Complete Wireless Design.pdf

Source: Complete Wireless Design

Wireless Essentials

Chapter

A firm understanding of how passive and active components function at high

frequencies, as well as a strong grasp of the fundamental concepts of lumped

and distributed transmission lines, S -parameters, and radio-frequency (RF)

propagation, is essential to successful circuit design.

1.1 Passive Components at RF

1.1.1 Introduction

At radio frequencies, lumped (physical) resistors, capacitors, and inductors are

not the “pure” components they are assumed to be at lower frequencies. As

shown in Fig. 1.1, their true nature at higher frequencies has undesirable

resistances, capacitances, and inductances—which must be taken into account

during design, simulation, and layout of any wireless circuit.

At microwave frequencies the lengths of all component leads have to be min-

imized in order to decrease losses due to lead inductance, while even the board

traces that connect these passive components must be converted to transmis-

sion line structures. Surface mount devices (SMDs) are perfect for decreasing

this lead length, and thus the series inductance, of any component (Fig. 1.2),

while the most common transmission line structure is microstrip, which main-

tains a 50-ohm constant impedance throughout its length—and without

adding inductance or capacitance.

As the frequency of operation of any wireless circuit begins to increase,

so does the requirement that the actual physical structure of all of the

lumped components themselves be as small as possible, since the part’s

effective frequency of operation increases as it shrinks in size: the smaller

package lowers the harmful distributed reactances and series or parallel

resonances.

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Wireless Essentials

2 Chapter One

Figure 1.1 A component’s real-life behavior at high frequencies (HF) and low

frequencies (LF).

Figure 1.2 A surface mount resistor.

1.1.2 Resistors

As shown in Fig. 1.3, a resistor’s actual value will begin to decrease as the fre-

quency of operation is increased. This is caused by the distributed capacitance

that is always effectively in parallel with the resistor, shunting the signal around

the component; thus lowering its effective value of resistance. As shown in the fig-

ure, this distributed capacitance is especially problematic not only as the fre-

quency increases, but also as the resistance values increase. If the resistor is not

of the high-frequency, thin-film type, a high-value resistor can lose much of its

marked resistance to this capacitive effect at relatively low microwave frequen-

cies. And since the series inductance of the leads of the surface-mount technology

resistor are typically quite low, the added reactive effect is negligible in assisting

the resistor in maintaining its marked resistance value.

1.1.3 Capacitors

Capacitors at RF and microwave frequencies must be chosen not only for their

cost and temperature stability, but also for their ability to properly function at

these high frequencies. As shown in Fig. 1.1, a capacitor has an undesired lead

inductance that begins to adversely change the capacitor’s characteristics as

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Wireless Essentials

Wireless Essentials 3

Figure 1.3 Ratio of an SMD resistor’s resistance at DC to its resistance at AC for increasing

frequencies.

the frequency is increased. This effect is most pronounced if the lead induc-

tance resonates with the capacitance of the physical capacitor, resulting in a

series resonance—or a total reactance of nearly zero ohms (resonating a capac-

itor can also be purposeful: a j0 capacitor is the type that becomes series reso-

nant at the frequency of interest by resonating its own parasitic inductance

with its own small value of marked capacitance, which creates a very low series

impedance, perfect for coupling and decoupling at very high frequencies). Above

this series resonant frequency the capacitor itself will actually become more

inductive than capacitive, making it quite important to confirm that the cir-

cuit’s design frequency will not be over the series resonance of the capacitor.

This is vital for coupling and decoupling functions, while a capacitor for tuned

circuits should have a series resonance comfortably well above the design fre-

quency. The higher the value of the capacitor, the lower the frequency of this

series resonance—and thus the closer the capacitor is to its inductive region.

Consequently, a higher-value capacitor will demonstrate a higher inductance,

on average, than a smaller value capacitor. This makes it necessary to compro-

mise between the capacitive reactance of the capacitor in coupling applications

and its series resonance. In other words, a coupling capacitor that is expected

to have a capacitive reactance at the frequency of interest of 0.1 ohm may actu-

ally be a much poorer choice than one that has a capacitive reactance of 5

ohms—unless the capacitor is chosen to operate as a j 0 type.

Only certain capacitor classifications are able to function at both higher fre-

quencies and over real-life temperature ranges while maintaining their capac-

itance tolerance to within manageable levels. The following paragraphs

discuss the various capacitor types and their uses in wireless circuits:

Electrolytic capacitors, both aluminum and tantalum, are utilized for very

low frequency coupling and decoupling tasks. They have poor equivalent series

resistance (ESR) and high DC leakage through the dielectric, and most are

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Wireless Essentials

4 Chapter One

F for

the aluminum types. Aluminum electrolytics have a limited life span of

between 5 to 20 years while tantalums, with their dry internal electrolyte,

have a much longer lifetime—and less DC dielectric leakage. Unfortunately,

tantalums have less of a range of values (between 0.047

F down to 1

F and 330

F) and

F, and include the polystyrene, metallized

paper, polycarbonate, and Mylar™ (polyester) families. Metallized film capac-

itors can be constructed by thinly metallizing the dielectric layers.

Silver mica capacitors are an older, less used type of high-frequency capaci-

tor. They have a low ESR and good temperature stability, with a capacitance

range available between 2 and 1500 pF.

Ceramic leaded capacitors are found in all parts of RF circuits up to a maxi-

mum of 600 MHz. They come as a single-layer type (ceramic disk) and as a

stacked ceramic (monolithic) structure. Capacitance values range from 1.5 pF to

0.047

F, with the dielectric available in three different grades: COG ( NPO ) for

critical temperature-stable applications with tight capacitance tolerance values

of 5 percent or better (with a capacitance range of 10 to 10,000 pF); X7R types,

with less temperature stability and a poorer tolerance (±10 percent) than COG

(with available values of 270 pF to 0.33

F); and Z5U types, which are typically

utilized only for bypass and coupling because of extremely poor capacitance tol-

erances (±20 percent) and bad temperature stability (with a range of values from

0.001 to 2.2

F). However, the dominant microwave frequency capacitors today

are the SMD ceramic and porcelain chip capacitors, which are used in all parts

of RF circuits up to about 15 GHz. Nonetheless, even for these ultra-high-quali-

ty RF and microwave chip capacitors, the capacitance values must be quite small

in order for them to function properly at elevated frequencies. Depending on the

frequency, a maximum value of 10 pF or less may be all that we can use in our

circuit because of the increasing internal inductance of the capacitor as its own

capacitance value is raised. These leadless microwave chip capacitors are also

available in multilayer and single-layer configurations, with the multilayer types

normally coming in a basic SMD package, while single-layer capacitors are more

difficult to mount on a board because of their nonstandard SMD cases.

Nonetheless, single-layer capacitors can operate at much higher frequencies—up

to tens of GHz—than multilayer; but they will also have a much lower capaci-

tance range. In addition, some ceramic and porcelain microwave SMD capacitors

will have a microstrip ribbon as part of their structure for easier bonding to the

microstrip transmission lines of the printed circuit board.

1.1.4 Inductors

A significant, real-world high-frequency effect in an inductor is undesired dis-

tributed capacitance—which is a capacitance that is in parallel with the actual

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polarized. However, they possess a very large amount of capacitance per unit

volume, with this value ranging from greater than 22,000

a lower maximum working voltage rating.

Metallized film capacitors are commonly good up to about 6 MHz and are

adopted for low-frequency decoupling. These capacitors are available in capac-

itance ranges from 10 pF to 10

Wireless Essentials

Wireless Essentials 5

desired inductance of the coil (Fig. 1.1). This also means that there must be

some frequency that will allow the coil’s inductance to be in parallel resonance

with the distributed capacitance, causing a high impedance peak to form at

that frequency. In fact, the impedance created by this parallel resonance would

be infinite if not for the small value of wire resistance found in series with the

inductor’s structure. The point of resonance is called the self-resonant fre-

quency (SRF) of the inductor and must be much higher than the circuit’s actu-

al frequency of operation if the inductor is to be used in a tuned resonant

circuit (to maintain the tank’s proper impedance). RF inductors for use at the

higher frequencies are built with small form factors in order to decrease this

distributed capacitance effect, and thus increase their SRF (this technique will

also lower the maximum inductance available, however).

An inductor parameter that is especially important for tuned circuits is the Q,

or quality factor, of the inductor. The Q indicates the quality of the inductor at a

certain test frequency; Q equals the inductive reactance divided by the combined

DC series resistance, core losses, and skin effect of the coil. At low frequencies Q

will increase, but at high frequencies the Q of an inductor will begin to decrease

as a result of the skin effect raising the resistance of the wire. (Even while this

is occurring, the distributed capacitance is also decreasing the desired induc-

tance of the coil. Thus, the Q will soon reach zero, which is the value at its SRF).

The coil’s DC series resistance is the amount of physical resistance, measured by

a standard ohmmeter, that is due to the innate resistance within the inductor’s

own wire. The DC series resistance affects not only the Q of a coil as mentioned

above (and can reach relatively high levels in physically small, high-value, high-

frequency inductors), but will also drop a significant amount of DC bias voltage.

This is important in choosing a coil for a circuit that demands that the inductor

must not have an excessive DC voltage drop across it, which can cause erratic cir-

cuit operation because of decreased bias voltages available to the active device.

The last major loss effect that can create problems in high-inductance coils at

high frequencies is created by coil-form losses, which can become substantial

because of hysteresis, eddy currents, and residual losses, so much so that the

only acceptable type of inductor core material is typically that of the air-core type.

Inductor coil design. There are times when the proper value or type of induc-

tor is just not available for a small project or prototype, and one must be

designed and constructed.

For a high-frequency, single-layer air-core coil (a helix ), we can calculate

the number of turns required to obtain a desired inductance with the follow-

ing formula.

d )

(

40 l )]

where n

number of single layer turns required to meet the desired

inductance ( L )

desired inductance of the air coil,

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L [(18

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