
ELECTRONIC DESIGN NOTES #1  POTENTIAL DIFFERENCE, CURRENT, IMPEDANCE

Commonly, people use the term
"voltage" to name Electrical Potential Difference. Things
are this way. Our Atomic Universe is composed of atoms, and we
know about 118 of them. Each atom has a nucleus with positively charged particles named
"protons". Around the
nucleus, at a certain distance, there are tiny electrons spinning continuously, very fast, and they hold the
mobile negative charges. The number of electrons varies from 1 to 118, plus or minus
a few more. Important to
remember is, the electrons are grouped in "electronic orbitals" around the nucleus.
In normal conditions, the electrons live happily within their electronic orbitals, and the atoms are balanced electricallywell, more or less. In particular conditions, however, the electrons on the last orbital may leave their
rightful place, and in that case the atom becomes electrically charged, as
follows:
1. if the electrons leave the last orbital, the atom becomes a "positively charged
ion"; 2. if external electrons come on the last orbital, the atom becomes a "negatively charged ion".
Because they can move form one atom to another, the electrons on the last orbital, in metals, are named
"free electrons". Only free electrons can leave the atom, in normal conditions.
Electricity is a generic term used to name various effects produced by electrons.
Historically, electricity is used on a large scale for about 100 years. However, electricity was known since old
times.
The name of "electron" and the idea that it is a mobile electrical charge was first defined by Thales
of Miletus (624546 BC) during the Hellenic Civilization. However, there are some proofs that electricity was used
5000 years ago during the Egyptian Civilization, and even 7000 years ago during the Sumerian one.
In order to present electricity in this page, the following (rudimentary) structure was employed:
1. Electrostatics
2. Electric Potential Difference
3. Insulators and Conductors
4. DC current
5. AC current
6. Impedance
7. Kirchhoff's Laws
NOTE The basic
notions highlighted in this page are related to a few electronic
design topics presented in the first part, Hardware Design, of
LEARN HARDWARE FIRMWARE AND SOFTWARE
DESIGN.

1. ELECTROSTATICS
Mr. Thales of Miletus did the following experience. He took an amber baguette, then he rubbed it
vigorously with a
piece of cloth. His baguette became charged with "electrostatic voltage". Next, he noticed the amber baguette was
able to attract small pieces of cloth, and paper. That experience, plus many similar ones, helped him define the
electron.
Later, his experience was repeated in laboratory conditions. The baguette was made of glass,
at that time, and it was
charged electrically by rubbing it with a piece of fur. The baguette was brought in touch with
the sphere
A, made of metal and isolated from ground via a wooden support. Next, the sphere A became charged positively
as it is presented in Fig 1.
If a second sphere, B, was brought close to sphere A, it was noticed that sphere B
also becomes electrically charged via "electrostatic
induction" although overall on its surface it is still neutral electrically. The distribution of
the electrical charges on sphere B surface is illustrated in Fig 1.
Fig1: Electrostatic Induction 

Electrostatic electricity
produces an "electrostatic field", very much similar to the magnetic one. Further, any body in proximity to an
electrostatic field becomes electrically polarized.
A French scientist, Charles Augustine de Coulomb (17361785), has discovered that:
1. two isolated bodies charged with the same electric polarity repel each other;
2. two isolated bodies charged with different electric polarity attract each other.
The attraction or repulsion forces are caused by the electrostatic field, and
they are sufficiently strong in close
proximity to the charged bodies. Consequently, Mr. Coulomb has stated a Law that bears his name:
Coulomb's Law:
F = k * Q_{1} * Q_{2}
/ r^{2 }[N]
F is the attraction/repulsion force in Newtons Q1 and Q2 are the values of the two electrical charges in Coulombs r^{2} is the square distance between the two charged bodies in meters k = 8.988*10^{9} [N*m/C^{2}] is a proportionality constant;
the constant k was calculated as: k = 1 / (4 * PI * ε) PI = 3.141592 is the PI number ε = 8.854 * 10^{12} in [C^{2}/(N*m^{2})] is
"electric permittivity" in vacuum
Definition One coulomb represents the electrical charge capable of repelling a similar electrical
charge positioned one meter away, in vacuum, with a force of 8.988*10^{9} [N]
Another great scientist, Mr. Michael Faraday (17911867), has made precise laboratory measurements, and he
defined Electric Field Intensity.
Electric Field
Intensity:
E = F / Q [N/C]
The enigmatic electric field lines have a radial distribution around the electrically charged body. On the surface
of an imaginary sphere, positioned at a certain distance from the electrically charged body, the intensity of the
Electric Field is constant.
By substituting in the above formula the force F with its expression calculated in Coulomb's Law, Electric Field
Intensity becomes:
Electric Field Intensity for one electrically charged point (body):
E = (1 / 4*PI*ε) * (Q / r^{2})
A German scientist, Mr. Carl Friedrich Gauss (17771855), has calculated the number of electric lines passing
through a closed surface (a sphere) enclosing an electric charge Q.
Gauss' Law:
N = Q / ε
N is the number of electric lines of force; it is independent of the radius
ε is electrical permittivity in vacuum 
2. ELECTRICAL POTENTIAL DIFFERENCE
Definition
Electrical potential difference between two electrically charged points A and B is the work
needed to move charge "Q" from A to B
Electric Potential Difference: ΔV = V_{A}  V_{B}
= W / Q
Definition
Electric potential difference between two points positioned 1 meter away is one volt if
it requires one Joule of external work to move a charge of one Coulomb from one point to the other.
Volt definition:
1 [V] = 1 [J] / 1 [C]
Because W = F*d and F = Q*E we have
W = Q*E*d and ΔV [N*m/C] = E * d
W is the work needed to move electrical charge q for distance d
NOTE Electrical potential difference, also known as "voltage", is a relation/state between two electrically charged
points; for example, the poles of a battery car. Technically, the two poles are "floating", unless we
connect one pole to car's body. However, even in that case, the two poles are still floating when they
are related to Earth's potential (true ground), because the body of the car is isolated by tires (rubber).
Floating voltages need to be avoided, because they could reach very high voltages when related to Earth's (true)
ground.

3. INSULATORS AND CONDUCTORS
We know 118 atomic elements, and about two hundred thousand substances, natural and synthetica substance is
built out of molecules which in turn are composed of atoms (or elements). All elements and substances may be
electrically polarized, but not all of them allow the conduction of electrical current. Generally, metals are
known to be good electrical conductors.
Electrical current conduction is a complex phenomenon. Suppose we connect the poles of a battery
via a metallic
wire. Electrical current starts "flowing" through that conductor almost instantly, because it
"moves" at lightspeed (2.998*10^{8} [m/s]).
The way this "current flow" happens is characterized by the
following considerations:
1. in order to have current flow, we need first of all
an Electrical Potential Difference; 2. as soon as we do have Electrical Potential Difference, on the surface of the conductor ONLY free electrons start
jumping to the adjacent atoms; 3. the "flow of current" is in fact billions of small jumps executed by billions of free electrons from
one atom to the next one, ONLY. That means, it is highly unlikely one electron will jump through the entire length
of the conductor; 4. the direction of the electrons movement (the jumps) is from the negative pole () to the positive one (+).
However, people/scientists have decided the positive sense of the current is from (+) to (); 5. the intensity of the electrical current is controlled only by the resistance of the conductor.
NOTE The first condition above may be replaced by: "in order to have
a current flow, we need to excite the atoms using: 1. Electrical Potential Difference; 2. light; 3. temperature; 4. moving magnetic or electromagnetic fields; 5. moving electrostatic fields; 6. nuclear radiations; 7. many more."
Definition
The resistance of a conductor (R) is directly proportional to
its resistivity (ρ) and the
length of the conductor (L), and inversely proportional to the crosssectional area (A) of that conductor.
Resistance is measured in ohms.
Resistance:
R = ρ * L / A [Ω]
"ρ" in the above formula should be read as "RO": it is a letter of the Latin alphabet used to mark resistivity, a constant particular to each material (both to conductors and insulators) A is the crosssectional area Ω is the symbol for ohm
Definition A conductor is a material (substance, pure element, alloy) which allows the electric
current to flow. For metallic conductors resistivity has very low values.
Definition An insulator (or non conductor) is a material (substance, pure element, alloy) which does
not allow the electric current to flow, in normal conditions. That means, its resistivity is very high.

4. DC CURRENT
Electrostatic electricity doesn't help us much because:
1. the electrostatic voltages are too high;
2. it ends up in an instance/flash once shorted by conductors.
For practical applications, we need continuous electric current having
(relatively) low voltages. The most known source of DC (Direct Current)
is a chemical battery, marked with E, and you can see its schematic representation in Fig2.
Ohm's Law: R = U / I [Ω]
In Fig 2 Ohm's Law is calculated as: 1000 [Ω] = 12[V] / 0.012[A] 

Fig 2: An elementary DC circuit 

5. AC CURRENT
The
AC (Alternative Current) is supplied by the power utility grid, and it alternates with a frequency of:
1. 50 Hz in Europe (and most of the World)
2. 60 Hz in N America (and in a few more places)
What everybody should know is, both 50 Hz and 60 Hz are very dangerous for the human body. For example, if you
touch a 110 V 60 Hz live wire you could die; if the frequency is 120 Hz the danger is way lower; at 300 Hz
frequency things are far safer.
Transformers and electrical motors built for 50 Hz work (relatively) well and safe at 60 Hz; if they are built for
60 Hz, however, they may not work well at 50 Hzthey generate excessive
heat, slower speeds, hum/noise, etc.
Due to the alternating frequency (f) the instantaneous voltage and current (at time
t) in the AC circuit picture in Fig 3 is:
V(t) = V_{max} * sin (2 * PI * f * t)
I(t) = I_{max} * sin (2 * PI * f * t)
Please note in Fig3 that one pole is grounded, although that is not mandatory. However, ungrounded circuits are
floating, and they may reach very high voltages; by grounding them "we pull the voltage down to the ground
reference potential". All AC circuits are grounded. In Fig 3 the "live" wire is violet in color,
and the "marked" (or polarized, or grounded) one is blue.
Fig 3: An elementary AC circuit 

Note in Fig 3 that we have a load R of 10 kilo ohms: it is a resistive load. That is the reason the AC current
sine wave in Fig 4 follows the AC voltage exactly.
Fig 4: Voltage and Current in AC resistive circuits 

Please take a look at the above two pictures; note the following:
1. if the load is inductive, the AC current will "lead" the voltage sine wave by PI/4
2. if the load is capacitive, the AC current will "lag" the voltage sine wave by PI/4
The following formulas are employed to define the AC flow:
Effective voltage is: V_{eff} = 0.707 V_{max}
Effective current is: I_{eff} = 0.707 I_{max}
Maximum voltage is: V_{max} = 1.414 V_{eff}
Maximum current is: I_{max} = 1.414 I_{eff}
The period T of the AC current/voltage sine wave is: T = 1 / f

6. IMPEDANCE
In AC circuits the Ohm's Law needs to be written as:
Ohm's Law in AC circuits:
Z = U / I [Ω]
Z in the above formula is the "impedance" in ohms of the circuit pictured in Fig 5, and it is calculated with:
Impedance: Z = √[R^{2} + (X_{L}  X_{C})^{2}]
The impedance formula has two terms; they are:
Inductive Reactance: X_{L} = 2 * PI * f * L
Capacitive Reactance:
X_{C} = 1 / (2 * PI * f * C)
Fig 5: Impedance in AC circuits 

ATTENTION In most DC circuits we work with pulses having two DC states:
1. False, for a DC voltage of 0 V
2. True, for a DC voltage of +5 V
However, each time a pulse changes its state from True to False, and back, that DC circuit ceases to be a DC one:
it becomes an AC/pulsing circuit, therefore all its elements need to be
(re)calculated accordingly!
NOTE In AC circuits (including most DC onessee the above ATTENTION) when the frequency becomes very high, Inductive
Reactance increases a lot, and the inductor behaves like an interrupted circuitsimilar
to a capacitor.
NOTE In AC circuits (including most DC onessee the above ATTENTION) when the frequency becomes very high, Capacitive
Reactance also increases, therefore capacitors behave like resistors having very low values. Due to that
aspect, capacitors are said they have a "leakage/parasitic current".

7. KIRCHOFF'S LAWS FOR ELECTRICAL CIRCUITS
Kirchoff's Laws for electrical circuits are sufficient to calculate all currents and voltages in any
section of any circuit. They are:
Definition
The algebraic sum of the currents at a junction is zero.
Kirchoff's Law for electrical nodes:
Σ I = 0
NOTE In the above formula, the currents entering the junction/node have the (+) sign; if they leave that junction the
currents take the () sign. According to Kirchoff's Law, the currents of a
junction/node are summed algebraically.
Examples: Node A in Fig 6: 9.4[mA]  6.4[mA]  3[mA] = 0
Node E: 2.4[mA] + 4[mA]  6.4[mA] = 0
Definition
In any closed loop of an electric circuit the algebraic sum of the generated
voltages is equal to the algebraic sum of the potential drops (differences) existing on that loop.
Kirchoff's Law for electrical loops:
Σ E = Σ( I * R)
Examples: Loop XAFY in Fig 6: 12[V] = 0.003[A]*4000[ohm] Loop ABEF: 0[V] = 0.0024[A]*5000[ohm]  0.003[A]*4000[ohm]
Please use Fig 6 to test the two Laws. The generated voltage E is 12V, and Potential Drops are developed on each
resistor. Examples of closed loops are: # XAFY; XABEFY; ABEF; BCDE; etc
NOTE In the second Law, the current keeps its sign, and
potential drops are summed algebraically, considering the CW (clockwise) direction to be the positive one.
Fig 6: Kirchhoff's Laws 

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