From f8a7225623cd07df53e70407ce4d67079d19fd95 Mon Sep 17 00:00:00 2001 From: "Robin P. Clark" Date: Tue, 4 Sep 2012 08:29:14 +0100 Subject: [PATCH] morning edit geddit --- submission_thesis/CH4_FMMD/copy.tex | 22 ++++++++++++---------- 1 file changed, 12 insertions(+), 10 deletions(-) diff --git a/submission_thesis/CH4_FMMD/copy.tex b/submission_thesis/CH4_FMMD/copy.tex index cb66df9..548f20b 100644 --- a/submission_thesis/CH4_FMMD/copy.tex +++ b/submission_thesis/CH4_FMMD/copy.tex @@ -474,11 +474,9 @@ In this way we can incrementally analyse an entire system. %% %% GARK BEGIN - - - To demonstrate the principles of FMMD, we use it to analyse a -commonly used circuit, a non-inverting amplifier built from an op amp~\cite{aoe}[p.234] and two resistors, a circuit schematic for this is shown in figure \ref{fig:noninvamp}. +commonly used circuit, a non-inverting amplifier built from an op amp~\cite{aoe}[p.234] and +two resistors, a circuit schematic for this is shown in figure \ref{fig:noninvamp}. % \begin{figure}[h+] \centering @@ -490,20 +488,24 @@ commonly used circuit, a non-inverting amplifier built from an op amp~\cite{aoe} \end{figure} % The function of the resistors in this circuit is to set the amplifier gain. -They operate as a potential divider, the resistors act as a potential divider --- assuming the op-amp has high impedance --- -and program the inverting input on the op-amp +The resistors act as a potential divider---assuming the op-amp has high impedance---and +program the inverting input on the op-amp to balance them against the positive input, giving the voltage gain ($G_v$) defined by $ G_v = 1 + \frac{R2}{R1} $ at the output. -\paragraph{Potential Divider.} +\paragraph{Analysing the failure modes of the Potential Divider.} \label{subsec:potdiv} -As the resistors work to provide a specific function, that of a potential divider, +As the resistors work to provide a clearly defined function, that of a potential divider, we can treat them as a collection of components with a specific functionality---which can be termed a `{\fg}'. This {\fg} has two members, $R1$ and $R2$. -Taken as an entity the potential divider can be viewed as a {\dc}. +% +The potential divider circuit can be considered as a component +that provides the function of splitting two voltages into three, +the third voltage being a ratio defined by the values of the resistors. +%Taken as an entity the potential divider can be viewed as a {\dc}. That is to say we can treat the potential divider, comprised of two resistors -to act as a component. +to act as a {\dc}. % Using the EN298 specification for resistor failure~\cite{en298}[App.A], we can assign failure modes of $OPEN$ and $SHORT$ to the resistors individually (assignment of failure modes