From c5c58ccfb9410c28d993bf28b3d3ba26c7750b85 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Tue, 29 Nov 2011 14:25:51 +0000 Subject: [PATCH] lunchtime edit (geddit) --- opamp_circuits_C_GARRETT/opamps.tex | 46 +++++++++++++++++++++++++++-- 1 file changed, 43 insertions(+), 3 deletions(-) diff --git a/opamp_circuits_C_GARRETT/opamps.tex b/opamp_circuits_C_GARRETT/opamps.tex index 64cac4d..1c618e9 100644 --- a/opamp_circuits_C_GARRETT/opamps.tex +++ b/opamp_circuits_C_GARRETT/opamps.tex @@ -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}