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Wednesday evening finish five pole LP filter

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analysis
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Robin Clark 2011-11-16 18:59:04 +00:00
parent d2c60a1915
commit 3250be53e3
4 changed files with 145 additions and 44 deletions
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opamp_circuits_C_GARRETT/opamps.tex
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@ -464,7 +464,7 @@ wihen it becomes a V2 follower).
\centering
\includegraphics[width=200pt]{./circuit2002.png}
% circuit2002.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331
\caption{circuit2}
\caption{circuit 2}
\label{fig:circuit2}
\end{figure}
@ -478,6 +478,16 @@ The output of this is passed into another Sallen~Key filter (which although it m
for its resistors/capacitors and thus a different frequency response) is idential from a failure mode perspective.
Thus we can analyse the first Sallen~Key low pass filter and re-use the results.
\begin{figure}[h]
\centering
\includegraphics[width=400pt,keepaspectratio=true]{./blockdiagramcircuit2.png}
% blockdiagramcircuit2.png: 689x83 pixel, 72dpi, 24.31x2.93 cm, bb=0 0 689 83
\caption{Signal Flow though the five pole low pass filter}
\label{fig:blockdiagramcircuit2}
\end{figure}
\paragraph{First Order Low Pass Filter.}
We begin with the first order low pass filter formed by $R10$ and $C10$.
%
@ -504,9 +514,11 @@ We will consider the latter type for this analysis.
\hline
FS1: R10 SHORT & & $No Filtering$ & & $LPnofilter$ \\ \hline
FS2: R10 OPEN & & $No Signal$ & & $LPnosignal$ \\ \hline
FS3: C10 SHORT & & $No Signal$ & & $LPnosignal$ \\ \hline
FS4: C10 OPEN & & $No Filtering$ & & $LPnofilter$ \\ \hline
FS3: C10 SHORT & & $No Signal$ & & $LPnosignal$ \\ \hline
FS4: C10 OPEN & & $No Filtering$ & & $LPnofilter$ \\ \hline
\hline
\end{tabular}
\end{table}
@ -527,17 +539,17 @@ from the $FirstOrderLP$ and the OPAMP component.
\centering % used for centering table
\begin{tabular}{||l|c|c|l|l||}
\hline \hline
\textbf{Test} & \textbf{Amplifier} & \textbf{ } & \textbf{General} \\
\textbf{Test} & \textbf{Circuit} & \textbf{ } & \textbf{General} \\
\textbf{Case} & \textbf{Effect} & \textbf{ } & \textbf{Symptom Description} \\
% R & wire & res + & res - & description
\hline
\hline
TC1: $OPAMP$ LatchUP & Output High & & LP1High \\
TC2: $OPAMP$ LatchDown & Output Low & & LP1Low \\ \hline
TC2: $OPAMP$ LatchDown & Output Low & & LP1Low \\
TC3: $OPAMP$ No Operation & Output Low & & LP1Low \\
TC4: $OPAMP$ Low Slew & Unwanted Low pass filtering & & LP1ExtraLowPass \\ \hline
TC5: $LPnofilter $ & No low pass filtering & & LP1NoLowPass \\ \hline
TC6: $LPnosignal $ & No input signal & & LP1low \\
TC4: $OPAMP$ Low Slew & Unwanted Low pass filtering & & LP1filterincorrect \\ \hline
TC5: $LPnofilter $ & No low pass filtering & & LP1filterincorrect \\
TC6: $LPnosignal $ & No input signal & & LP1nosignal \\ \hline
\hline
\hline
@ -549,7 +561,20 @@ From the table~\ref{tbl:firststage} we can see three symptoms of failure of
the first stage of this circuit (i.e. R10,C10,IC1).
We can create a derived component for it, lets call it $LP1$.
$$ fm(LP1) = \{ LP1High, LP1Low, LP1ExtraLowPass, LP1NoLowPass \} $$
$$ fm(LP1) = \{ LP1High, LP1Low, LP1filterincorrect, LP1nosignal \} $$
In terms terms of the circuit we have modelled the functional groups $FirstOrderLP$, and
$LP1$. We can represent these on the circuit diagram by drawing contours around the components
on the schematic as in figure~\ref{fig:circuit2002_LP1}.
\begin{figure}[h]
\centering
\includegraphics[width=200pt,keepaspectratio=true]{./circuit2002_LP1.png}
% circuit2002_LP1.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331
\caption{Circuit showing functional groups modelled so far.}
\label{fig:circuit2002_LP1}
\end{figure}
\paragraph{Second order Sallen Key Low Pass Filter.}
@ -562,27 +587,30 @@ We can analyse one and re-use the results for the second.
\centering % used for centering table
\begin{tabular}{||l|c|c|l|l||}
\hline \hline
\textbf{Test} & \textbf{Amplifier} & \textbf{ } & \textbf{General} \\
\textbf{Test} & \textbf{Circuit} & \textbf{ } & \textbf{General} \\
\textbf{Case} & \textbf{Effect} & \textbf{ } & \textbf{Symptom Description} \\
% R & wire & res + & res - & description
\hline
\hline
TC1: $OPAMP$ LatchUP & Output High & & SKLPHigh \\
TC2: $OPAMP$ LatchDown & Output Low & & SKLPLow \\ \hline
TC2: $OPAMP$ LatchDown & Output Low & & SKLPLow \\
TC3: $OPAMP$ No Operation & Output Low & & SKLPLow \\
TC4: $OPAMP$ Low Slew & Unwanted Low pass filtering & & SKLPIncorrect \\ \hline
TC5: $R1 OPEN$ & No input signal & & SKLPIncorrect \\ \hline
TC6: $R1 SHORT$ & incorrect low pass filtering & & SKLPIncorrect \\
TC7: $R2 OPEN$ & No input signal & & SKLPnosignal \\ \hline
TC8: $R2 SHORT$ & incorrect low pass filtering & & SKLPIncorrect \\
TC9: $C1 OPEN$ & reduced/incorrect low pass filtering & & SKLPIncorrect\\ \hline
TC10: $C1 SHORT$ & reduced/incorrect low pass filtering & & SKLPIncorrect \\
TC11: $C2 OPEN$ & reduced/incorrect low pass filtering & & SKLPIncorrect \\ \hline
TC12: $C2 SHORT$ & No input signal, low signal & & SKLPnosignal \\
TC4: $OPAMP$ Low Slew & Unwanted Low pass filtering & & SKLPfilterIncorrect \\ \hline
TC5: R1 OPEN & No input signal & & SKLPfilterIncorrect \\
TC6: R1 SHORT & incorrect low pass filtering & & SKLPfilterIncorrect \\ \hline
TC7: R2 OPEN & No input signal & & SKLPnosignal \\
TC8: R2 SHORT & incorrect low pass filtering & & SKLPfilterIncorrect \\ \hline
TC9: C1 OPEN & reduced/incorrect low pass filtering & & SKLPfilterIncorrect\\
TC10: C1 SHORT & reduced/incorrect low pass filtering & & SKLPfilterIncorrect \\ \hline
TC11: C2 OPEN & reduced/incorrect low pass filtering & & SKLPfilterIncorrect \\
TC12: C2 SHORT & No input signal, low signal & & SKLPnosignal \\ \hline
\hline
\hline
\end{tabular}
\label{tbl:firststage}
\label{tbl:sallenkeylp}
\end{table}
We now can create a derived component to represent the Sallen Key low pass filter, which we can call $SKLP$.
@ -593,29 +621,32 @@ $$ fm ( SKLP ) = \{ SKLPHigh, SKLPLow, SKLPIncorrect, SKLPnosignal \} $$
\paragraph{A failure mode model of Op-Amp Circuit 2.}
We now have {\dcs} representing the three stages of this filter.
We represent this as a block diagram to represent the signal flow, in figure~\ref{fig:blockdiagramcircuit2}.
We now have {\dcs} representing the three stages of this filter
and this follows the signal flow in the filter circuit (see figure~\ref{fig:blockdiagramcircuit2}).
\begin{figure}[h]
\centering
\includegraphics[width=400pt,keepaspectratio=true]{./blockdiagramcircuit2.png}
% blockdiagramcircuit2.png: 689x83 pixel, 72dpi, 24.31x2.93 cm, bb=0 0 689 83
\caption{Signal Flow though five pole low pass filter}
\label{fig:blockdiagramcircuit2}
\end{figure}
As the signal has to pass though each block/stage
in order to be `five~pole' filtered, we need to bring these three blocks together into a {\fg}
in order to get a failure mode model for the whole circuit.
We can index the Sallen Key stages, and these are marked on the ciruit schematic in figure~\ref{fig:circuit2002_FIVEPOLE}.
\begin{figure}[h]+
\centering
\includegraphics[width=200pt]{./circuit2002_FIVEPOLE.png}
% circuit2002_FIVEPOLE.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331
\caption{Functional Groups in Five Pole Low Pass Filter on schematic}
\label{fig:circuit2002_FIVEPOLE}
\end{figure}
\pagebreak[4]
So our final {\fg} will consist of the derived components $\{ LP1, SKLP_1, SKLP_2 \}$.
We represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}.
We can represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}.
\begin{figure}[h]
\begin{figure}[h]+
\centering
\includegraphics[width=300pt]{./circuit2h.png}
% circuit2h.png: 676x603 pixel, 72dpi, 23.85x21.27 cm, bb=0 0 676 603
@ -623,9 +654,82 @@ We can represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}.
\label{fig:circuit2h}
\end{figure}
%\pagebreak[4]
%$$ fm ( SKLP ) = \{ SKLPHigh, SKLPLow, SKLPIncorrect, SKLPnosignal \} $$
%$$ fm(LP1) = \{ LP1High, LP1Low, LP1ExtraLowPass, LP1NoLowPass \} $$
\begin{table}[ht]+
\caption{Five Pole Low Pass Filter: Failure Mode Effects Analysis: Single Faults} % title of Table
\centering % used for centering table
\begin{tabular}{||l|c|l|l|l||}
\hline \hline
\textbf{Test} & \textbf{Circuit} & \textbf{ } & \textbf{General} \\
\textbf{Case} & \textbf{Effect} & \textbf{ } & \textbf{Symptom Description} \\
% R & wire & res + & res - & description
\hline
\hline
TC1: $LP1$ LP1High & signal HIGH & & HIGH \\
TC2: $LP1$ SKLPLow & signal LOW & & LOW \\
TC3: $LP1$ LP1filterIncorrect & filtering incorrect & & FilterIncorrect \\
TC4: $LP1$ LP1nosignal & no signal propogated & & NO\_SIGNAL \\ \hline
TC5: $SKLP_1$ High & signal HIGH & & HIGH \\
TC6: $SKLP_1$ Low & signal LOW & & LOW \\
TC7: $SKLP_1$ filterIncorrect & filtering incorrect & & FilterIncorrect \\
TC8: $SKLP_1$ nosignal & no signal propogated & & NO\_SIGNAL \\ \hline
TC9: $SKLP_2$ High & signal HIGH & & HIGH \\
TC10: $SKLP_2$ Low & signal LOW & & LOW \\
TC11: $SKLP_2$ filterIncorrect & filtering incorrect & & FilterIncorrect \\
TC12: $SKLP_2$ nosignal & no signal propogated & & NO\_SIGNAL \\ \hline
\hline
\hline
\end{tabular}
\label{tbl:fivepole}
\end{table}
We now can create a {\dc} to represent the circuit in figure~\ref{fig:circuit2}, we can call it
$FivePoleLP$ and applying the $fm$ function to it (see table~\ref{tbl:fivepole}) yields $fm(FivePoleLP) = \{ HIGH, LOW, FilterIncorrect, NO\_SIGNAL \}$.
\pagebreak[4]
The failure modes for the low pass filters are very similar, and the propogation of the signal
is simple (as it is never inverted). The circuit under analysis is -- as shown in the block diagram (see figure~\ref{fig:blockdiagramcircuit2}) --
three opamp driven non-inverting low pass filter elements; It is not suprising therefore that they have very similar failure modes.
From a safety point of view, the failure modes $LOW$, $HIGH$ and $NO\_SIGNAL$
could be easily detected; the failure symptom $FilterIncorrect$ may be less observable.
So out final {\fg} will consist of the derived components
$\{ LP1, SKLP_1, SKLP_2 \}$.
\clearpage
\section{Op-Amp circuit 3}
@ -637,12 +741,9 @@ $\{ LP1, SKLP_1, SKLP_2 \}$.
\caption{Circuit 3}
\label{fig:circuit3}
\end{figure}
\end{tabular}
\label{ampfmea}
\end{table}
\clearpage
\section{Standard Non-inverting OP AMP}
%\clearpage
%\section{Standard Non-inverting OP AMP}
\clearpage
@ -662,7 +763,7 @@ $\{ LP1, SKLP_1, SKLP_2 \}$.
\paragraph{ Creating a fault hierarchy.}
The main concept of FMMD is to build a hierarchy of failure behaviour from the {\bc}
level up to the top, or system level, with analysis stages between each
transition to a higher level in the hierarchy.
transition to a higher level in the hierarchy. $$ fm(LP1) = \{ LP1High, LP1Low, LP1ExtraLowPass, LP1NoLowPass \} $$
The first stage is to choose
{\bcs} that interact and naturally form {\fgs}. The initial {\fgs} are collections of base components.
@ -846,7 +947,7 @@ they always have a small number of system failure modes.
Idea stage on this section
\begin{itemize}
\item Look at OPAMP circuits
\item Look at OPAMP circuits, pick one (say $\mu$741)
\item examine number of components and failure modes
\item outline a proposed FMMD analysis
\item Show FMD-91 OPAMP failure modes -- compare with FMMD