1 Analyzing a Scope Plot
(written test, approx. 12 % of a 60-minute written test, SS2023)
On an oscilloscope is the following plot visible.
The measured current curve shall be visible as a dashed line.
The continuous line shows the voltage.
Use the correct symbols and units in your answers!
1. Calculate the frequency $f$ of the periodic signals.
- The sine waves repeat after $6 ~\rm divisions$ (e.g. from falling turning point to falling turning point of one curve)
- The scale is $0.1 ~\rm ms/Div$
\begin{align*} f &= {{1} \over {T}} \\ T &= 6 ~\rm Div \cdot 0.1 ~ms/Div \\ \rightarrow f &= {{1} \over {6 ~\rm Div \cdot 0.1 ~ms/Div}} \end{align*}
2. Write down the amplitude values for the voltage and current.
- The amplitude of the voltage is $3 ~\rm divisions$
- The scale is $5 ~\rm V/Div$
\begin{align*} \hat{U} &= 3 ~\rm Div \cdot 5 ~\rm V/Div \end{align*}
Similar for the current.
3. What are the RMS values of voltage and current?
\begin{align*} U_{\rm RMS} & ={{1} \over {2} } \sqrt{2} \cdot \hat{U} ={{1} \over {2} } \sqrt{2} \cdot 15 ~\rm V \\ I_{\rm RMS} & ={{1} \over {2} } \sqrt{2} \cdot \hat{I} ={{1} \over {2} } \sqrt{2} \cdot 0.5 ~\rm A \end{align*}
4. What is the phase shift on the system under test (in radiant and degree)?
A full period has an angle of $360°$ or $2\pi$ in $\rm radian$.
One has to find out the phase shift as a fraction of a period to get the value of the phase shift:
\begin{align*} \varphi &= \rm -{{0.5 ~Div} \over { 6 ~Div}} \cdot 2\pi \end{align*}