5.1 Introduction

The number of circuit board applications that involve transmitting or radiating signals is growing steadily. Radio, television, and garage door openers held center stage for a long while. Today, global positioning, cordless phones, cell phones, remote monitors, automobile keys, and communications links of all types are taking over. Most devices require a circuit board that receives and/or transmits data. Many devices are battery operated, so efficiency is often an issue. It is interesting that the same technology that allows the rapid processing of digital data can also transmit and receive data in the form of modulated carriers.

The general radiation problem involves sine wave signals, active circuits, transmission lines, multiple ports, and antennas. A practical approach to handling rf design is to measure the reflection and transmission coefficients at each port. These coefficients are known as scattering or S parameters. This approach is practical because these parameters can be acquired without using short and open circuits. Just as a reminder, we are leaving the world of step functions and entering the world of sine waves. In most cases, we deal with single‐frequency phenomena where the language of circuit theory is appropriate.

On a circuit board, an antenna must couple energy into free space which has a characteristic impedance 377 ohms. A driver usually connects to a transmission line with a characteristic impedance of 50 ohms. At the antenna, the impedance might be complex and near 100 ohms. To optimize the flow of energy there needs to be a matching network placed between the transmission line supplying energy and the antenna. This network plus the antenna must look like a 50‐ohm termination so that there is no reflection at this junction. In applications where the radiated frequency is varied, this matching problem becomes a compromise.

5.2 Standing Wave Ratio

On terminated transmission lines, when there are reflected sine waves, they combine with the incident waves to form a standing voltage pattern. There are fixed points along a transmission line where the voltage peaks and other fixed points where the voltage never exceeds a minimum value. This pattern is static and depends on frequency and line length. For long lines, there are multiple peaks and valleys. The ratio of maximum to minimum voltage along the line is called the standing wave ratio (SWR). This ratio is used as a guide as to just how closely a transmission line is matched to its termination. When large amounts of power are involved or where there is limited power available, this ratio is important. In an ideal case, the ratio is unity. Where the voltages peak, the currents are a minimum. This means that where the electric field energy peaks, the magnetic field energy is minimum. A pattern of superposed waves is shown in Figure 5.1.

5.3 The Transmission Coefficient τ

In Section 2.10, the transmission coefficient τ was introduced. In this discussion all impedances were resistances or real numbers, so τ was a real number.

(5.1)

This equation is valid for real and complex terminating impedances. As an example, if a capacitor terminates a transmission line, the impedance Z_L is a reactance of −j/ωC. If C = 2 and ω = 1, then Z_L = −0.5j ohms. If Z₀ = 1 then using Equation 5.1

(5.2)

If the forward wave is a 5‐V sine wave at ω = 1, the transmitted wave is 5τ = (2 − 4 j) V.

For a review of circuit theory and complex numbers see Appendix A.

5.4 The Smith Chart

The Smith chart can be used as a work sheet for designing matching networks to terminate a transmission line in its matching impedance. The chart deals with sine waves at one frequency. The chart treats the S parameter problem of one port and one reflection coefficient. Working charts are available on the internet. A Smith chart with limited resolution is shown in Figure 5.2.

A Smith chart¹ is a plot of the complex transmission coefficient τ for a transmission line with a characteristic impedance of 1 ohm terminated in any impedance Z_L. Assume Z_L = r + jx. The point Z_L on the chart is at the intersection of circle r and circle x. The value of τ is the distance from the point (0,0) to the intersection of circles r and x. The Smith chart works for any transmission line length at any frequency. An examination of the chart shows that x and r can be any value from 0 to ∞. Note that x can be of either polarity. The value of τ is not shown on the graph as it is not needed for most applications.

The center or origin of the Smith chart is where τ = 1 and there is no reflection. The distance from the point (1,0) to Z_L. is (τ − 1). Since

(5.3)

then

(5.4)

Thus, the distance from the point (1,0) to the terminating impedance Z_L is the complex reflection coefficient ρ. This equation was introduced in Section 2.10.

The circles on the Smith chart are marked r and x where r stands for real value and x stands for imaginary value. This makes it possible to interpret the curves to mean a value of impedance or admittance. For impedances, x stands for reactance and r stands for resistance. For admittances, x stands for susceptance and r stands for conductance. The user must decide when the chart represents impedance and when it represents admittance. For an impedance chart, the point Z_L = 0 is where x and r are equal to 0. This is where the terminating impedance is a short circuit. The point at the far right, where x and r are infinite, is an open circuit. If the chart represents admittance, then the point where x and r are 0 represents an open circuit and the point where x and r are infinite represents a short circuit. To use the chart for admittance the value of Z_L can be reflected about the origin. A resistor of 5 ohms is on the circle r = 5. A conductance of 0.2 S is on the circle r = 0.2. A reactance of 2 j is on a circle of x = 2. A susceptance of −0.5 j siemens is on a circle of x = −0.5.

In a typical design, it is desirable to carry energy on a 50‐ohm line to an antenna structure and match its driving point impedance. To work with a Smith chart, the antenna impedance needs to be scaled down by a factor of 50. The Smith chart can then be used to change the terminating impedance to 1 ohm. This is done by adding impedances and admittances to the antenna at the interface. The added elements are then scaled up in impedance by a factor of 50. This matching of impedance only works at one frequency.

If the Smith chart represents impedances, then moving along a circle of constant resistance adds or subtracts reactance. Adding reactance means adding a series inductor or reducing an existing capacitor. Subtracting reactance means adding a series capacitor or reducing an existing inductor. Moving along a circle of constant reactance adds or subtracts resistance. A negative resistance is not allowed. If there is a resistor present it can be reduced.

If the Smith chart represents admittances then moving along a circle of constant conductance adds or subtracts susceptance. Adding susceptance means adding more shunt capacitance. Subtracting susceptance means adding a shunt inductance or reducing an existing capacitor. Moving along a circle of constant susceptance adds or subtracts conductance. Adding conductance means reducing the value of a shunt resistor.

The technique used to match impedances usually does not add resistance or conductance as these components dissipate energy. This means that the correcting impedance is usually built up of inductors and capacitors. The idea in construction is to add or subtract impedances or admittances until the transmission line has an input impedance (admittance) of one real ohm (one real siemen). The only orthogonal circle that crosses the (1,0) coordinate is r = 1. This real circle is thus key to designing a terminating network. The usual procedure is to add reactances or susceptances to reach this circle. This makes it easy to reach the point (1,0) by adding the last reactance or susceptance.

To illustrate the use of the Smith chart, consider a termination of 100 ohms on a 50‐ohm line. On a Smith chart this is a termination of 2 ohms. This impedance must be modified to where the input impedance is 1 ohm. We rule out paralleling the 2 ohms with a resistor of 2 ohms as half of the energy will be lost. Since parallel elements must be used to reduce the impedance, the admittance form of the chart is used first. The reciprocal of 2 ohms is 0.5 S. This point is located diametrically opposite the midpoint of the chart. This move is shown as step A on Figure 5.2. The chart is now in admittance mode. We need to place a shunt capacitor across this conductance that will add to the susceptance to reach the dotted admittance circle. The path B is a distance of 0.5 j siemens along the r = 0.5 circle. This move represents a shunt capacitor with a reactance of −2 j ohms.

We now convert back to an impedance Smith chart. The reciprocal of the point 0.5 + 0.5 j is the point 1.0 and −1.0 j on the path C. If an inductor of 1.0j is added, the resulting impedance will be 1 + 0 j which is our objective. In review, we now have an impedance of 2 ohms in parallel with a reactance of −2.0 j ohms in series with a reactance of 1.0 j. The transmission line is now terminated so that the input impedance is 1 ohm.

These reactances can be related to capacitors and inductors once a frequency is selected. At 500 MHz for a 50‐ohm line the inductance is 159 nH and the capacitor is 6.7 pF.

This problem can be solved using circuit analysis. The impedance of an inductor in series with an admittance consisting of 2 ohms in parallel with a capacitor C is

(5.5)

The real and imaginary terms must balance separately. It is easy to show that ωC = ½ and ωL = 1 which agrees with the Smith chart procedure.

A second solution is practical where the capacitor and inductor are interchanged but with different values. This solution is shown in Figure 5.3b. Step A is the same as before where the chart is in the admittance form. Step B shunts the line with an inductor to reach the mirror image of the r = 1 circle at x = −1/2 j. Step C returns the chart to the impedance form. Step D adds a series capacitor to reach the (1 + 0 j) point. Again, the input impedance to the transmission line is 1 ohm.

When parasitics are included in the problem, the mathematics can become complex and a graphical solution can be very useful. In general, accuracy is not an issue in designs as there are many parasitics that are not considered. The Smith chart provides a visual tool that directs finding the path to a solution.

5.5 Smith Chart and Wave Impedances (Sine Waves)

A transmission line terminated in its characteristic impedance has an input impedance that is the characteristic impedance of the line. This impedance is independent of line length. If a transmission line is terminated in any other impedance, the input impedance varies with line length and frequency. The input impedance varies because the reflected wave modifies how much current the source must supply. The line length determines the phase of the reflected voltage at the source and this affects the input impedance.

On a Smith chart the reflection coefficient vector ρ is drawn from the center of the graph to the terminating impedance. The terminating impedance is the wave impedance of the line at the termination point. To determine the impedance at the driving point, the reflection vector can be rotated back (clockwise) toward the source. The angle of rotation is a measure of length on the transmission line. One half wavelength corresponds to 360° on the Smith chart. The reflection coefficient vector points to an impedance that is the input impedance of the transmission line for that line length and for that termination.

To determine the SWR along a line, the reflection coefficient vector is rotated to where it crosses the real positive axis of the chart. The crossing point is the SWR. The proof is as follows.

The SWR is the maximum voltage on a transmission line divided by the minimum voltage. The maximum voltage occurs where the forward and reflected waves add together. The minimum occurs when they subtract. The SWR at an arbitrary point on the line is

(5.6)

where V_F is the amplitude of the forward wave and V_R is the amplitude of the reflected wave. The reflection coefficient ρ relates the forward wave to the reflected wave or

(5.7)

Substituting Equation 5.7 into Equation 5.6 yields

(5.8)

On the Smith chart the reflection coefficient ρ is the vector distance from the point Z = 1 real ohm to the terminating impedance Z_L.

The reflection coefficient is given by

(5.9)

Solving for Z_L where Z₀ = 1 we get

(5.10)

Thus, on the Smith chart, the value of the terminating impedance is the value of the SWR at that point. At a general point on the chart, the ratio of voltages is complex. The ratio of voltages we are interested in is a real number. This real number is obtained by rotating the vector ρ to where it crosses the positive real axis of the Smith chart. The angle that is rotated defines the location on the transmission line where the largest voltage ratio occurs. This real value of ρ is the SWR.

The peaks of sine wave voltage along a transmission line repeat every half wavelength. The Smith chart provides information for each one‐half wavelength section. If the line length is not a multiple of a half wavelength, the Smith chart applies to the partial section up to the generator (voltage source). The reflection vector ρ points to the load impedance Z_L at the end of the line. If the vector ρ is rotated clockwise the number of electrical degrees on the transmission line, it will point to the input impedance of the transmission line when the line is terminated in Z_L. Remember that each 360° rotation of ρ represents a half wavelength along the line.

5.6 Stubs and Impedance Matching

Stubs can often be used as a reactance to match a transmission line to a load. The reactance of a stub depends on the length of the stub and whether the stub is terminated in a short circuit or left open (unterminated). Since there are no resistors involved in the termination, the stub can only be reactive which means it looks like a single capacitor or inductor. The matching process simply adds a stub to the transmission line at a calculated point on the transmission line. The characteristic impedance and the length of the stub determines the reactance that is added.

The reactance of a stub can be determined by using a second Smith chart. In the impedance form of the chart, the point where the termination is a short circuit is at the far left. The reflection coefficient is a vector from the origin to this point. When this vector is rotated counterclockwise, it points to the reactance of a shorted line where the angle is proportional to stub length. One revolution of the vector corresponds to one‐half wavelength at the frequency of interest. The vector first points to a negative reactance and zero resistance. As the angle increases the point on the stub length increases and the negative reactance increases. At 180° the line looks like an infinite capacitance or a short circuit. In the next 180° the reactance is positive which means the stub looks like a decreasing inductive reactance. Thus, a shorted stub can take on any value of reactance depending on stub length.

A Smith chart can be used to determine the stub length required to provide a required reactance when the stub is open circuited. The reflection coefficient vector points from the origin to the far right. As the vector rotates counterclockwise the positive reactance decreases which means the inductance is decreasing. At an angle of 180° the inductance is 0. As the angle increases the reactance goes negative which means the stub looks capacitive. The stub can take on any reactive value depending on stub length. In general, a shorted stub is preferred over an open stub as it is less apt to radiate.

To match a transmission line to a termination, a stub is added to the line at a point that has a real normalized resistance of 1 ohm. The reflection coefficient is rotated from the terminating impedance point until it crosses the r = 1 circle. The angle of rotation defines the point on the line where the stub must be attached. In general, it can be located at one of two points. If the reflection coefficient crosses the 1‐ohm circle at 2 j, the stub must have an input impedance of −2 j. With this correction, the input impedance to the transmission line is 1 ohm.

Electrical degrees around a Smith chart and distance along a transmission line are proportional. At 100 MHz in a vacuum, one wavelength is 30 cm. If the dielectric constant is 4 the distance is 15 cm. A half wavelength is 7.5 cm. This is 360° on the Smith chart. Thus, 45° represents 0.93 cm along the transmission line.

5.7 Radiation—General Comments

Transmission lines by their very nature confine electromagnetic fields. We have discussed cases where reflections take place where there are transitions in conductor geometry. When sine waves are used on transmission lines, the same rules apply. In logic, reflections at open circuits are desired. For sine wave transmissions, reflections are undesirable as they imply an SWR and this limits the antenna radiation.

There are two basic radiator geometries on circuit boards. These are loops and isolated conductors that should be correctly called antennas. Loops are generally considered low‐impedance radiators while isolated conductors are considered high‐impedance radiators. Near a loop, the magnetic field dominates and the ratio between E and H fields is low. Near a conductor where the return current is the D field in space, the electric field dominates and the ratio between E and H fields is high. At a distance from a radiating structure, the ratio E/H approaches 377 ohms, the characteristic impedance of free space. This distance is λ/2π where λ is the wavelength. This transition point is referred to as the near‐field/far‐field interface distance.

5.8 Radiation from Dipoles

The simplest radiator is the half‐dipole antenna. On the earth, the antenna is usually mounted vertically and driven from a sinusoidal voltage source at the base. The current supplied to the antenna flows in space and returns near the transmission line on the surface of the earth at the base of the antenna. In space, this current is correctly called a displacement current. In almost all cases the driving voltage is a sinusoid. The information being transmitted can modulate the amplitude, frequency, or phase of transmission. In many schemes, the modulation is a combination of phase and amplitude. If there are four amplitude levels and eight phase possibilities, a length of carrier can represent a 32‐bit word.

In a typical circuit carrying sinusoids, the energy stored in an inductance or capacitor is returned to the circuit in each half cycle. Most of the energy is stored in the component or in the nearby space. When a radiator is built, the field energy is allowed to extend out into space. There is a delay associated with returning this energy to the circuit. The returning energy can be divided into two components. The component that is 90° out of phase cannot re‐enter the circuit and is radiated. The higher the frequency, the more efficient the radiator can be.

The electric field dominates near a dipole. This higher field impedance makes it easier to shield. The relative field intensities at a distance from the radiator are shown in Figure 5.4. Beyond the near‐field/far‐field interface, the E and H field intensities fall off proportional to distance, not distance squared. The energy density falls off as the square of the distance.

The field intensity around a dipole is independent of direction and falls to zero in the vertical direction. In many applications, omnidirectional radiation is preferred. The antenna geometry is not limited to simple dipoles or loops. Right‐angle structures that are asymmetrical and use conducting plates are often effective in radiating in all directions. Some antennas are in the form of paddles. The presence of nearby circuitry makes it difficult to predict the actual radiation pattern.

Vias often extend through a board where the path for current flow uses only a part of the via. This unused part of the via forms a short segment of antenna that can radiate in the GHz range. To avoid this radiation, the extra via segment can be removed by drilling. A second solution is to provide a return current path next to the via so that a radiating structure is not formed. This points out the fact that field control gets more difficult as the frequency content rises.

5.9 Radiation from Loops

Loops are characterized by currents that follow a closed path on conductors. The radiation from logic traces is considered a loop in character and the wave impedance is 50 ohms. Radiation is limited to that part of trace where the voltage is in transition. At a distance equal to the near‐field/far‐field interface, the ratio of field intensity will be 377 ohms. Inside this distance, the H field dominates. Outside of the interface distance the E and H field intensities fall off linearly with distance, not distance squared. The field intensities are shown in Figure 5.5.

The current levels on a typical circuit board are limited by the characteristic impedance of traces. The characteristic impedance of free space is 377 ohms. Dipoles are, in general, a better way to bridge this impedance mismatch if radiation is to be efficient.

5.10 Effective Radiated Power for Sinusoids

The power W crossing a small area A at a distance from a transmitting antenna is

(5.11)

where E and H are the electric and magnetic field vectors.

At a far distance r from a radiator, the field is spherical in shape and the total radiated power crossing a spherical surface would be

(5.12)

In the far field the ratio of E/H is 377 ohms. Solving for H, Equation 5.12 can be written as

(5.13)

Using Equation 5.8, the electric field E at a distance r can be written as

(5.14)

As an example, assume a cell phone transmits ½ W uniformly in all directions. At a distance of 100 m the E field strength is 40 mV/m.

A radar pulse of 10 kW in a solid angle of 1° has an effective radiated power of 360 times 10 kW or 3.6 MW.

5.11 Apertures

Every electrical device that is housed in a metal enclosure requires seams and holes for construction, ventilation, power, and signal transport. These apertures are a path for fields to move in or out of a structure. A single conductor allows the penetration of fields at all frequencies while a hole or seam attenuates a field depending on maximum dimension. In general, the orientation of the field is unknown and the assumption that must be made is to treat the worst case scenario. If the field has a half wavelength equal to the diameter of the hole or the length of the seam, we assume the field enters or leaves unattenuated. It seems counterintuitive to consider a narrow seam as being an opening but it is the only safe interpretation. In fact, a seam is defined as an opening in a conductor where surface currents cannot freely cross the seam. The author has seen radiation from a vacuum chamber formed from two machined metal surfaces over 1 inch wide. This seam had to be closed by using a gasket that made a continuous connection across the gap. In this case, the field strength was very high and there was attenuation but not enough.

Seams formed by overlapping metal surfaces can be reduced in length by adding point contacts such as screws. The initial aperture is now a group of shorter apertures. Apertures closed in this manner are said to be dependent. The dependence arises because surface currents cannot circulate freely around each opening. The result is a group of apertures that behave as a single opening. If the attenuation factor must be 100, then 100 screws would be required to close the seam. A large screw count is not a viable solution. This is the reason why a gasket is needed as it makes hundreds of connections. Conductive surfaces such as steel or aluminum will oxidize and the metal must be plated where a gasket makes electrical contact.

Seams that form a flange can be considered a waveguide. In most situations the depth of the flange is much shorter than the length of the seam and there is very little attenuation.

Consider a hole that attenuates a field by 20 dB which is a factor of 10. A similar hole at a distance from the first hole will allow equal field penetration. This second aperture is said to be independent because currents can circulate freely around the opening. To calculate the total field penetration from independent apertures, the field intensities add directly. If the external field is 60 dBμV/m, the field inside the structure is 40 dBμV/m from each aperture. This is 100 μV for each aperture or a total field strength of 200 μV. Expressed in dB notation, the resulting intensity is 46 dBμV. Notice that we cannot add intensities using the dB notation. Obviously, this is a worst case approximation. When there are many openings, the field intensity inside an enclosure cannot be greater than the external field intensity.

An array of ventilation holes behaves as a single hole if the holes are closely spaced. A screen mesh behaves as a single opening provided the mesh is bonded at each wire crossing and the edges of the mesh are bonded to the conducting surface. Aluminum mesh is unsatisfactory because of oxidation.

Connectors, displays, and line filters form apertures that must often be sealed. Conducting gaskets are needed to close these apertures. It is necessary to close all apertures to solve an interference problem. One unfiltered conductor entering or leaving a controlled space can carry interference and negate all other attempts at control. In trouble shooting, it is advised that all fixes remain in place until a solution is found. Then the fixes are removed one at a time. This is the only way to find a solution when two or more changes are required.

5.12 Honeycomb Filters

A honeycomb filter is formed by soldering together a group of hexagonal conducting channels. The channel diameter must be less than a half wavelength at the highest frequency that is to be attenuated. At 15 GHz a half wavelength is 1.0 cm, so a honeycomb channel width of 1 cm would work. A honeycomb made of a hundred channels would form a unit that is about 10 cm in diameter. These channels are independent apertures as current can circulate freely around each opening. In this example, the attenuation factor is given by Equation 3.7 or A = 30 h/d dB where h is the depth and d is the diameter of the opening. If the ratio h/d is 3 then the attenuation factor is 90 dB. Since there are 100 apertures the resulting attenuation factor is 50 dB. This is a large attenuation factor and it tells us that very little field will enter through the honeycomb. If the interfering field is at 150 MHz there is an additional attenuation factor of 40 dB. This is the ratio of half the wavelength to the aperture opening.

The biggest problem involving honeycomb filters is the aperture that mounts the honeycomb. This aperture must be sealed with a conducting gasket that is near perfect if the waveguide is to be effective. If the mounting seal in the example above has a 1 cm long gap, the honeycomb can be totally ineffective. This means the mounting gasket must be correctly installed using a plated surface.

5.13 Shielded Enclosures

The testing of electronics for radiation requires controlled spaces. In some cases this testing can be done in a remote open area, a distance from known radiators. In other cases it is necessary to use a conductive enclosure that can limit the presence of unwanted electromagnetic activity. Scientific experimentation often requires a controlled electromagnetic environment. Supplying power to operate the hardware and test equipment becomes a part of the problem. Vents that supply air can allow the entry of unwanted fields. Lighting, physical access, and communication can also provide entry for unwanted fields. The level of interference that can be tolerated obviously determines just how difficult it is to construct the controlled space. Shielding against power‐related magnetic fields is the most difficult part of the general problem. For logic hardware, interference in the power part of the spectrum is usually not a problem. We discuss the general problem as this sheds light on all the issues.

5.14 Screened Rooms

A screened room that limits magnetic field penetration at power frequencies is made from panels of silicon steel. The permeability of the steel is very nonlinear and does not provide very much attenuation for weak magnetic fields at 60 Hz and its harmonics. Since power must be used to operate test hardware and lights, some magnetic field must be brought into the room. For logic circuit boards, the emphasis is on measuring radiation above 1 MHz and low‐frequency magnetic fields are usually not an issue. There are some best practices that should be followed in providing power to a screened room that adds very little cost.

Power should not be routed along the external walls of the room. The changing magnetic field from power conductors will cause current flow on the exterior walls. This occurs even if the wiring is in conduit. Some of this current crosses into the inner surfaces. Ideally, the conduit carrying power should arrive perpendicular to an exterior wall. The room should not be located near existing power panels. Multiple grounding of the screen room will provide current paths that can allow some current to cross to the inner surfaces. This means that there is field penetration. It is preferred that all electrical connections to the room be located in one area. This includes power line filters and communication links. Fiber optics is a good way to communicate to outside hardware. Any steel supporting the optics cable should be bonded to the room wall. Any hole in the wall should be extended into a metal tube so that it is a waveguide beyond cutoff. The tube can run parallel to the wall surface.

The one ground for a screened room is equipment ground. There is capacitance from the screened room to any building steel under the room. This reactive grounding path can be limited by placing the room on blocks.

Air should be provided through a honeycomb filter. The duct carrying the air should have a plastic section, so the room is not regrounded. Air filters should not require removal of the honeycomb section. Florescent lighting is electrically noisy and should not be used. A weak spot is usually the finger stock used to seal the door. If the stock is protected by a metal channel it will not catch on clothing.

5.15 Line Filters

Power line filters usually consist of series inductors and shunt capacitors. The ungrounded (hot) lead is often filtered with respect to the neutral or grounded lead. The code prohibits grounding the neutral conductor, so it must be filtered separately. All leads carried in a power connection should be filtered to the common outer surface of the conducting enclosure. In a screened room this common conductor is the outer wall. The electrical code does not allow any components to be placed in the equipment grounding conductor path. This means that equipment ground (green wire) must be connected directly to the local housing. If the equipment ground conductor enters the hardware, it will bring in interference. Electrically any filter associated with the hardware must be located external to the hardware but physically the connection can be hidden from view. This means that line filters should be supplied in a metal housing so the unit can be mounted inside of the hardware without allowing fields to enter. This mounting cannot be on a painted or anodized surface. Filters in plastic housings are very suspect.

Filtering must often cover a very wide frequency spectrum which means that several filter sections may be required. For a screened room, the line filter can be an expensive component as conductors must carry many amperes, both power leads must be filtered, and filtering must cover a wide spectrum. In designing the power entrance, the path for interference should be treated in terms of fields and the process a reflection of field energy. Power lines are not broadband transmission lines and obviously the process of reflection will not be perfect. It is wise to review the path taken by interference currents so that interference fields can be traced. If fields can enter the hardware the filter is ineffective.

The inductances used in a power filter must carry the line current. Ampere‐turns can easily saturate any magnetic materials. The permeability of magnetic materials above 1 MHz is also an issue. This means that inductors used in line filters will usually be built as a solenoid in air. The parasitic capacitance of the inductors limits the high frequency filter performance. This is the reason that line filters must be built in sections. To further complicate the issue, the filter sections must be shielded from each other. All of these factors make line filters for screened rooms large and expensive. It also brings into focus the fact that many line filters are ineffective and can be omitted with little performance impact.

Glossary

Active circuit

 Any semiconductor component or product that uses transistors or FETs.

Admittance

 The reciprocal of impedance. It has a real part called a conductance and an imaginary part called a susceptance. The units of admittance are the siemens.

Admittance Smith chart

 The impedance Smith chart rotated 180°.

Complex notation

 The use of complex numbers to represent the 90° phase relationship between sine wave measures of current and voltage in inductors and capacitors. This notation extends to reflection and transmission coefficients. This notation is explained in Appendix A.

Conductance

 The reciprocal of resistance. The units are real siemens.

Dipole

 An antenna configuration. A full dipole is a length of the conductor fed from a center point. A half dipole is a conductor perpendicular to a conducting surface such as the earth.

Effective radiated power

 The power required to establish a field of uniform intensity in all directions.

Full dipole

 An antenna consisting of two in‐line conductors driven by a balanced signal.

Half dipole

 An antenna consisting of a single conductor usually mounted perpendicular to a conducting surface.

Impedance

 The opposition to current flow in any network. It generally applies to sine waves. It is used as the ratio of electric to magnetic field intensities in space and along transmission lines. For a transmission line, it is usually a real number. In a network, it is usually a complex number. Impedance has a real component called resistance and a complex component called a reactance.

Impedance of free space

 377 ohms. The ratio of the electric field intensity to the magnetic field intensity in space at a distance from the radiator (Section 5.1).

Interface distance

 The distance from the radiator where the wave impedance is approximately 377 ohms. This distance is λ/2π.

Near‐field/far‐field interface distance

 The distance from a radiator where the wave impedance E/H is equal to 377 ohms.

Radiation

 The release of electromagnetic energy that does not return to the generating source.

Reactance

 The opposition to current flow in capacitors and inductors. An inductor has a positive reactance and a capacitor a negative reactance. The unit of reactance is the ohm.

Siemens

 The unit of admittance. Admittance has a real part called conductance and an imaginary part called susceptance.

Smith chart

 A plot of the complex transmission coefficients τ for a terminated transmission line with a characteristic impedance of 1 ohm terminated in any impedance. The terminating impedances are found on orthogonal circles located inside a unit circle. The center of this circle is where there is full transmission and τ = 1 (Section 5.4).

Solid angle

 Consider a circular cone with its tip at the center of a unit sphere. The surface area intersected by the cone is a measure of solid angle. The total surface area of a sphere is 4πr². The full solid angle is 4π steradians.

Standing wave ratio

 The ratio of peak voltage to minimum voltage along a transmission line carrying a steady sine wave signal. Abbreviated SWR. This pattern is stationary along the transmission line. For an ideal transmission the SWR is unity (Section 5.2).

Stub

 A short section of transmission line. It can be shorted or open circuited at the far end.

Susceptance

 For sine waves. The reciprocal of reactance. The ratio of current to voltage for a capacitor or inductor when a voltage is applied. In circuit theory, the susceptance of a capacitor is a positive imaginary number of siemens. The susceptance of an inductor is a negative imaginary number of siemens.

SWR

 See standing wave ratio.

Wavelength

 The distance between positive peaks for a sine wave pattern.