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@@ -246,35 +246,46 @@ When working with resistors at high frequencies, one must care for the parasitc
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Chapter 3.1.6 \cite{theCircuitDesignersCompanion}
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+\autoref{fig:nonIdealResistor}. \cite{theElectricalEngineeringHandbook}
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+
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+\begin{figure}[h]
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+ \includegraphics[width=0.5\textwidth]{nonIdealResistor}
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+ \caption{At high frequencies a resistors parasitic inductance and capacitance will affect the behavior of the circuit.}
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+ \label{fig:nonIdealResistor}
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+\end{figure}
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+
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\section{Measurement}
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-There are several measurement methods needed during the project. To verify the test pulses, voltage has to be measured over time. To verify the dummy loads, resistance has to be measured. To verify the attenuators, the magnitude response has to be measured. This chapter describes the necessary measurement theory required for this project.
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+There are several measurement methods needed during the project. To verify the test pulses, voltage has to be measured over time. To verify the dummy loads, resistance has to be measured. To verify the attenuators, their magnitude response has to be measured. This chapter describes the necessary measurement theory required for this project.
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\subsection{Resistance}
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-The circuit designers companion p.99
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+To measure resistance, a current is fed through the resistor and the resulting voltage is measured to calculate the resistance using ohms law. This is typically carried out using a multimeter and two probe wires connecting to each terminal of the resistor. When measuring very low valued resistors, however, the resistance in the probe wires can be significant in relation to the resistor measured and will affect the accuracy. One way of overcoming this is to perform a 4-wire measurement using a so called \emph{Kelvin connection}. In this method the current that is fed through the resistor using one pair of wire, and the resulting voltage is measured at the desired point using another pair according to \autoref{fig:kelvin_measurement}.\cite{theCircuitDesignersCompanion}
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+
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+\begin{figure}
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+ %\captionsetup{width=.5\linewidth}
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+ \includegraphics[width=0.5\textwidth]{kelvin_measurement}
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+ \caption{When measuring a low value resistor, the \emph{Kelvin connection} can be used to determine the resistance at the point where the voltmeter is connected without the resistance in the probe leads affecting the result.}
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+ \label{fig:kelvin_measurement}
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+\end{figure}
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\subsection{High Voltage}
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The highest voltage that can be generated by the pulse generators is 1500~V, which is higher than any of the standards require but will serve as the design goal for the verification equipment. This is a higher voltage than most acquisition devices can measure without the use of external attenuators \cite{source}.
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Resistive attenuators.. \todo[fyll på]
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-\subsection{Bandwidth and rise time}
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-The shortest rise time is xxx ns, which can roughly be compared to yyy MHz. \cite{source}
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-
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-The relationship and requirements, addition of rise time limitations etc
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-Combined rise time \cite{vilken_bok_menar_jag}.
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-
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-high speed digital design 83
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+\subsection{Oscilloscopes, bandwidth, rise time and probes}
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+When using an oscilloscope to measure voltage over time, there are several limiting factors to how fast signals one can measure. The oscilloscope itself has a specified bandwidth, as do the probe and any attenuators used. All of these combined determine how short rise times that can be measured accurately. The rise time of the measured will be affected by these properties and the rise time displayed on the oscilloscope screen will be approximately according to \autoref{equ:riseComposite}, where $T_N$ is the \SI{10-90}{\percent} rise time limit for each part in the chain. \cite{highSpeedDigitalDesign}
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-\subsection{Oscilloscope and probes}
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-\todo[Put good theory here]
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-
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-An oscilloscope measures voltage over time, using voltage probes.
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-
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-The oscilloscope has properties bandwidth...
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+\begin{equation}
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+\label{equ:riseComposite}
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+T_{rise~composite} = \sqrt{ T_1^2 + T_2^2 + ... + T_N^2}
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+\end{equation}
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-The probe also has properties..
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+Since \autoref{equ:riseComposite} is based on the rise time limitation but the specification usually tells the \SI{3}{\deci\bel} bandwidth, a conversion can be made according to \autoref{equ:bwToRise}. \cite{highSpeedDigitalDesign}
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-Commercial probes are expensive
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+\begin{equation}
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+\label{equ:bwToRise}
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+T_{10-90} = \frac{0.338}{F_{ \SI{3}{\deci\bel}}}
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+\end{equation}
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\subsection{Measurement errors}
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\todo[Put good theory here]
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Jonatan Gezelius
