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Robin Clark 2011-11-29 14:25:51 +00:00
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opamp_circuits_C_GARRETT/opamps.tex
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@ -503,6 +503,7 @@ Thus we can analyse the first Sallen~Key low pass filter and re-use the results.
\paragraph{First Order Low Pass Filter.}
\label{sec:lp}
We begin with the first order low pass filter formed by $R10$ and $C10$.
%
This configuration (or {\fg}) is very commonly
@ -770,7 +771,7 @@ could be easily detected; the failure symptom $FilterIncorrect$ may be less obs
This circuit is described in the Analog Applications Journal~\cite{bubba}.
The circuit uses four 45 degree phase shifts, and an inverting amplifier to provide
gain and the final 180 degrees of phase shift.
gain and the final 180 degrees of phase shift (making a total of 360 degrees of phase shift).
We identifiy three functional groups, the inverting amplifer (analysed in section~\ref{fig:invamp}),
a 45 degree phase shifter (a {$10k\Omega$} resistor and a $10nF$ capacitor) and a noninverting buffer
@ -798,12 +799,51 @@ $$ fm(INVAMP) = \{ OUT OF RANGE, ZERO OUTPUT, NO GAIN, LOW PASS \} $$
\subsection{Phase shifter: PHS45}
\subsection{Non Inverting Buffer: NIBUFF}
This consists of a resistor and a capacitor. We already have failure mode models for these components -- $ fm(R) = \{OPEN, SHORT\}$, $fm(C) = \{OPEN, SHORT\}$ --
we now need to see how these failure modes would affect the phase shifter. Note that the circuit here
is idential to the low pass filter in structure (see \ref{sec:lp}), but its intended use is different.
We have to analyse this circuit from the perspective of it being a {\em phase~shifter} not a {\em low~pass~filter}.
\begin{table}[h+]
\caption{PhaseShift: Failure Mode Effects Analysis: Single Faults} % title of Table
\label{tbl:firstorderlp}
\subsection{Bringing the functional Groups Together: The `Bubba' Oscillator}
\begin{tabular}{|| l | l | c | c | l ||} \hline
\textbf{Failure Scenario} & & \textbf{First Order} & & \textbf{Symptom} \\
& & \textbf{Low Pass Filter} & & \\
\hline
FS1: R SHORT & & 90 degree's of phase shift & & $90\_phaseshift$ \\ \hline
FS2: R OPEN & & No Signal & & $nosignal$ \\ \hline
FS3: C SHORT & & Grounded,No Signal & & $nosignal$ \\ \hline
FS4: C OPEN & & 0 degree's of phase shift & & $0\_phaseshift$ \\ \hline
\hline
\end{tabular}
\end{table}
% PHS45
$$ fm (PHS45) = \{ 90\_phaseshift, nosignal, 0\_phaseshift \} $$
\subsection{Non Inverting Buffer: NIBUFF.}
The non-inverting buffer functional group, is comrised of one component, an op-amp.
We use the failure modes for an op-amp to represent this group.
% GARK
$$ fm(NIBUFF) = fm(OPAMP) = \{L\_{up}, L\_{dn}, Noop, L\_slew \} $$
%\subsection{Forming a functional group from the PHS45 and NIBUFF.}
% describe what we are doing, a buffered 45 degree phase shift element
\subsection{Bringing the functional Groups Together: The `Bubba' Oscillator.}
We could at this point bring all the {\dcs} together into one large functional group (see figure~\ref{fig:poss1finalbubba})
or we could try to merge smaller stages. We could merge the $NIBUFF$ and $PHS45$
{\dcs}, and then with those three, form a $PHS135BUFFERED$ functional group -- with the remaining $PHS45$ and the $INVAMP$ in a second group $PHS225AMP$,
and then merge $PHS135BUFFERED$ and $PHS225AMP$ in a final stage (see figure~\ref{fig:poss2finalbubba})
\clearpage
\section{Basic Concepts Of FMMD}