fix: wrong R2? value given

Final.tex

@@ -2,6 +2,34 @@
 % \IEEEoverridecommandlockouts
 % The preceding line is only needed to identify funding in the first footnote. If that is unneeded, please comment it out.
 \usepackage{cite}
+\usepackage{xcolor}
+\definecolor{codegreen}{rgb}{0,0.6,0}
+\definecolor{codegray}{rgb}{0.5,0.5,0.5}
+\definecolor{codepurple}{rgb}{0.58,0,0.82}
+\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
+
+\usepackage{listings}
+\lstdefinestyle{mystyle}{
+  backgroundcolor=\color{backcolour},
+  commentstyle=\color{codegreen},
+  keywordstyle=\color{magenta},
+  numberstyle=\tiny\color{codegray},
+  stringstyle=\color{codepurple},
+  basicstyle=\ttfamily\footnotesize,
+  breakatwhitespace=false,
+  breaklines=true,
+  captionpos=b,
+  keepspaces=true,
+  numbers=left,
+  numbersep=5pt,
+  showspaces=false,
+  showstringspaces=false,
+  showtabs=false,
+  tabsize=2
+}
+
+\lstset{style=mystyle}
+
 \usepackage{amsmath,amssymb,amsfonts}
 \usepackage{algorithmic}
 \usepackage{graphicx}
@@ -10,7 +38,7 @@
 \usepackage{framed}
 \usepackage{longtable,booktabs,array}
 \usepackage{caption}
-\usepackage{xcolor}
+
 \usepackage{siunitx}
 \usepackage{circuitikz}
 \def\BibTeX{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em
@@ -22,7 +50,7 @@
 \author{\IEEEauthorblockN{Martin Kennedy}
 \IEEEauthorblockA{\textit{College of Engineering and Mathematical Sciences} \\
 \textit{University of Vermont}\\
-So. Burlington, Vermont, USA \\
+Burlington, Vermont, USA \\
 martin.kennedy@uvm.edu}
 }
 
@@ -54,7 +82,7 @@ the frequency response of the open-loop gain.
 
 One of the most well-known op-amps is the LM741. In no small part to
 demonstrate one weakness of the LM741, a cutoff frequency of
-$\SI{40}{kHz}$ is selected for the high-pass filter design. To compare,
+$\SI{400}{kHz}$ is selected for the high-pass filter design. To compare,
 three op-amps are selected beyond the LM741:
 
 \begin{enumerate}
@@ -67,15 +95,16 @@ three op-amps are selected beyond the LM741:
 \end{enumerate}
 
 To focus on the real-world impact of the variations in performance of
-these op-amps: imagine that the application for our high-pass filter
-is as a pre-amplifier for a hobbyist kit, to be sold in the United
-Kingdom, which can use the MSF signal ($\SI{60}{\kHz}$) \cite{b4} to
-tell the current time.
+these op-amps at higher frequencies: imagine that the application for
+our high-pass filter is as a pre-amplifier for a hobbyist AM receiver
+kit to receive emergency weather and traffic alerts in the Northeast
+US. These alerts are broadcast between $\SI{530}{\kHz}$ AM and
+$\SI{1650}{\kHz}$ \cite{b4}.
 
 \section{Design of a High-pass Active Filter}
 
 A design for a first-order inverting active high-pass filter with
-amplification is depicted below in Figure \ref{fig:hpf}.
+amplification is depicted in Figure \ref{fig:hpf}.
 
 \begin{figure}[h]
   \caption{A first-order high-pass filter}
@@ -110,27 +139,27 @@ which flows from $v_{in}$ into $v_n$ then flows from $v_n$ into
 $v_{out}$, the network of $R_1$ and $C_1$ into $R_2$ forms a voltage
 divider, and so
 
-\begin{equation}
+\begin{equation}\label{eqn:hpf_tf}
   \frac{v_{out}}{v_{in}} = - \frac{R_2}{R_1+Z_{C_1}}
 \end{equation}
 
-The high-pass filter design is a common one, with a well-known cutoff
+This high-pass filter design is a common one, with a well-known cutoff
 frequency $\omega_c = \frac{1}{R_1 C}$ and gain $K = \frac{R_2}{R_1}$
 \cite{b3}. To acquire a cutoff frequency of
-$\omega_c = \SI{40}{\kHz} \approx \SI{2.51E5}{}$ rad/s,
-$R_1 = \SI{100}{\ohm}$ and $C_1 = \SI{39}{\nano\farad}$ will
+$\omega_c = \SI{400}{\kHz} \approx \SI{2.51E6}{}$ rad/s,
+$R_1 = \SI{100}{\ohm}$ and $C_1 = \SI{3.9}{\nano\farad}$ will
 suffice. Only $R_2$ remains to be selected to determine the limit on
 gain; selecting $R_2 = \SI{100}{\kohm}$ yields
-$K = 1000 = \SI{30}{dB}$.
+$K = 1000 = \SI{60}{dB}$.
 
 \subsection{Toward a more perfect Model}
-A more accurate representation of the op-amp foregoes the
-assumption, oft made regarding op-amps wired in a feedback
-configuration, that $v_n = v_p$. Avoiding this assumption requires a
-more precise description of the properties of the op-amp itself,
-describing its input resistance $R_i$, output resistance $R_o$, and
-the relationship between the input and output - the open-loop gain
-$A$. Figure \ref{img:opamp_internal} depicts such a model.
+A more accurate representation of the op-amp foregoes the assumption,
+often made regarding op-amps wired in a feedback configuration, that
+$v_n = v_p$. Avoiding this assumption requires a more precise
+description of the properties of the op-amp itself, describing its
+input resistance $R_i$, output resistance $R_o$, and the relationship
+$A$ between the input and output, also known as the open-loop
+gain. Figure \ref{img:opamp_internal} depicts such a model.
 
 \begin{figure}[h]
   \caption{A more accurate depiction of an op-amp \cite{b2}}
@@ -156,19 +185,24 @@ and input of the op-amp. This measure is useful, as it describes the
 absolute maximum gain performance of the op-amp: notice, for example,
 that the feedback resistor $R_2$ in the selected high-pass filter
 design only serves to limit the gain and has no bearing on the cutoff
-frequency.
+frequency; its value can be increased until the gain is restricted by
+the op-amp itself instead of the resistor (otherwise, an op-amp
+would have infinite gain if it lacked a feedback resistor).
 
 In some cases, manufacturers give more precise details about op-amp
 operation than would be specified under generic ``open-loop gain'':
 for example, the LM741 datasheet documents the \textit{Open-Loop
- Large-Signal Differential Voltage Amplification} as a function of
+  Large-Signal Differential Voltage Amplification} as a function of
 frequency, as seen in Figure \ref{img:lm741_oclsg}. Despite being
 closely related to ``open-loop gain'', it is distinct in that it is
 measured with an output load (in this case, $R_L = \SI{2}{\kohm}$),
 and under conditions such that the load is significant, i.e. that the
 operating output is known to be a meaningful fraction of the supply
 voltage \cite{b1}. Here, it is $V_o = \SI{10}{V}$ for
-$V_{CC} = \pm \SI{15}{V}$.
+$V_{CC} = \pm \SI{15}{V}$. Still, for the purposes of this paper,
+``open-loop gain'' is treated as ``open-loop large-signal differential
+voltage amplification'', with caution made to stay away from
+specifically small-signal measurements.
 
 \begin{figure}[h]
   \caption{The large-signal open-loop gain of the LM741}
@@ -222,8 +256,8 @@ Combining equations \ref{eqn:kcl} and \ref{eqn:known},
 \begin{align}
   \begin{split}
     0 &= \frac{v_{in}-v_n}{R_1+\frac{1}{s C_1}} - \frac{v_n - A(-v_n)}{R_2} \\
-      &= \frac{v_{in}}{R_1+\frac{1}{s C_1}} - v_n \left(\frac{1}{R_1+s C_1} + \frac{A+1}{R_2} \right) \\
-      &= \frac{v_{in}}{R_1+\frac{1}{s C_1}} + \frac{v_{out}}{A} \left(\frac{1}{R_1+s C_1} + \frac{A+1}{R_2} \right) \\
+      &= \frac{v_{in}}{R_1+\frac{1}{s C_1}} - v_n \left(\frac{1}{R_1+\frac{1}{s C_1}} + \frac{A+1}{R_2} \right) \\
+      &= \frac{v_{in}}{R_1+\frac{1}{s C_1}} + \frac{v_{out}}{A} \left(\frac{1}{R_1+\frac{1}{s C_1}} + \frac{A+1}{R_2} \right) \\
   \end{split}
 \end{align}
 
@@ -231,10 +265,9 @@ So,
 
 \begin{align}
   \begin{split}
-    \frac{v_{out}}{A} \left(\frac{1}{R_1+s C_1} + \frac{A+1}{R_2} \right) &= -\frac{v_{in}}{R_1+\frac{1}{s C_1}} \\
+    \frac{v_{out}}{A} \left(\frac{1}{R_1+\frac{1}{s C_1}} + \frac{A+1}{R_2} \right) &= -\frac{v_{in}}{R_1+\frac{1}{s C_1}} \\
     H(s) = \frac{v_{out}}{v_{in}} &= -A \frac{R_2}{R_2+(A+1)(R_1+\frac{1}{s C_1})} \\
-                                                                          &= -A\frac{\SI{10}{\kohm}}{\SI{10}{\kohm} + (A + 1) (\SI{100}{\ohm} + \frac{1}{s \SI{39}{\nano\farad}})} \\
-                                                                          &= -A\frac{\SI{E4}{}}{\SI{E4}{} + (A + 1) (\SI{E2}{} + \frac{\SI{2.56E7}{}}{s})}
+                                                                          &= -A\frac{\SI{100}{\kohm}}{\SI{100}{\kohm} + (A + 1) (\SI{100}{\ohm} + \frac{1}{s \SI{3.9}{\nano\farad}})} \\
   \end{split}
 \end{align}
 
@@ -262,10 +295,13 @@ $\tau = \frac{1}{\omega_c}$ and $A_0$:
   A(s) = \frac{A_0}{\tau s + 1}
 \end{equation}
 
-$A_0$ represents the peak gain; here, $\SI{106}{dB} \approx
-\SI{2E5}{}$. Since $\omega_c = 25$ rad/s.
+$A_0$ represents the peak gain; we can see from Figure
+\ref{img:lm741_oclsg} that this is about
+$\SI{106}{dB} \approx \SI{2E5}{}$. The cut-off frequency is that for
+which the gain is $\SI{6}{dB}$ less than this peak - this is
+approximately $\omega_c = 25$ rad/s. This yields:
 
-\subsection{An improvement: The TL081}
+\subsection{An improvement: the TL081}
 
 \begin{figure}[h]
   \caption{The large-signal open-loop gain of the TL081}
@@ -274,207 +310,195 @@ $A_0$ represents the peak gain; here, $\SI{106}{dB} \approx
   \includegraphics[width=0.4\textwidth]{tl08xx_oclsg}
 \end{figure}
 
-\section{Prepare Your Paper Before Styling}
-Before you begin to format your paper, first write and save the content as a
-separate text file. Complete all content and organizational editing before
-formatting. Please note sections \ref{AA}--\ref{SCM} below for more information on
-proofreading, spelling and grammar.
+In this case, the peak gain $A_0$ is still approximately $\SI{2E5}{}$
+(agreeing with earlier content of the datasheet, noting
+$A_{VD}= 200V/mV$ typical). The cut-off frequency, however, is higher,
+closer to $\omega_c = 210$ rad/s.
 
-Keep your text and graphic files separate until after the text has been
-formatted and styled. Do not number text heads---{\LaTeX} will do that
-for you.
+\subsection{A whole new world: the OPA818}
 
-\subsection{Abbreviations and Acronyms}\label{AA}
-Define abbreviations and acronyms the first time they are used in the text,
-even after they have been defined in the abstract. Abbreviations such as
-IEEE, SI, MKS, CGS, ac, dc, and rms do not have to be defined. Do not use
-abbreviations in the title or heads unless they are unavoidable.
+The TI OPA818 is a much higher-cost, much higher-bandwidth, and much
+less common op-amp than either the LM741 or the TL08X. It was selected
+in case neither of the previous two op-amps were able to perform well
+enough in this application.
 
-\subsection{Units}
-\begin{itemize}
-\item Use either SI (MKS) or CGS as primary units. (SI units are encouraged.) English units may be used as secondary units (in parentheses). An exception would be the use of English units as identifiers in trade, such as ``3.5-inch disk drive''.
-\item Avoid combining SI and CGS units, such as current in amperes and magnetic field in oersteds. This often leads to confusion because equations do not balance dimensionally. If you must use mixed units, clearly state the units for each quantity that you use in an equation.
-\item Do not mix complete spellings and abbreviations of units: ``Wb/m\textsuperscript{2}'' or ``webers per square meter'', not ``webers/m\textsuperscript{2}''. Spell out units when they appear in text: ``. . . a few henries'', not ``. . . a few H''.
-\item Use a zero before decimal points: ``0.25'', not ``.25''. Use ``cm\textsuperscript{3}'', not ``cc''.)
-\end{itemize}
+\begin{figure}[h]
+  \caption{The open-loop gain of the OPA818}
+  \label{img:opa818_olgm}
+  \centering
+  \includegraphics[width=0.4\textwidth]{opa818_olgm}
+\end{figure}
 
-\subsection{Equations}
-Number equations consecutively. To make your
-equations more compact, you may use the solidus (~/~), the exp function, or
-appropriate exponents. Italicize Roman symbols for quantities and variables,
-but not Greek symbols. Use a long dash rather than a hyphen for a minus
-sign. Punctuate equations with commas or periods when they are part of a
-sentence, as in:
-\begin{equation}
-a+b=\gamma\label{eq}
-\end{equation}
+While the OPA818 has a lower peak gain of
+$A_0 \approx \SI{92}{dB} \approx \SI{4E4}{}$, it is a much
+higher-bandwidth part, with a cutoff frequency of approximately
+$\SI{7E5}{}$ rad/s.
 
-Be sure that the
-symbols in your equation have been defined before or immediately following
-the equation. Use ``\eqref{eq}'', not ``Eq.~\eqref{eq}'' or ``equation \eqref{eq}'', except at
-the beginning of a sentence: ``Equation \eqref{eq} is . . .''
+\subsection{The ideal op-amp}
 
-\subsection{\LaTeX-Specific Advice}
+In the case of the ideal op-amp, the transfer function is much
+clearer: $A \to \infty$, so, substituting $A$ back in the overall
+transfer function approaches
+$-\frac{AR_2}{A(R_1 + \frac{1}{sC_1})} = -\frac{R_2}{R_1 +
+  \frac{1}{sC_1}}$. This is, unsurprisingly, exactly the transfer
+function seen in Equation \ref{eqn:hpf_tf} for the inverting ideal
+active high-pass filter.
 
-Please use ``soft'' (e.g., \verb|\eqref{Eq}|) cross references instead
-of ``hard'' references (e.g., \verb|(1)|). That will make it possible
-to combine sections, add equations, or change the order of figures or
-citations without having to go through the file line by line.
+\section{A complete comparison}
+MATLAB is used to compare the final transfer functions of all four
+cases; the result is shown in Figure \ref{img:bode_plots}. Of
+particular note: MATLAB's symbolic handling does some heavy lifting to
+generate Bode plots without having to further simplify the transfer
+functions, beyond substituting each $A(s)$ into place.
 
-Please don't use the \verb|{eqnarray}| equation environment. Use
-\verb|{align}| or \verb|{IEEEeqnarray}| instead. The \verb|{eqnarray}|
-environment leaves unsightly spaces around relation symbols.
+\begin{figure}[h]
+  \caption{Bode plots of our four filters}
+  \label{img:bode_plots}
+  \centering
+  \includegraphics[width=0.5\textwidth]{bode_plots}
+\end{figure}
 
-Please note that the \verb|{subequations}| environment in {\LaTeX}
-will increment the main equation counter even when there are no
-equation numbers displayed. If you forget that, you might write an
-article in which the equation numbers skip from (17) to (20), causing
-the copy editors to wonder if you've discovered a new method of
-counting.
+Figure \ref{img:bode_plots} clearly shows that while the ideal op-amp
+has no problem enabling a 'proper' $\omega_c = \SI{400}{\kHz}$, both
+the LM741 and TL081 miss the mark substantially, and act in practice
+more like band-pass filters with upper cutoff frequencies of around
+$\SI{1.2E5}{}$ rad/s and $\SI{3.0E5}{}$ rad/s, respectively, both
+\textit{below} the intended \textit{lower} cutoff frequency of our
+high-pass filter.
 
-{\BibTeX} does not work by magic. It doesn't get the bibliographic
-data from thin air but from .bib files. If you use {\BibTeX} to produce a
-bibliography you must send the .bib files.
+Ultimately, even the much more capable OPA818 acts as a band-pass
+filter rather than a high-pass filter. Nevertheless, it succeeds in
+reaching an upper $\omega_{c_2} = \SI{4E7}{}$ rad/s
+$\approx \SI{6.37}{\MHz}$, making it functional, if not necessarily
+suitable, for the intended application.
 
-{\LaTeX} can't read your mind. If you assign the same label to a
-subsubsection and a table, you might find that Table I has been cross
-referenced as Table IV-B3.
+\subsection{Gain response}
+In terms of the frequency response of gain, it is clear that only
+exceptional op-amps succeed in higher-frequency circumstances. Note as
+well that the application described -- AM radio reception -- is,
+compared to other types of radio amplification, relatively
+low-frequency. Compare, for example, FM radio, which operates in the
+$\SI{87.9}{\MHz}$ through $\SI{107.9}{\MHz}$ band. Of our models, the
+only one that comes out unscathed is the ideal op-amp model.
 
-{\LaTeX} does not have precognitive abilities. If you put a
-\verb|\label| command before the command that updates the counter it's
-supposed to be using, the label will pick up the last counter to be
-cross referenced instead. In particular, a \verb|\label| command
-should not go before the caption of a figure or a table.
+\subsection{Phase response}
+The phase response of the three non-ideal op-amps is consistent: below
+the cutoff frequency, the phase is delayed by 270 degrees; in the
+effective pass-band, the phase shift moves towards 180 degrees, and
+after the pass-band, it reduces to 90 degrees.
 
-Do not use \verb|\nonumber| inside the \verb|{array}| environment. It
-will not stop equation numbers inside \verb|{array}| (there won't be
-any anyway) and it might stop a wanted equation number in the
-surrounding equation.
+Note that for any time-sensitive applications, where the bandwidth of
+the signal being carried is a substantial portion of the frequency of
+the signal, this phase shift would be problematic. An additional
+phase-shift is entirely expected since we are using it as an inverting
+op-amp, obligating an 180 degree phase-shift in the passband.
 
-\subsection{Some Common Mistakes}\label{SCM}
-\begin{itemize}
-\item The word ``data'' is plural, not singular.
-\item The subscript for the permeability of vacuum $\mu_{0}$, and other common scientific constants, is zero with subscript formatting, not a lowercase letter ``o''.
-\item In American English, commas, semicolons, periods, question and exclamation marks are located within quotation marks only when a complete thought or name is cited, such as a title or full quotation. When quotation marks are used, instead of a bold or italic typeface, to highlight a word or phrase, punctuation should appear outside of the quotation marks. A parenthetical phrase or statement at the end of a sentence is punctuated outside of the closing parenthesis (like this). (A parenthetical sentence is punctuated within the parentheses.)
-\item A graph within a graph is an ``inset'', not an ``insert''. The word alternatively is preferred to the word ``alternately'' (unless you really mean something that alternates).
-\item Do not use the word ``essentially'' to mean ``approximately'' or ``effectively''.
-\item In your paper title, if the words ``that uses'' can accurately replace the word ``using'', capitalize the ``u''; if not, keep using lower-cased.
-\item Be aware of the different meanings of the homophones ``affect'' and ``effect'', ``complement'' and ``compliment'', ``discreet'' and ``discrete'', ``principal'' and ``principle''.
-\item Do not confuse ``imply'' and ``infer''.
-\item The prefix ``non'' is not a word; it should be joined to the word it modifies, usually without a hyphen.
-\item There is no period after the ``et'' in the Latin abbreviation ``et al.''.
-\item The abbreviation ``i.e.'' means ``that is'', and the abbreviation ``e.g.'' means ``for example''.
-\end{itemize}
-An excellent style manual for science writers is \cite{b7}.
+The ideal op-amp yields a true high-pass filter, which is reflected as
+well in the fact that the phase shift never decreases past 180
+degrees.
 
-\subsection{Authors and Affiliations}
-\textbf{The class file is designed for, but not limited to, six authors.} A
-minimum of one author is required for all conference articles. Author names
-should be listed starting from left to right and then moving down to the
-next line. This is the author sequence that will be used in future citations
-and by indexing services. Names should not be listed in columns nor group by
-affiliation. Please keep your affiliations as succinct as possible (for
-example, do not differentiate among departments of the same organization).
+\section{Summary}
+The exploration of op-amps applied to a higher-frequency application
+makes for an excellent illustration for the extremely limited
+applicability of some op-amps in this application. While an LM741 or
+TL081 would make for a fine low-power audio amplifier, they are, due
+to their low cutoff frequency, not suitable for $\ge \SI{100}{\kHz}$
+applications; indeed, even more performant op-amps have limits in
+amplifying higher-frequency signals.
 
-\subsection{Identify the Headings}
-Headings, or heads, are organizational devices that guide the reader through
-your paper. There are two types: component heads and text heads.
+\section{Code appendix}
 
-Component heads identify the different components of your paper and are not
-topically subordinate to each other. Examples include Acknowledgments and
-References and, for these, the correct style to use is ``Heading 5''. Use
-``figure caption'' for your Figure captions, and ``table head'' for your
-table title. Run-in heads, such as ``Abstract'', will require you to apply a
-style (in this case, italic) in addition to the style provided by the drop
-down menu to differentiate the head from the text.
+\begin{lstlisting}[style=mystyle,breaklines=true,language=Octave]
+% Define symbolic variables
+syms s
 
-Text heads organize the topics on a relational, hierarchical basis. For
-example, the paper title is the primary text head because all subsequent
-material relates and elaborates on this one topic. If there are two or more
-sub-topics, the next level head (uppercase Roman numerals) should be used
-and, conversely, if there are not at least two sub-topics, then no subheads
-should be introduced.
+r_1 = 1.e2
+r_2 = 1.e5
+c_1 = 3.9e-9
 
-\subsection{Figures and Tables}
-\paragraph{Positioning Figures and Tables} Place figures and tables at the top and
-bottom of columns. Avoid placing them in the middle of columns. Large
-figures and tables may span across both columns. Figure captions should be
-below the figures; table heads should appear above the tables. Insert
-figures and tables after they are cited in the text. Use the abbreviation
-``Fig.~\ref{fig}'', even at the beginning of a sentence.
+% Transfer function setup: LM741 %
+A_0_LM741 = 2.e5;
+tau_LM741 = 1./25;
+A_sym_LM741 = A_0_LM741 / (tau_LM741 * s + 1);
 
-\begin{table}[htbp]
-\caption{Table Type Styles}
-\begin{center}
-\begin{tabular}{|c|c|c|c|}
-\hline
-\textbf{Table}&\multicolumn{3}{|c|}{\textbf{Table Column Head}} \\
-\cline{2-4}
-\textbf{Head} & \textbf{\textit{Table column subhead}}& \textbf{\textit{Subhead}}& \textbf{\textit{Subhead}} \\
-\hline
-copy& More table copy$^{\mathrm{a}}$& &  \\
-\hline
-\multicolumn{4}{l}{$^{\mathrm{a}}$Sample of a Table footnote.}
-\end{tabular}
-\label{tab1}
-\end{center}
-\end{table}
+% Symbolic setup and consumption: LM741 %
+sym_LM741 = -A_sym_LM741 * (r_2) / (r_2 + (A_sym_LM741 + 1) * (r_1 + 1 / (s * c_1)));
+tf_sym_LM741 = subs(sym_LM741, A_sym_LM741, A_0_LM741 / (tau_LM741 * s + 1));
 
-% \begin{figure}[htbp]
-% \centerline{\includegraphics{fig1.png}}
-% \caption{Example of a figure caption.}
-% \label{fig}
-% \end{figure}
+% Perform sym extraction for LM741, and generate polynomial num/denom %
+[nH_LM741um_sym_LM741, den_sym_LM741] = numden(tf_sym_LM741);
+num_coeffs_LM741 = sym2poly(num_sym_LM741);
+den_coeffs_LM741 = sym2poly(den_sym_LM741);
 
-Figure Labels: Use 8 point Times New Roman for Figure labels. Use words
-rather than symbols or abbreviations when writing Figure axis labels to
-avoid confusing the reader. As an example, write the quantity
-``Magnetization'', or ``Magnetization, M'', not just ``M''. If including
-units in the label, present them within parentheses. Do not label axes only
-with units. In the example, write ``Magnetization (A/m)'' or ``Magnetization
-\{A[m(1)]\}'', not just ``A/m''. Do not label axes with a ratio of
-quantities and units. For example, write ``Temperature (K)'', not
-``Temperature/K''.
+% Create the numeric transfer function object for LM741 %
+LM741 = tf(num_coeffs_LM741, den_coeffs_LM741);
 
-\section*{Acknowledgment}
 
-The preferred spelling of the word ``acknowledgment'' in America is without
-an ``e'' after the ``g''. Avoid the stilted expression ``one of us (R. B.
-G.) thanks $\ldots$''. Instead, try ``R. B. G. thanks$\ldots$''. Put sponsor
-acknowledgments in the unnumbered footnote on the first page.
+% Transfer function setup: TL081 %
+A_0_TL081 = 2.e5;
+tau_TL081 = 1./210;
+A_sym_TL081 = A_0_TL081 / (tau_TL081 * s + 1);
 
-\section*{References}
+% Symbolic setup and consumption: TL081 %
+sym_TL081 = -A_sym_TL081 * (r_2) / (r_2 + (A_sym_TL081 + 1) * (r_1 + 1 / (s * c_1)));
+tf_sym_TL081 = subs(sym_TL081, A_sym_TL081, A_0_TL081 / (tau_TL081 * s + 1));
 
-Please number citations consecutively within brackets \cite{b1}. The
-sentence punctuation follows the bracket \cite{b2}. Refer simply to the reference
-number, as in \cite{b3}---do not use ``Ref. \cite{b3}'' or ``reference \cite{b3}'' except at
-the beginning of a sentence: ``Reference \cite{b3} was the first $\ldots$''
+% Perform sym extraction for TL081, and generate polynomial num/denom %
+[num_sym_TL081, den_sym_TL081] = numden(tf_sym_TL081);
+num_coeffs_TL081 = sym2poly(num_sym_TL081);
+den_coeffs_TL081 = sym2poly(den_sym_TL081);
 
-Number footnotes separately in superscripts. Place the actual footnote at
-the bottom of the column in which it was cited. Do not put footnotes in the
-abstract or reference list. Use letters for table footnotes.
+% Create the numeric transfer function object for TL081 %
+TL081 = tf(num_coeffs_TL081, den_coeffs_TL081);
 
-Unless there are six authors or more give all authors' names; do not use
-``et al.''. Papers that have not been published, even if they have been
-submitted for publication, should be cited as ``unpublished'' \cite{b4}. Papers
-that have been accepted for publication should be cited as ``in press'' \cite{b5}.
-Capitalize only the first word in a paper title, except for proper nouns and
-element symbols.
 
-For papers published in translation journals, please give the English
-citation first, followed by the original foreign-language citation \cite{b6}.
+% Transfer function setup: OPA818 %
+A_0_OPA818 = 4.e4;
+tau_OPA818 = 1./7.E5;
+A_sym_OPA818 = A_0_OPA818 / (tau_OPA818 * s + 1);
+
+% Symbolic setup and consumption: OPA818 %
+sym_OPA818 = -A_sym_OPA818 * (r_2) / (r_2 + (A_sym_OPA818 + 1) * (r_1 + 1 / (s * c_1)));
+tf_sym_OPA818 = subs(sym_OPA818, A_sym_OPA818, A_0_OPA818 / (tau_OPA818 * s + 1));
+
+% Perform sym extraction for OPA818, and generate polynomial num/denom %
+[num_sym_OPA818, den_sym_OPA818] = numden(tf_sym_OPA818);
+num_coeffs_OPA818 = sym2poly(num_sym_OPA818);
+den_coeffs_OPA818 = sym2poly(den_sym_OPA818);
+
+% Create the numeric transfer function object for OPA818 %
+OPA818 = tf(num_coeffs_OPA818, den_coeffs_OPA818);
+
+% Create a numeric TF for the ideal op-amp %
+% Symbolic consumption: ideal %
+tf_sym_ideal = - (r_2) / (r_1 + 1 / (s * c_1));
+
+% Perform sym extraction for OPA818, and generate polynomial num/denom %
+[num_sym_ideal, den_sym_ideal] = numden(tf_sym_ideal);
+num_coeffs_ideal = sym2poly(num_sym_ideal);
+den_coeffs_ideal = sym2poly(den_sym_ideal);
+
+% Create the numeric transfer function object for the ideal op-amp %
+ideal = tf(num_coeffs_ideal, den_coeffs_ideal);
+
+% Generate the Bode plot
+hold on;
+bode(LM741);
+bode(TL081);
+bode(OPA818);
+bode(ideal);
+legend('LM741','TL081','OPA818','ideal');
+
+grid on;
+title('Frequency responses of op-amp driven high-pass filters');
+hold off;
+\end{lstlisting}
 
 \begin{thebibliography}{00}
 \bibitem{b1} J. Karki, ``Understanding Operational Amplifier Specifications.'' Accessed: May 05, 2025. [Online]. Available: https://www.ti.com/lit/an/sloa011b/sloa011b.pdf, p. 14.
 \bibitem{b2} J. W. Nilsson and S. A. Riedel, Electric Crircuits, 12th ed., Hoboken: Pearson, 2022, p.168
 \bibitem{b3} J. W. Nilsson and S. A. Riedel, Electric Crircuits, 12th ed., Hoboken: Pearson, 2022, p.576
-\bibitem{b4} ``MSF radio time signal,'' NPLWebsite. https://www.npl.co.uk/msf-signal
-\bibitem{b5} R. Nicole, ``Title of paper with only first word capitalized,'' J. Name Stand. Abbrev., in press.
-\bibitem{b6} Y. Yorozu, M. Hirano, K. Oka, and Y. Tagawa, ``Electron spectroscopy studies on magneto-optical media and plastic substrate interface,'' IEEE Transl. J. Magn. Japan, vol. 2, pp. 740--741, August 1987 [Digests 9th Annual Conf. Magnetics Japan, p. 301, 1982].
-\bibitem{b7} M. Young, The Technical Writer's Handbook. Mill Valley, CA: University Science, 1989.
+\bibitem{b4} N. US Department of Commerce, ``NOAA Weather Radio Frequently Asked Questions,'' www.weather.gov. https://www.weather.gov/phi/nwrfaq
 \end{thebibliography}
 \vspace{12pt}
-\color{red}
-IEEE conference templates contain guidance text for composing and formatting conference papers. Please ensure that all template text is removed from your conference paper prior to submission to the conference. Failure to remove the template text from your paper may result in your paper not being published.
-
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