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diff --git a/exercise05/exercise05.tex b/exercise05/exercise05.tex index 0591f3c..0c1ae31 100644 --- a/exercise05/exercise05.tex +++ b/exercise05/exercise05.tex @@ -12,6 +12,137 @@ \addcontentsline{toc}{section}{Exercise 5} \section*{Exercise 5} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{question}[subtitle={Mixers}] + \begin{tasks} + \task + Is the mixer a linear device like filters and amplifiers? + \task + What is the difference between unbalanced and balanced mixers? + \task + Why do mixers need a non-linear component? + \end{tasks} +\end{question} + +\begin{solution} + \begin{tasks} + \end{tasks} +\end{solution} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{question}[subtitle={Mirror frequencies}] + This is simplified block diagram of a receiver. + \begin{figure}[H] + \centering + \begin{adjustbox}{scale=0.8} + \begin{circuitikz} + \node[mixer](Mixer){}; + \node[oscillator, below=1cm of Mixer](LO){}; + \node[adcshape, right=2cm of Mixer](ADC){}; + \node[block, draw, right=1cm of ADC](Baseband){Digital signal\\ processing}; + + \draw (LO.south) node[below,align=center,yshift=-5mm]{LO}; + \draw (Mixer.north) node[above,align=center,yshift=3mm]{Mixer}; + + \draw (Mixer.west) -- ++(-1cm,0) node[rxantenna,xscale=-1]{}; + + \draw[-latex] (LO.north) -- (Mixer.south); + \draw[-latex] (Mixer.east) to[lowpass] (ADC.west); + \draw[-latex] (ADC.east) -- (Baseband.west); + \end{circuitikz} + \end{adjustbox} + \end{figure} + A signal of \SI{868}{MHz} should be received. The baseband is not zero-IF. The signal shall be mixed to \SI{1}{MHz} centre frequency. + + \begin{tasks} + \task + How much is the minimum ADC sampling rate? + \task + To which frequencies can the LO be tuned to? + \task + The \SI{868}{MHz}-band is shared with lots of other users. Which important piece is missing in the receiver signal chain? + \task + An IQ demodulator is used instead of the single mixer. Sketch the spectrum of the complex-valued baseband signal for both possible LO frequencies! + \end{tasks} +\end{question} + +\begin{solution} + \begin{tasks} + \end{tasks} +\end{solution} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{question}[subtitle={Constellation diagrams}] + Draw a constellation diagram of: + \begin{tasks} + \task + ASK (with 2 steps) + \task + BPSK + \task + QPSK + \task + 16-QAM + \end{tasks} +\end{question} + +\begin{solution} + \begin{tasks} + \end{tasks} +\end{solution} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{question}[subtitle={Constellation diagrams}] + A QPSK modulator has the following mapping and symbol constellation: + \begin{table}[H] + \centering + \begin{tabular}{|l|l|l|} + \hline + Data & Symbol & Phasor \\ + \hline + \hline + $(00)_2$ & 0 & $\SI{2}{mV} \cdot e^{j 0}$ \\ + \hline + $(01)_2$ & 1 & $\SI{2}{mV} \cdot e^{j \frac{\pi}{2}}$ \\ + \hline + $(10)_2$ & 2 & $\SI{2}{mV} \cdot e^{j \pi}$ \\ + \hline + $(11)_2$ & 3 & $\SI{2}{mV} \cdot e^{j \frac{3 \pi}{2}}$ \\ + \hline + \end{tabular} + \end{table} + The carrier is: + \begin{equation} + x_C(t) = \SI{2}{mV} \cdot \cos\left(2\pi \cdot \SI{50}{MHz} \cdot t\right) + \end{equation} + The symbol rate is $\SI{25}{MHz}$. After the DAC, an ideal low-pass filter with $\SI{25}{MHz}$ cut-off frequency is applied. + + \begin{tasks} + \task + How much is the transmission bandwidth? + \task + How many bits can be encoded per QPSK symbol? How many symbols are required to encode one byte (8 bits)? + \task + Draw the constellation diagram! + \task + The data byte $(2E)_{16}$ shall be transmitted. Give the sequence of phasors representing the data byte! + \task + Describe the problem with inter-symbol interference! + \task + Plot the I and Q baseband signals! Plot the RF signal after IQ modulation! + \task + The following phasors are received at the receiver: + \begin{equation} + [\SI{1.5}{mV} e^{j \SI{120}{\degree}}, \SI{1.5}{mV} e^{j \SI{300}{\degree}}, \SI{1.5}{mV} e^{j \SI{30}{\degree}}, \SI{1.5}{mV} e^{j \SI{210}{\degree}}] + \end{equation} + What would the decoded data be? What is the matter? + \end{tasks} +\end{question} + +\begin{solution} + \begin{tasks} + \end{tasks} +\end{solution} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\begin{question}[subtitle={Decibel}] |