The Field Of An Oscillating Charge

A charge moving in a circle experiences sinusoidal acceleration. In fact, sinusoidal acceleration will occur for a charge moving in any oscillatory manner. In this case, the kinks in the field will be continuously varying and sinusoidal and the electromagnetic radiation will occur only at the frequency of oscillation. As shown in Figure 5.6B, an oscillating charge produces a rippling of waves that propagate outward, in some ways similar to the water waves produced by tossing a rock into a pool...

The Field Of An Alternating Current

If we allow the voltage source across a wire to slowly oscillate in time at frequency, fo, the accompanying electric field will take the same form as that of the DC charge, except that the magnitude will vary between positive and negative values (see Figure 5.8). Relating frequency to wavelength by l c f, we define slow oscillation as any frequency whose corresponding wavelength is much greater than the length of the wire. This condition is often called quasi-static. In this case, the current...

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...

Circuits As Guides For Waves And Sparameters

In the previous chapter, I mentioned that waves do not propagate well in conductors. They attenuate down to miniscule levels after traveling a few skin depths. Keep in mind that the conductor actually becomes more lossy at higher frequencies because the current must travel through a smaller cross-sectional area. High-voltage power lines often use multiple parallel wires for each phase partly because of the skin effect. At 60 Hz, the skin depth is about 8 mm. By splitting the current into...

Explanation Of The Magnetic Vector Potential

In Chapter 3, I promised to give a conceptual meaning to the magnetic vector potential. This explanation involves the electrons of a superconducting circuit. In a superconductor, the electrons can move freely without colliding with the positive ions of the metal. Suppose that a DC current is applied to a superconducting wire. Without collisions, the electrons form a collective system that has a wave nature. In other words, the wave nature of the electrons dominates over the particle nature....

Power Supply Decoupling Problems And Techniques

Decoupled Supply

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...

The Quantum Vacuum And Virtual Photons

Now what about the energy in nonradiating electromagnetic fields, that is, the static field and the near field Quantum physics states that any energy must consist of individual packets or quanta, but this implies that even the static field must consist of particles. In fact, the static field does consist of particles virtual photons. To explain virtual photons, let's step further into the strange world of quantum physics. If we think about the uncertainty principle from another point of view,...

And Maxwell Said Let There Be Light

In addition to being a physicist, Maxwell was also an extraordinarily talented mathematician. When he added his new term to the existing equations for electricity and magnetism, he quickly noticed that the mathematics implied that propagating electromagnetic waves could be created. Such waves had never been observed. This was a monumental discovery. Furthermore, when he performed the mathematical derivations, the speed of these new waves was predicted to be that of the speed of light Before...

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...

Multiturn Loop Antennas

I have focused on electric antennas, because these antennas are used most often in practice. One reason is that loops tend to take up more space than electric dipoles. However, the loop antenna can actually save space in low-frequency radio applications, where wavelength is tremendous. For instance, the wavelength at the center of the AM radio band is about 300 m. Creating an electrically long antenna at this wavelength is not feasible, except for the broadcast companies. An alternative to the...

Antenna Pattern Versus Electrical Length

Magnetic Loop Antenna Radiation Pattern

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...

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...