Capacitors hold charge.  Capacitors do not conduct.

We measure capacitance in farads and charge in coulombs (equivalent to the charge 6×10^18 electrons).

a capacitor with 1 farad of capacity will charge 1 coulomb of charge after 1 volt has been applied across its terminals for 1 second.

Q=CV

The capacitor is basically plates of two conductors separated by a non-conductor.  When a voltage is applied, the charge accumulates.  And when the voltage has been removed, then it can release that charge.

I found this really cute video that explains a capacitor:

The total capacitance of capacitors in parallel is the sum of the capacitors.

Ctotal = C1+C2+C3…

Capacitors in parallel will always result in a BIG capacitance.

However capacitors in series will always result in a smaller capacitance.  Two capacitors in series have the capacitance of:

Ctotal = (C1C2)/(C1+C2)

Capacitors in series will always result in a capacitance smaller than the smaller capacitor.

Since capacitors do not conduct current, they do not dissipate power.

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Let’s cover two sections today:
1.09 Other signals
1.10 Logic Levels

We have been looking at Voltage as a function of time and seeing how it will look on a graph.  The past few days we have talked about graphs that are sine wave.

But there could be other ways that this could look too.  Consider if voltage started out at zero and continued to increase.  It would look something like this:

But it is not possible to increase voltage indefinitely and so the graph would really look like this:  (Ramp with limit)

But there are other interesting graphs to.  Consider the case of voltage increasing to a point, and then when it reaches a certain point it goes to zero and then begins again.  Let’s say you have a circuit that triggers at a certain voltage, and a capacitor that you are charging up till that point.  It might looks something like this sawtooth wave:

But you can also imagine a case where it reaches a point and decreases at the same linear rate.  This would look like a triangle wave:

And then there is noise, a complex, background static that we always need to consider and usually minimize:

Square waves

Steps

Spikes

But in digital electronics we concern ourselves with logic levels and interrupting a particular voltage as either a true or a false; as a on or a off; as a 1 or 0.  Most digital electronics have a threshold voltage.  Above that voltage it is considered to be true/on/1.  Below that voltage it is considered to be false/off/0.

The next few sections in The Arts of Electronics deals with signals.  What are the characteristics of signals?  Amplitude, frequency, shape, etc.

The values we are looking at is voltage as a function of time.  The most basic signal is the sinusoidal signal.  Have you ever graphed y=sin(x) and end up with:

But how would you compare this wave to the following:

There are two key things to think about when comparing sine waves:  frequency and amplitude.    The amplitude is the distance from y=0 to the top of the sine wave.  The frequency is how many times the wave repeats in a given period of time.  We typically use the unit hertz (Hz) for frequency, which is one cycle (or period) per second.  Lets take a look at period and amplitude in our original sine graph:

The formula that you should remember is

V=A*sin(2*pi*f*t)

A is the amplitude in volts, f is the frequency in Hz and t is the time in seconds.

Ohm’s law is R=V/I.  For the ordinary resistance, this is a constant proportion for a large range of V.  But this is not true for all devices.  Today we look at the Zener diode which has a high resistance up to a point and then almost no resistance for a large range of V.  Also, we look at the tunnel diode (also known as the Esaki diode) which actually has a negative resistance over a particular range of V.

Any two terminal network of voltage sources and resistors can be replace by a single voltage source in combination with a single resistor.  This is called the Thevenin’s equivalent circuit:

The first step is to identify the two terminals of the network.

Then to figure out Rth, replace any voltage sources with short circuits and any current sources with open circuits.

Calculate the voltage between the two terminals.

Then figure out Vth between the two terminals.

To figure this out using testing and measuring, it is only necessary to find the voltage at the two terminals with power on, and the resistance with power off.

This can greatly simplify circuit analysis of complex circuits.

Check out videos on YouTube with more detailed information:

www.youtube.com/results?search_query=thevenin+equivalent+circuit

Let’s take a look at the symbols for voltage sources and current sources. Also, let’s discuss the properties of the ideal voltage source and the ideal current source.

The ideal voltage source will maintain the same voltage between its terminals regardless of the load. This is easiest with an open circuit but becomes impossible with a short circuit.

The ideal current source will maintain the same current regardless of the resistance of the load. This is easy with an open circuit but becomes more and more difficult as the resistance increases.

Voltage Dividers take an input voltage and gives you a smaller, fractional output voltage. This can be useful for volume control or when interfacing between logic circuits that run at 5V with new/lower power devices that run at 3.3V.

A voltage divider is a simple circuit made up of only two resistors (R1 & R2 in the diagram below).

Art of Electronics 2nd Edition p 4-7

What you MUST learn

Resistance (represented in formulas as “R”) measured in Ohms which is represented using the symbol:

Resistance is the relationship between Current (I) and Voltage (R).

This relationship is defined by Ohm’s law:  R = V/I.

Circuit diagrams represent resistors as

Resistors in Series: (Always bigger)

R= R1 + R2

Resistors in Parallel: (Always smaller)

R = (R1*R2)/(R1+R2)

Shortcut #1:

A large resistor in series with a small resistor has the resistance of the larger one, roughly.

A large resistor in parallel with a  small resistor has the resistance of the smaller one, roughly.

Try to develop an intuitive sense of the voltage and current in the parts of the circuit.  Do not try to calculate to be extremely precise because the precision of the components will make this pointless.  Also, good circuit design should be tolerant of variations.

Power:

P=IV

Using Ohm’s law you get:

P=(I^2)R

P=(V^2)/R

Things good to learn

The inverse of resistance is conductance (represented by “G” in formulas)  G=1/R

Restatement of Ohm’s law:  I=GV

Conductance is measured in siemens

siemens is also known as mho (ohm spelled backwards)