{figure}

\end{multicols}

The ideal RMS voltage is described by the linear function $V_\mathrm{rms,ideal}(\mathrm{ASF})=\frac{V_\mathrm{rms}(0.1)}{0.1}*\mathrm{ASF}$.
The measured RMS voltage divided by the full scale ideal RMS voltage (i.e. $V_\mathrm{rms,ideal}(1)$) is shown below.

\begin{figure}[H]
    \centering
    \begin{tikzpicture}
        \begin{axis}[
            xlabel={AD9910 Amplitude Scale Factor},
            ylabel={Scaled RMS Voltage},
            xmin=0, xmax=1,
            ymin=0, ymax=1.1,
            xtick={0, 0.2, 0.4, 0.6, 0.8, 1},
            ytick={0, 0.2, 0.4, 0.6, 0.8, 1},
            legend pos=north west,
            ymajorgrids=true,
            grid style=dashed,
            width=0.7\textwidth
        ]

        \addplot[
            color=black,
            samples=2,
            ultra thick,
            dotted
        ] {x};

        \addplot[
            color=blue,
            mark=square,
            samples=11,
            y filter/.expression={y/0.089807 * 0.1}
        ] coordinates {
            (0.0, 0) (0.1, 0.089807) (0.2, 0.179723) (0.3, 0.268852) (0.4, 0.354310) (0.5, 0.441055)
            (0.6, 0.526386) (0.7, 0.61233) (0.8, 0.69044) (0.9, 0.75856) (1.0, 0.81703)
        };

        \addplot[
            color=orange,
            mark=square,
            samples=11,
            y filter/.expression={y/50.0729 * 0.1}
        ] coordinates {
            (0, 0) (0.1, 50.0729) (0.2, 100.309) (0.3, 150.996) (0.4, 200.905) (0.5, 250.004)
            (0.6, 297.000) (0.7, 345.980) (0.8, 394.391) (0.9, 442.869) (1.0, 490.651)
        };

        \addplot[
            color=green,
            mark=square,
            samples=11,
            y filter/.expression={y/28.4696 * 0.1}
        ] coordinates {
            (0, 0) (0.1, 28.4696) (0.2, 57.143) (0.3, 85.776) (0.4, 114.694) (0.5, 143.302)
            (0.6, 171.911) (0.7, 200.098) (0.8, 227.816) (0.9, 256.321) (1.0, 281.930)
        };

        \addplot[
            color=red,
            mark=square,
            samples=11,
            y filter/.expression={y/16.6691 * 0.1}
        ] coordinates {
            (0, 0) (0.1, 16.6691) (0.2, 33.3762) (0.3, 49.8844) (0.4, 67.055) (0.5, 83.652)
            (0.6, 99.970) (0.7, 116.906) (0.8, 133.368) (0.9, 150.839) (1.0, 167.033)
        };
        \legend{Ideal response, 0dB attenuation, 5dB attenuation, 10dB attenuation, 15dB attenuation}

        \end{axis}
    \end{tikzpicture}
\caption{RMS voltage scaled by ideal voltage at ASF=1, 100 MHz}
\end{figure}

\newpage

\begin{multicols}{2}

\begin{figure}[H]
    \includegraphics[width=3.3in]{urukul_xo_phase_noise.jpg}
    \caption{Phase noise of Urukul clocked by\\internal oscillator}
\end{figure}

\begin{figure}[H]
    \includegraphics[width=3.3in]{urukul_clock_phase_noise.jpg}
    \caption{Phase noise of 200 MHz DDS Output}
\end{figure}

\begin{figure}[H]
    \includegraphics[width=3.3in]{urukul_harmonics.png}
    \caption[]{Harmonic content of 200 MHz DDS Output\footnotemark}
\end{figure}

\begin{figure}[H]
    \includegraphics[width=3.3in]{urukul_6dbm_harmonics.png}
    \caption{Harmonic content of 80 MHz DDS Output (6 dBm)\repeatfootnote{sinara354}}
\end{figure}

\begin{figure}[H]
    \includegraphics[width=3.3in]{urukul_10dbm_harmonics.png}
    \caption{Harmonic content of 80 MHz DDS Output (10 dBm)\repeatfootnote{sinara354}}
\end{figure}

\begin{figure}[H]
    \includegraphics[width=3.3in]{rf_transient.jpg}
    \caption{RF switch turn on transient\repeatfootnote{sinara354}}
\end{figure}

\begin{figure}[H]
    \includegraphics[width=3.3in]{nyquist_rejection_400mhz.png}
    \caption{Nyquist rejection 400 MHz to 600 MHz\repeatfootnote{sinara354}}
\end{figure}

\end{multicols}

\footnotetext{\label{urukul64}\url{https://github.com/sinara-hw/Urukul/issues/64}}

\begin{figure}[H]
    \centering
    \includegraphics[width=3.3in]{nyquist_rejection_450mhz.png}
    \caption{Nyquist rejection 450 MHz to 550 MHz\repeatfootnote{sinara354}}
\end{figure}

\begin{figure}[H]
    \centering
    \includegraphics[width=3.3in]{att_glitch_bitflip.png}
    \caption{Attenuator step from 20 to 60 digital\\(16+4dB switch glitch)\repeatfootnote{sinara354}}
\end{figure}

\begin{figure}[H]
    \centering
    \includegraphics[width=3.3in]{att_glitch_carry.png}
    \caption{Attenuator step from 31 to 32 digital\\(major carry glitch)\repeatfootnote{sinara354}}
\end{figure}

\newpage
\section{Configuring Operation Mode}
Mode of operation is specified by a DIP switch. The DIP switch can be found at the top right corner of the card. The following table summarizes the required setting for each mode.
\ding{51} indicates ON, while \ding{53} indicates OFF.

\begin{multicols}{2}

\begin{center}
\captionof{table}{DIP switch configurations}
    \begin{tabular}{|l|cccc|}
    \hline
    \multicolumn{1}{|c|}{\multirow{2}{*}{Mode}} & \multicolumn{4}{c|}{DIP Switch}                                            \\ \cline{2-5}
    \multicolumn{1}{|c|}{}                      & \multicolumn{1}{c|}{1} & \multicolumn{1}{c|}{2} & \multicolumn{1}{c|}{3} & 4 \\ \hline
    Default                                     & \multicolumn{1}{c|}{\ding{53}}  & \multicolumn{1}{c|}{\ding{53}}  & \multicolumn{1}{c|}{\ding{53}}  & \ding{53}  \\ \hline
    SU-Servo                                    & \multicolumn{1}{c|}{\ding{51}}  & \multicolumn{1}{c|}{\ding{51}}  & \multicolumn{1}{c|}{\ding{53}}  & \ding{53}  \\ \hline
    \end{tabular}
\end{center}

\columnbreak

\begin{center}
    \centering
    \includegraphics[height=1.5in]{urukul_dip_switch.jpg}
    \captionof{figure}{Position of DIP switch}
\end{center}

\end{multicols}

\section{Urukul Single-/Double-EEM Modes}

4410/4412 DDS Urukul cards can operate with either a single or double EEM connections. When only EEM0 is connected, the card will act in single-EEM mode; when both EEM0 and EEM1 are connected, the card will act in double-EEM mode.  2-EEM mode when both EEM0 \& EEM1 are connected. Double-EEM mode provides these additional features in comparison to single-EEM mode:
\begin{itemize}
    \item \textbf{1 ns temporal resolution RF switches} \\
    Without EEM1, the only way to access the switches is through the CPLD, using SPI. \\
    With EEM1, RF switches can be controlled as a TTL output through the LVDS transceiver. 1 ns temporal resolution can then be achieved using the ARTIQ RTIO system.

    \item \textbf{SU-Servo (4410 DDS Urukul feature)} \\
    SU-Servo requires both EEM0 \& EEM1 to allow the control of multiple DDS channels simultaneously using the QSPI interface.

\end{itemize}

\newpage

\codesection{4410/4412 DDS Urukul}

\subsection{10 MHz sinusoidal wave}
Generates a 10MHz sinusoid from RF0 with full scale amplitude, attenuated by 6 dB. Both the CPLD and the DDS channels should be initialized. By default, AD9910 single-tone profiles are programmed to profile 7.

\inputcolorboxminted{firstline=11,lastline=18}{examples/dds.py}

If the synchronization feature of AD9910 is enabled, RF signal across different channels of the same Urukul can be synchronized. For example, phase-coherent RF signal can be produced on both channel 0 and channel 1 after configuring an appropriate phase mode.

\inputcolorboxminted{firstline=28,lastline=43}{examples/dds.py}

Note that the phase difference between the 2 channels might not be exactly 0.25 turns, but it is a constant. It can be negated by adjusting the \texttt{phase} parameter.

\newpage
\subsection{Periodic RF pulse (AD9910 Only)}
This example demonstrates that the RF signal can be modulated by amplitude using the RAM modulation feature of the AD9910. By default, RAM profiles are programmed to profile 0.

\inputcolorboxminted{firstline=53,lastline=91}{examples/dds.py}

The generated RF output of the above example consists of the following features in sequence:
\begin{enumerate}
    \item A 5 MHz RF pulse for 2 microseconds.
    \item No signal for 1 microseconds.
    \item A 5 MHz RF pulse for 1 microseconds.
    \item No signal for 3 microseconds.
    \item Go back to item 1.
\end{enumerate}
The expected waveform is plotted on the following figure. Note that phase of the RF pulses may drift gradually.
Urukul was operated with a 50$\Omega$ termination to produce the waveform.

\begin{tikzpicture}[
    declare function={
        func(\x)= (\x<0) * (0) +
            and(\x>=0, \x<2) * (0.42*cos(deg(10*pi*\x))) +
            and(\x>=2, \x<3) * (0) +
            and(\x>=3, \x<4) * (0.42*cos(deg(10*pi*\x))) +
            and(\x>=4, \x<7) * (0) +
            and(\x>=7, \x<7.5) * (0.42*cos(deg(10*pi*\x)));
    }
]
\begin{axis}[
    axis x line=middle, axis y line=middle,
        every axis x label/.style={
            at={(ticklabel* cs:1.05)},
            anchor=west,
        },
        every axis y label/.style={
            at={(ticklabel* cs:1.05)},
            anchor=south,
        },
    height=5cm,
    width=16cm,
    ymin=-0.5, ymax=0.5, ytick={-0.42,0.42}, ylabel=Voltage ($V$),
    xmin=-0.5, xmax=7.5, xtick={0,...,7}, xlabel=Time ($\mu s$),
]

\addplot[blue, samples=1000, domain=-0.5:7.5]{func(x)};
\end{axis}
\end{tikzpicture}

\subsection{Simple amplitude ramp (AD9910 only)}
An amplitude ramp of an RF signal can be generated by modifying the \texttt{self.amp} array in the previous example.

\inputcolorboxminted{firstline=95,lastline=98}{examples/dds.py}

The generated RF output has an incrementing amplitude scale factor (ASF), increasing by 0.1 at every microsecond. Once the ASF reaches 1.0, it drops back to 0.0 at the next microsecond. The expected waveform over 1 cycle is plotted on the following figure. Note that phase of the RF pulses may drift gradually.
Urukul was operated with a 50$\Omega$ termination to produce the waveform.

\begin{tikzpicture}[
    declare function={
        func(\x)= and(\x>=0, \x<1) * (0) +
            and(\x>=1, \x<2) * (0.05*cos(deg(10*pi*\x))) +
            and(\x>=2, \x<3) * (0.1*cos(deg(10*pi*\x))) +
            and(\x>=3, \x<4) * (0.15*cos(deg(10*pi*\x))) +
            and(\x>=4, \x<5) * (0.2*cos(deg(10*pi*\x))) +
            and(\x>=5, \x<6) * (0.25*cos(deg(10*pi*\x))) +
            and(\x>=6, \x<7) * (0.3*cos(deg(10*pi*\x))) +
            and(\x>=7, \x<8) * (0.35*cos(deg(10*pi*\x))) +
            and(\x>=8, \x<9) * (0.4*cos(deg(10*pi*\x))) +
            and(\x>=9, \x<10) * (0.45*cos(deg(10*pi*\x))) +
            and(\x>=10, \x<11) * (0.5*cos(deg(10*pi*\x)));
    }
]
\begin{axis}[
    axis x line=middle, axis y line=middle,
    every axis x label/.style={
        at={(ticklabel* cs:1.05)},
        anchor=west,
    },
    every axis y label/.style={
        at={(ticklabel* cs:1.05)},
        anchor=south,
    },
    minor tick num=4,
    grid=both,
    height=8cm,
    width=16cm,
    ymin=-0.7, ymax=0.7, ytick={-0.5,...,0,...,0.5}, ylabel=Voltage ($V$),
    xmin=0, xmax=11.5, xtick={0,...,11}, xlabel=Time ($\mu s$),
]

\addplot[blue, samples=1500, domain=0:11]{func(x)};
\end{axis}
\end{tikzpicture}

\newpage

\subsection{RAM synchronization (AD9910 only)}
Multiple RAM channels can also be synchronized. Similar to the 10 MHz single-tone RF signals, specify \texttt{phase} when calling \texttt{dds.set()} in \texttt{configure\char`_ram\char`_mode}. For example, set phase to 0 for the channels (\texttt{phase=0.0}):

\inputcolorboxminted{firstline=116,lastline=116}{examples/dds.py}

Then, replace the \texttt{run()} function with the following:

\inputcolorboxminted{firstline=122,lastline=134}{examples/dds.py}

Two phase-coherent RF signal with the same waveform as the previous figure (from either RAM examples) should be generated.

\subsection{Voltage-controlled DDS amplitude (SU-Servo only)}
The SU-Servo feature can be enabled by integrating the 4410 DDS Urukul with a 5108 Sampler. Amplitude of the DDS output can be controlled by the ADC input of the Sampler through PI control, characterised by the following transfer function:

\[H(s)=k_p+\frac{k_i}{s+\frac{k_i}{g}}\]

In the following example, the amplitude of DDS is proportional to the ADC input from Sampler.  First, initialize the RTIO, SU-Servo and its channel. Note that the programmable gain of the Sampler is $10^0=1$ and the input range is [-10V, 10V].

\inputcolorboxminted{firstline=10,lastline=17}{examples/suservo.py}

Next, setup the PI control as an IIR filter. It has -1 proportional gain $k_p$ and no integrator gain $k_i$.

\inputcolorboxminted{firstline=18,lastline=25}{examples/suservo.py}

Then, configure the DDS frequency to 10 MHz with 3V input offset.
When input voltage $\geq$ offset voltage, the DDS output amplitude is 0.

\inputcolorboxminted{firstline=26,lastline=30}{examples/suservo.py}

SU-Servo encodes the ADC voltage in a linear scale [-1, 1]. Therefore, 3V is converted to 0.3. Note that the ASF of all DDS channels are capped at 1.0 and the amplitude clips when ADC input $\leq -7V$ with the above IIR filter.

Finally, enable the SU-Servo channel with the IIR filter programmed beforehand:

\inputcolorboxminted{firstline=32,lastline=33}{examples/suservo.py}

A 10 MHz DDS signal is generated from the example above, with amplitude controllable by ADC. The RMS voltage of the DDS channel against the ADC voltage is plotted. The DDS channel is terminated with 50\textOmega.

\begin{center}
\begin{tikzpicture}[
    declare function={
        func(\x)= and(\x>=-10, \x<-7) * (160) +
            and(\x>=-7, \x<3) * (16*(3-x)) +
            and(\x>=3, \x<10) * (0);
    }
]
\begin{axis}[
    axis x line=middle, axis y line=middle,
    every axis x label/.style={
        at={(axis description cs:0.5,-0.1)},
        anchor=north,
    },
    every axis y label/.style={
        at={(ticklabel* cs:1.05)},
        anchor=south,
    },
    minor x tick num=3,
    grid=both,
    height=8cm,
    width=12cm,
    ymin=-5, ymax=180, ytick={0,16,...,160}, ylabel=DDS RMS Voltage ($mV_{rms}$),
    xmin=-10, xmax=10, xtick={-10,-8,...,10}, xlabel=Sampler Voltage ($V$),
]

\addplot[very thick, blue, samples=21, domain=-10:10]{func(x)};
\end{axis}
\end{tikzpicture}
\end{center}

DDS signal should be attenuated. High output power affects the linearity due to the 1 dB compression point of the amplifier at 13 dBm output power. 15 dB attenuation at the digital attenuator was applied in this example.

\ordersection{4410/4412 DDS Urukul}

\finalfootnote

\end{document}