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Robin P. Clark 2012-09-04 08:29:14 +01:00
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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 %% GARK BEGIN
To demonstrate the principles of FMMD, we use it to analyse a 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+] \begin{figure}[h+]
\centering \centering
@ -490,20 +488,24 @@ commonly used circuit, a non-inverting amplifier built from an op amp~\cite{aoe}
\end{figure} \end{figure}
% %
The function of the resistors in this circuit is to set the amplifier gain. 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 --- The resistors act as a potential divider---assuming the op-amp has high impedance---and
and program the inverting input on the op-amp program the inverting input on the op-amp
to balance them against the positive input, giving the voltage gain ($G_v$) to balance them against the positive input, giving the voltage gain ($G_v$)
defined by $ G_v = 1 + \frac{R2}{R1} $ at the output. 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} \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}'. 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 $R2$. 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 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], 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 we can assign failure modes of $OPEN$ and $SHORT$ to the resistors individually (assignment of failure modes