Electric Field And Magnetic Field Become The Electromagnetic Field

The 4-vector concept also allows us to condense the mathematics of electromagnetics, and reveals the true nature of the electromagnetic field. By combining the magnetic vector potential with voltage into a four vector A Ax,Ay,Az,V c , a single electromagnetic potential is formed. Using this 4-potential, the electric and magnetic fields combine to form a single electromagnetic field, which can be represented by a mathematical object called a tensor. In the mathematical system called Clifford...

The Moving Charge

Right Hand Rule Electromagnetics

Another, more fundamental, test particle for the magnetic field is a free charge moving with velocity, v. As you learned earlier in this chapter, the magnetic field arises from moving charges. Therefore, a moving charge serves as a good test particle. You can better understand the effect that a magnetic field has on a moving charge by first understanding a similar mechanical effect, that of the Coriolis force. Without knowing it, you are probably very familiar with the Coriolis force. Imagine...

The Electromagnetic Spectrum

For electrical engineers the word electromagnetics typically conjures up thoughts of antennas, transmission lines, and radio waves, or maybe boring lectures and all-nighters studying for exams. However, this electrical word also describes a broad range of phenomena in addition to electronics, ranging from X-rays to optics to thermal radiation. In physics courses, we are taught that all these phenomena concern electromagnetic waves. Even many nontechnical people are familiar with this concept...

Power Supply Decoupling Problems And Techniques

Parallel Decoupling Capacitors

Power supply decoupling is the term given to the technique of making sure the DC power line variations do not affect the loads amplifier, ICs, logic gates, etc. and vice versa. Since most ICs have AC signals as inputs and outputs, the current drawn from the power supply will vary in an AC manner. For example, an RF circuit that amplifies a 900 MHz signal will draw a supply current that varies at 900 MHz. A digital CMOS circuit that buffers a 100 MHz digital signal will also draw a supply...

Near And Far Field

As mentioned earlier, an AC circuit will have a reactive field and a radiating field. The reactive field of an AC source circuit or system is often referred to as the near field because it is concentrated near the source. Similarly, the radiating field is referred to as the far field because its effects extend far from the source. Let's examine why. The power density of an electromagnetic field at a distance, r, from the source can be represented by a series in 1 r, Field power density Pd Q r2...

Electrostatic Induction And Capacitance

To understand capacitance, you need to first understand the process of electrostatic induction. For example, consider that you have a metal ball that is positively charged, near which you bring a neutral metal ball. Even though the second ball has overall neutrality, it still contains many charges. Neutrality arises because the positive and negative charges exist in equal quantities. When placed next to the first ball, the second ball is affected by the electric field of the charged ball. The...

Mesh Shields and Faraday Cages

Due to the radiation limiting effects of small apertures, shields can be made from a mesh of wires or from a metallic cage, as an alternative to using a solid sheet of metal. From the results of apertures, you can deduce that the holes in the mesh or cage should be considerably less than half a wavelength for such shields to work properly. Moreover, the mesh will be mostly transparent to signals with wavelengths smaller than the mesh holes. When the shield takes the form of a wire cage, it is...

Antenna Pattern Versus Electrical Length

Half Wave Dipole Radiation Patterns

Antennas do not radiate equally to all directions. The directional dependence of antenna radiation is aptly called the antenna pattern. An electric dipole that is 1 2 1 in length or smaller exhibits a fairly simple antenna pattern. The most power is radiated in the direction broadside to the antenna that is, perpendicular to the antenna's length. The power decreases with decreasing angle such that at zero degrees, no power is radiated. In other words, no power is radiated in the direction of...

Conducted Versus Induced Versus Radiated Interference

High Frequency Interference

In EMC literature and EMC regulations the mechanisms of electromagnetic interference are divided into two categories, conducted and radiated. Historically, this categorization has been used in the regulations and, unfortunately, it continues today. I use the word unfortunately because both near-field coupling and far-field radiation are lumped under the term radiated emissions. While experts in electromagnetics are quite familiar with the difference between near-field coupling and far-field...

Differential Mode And Common Mode Radiation

Common Mode Choke Symbol

Unintentional radiation can be described as either differential mode or common mode. The two terms relate to the currents that create the radiation. Differential mode currents are equal but travel in opposite directions. Common mode currents travel in the same direction. On any transmission line, the signal current and the return current travel in opposite directions. As long as the two currents are close together the radiation is very small, albeit non-zero. The two currents Figure 12.18 Here...

Voltage And Potential Energy

A quantity that goes hand in hand with the electric field is voltage. Voltage is also called potential, which is an accurate description since voltage quantifies potential energy. Voltage, like the electric field, is normalized per unit charge. Voltage Potential energy of a unit charge In other words, multiplying voltage by charge gives the potential energy of that charge, just as multiplying the electric field by charge gives the force felt by the charge. Mathematically we represent this by...

The Path Of Least Impedance

Via Inductance High Speed Design Rules

One of the most fundamental relations taught in basic circuit theory is that current follows the path of least resistance. At high frequencies this relation is modified to current follows the path of least impedance. The path of least resistance and the path of least impedance may or may not be the same, depending on the circuit geometry and the signal frequency. In any circuit, the signal consists of the flow of two currents, typically called the signal and return. Since the return current...

Static Electricity And Lightning

Static Electricity Free Energy

Let's go back to the charged sphere of Figure 2.5. If the second metal ball is placed closer to the charged ball so that they actually touch, the Figure 2.11 A Water molecule. B Water molecules in random orientation with no field applied. C Water molecules line up when an electric field is applied. Figure 2.11 A Water molecule. B Water molecules in random orientation with no field applied. C Water molecules line up when an electric field is applied. negative charge will now redistribute itself...

The Vector Magnetic Potential And Potential Momentum

Magnetic Vector Potential

In the previous chapter, which covered electric fields, one of the first concepts covered was the electric field potential, more commonly known as voltage. You may be wondering if a similar potential exists for the magnetic field. If so, you are correct. However, the magnetic potential is a vector quantity. It has both magnitude and direction. The vector potential around a current is shown in Figure 3.16. As you can see, its main characteristic is that it points in a direction parallel to the...