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the data by setting enable low again.
We strongly suggest that you wire up your two-digit display right away. While it is
fairly straightforward, it is as much wiring as you have done in any of the labs to
date. It should now be clear why we used common anode LED displays rather than
common cathode. Because the MM5484 connects outputs to ground, it only works
with a common anode display. Of course, you will still need resistors on each of the
outputs to limit the current through the LED segments. Each output in the MM5484
is rated for a maximum current of 15mA, so be careful not to exceed this specifica-
tion.
52 A Pragmatic Introduction to the Art of Electrical Engineering
What is a Capacitor?
What is a Capacitor?
In comedy, the stock market, and life in general, timing is everything. But up until
now, we have carefully avoided talking about timing when analyzing circuits. In
fact, all of the circuits we solved fall under the rubric of  DC circuits , that is, no
voltages or currents have been specified as functions of time. However, as we men-
tioned in the problem statement, we will be building a circuit that will give us a
pulse, the width of which will vary according to the pot setting. You can t do that
with just resistors and voltage sources.
In this chapter, we introduce the capacitor, often called a cap for short. Unlike the
devices we have study so far, it can not be characterized by a simple I-V curve. In
fact, if you attached a capacitor to almost any curve tracer, you would get a loop
instead of a single line. Clearly, this is not a single valued function, so something
weird is going on.
In order to understand this, we ll have to once again wallow in some basic physics.
The prototypical capacitor consists of two parallel conductive plates separated by
some insulator as shown in the figure below. Although charges do not actually flow
I
+Q
V
-Q
between the plates, placing some positive charge +Q on the top plate will push
away an equivalent amount of charge from the bottom plate, leaving it charged to -
Q. So in fact, from the outside, it looks as if current can flow through the capacitor.
The fundamental relationship for a capacitor is that the voltage across it will be pro-
portional to the charge stored on it. Recall that when we defined voltage, we said it
was the potential of separated charges. You might think that adding more charge
doesn t change the separation, and thus it wouldn t change the voltage. However,
adding additional charges becomes increasingly more difficult because the plate is
A Pragmatic Introduction to the Art of Electrical Engineering 53
Timing is Everything
already charged, and repels the new charges. Thus, adding each new charge takes
progressively more work, and this energy ultimately increases the potential.
An analogy with a fluid system might be helpful here. A capacitor is like a tank of
water. If you are pumping water in at the bottom of the tank you will need increas-
ingly more pressure as the tank starts to fill. The pressure at the bottom, a measure
of the potential, rises with the rising fluid level. In fact, for a tank of constant cross
section, the pressure will rise linearly with the amount of fluid in the tank just as the
voltage across a capacitor rises linearly with the amount of charge stored in it.
In equation form, the defining relationship for a capacitor is:
Q = CV
The constant of proportionality, C, is called the capacitance, and is measured in
farads, often abbreviated F. One Coulomb of charge stored on a one farad capacitor
produces one volt. One Farad is a huge amount of capacitance. In the lab, we will
generally be talking about capacitances ranging from 10-12 farads (or simply, one
picofarad, written 1 pF, and often pronounced  one puff ) to 10-3 farads (generally
written as 1000µF).
As nice as this equation may be, it doesn t tell us what we want to know: namely
what is the current as a function of the voltage. Current is the rate of change of
charge with respect to time, so we can take the derivative of this equation to yield:
-------
I = CdV
dt
In plain english, the current through a capacitor is proportional to the rate of change
of voltage across it. We can rewrite this in integral form as:
1-
V = ---
+"idt
C
This just says that the voltage across the cap will be proportional to the integral of
the current into the cap - just like the height of water in the constant cross section
tank is proportional to the integral of the fluid flow into it. So the voltage across the
capacitor depends upon the whole history of current flow into it. Now you can see [ Pobierz całość w formacie PDF ]