\section{E-6: Cathode Ray Oscilloscope and Differential Amplifiers}\label{e08_scope}
\noindent OBJECTIVES:  To learn the basic operation of an oscilloscope in order to
observe the voltage {\it vs} time relationships of basic electrical signals.

%\subsection{
\noindent {\em Preliminary Question:}\begin{itemize}
\item \latex{\vspace*{-.08in}}
What signal (voltage or otherwise) {\it vs} time displays do you have in your house?
\end{itemize}

\noindent APPARATUS: 
\begin{enumerate}
\item[] \latex{\vspace*{-.08in}}Dual-trace oscilloscope plus manual, 
signal generator plus 
frequency counter, digital multimeter, (DMM);
circuit plug board \& component kit; differential amplifier.
\end{enumerate}


\begin{center}
{\bf Part~A -- Operation~of~the~Oscilloscope}\\
(Leader, Model 1021, or Hitachi, Model V-202F)
\end{center}

\noindent INTRODUCTION: 
\begin{enumerate}
\item[] \latex{\vspace*{-.08in}}
The oscilloscope is basically a graph-displaying device --
it draws a graph of an electrical signal. In most applications
the graph shows how signals change over time: the vertical
(Y) axis represents {\em voltage} and the horizontal (X) axis
represents {\em time}. The intensity or brightness of the display is
sometimes called the Z axis. This simple
graph can tell you many things about a electrical signal. Here are just
a few, you can ... 
\begin{itemize}
\item \latex{\vspace*{-.07in}}determine the time and voltage values of a signal. 
\item \latex{\vspace*{-.07in}}measure the frequency of an oscillating signal. 
\item \latex{\vspace*{-.07in}}see the ``moving parts'' of a circuit represented by the signal. 
\item \latex{\vspace*{-.07in}}tell how often a particular portion of the signal is occurring relative to other portions. 
\item \latex{\vspace*{-.07in}}find out how much of a signal is direct current (DC) or alternating current (AC). 
\item \latex{\vspace*{-.07in}}tell how much of the signal is noise and whether the noise is changing with time. 
\end{itemize}

\item[] \latex{\vspace*{-.08in}}Your dual trace analog oscilloscopes have circuits which 
can alternately 
display sweep signals from two different input channels (Y$_1$ and Y$_2$).  
Unfortunately this instrument can address
only a single point on the display window at one instant in time.
However the screen is coated with a phosphor coating which whose image
persists for a short time.  When this property is combined with
the finite time resolution of the eye one can observe ``simultaneous'' 
dual traces. 

\begin{center} 
\fbox{{\em CAUTION:} 
Avoid placing signal generator on top of scope.}
\end{center} 
[Stray
magnetic fields from power supplies can interfere with the cathode ray tube
(i.e., the display or CRT) operation and create a noisy (fuzzy) ``trace.''] 

If you are unfamiliar with the various control knobs and switches you should
read through this section carefully. 
\end{enumerate}

\noindent SUGGESTED PROCEDURE (refer to Fig.~1):
\begin{enumerate}                                             
\item \latex{\vspace*{-.07in}}Using a BNC cable and the sinusoidal wave signal output from the function 
generator (1kHz, 1V rms) connect the signal to the CH1 input (\# 7) oscilloscope (or {\em scope}).  
Note that each input, CH1 and CH2,  has a three position switch (\#6 or \#15) for 
either grounding the input (GND), coupling the signal through a capacitor (AC), or a 
direct connection (DC).  Using the AC input ({\em use this position}) 
removes all DC components of the input signal. \latex{\vspace*{-.08in}}
%\begin{figure}[h] \centering
\begin{center} 
\latex{\hspace*{-.15in}\includegraphics[height=6.2in]{figs/e8-01.eps}
\\ Figure 1}
\html{ {\bf Figure 1} \\
      \includegraphics[height=7.2in]{figs/e8-01.eps}}
\end{center}
%\end{figure}
\latex{\vspace*{-.05in}}

\item \latex{\vspace*{-.1in}}Turn on the scope (\#1)and note the {\em four} main groups of 
controls:   
\begin{enumerate}
\item[i.] \latex{\vspace*{-.06in}}those associated with the {\em intensity} and {\em focus} of the trace 
\item[ii.] \latex{\vspace*{-.06in}}those controlling {\em vertical deflection} (\#6 thru 15).
\item[iii.] \latex{\vspace*{-.06in}}those controlling {\em horizontal deflection} (\#16 thru 19).  
\item[iv.] \latex{\vspace*{-.06in}}those associated with initiating the trace movement, TRIGGER,(\#20 thru 24).  
\end{enumerate}
\item  \latex{\vspace*{-.12in}}Nominal starting positions:  (If you have trouble finding the 
beam consult your instructor.) \latex{\vspace*{.02in}} \\
\begin{tabular}{|ll|ll|} \hline
 LEVEL(20) & 0 (or so) & VMODE(10)    & CH1 \\ 
 MODE(22)  & NORM    & VOLT/DIV & 0.2 V \\
 COUPLING(23) & DC     & RED knobs & fully CW (to CAL) \\
 SOURCE(24) & CH1      & AC/GND/DC & AC \\
 HOLDOFF(19) & fully CCW & POSITIONs (9,12,17) & centered \\ 
 TIME VARIABLE(16) & fully CW & INTEN/FOCUS/ILLUM & centered \\
 TIME/DIV(18)  & 0.2 ms & 9,12 and 16 & pushed in \\ \hline
\end{tabular}   
\end{enumerate}

\begin{center} {\bf Additional desciption of oscilloscope controls}   \end{center}
\begin{enumerate}
\item[A:] \latex{\vspace*{-.1in}}The {INTENSITY} knob controls the trace 
brightness\footnote{CAUTION: a stationary intense spot may damage the screen}
by varying the 
potential of a control grid or an aperture near the electron emitting 
cathode.  The {FOCUS} adjusts the trace sharpness by varying the 
potential on the focusing anode. {POSITION} knobs 
move the traces up 
and down, and also right and left.
\item[B:] \latex{\vspace*{-.07in}}The {VOLTS/DIV} and {red VARIABLE} knobs provide coarse and 
fine adjustment of the pattern height by varying the amplification of the 
signals from the input terminals.  To read the {\em correct} volts/division 
shown on the scales, the red variable knobs {\em must} be in the {CAL}
(calibrated) position (fully clockwise).\latex{\vspace*{.02in}}

\noindent The {V MODE} lever permits display of either or both channels; for 
both use either {ALT} for alternate sweeps, or {CHOP} which switches 
channels at a 250~kHz rate.
(Hitachi's {DUAL}
automatically switches from {ALT} to {CHOP} at a {TIME/DIV} setting =~1~ms/DIV).\latex{\vspace*{.02in}}

\noindent Except for the Hitachi, pulling out the {CH1 POSITION} control ({PULL ADD}) 
adds both channels (CH1 + CH2), and
pulling out the {CH2 POSITION} control ({PULL INV}) inverts its 
signal (-CH2). Hence using 
both {PULL ADD and PULL INV} gives the {\em difference} of the two channels (CH1 + -CH2). 
(For the Hitachi use the {ADD or DIFF} on
the vertical {MODE} lever).
\item[C:] The {TIME/DIV and VARIABLE or SWP/VAR}
knobs give coarse and fine control of the trace horizontal sweep motion.  Again for the 
{TIME/DIV} scales to be {\em correct}, set the {VARIABLE}
(or {SWP/VAR}) knob at the {CAL} position (fully clockwise).

\noindent Once the trigger requirements have been satisfied, the scope 
sweeps the trace horizontally from left to right 
at a uniform rate (set by the TIME/DIV knob), and then quickly returns the trace to the 
start position.  These trigger circuits are useful for
synchronizing the sweep start with some common feature of the input signal although the signal
itself may not be perfectly periodic (e.g.~your heartbeat).
(see Fig.~2).

%\begin{figure}[h] \centering
\latex{\vspace*{-.1in}}
\begin{center} 
\latex{\hspace*{.0in}\includegraphics[height=2.75in]{figs/e8-02.eps}
\\ Figure 2}
\html{ {\bf Figure 2} \\
      \includegraphics[height=3.8in]{figs/e8-02.eps}}
\end{center}
\latex{\vspace*{-.1in}}
%\end{figure}

\item [D:] The {TIME/DIV} knob, when set to the \framebox{X-Y} position,
disconnects the internal horizontal sweep generator and uses the {CH1~X} input to specify 
the  horizontal sweep; {CH2} is still connected for vertical 
displacements and thus becomes {Y}. (For Hitachi also set {MODE} 
lever to {CH 2 X-Y}).  The resultant {X-Y} pattern forms a Lissajous figure.


\item[E:] Other triggering options:
 \begin{itemize}
\item \latex{\vspace*{-.07in}}{\bf To~sweep~automatically:}  Set trigger {MODE} lever (22) to {AUTO}.
\item \latex{\vspace*{-.07in}}{\bf To~trigger~and~sweep~only~on~a~large~signal:}  Set trigger 
{\em MODE} lever (or 
Hitachi horizontal {MODE}) to {NORM} and set {SOURCE} lever to the appropriate 
{CH1 or CH2}; then adjust trigger {LEVEL} knob (20) to desired amplitude.
\item \latex{\vspace*{-.07in}}The trigger {COUPLING} lever can also couple the  
trigger input signal  
directly (DC); through a large capacitance, (AC); or (except 
Hitachi) through a filter
({HF REJ or LF REJ}) which can reject high or low 
frequencies: $>$~4~kHz or $<$~4~kHz.  
\item \latex{\vspace*{-.07in}}The trigger {SOURCE} lever has options of triggering at 60 Hz 
({LINE}) or by using an external trigger ({EXT}) signal.

\end{itemize}
\end{enumerate}

\begin{center} {\bf Part~B~-~Suggested~Oscilloscope~Experiments}
\end{center}

\begin{enumerate}
\item \latex{\vspace*{-.07in}}{\em Observe both sine and square wave signals of various frequencies.}  
Experiment with setting to learn the effect of different controls, (e.g. automatic {\em vs}
triggered sweeps).  For the square waves look both at low frequencies and 
at maximum frequencies.  Notice any effects of changing the input coupling (\#6 or 15) 
(switch back and forth from AC to DC).  Sketch the appearance of ``square'' 
waves at high and low frequencies.  If possible, explain the differences.

\begin{enumerate}
\item[i.] \latex{\vspace*{-.07in}}Verify the calibration of the scope's Y scaling by using the 0.5 volt peak 
to peak square wave signal from the calibration terminal {(CAL or \#11)}. 
To connect this signal to the scope, just 
touch the exposed calibration terminal with the center gold pin of the 
{\em bayonet coaxial} (BNC) connector 
on the input cable.  

\item[ii.] \latex{\vspace*{-.07in}}Use a digital multimeter (DMM) to {\em measure} both the {\em sine}
wave and {\em square} wave voltage output of the signal generator.  
Avoid very high frequencies since
capacitative loading may then be a problem when the signal generator is 
also connected to the scope.

\item[iii.] \latex{\vspace*{-.07in}}Compare the DMM readings (which are r.m.s.~or 
``effective'' voltages) 
with the {\em peak-to-peak} voltages reading directly off 
the scope screen.  Are they consistent? \\ Remember the voltage amplitude is 
one-half the peak to peak voltage and the rms voltage is 
$$\frac{\mbox{peak voltage}}{\sqrt{2}}=\frac{\mbox{peak-to-peak voltage}}{2.818}~~!$$
\end{enumerate}
\item OPTIONAL: Check the calibration of the 
scope's  X (horizontal) scaling  by 
using the TIME/DIV reading to measure the period for one wavelength of the 
signal.
Compare the deduced frequency with signal generator scale setting and/or 
that of a frequency meter.
\end{enumerate}


\noindent OPTIONAL:
\begin{enumerate}
\item[] \latex{\vspace*{-.07in}}{\em Lissajous~Figures:}  When two periodic motions at right angles 
combine, the resulting pattern is generally very complex.  However, sine 
waves whose frequencies are in small integer ratios give simple 
stationary patterns.  For example see Fig.~3.

To produce {\em Lissajous} figures on the scope, set the {TIME/DIV}
control to \framebox{X-Y}.  Connect the 60 Hz terminal to the 
{CH1~X} input.  To the {CH2~Y} input apply a sine wave input
whose frequency bears a simple ratio with respect to 60 Hz. (For the Hitachi,             
also set the vertical MODE lever to CH 2, {X-Y}.) 

A Lissajous pattern should 
result.  Adjust amplitudes and positions to locate the figure properly
on the screen.  
The frequency scale on the signal generator may not be accurate,
but the 60 Hz power line is an excellent frequency standard. \\  
{\em Use Lissajous figures to calibrate your signal generator at 120~Hz and 
180~Hz}.

Observe and explain patterns with the frequency ratios of Fig.~3.  Also try 
a ratio 2:3.
%\begin{figure}[h] \centering
\begin{center} 
\latex{\hspace*{.0in}\includegraphics[height=2.2in]{figs/e8-04.eps}
\\ Figure 3:  Examples of Lissajous figures.}
\html{ {\bf Figure 3:} Examples of Lissajous figures. \\
      \includegraphics[height=2.2in]{figs/e8-04.eps}}
\end{center}
%\end{figure}
%\latex{\vspace*{-.1in}}
\end{enumerate}

\newpage

\begin{center}
{\bf Part~C~--~Differential~Amplifiers} 
\end{center}
\noindent INTRODUCTION:
\begin{enumerate}
\item[] \latex{\vspace*{-.07in}}
Amplifiers are devices which usually increase the amplitude 
of the output signal compared to the input signal.  The customary symbol 
for an amplifier is a triangular shape:

%\begin{figure}[h] \centering
\begin{center} 
\latex{\hspace*{-.25in}\includegraphics[height=1.4in]{figs/e8-05.eps}
\\ Figure 4}
\html{ {\bf Figure 4} \\
      \includegraphics[height=1.4in]{figs/e8-05.eps}}
\end{center}
%\end{figure}
%\latex{\vspace*{-.1in}}

In the sine wave example above, the gain is 10 and the input signal is 
between an input terminal and ground.  The internal oscilloscope amplifiers for
channels Y$_1$ and Y$_2$ are of this type and have a common ground.  Because of 
this common ground, one has problems 
in using a scope to examine 
{\bf simultaneously} voltages across individual circuit elements that are in 
series (see below, also E9 lab).

\noindent We can avoid these problems by interposing ``differential 
amplifiers'' which 
have two inputs $V'$ and $V''$, (neither at ground), and which 
amplify only the voltage 
difference ($V'-V''$).  Symbolically:

%\begin{figure}[h] \centering
\begin{center} 
\latex{\hspace*{.0in}\includegraphics[height=1.4in]{figs/e8-06.eps}
\\ Figure 5}
\html{ {\bf Figure 5} \\
      \includegraphics[height=1.5in]{figs/e8-06.eps}}
\end{center}
%\end{figure}
%\latex{\vspace*{-.1in}}

Note now that the ground of the output signal is independent of any input 
ground.
\end{enumerate}

\noindent SUGGESTED~EXPERIMENTS: 
\begin{enumerate}
\item[1.]  \latex{\vspace*{-.06in}}{\em Become familiar with the circuit plug board (Fig.~6) and the banana type 
plug-in components}.  Note there are 24 groups with 9 socket plug-in holes in each group.  
While the 9 plug-in holes in each group are electrically connected together, each of the 24 groups 
is isolated unless connected by plug-in components.  Two isolated metal 
bus bars (with banana plug-in holes) on the sides may facilitate common 
connections for some circuits.


%\begin{figure}[h] \centering
\begin{center} 
\latex{\vspace*{-.1in}}
\latex{\hspace*{.0in}\includegraphics[height=2.7in]{figs/l104/e08-2r.eps}
\\ Figure 6}
\html{ {\bf Figure 6} \\
      \includegraphics[height=3.2in]{figs/l104/e08-2r.eps}}
\end{center}
%\end{figure}

\latex{\vspace*{-.1in}}
\html{\begin{tabular}{p{3.5in}l} }
\latex{\parbox{0.57\linewidth}}
{The plug-in components (metal bridges, resistors, 
capacitors, inductors, or 
other circuit elements) will only connect between adjacent groups of the 9 
(already connected) plug-in holes or from the edge metal bus bars to an 
adjacent 9 hole group.  We also provide coaxial cable to 
banana plug-in connectors:
these facilitate using signal generators, scopes, etc.~with the 
circuit plug-in board. {\em Be sure to notice the raised retangular 
protuberance on one side of the connector.} 
This indicates the connector ground bar side.}
\html{ & }
\latex{\parbox{0.40\linewidth}}
{\latex{\hspace*{.2in}}
\latex{\includegraphics[height=2.2in]{figs/l104/n02-3.eps}}
\html{\includegraphics[height=2.2in]{figs/l104/n02-3.eps}}
%begin{center} {\bf Figure~1:} Dual differ .
%end{center}
}
\html{ \cr \end{tabular}  }

As a first configuration use the RC series circuit sketched in 
Fig.~6 as a guide using the scope to observe simultaneously the output of the
AC signal generator and the signal across the resistor.  How do the relative
$V_{\mbox{\tiny peak}}$-to-$V_{\mbox{\tiny peak}}$ amplitudes compare at low, 
medium and high frequencies.  It may help to know that the reactance $X_C$ of a 
capacitor is $X_C = 1/\omega C$, the impedence $Z$ is $Z=\sqrt{R^2+X^2_C}$ and
medium frequencies are given by $X_C  \approx R$. 
Qualitatively explain the behavior.  

Do to voltage peaks always occur at the same time?

\item[2.] \latex{\vspace*{-.08in}}The {\em phase shift} $\phi$  between the current (monitored by the voltage drop across the
resistor) and the voltage has the relation $\tan \phi =
-X_C/R=V_C/V_R$.  To observe this behavior you must simultaneously monitor the signal across the
resistor and capactors.  Unfortunately, only one of these components does reference to ground; a
necessary aspect of your scope inputs. (Which
one?)  To compensate for this short coming a module containing dual differential amplifiers
is provided.    

Connect the resistor and capacitor signal to the differential amplifiers as shown in the
figures below.  Connect the outputs of the differential amplifiers to 
the scope CH~1 and CH~2 inputs, and set both gains to 1. \latex{\vspace*{-.15in}} 

\latex{\hspace*{-.25in}\parbox{0.50\linewidth}{
        \begin{center}
        \includegraphics[height=2.5in]{figs/l104/e08-7.eps} \\ 
        Figure~7: Dual differential amplifier module.
	\end{center}}
        \parbox{0.50\linewidth}{\begin{center}
        \includegraphics[height=2.in]{figs/l104/e08-8.eps}\\  
	Figure~8: Inputs to differential amplifiers.\end{center}}
	\vspace*{-.15in}}
	
\html{\begin{tabular}{p{4.in}p{4.in}}
       \includegraphics[width=2.2in]{figs/l104/e08-7.eps} 
       {\bf Figure~7: Dual differential amplifier module.} &
       \includegraphics[width=3.6in]{figs/l104/e08-8.eps} 
       {\bf Figure~8: Inputs to differential amplifiers.} 
        \cr 
	\end{tabular} }
  
Sketch the oscilloscope display when $X_C=R$ and show how you can use this information to
obtain the phase shift.  Compare your result to that of the $\tan \phi$ formula.  

\item[3.] \latex{\vspace*{-.1in}}Replace the capacitor with the diode and use the differential amplifiers to 
now observe the action of a 
silicon diode on an A.C.~signal. 
\end{enumerate}

\begin{description}
\item \latex{\vspace*{-.1in}}NOTE:
Silicon diodes (Fig.~9) are junctions between silicon semiconductors 
with different type doping: n-type with an impurity which easily donates 
electrons, e.g.~phosphorus (P) in silicon;\footnote{As one might 
expect since silicon has valence 4, phosphorus valence 5, 
and aluminum valence 3} 
and p-type with an ``acceptor'' impurity, 
e.g.~aluminium (Al) in silicon$^5$. 
The junction between the two types
becomes a very non-linear device which if subjected to an electric field
acts almost as a one way valve to current flow.  The diode symbol 
has the arrow pointed in the direction of conventional easy current flow 
(from p-type to n-type) though actual electron flow may be in the opposite 
direction.
\end{description}
\latex{\vspace*{-.1in}}
%\begin{figure}[h] \centering
\begin{center} 
\latex{\hspace*{.0in}\includegraphics[height=1.3in]{figs/e8-08.eps}
\\ Figure 9}
\html{ {\bf Figure 9} \\
      \includegraphics[height=1.7in]{figs/e8-08.eps}}
\end{center}
%\end{figure}
\latex{\vspace*{-.1in}}

\noindent {SUGGESTED EXPERIMENT:}
\begin{enumerate}
\item[]  \latex{\vspace*{-.06in}}Set up the circuit plug board as shown in Fig.~10. Connect Y$_1$ and Y$_2$ to 
the two scope inputs.  

%\begin{figure}[h] \centering
\begin{center} 
\latex{\hspace*{.0in}\includegraphics[height=1.7in]{figs/e8-09.eps}
\\ Figure 10}
\html{ {\bf Figure 10} \\
      \includegraphics[height=2.0in]{figs/e8-09.eps}}
\end{center}
%\end{figure}
\latex{\vspace*{-.1in}}
Vary the amplitude of the signal generator input 
and sketch the resultant waveforms across the resistor and across the 
diode.
\end{enumerate}
\hfil
