EC Fundamentals - Basic Electricity
EC basics
A firmware engineer, in addition to software coding skills, must also possess basic hardware knowledge. This is because firmware engineers often need to collaborate with hardware engineers to troubleshoot and resolve issues; therefore, hardware fundamentals are an indispensable skill for firmware engineers. This article will use basic electrical knowledge as an introduction to lay a solid foundation for becoming a firmware engineer.
Basic Electricity
Fundamental electricity is built upon the theories proposed by modern electrical scientists through experiments, and it forms the foundation of electrical-related technologies. It is thanks to the contributions of these scientists that the modern technology industry has developed and profoundly changed human lifestyles. Therefore, this article will introduce these important electrical scientists and the theoretical foundations established by their experiments.
Coulomb's Law
Francephysicist
Coulomb's law is the first quantitative law in the history of electricity.
The interaction force between two stationary point charges in a vacuum is inversely proportional to the square of the distance between them and directly proportional to the product of their charges.
The direction of the forces is along the line connecting them; like charges repel, and unlike charges attract.
The unit of electric charge, "coulomb," refers to 1 ampere of current, which is the amount of electric charge that accumulates through a cross-sectional area in one second.
Ampere's Law
Francephysicist
An electric current in a conductor will create a magnetic field in space, and the magnitude of the current is proportional to the integral of the magnetic field.
The unit of electric current, the ampere, refers to the amount of electric charge that passes through the cross-section of a conductor per second. One ampere is equivalent to one coulomb of electric charge.
Ohm's Law
German physicist
In terms of steady current, the magnitude of the current in a circuit is directly proportional to the electromotive force applied to the circuit and inversely proportional to the total resistance of the circuit.
V (volt) = I (ampere) × R (ohm)
A thermistor with a positive temperature coefficient (PTC) means that its resistance increases as the temperature rises (non-linear).
A thermistor with a negative temperature coefficient (NTC) is one whose resistance decreases as the temperature rises (non-linear).
Joule's law
British physicist
The heat generated in a current-carrying conductor (called Joule heating) is proportional to the square of the current I, the conductor's resistance R, and the time t during current flow.
I = Q/T , Q = I × T
V = I× R
Example -
W [watts] = Q × V = (I × T) × (I × R) = I2 × R × T
EX: How many watts does an 8-cell (4.4Ahr) 14.8Volt Lion battery provide?
W= Q × V = I × T × V = 4.4 × 14.8 = 65.12 (W)
capacitor
An insulating material is placed between the two plates to enable the element to store electrical charge.
C (farad) = Q (coulomb) ÷ V (volt)
During the moment of charging, the capacitor is considered a short circuit; however, once fully charged, the capacitor is considered an open circuit.
Time > RC: 0.632 * Capacitor full charge voltage.
Time > 5RC: The capacitor is fully charged.
When capacitors are connected in parallel, the total current in the circuit increases because Q = I × T, and the voltage remains constant. Therefore, the total current in the circuit increases when capacitors are connected in parallel (C).T = C1 + C2 + …
When capacitors are connected in series, the circuit current remains constant, and the voltage is the sum of the voltages across all the series-connected capacitors. That is, VT=VC1+VC2+…and V=Q/C. Therefore, the capacitor is connected in series with 1/C.T = 1/C1 + 1/C2 + …
Inductor
A component with inductive properties, formed by winding a wire into a coil, typically has a single coil and exhibits self-inductance; while a component with more than one coil exhibits mutual inductance.
L (Henry) = (N (number of coil turns) × Φ (magnetic flux)) ÷ I (current)
The inductor is considered an open circuit the instant power is applied; however, it is considered a short circuit after power is applied.
Factors determining the magnitude of inductance:
Number of coil turns
Cross-sectional area and length or average length of magnetic field lines path
Types of materials through which magnetic circuits pass
Inductors in series: LT = L1 + L2 + …
Inductors in parallel: 1/LT = 1/L1 + 1/L2 + …
Kirchhoff's Current Law
German physicist
In any circuit, the sum of the currents flowing into a node (mesh) is always equal to the sum of the currents flowing out of that node (mesh), that is, the algebraic sum of the currents in a node (mesh) is zero.
Kirchhoff's Voltage Law
In any closed loop, the algebraic sum of the electromotive forces of the power sources is equal to the algebraic sum of the voltage drops of each component.。
Nodal voltage method
By using Kirchhoff's current law to determine the current in each branch circuit based on the potential of each node in the network.
Choose an appropriate node as the reference node, which is at zero potential.
Mark the direction of each unknown master node and each branch current.
Use Kirchhoff's current law to formulate the current equations for each principal node.
Solve the equations for the steps to determine the potential of each node and the current of each branch.
Loop analysis method
In each loop of the network to be determined, apply Kirchhoff's voltage law to write a set of loop equations to determine the current in each loop.
Each mesh in the network is plotted as a loop current. The assumed direction is the direction in which the voltage or current source in the mesh flows out, but this direction is not important. If the solved current is negative, it means that the assumed direction is opposite to the actual current direction.
On each branch, mark the polarity of the voltage drop according to the direction of the loop current.
Write the voltage equation based on Kirchhoff's voltage law. This equation must include the power sources and voltage drops in the network.
The current in each common branch is equal to the algebraic sum of the currents in the two adjacent branches.
Solve the voltage equations to determine the loop current of each mesh and the current of each branch.
Overlap Theorem
In a multi-power circuit, the current in a branch or the voltage at a node is equal to the algebraic sum of the currents in that branch or the voltages at that node when each power source acts on the network individually.
First, consider the first power source. Remove the other power sources, which means short-circuiting the voltage sources and disconnecting the current sources in the other power sources.
Determine the effect of the power supply on the component (in terms of voltage or current).
For each power source in the circuit, repeat steps 1 and 2.
After calculating the power supply individually, add or subtract all the calculated currents. If the polarities are the same, add; otherwise, subtract. The result is the total effect of all power supplies on this component.
Thevenin's theorem
French Telegraph Engineer
Removing the component from the desired branch circuit creates an open circuit.
Short-circuit all voltage sources and open-circuit all current sources in the network. Find the equivalent resistance Rth across the network after the components are removed.
By replacing the voltage and current sources and applying various circuit solving methods, the voltage across the network after the components are removed is obtained, which is the equivalent voltage Eth.
Draw the Thevenin equivalent circuit and explain the steps.
By replacing the removed component with the Thevenin equivalent circuit, the effect of the removed component (e.g., IL, VL, PL, ...) can be easily determined.
Voltage source short circuit or current source open circuit: Rth = R1 // R2
Open circuit load: Eth = E * R2 / (R1+R2)
Norton's Theorem
In 1926, Edward Lawry Norton of Bell Labs (1898-1983) published a paper stating that in any network containing linear resistance and independent power sources, any circuit connected between two points can be represented by the Norton equivalent current I.NNorton equivalent resistance RNThey are connected in parallel.
Remove or open the desired branch component.
Short-circuit all voltage sources in the network. Disconnect the current sources. Find the equivalent resistance R of the component after removing its terminals.N。The first two steps and the Thevenin equivalent resistance RTHThe method for finding R is the same.N=RTH。
The voltage and current sources are replaced, and the two ends of the removed component are short-circuited. Using the aforementioned circuit-solving methods, the current flowing through this short-circuit is calculated, which is the equivalent current I.N。
Then draw the Norton equivalent circuit and put the removed components back in.
Finally, the effect of removing components can be determined from the simplified Norton equivalent circuit (e.g., IL, VL, PL, ...).
Voltage source short circuit or current source open circuit: RN = R1 // R2
Load short circuit: IN = E / R1
Glossary
Maximum value (Vm)The maximum instantaneous value in a current or voltage waveform.
Average value (Vav)The value of the total average area encompassed within one cycle of current or voltage.
Valid values (Vrms)The DC voltage or current when the heat generated by an alternating current applied to a resistor is equal to the heat generated by a direct current applied to the same resistor.
Peak-to-peak value (Vp-p)The value between the peaks and troughs of a current or voltage waveform. Also known as the ripple value.
For example: EC uses PWM to control the fan, but how much energy is applied to the fan by the PWM?
(The work done by the fan in PWM is the effective value of DC.)
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