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Robin P. Clark 2012-09-04 08:29:14 +01:00
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22
submission_thesis/CH4_FMMD/copy.tex
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@ -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