05.pdf

(4808 KB) Pobierz

Contents

5.1 Introduction

5.2 Lumped-Element versus Distributed Characteristics

5.3 Effects of Parasitic Characteristics

5.3.1 Parasitic Inductance

5.3.2 Parasitic Capacitance

5.3.3 Inductors at Radio Frequencies

5.3.4 Skin Effect

5.3.5 RF Heating

5.3.6 Effect on Q

5.3.7 Self-Resonance

5.3.8 Dielectric Breakdown and Arcing

5.3.9 Radiative Losses

5.3.10 Bypassing and Decoupling

5.3.11 Effects on Filter Performance

5.4 Semiconductor Circuits at RF

5.4.1 The Diode at High Frequencies

5.4.2 The Transistor at High Frequencies

5.4.3 Amplifier Classes

5.4.4 RF Amplifiers with Feedback

5.5 Ferrite Materials

5.5.1 Ferrite Permeability and Frequency

5.5.2 Resonances of Ferrite Cores

5.5.3 Ferrite Series and Parallel

Equivalent Circuits

5.5.4 Type 31 Material

5.6 Impedance Matching Networks

5.6.1 L Networks

5.6.2 Pi Networks

5.6.3 T Networks

5.6.4 Impedance Inversion

5.7 RF Transformers

5.7.1 Air-Core Nonresonant RF Transformers

5.7.2 Air-Core Resonant RF Transformers

5.7.3 Broadband Ferrite RF Transformers

5.8 Noise

5.8.1 Noise Power

5.8.2 Signal to Noise Ratio

5.8.3 Noise Temperature

5.8.4 Noise Factor and Noise Figure

5.8.5 Losses

5.8.6 Cascaded Amplifiers

5.8.7 Antenna Temperature

5.8.8 Image Response

5.8.9 Background Noise

5.9 Two-Port Networks

5.9.1 Two-port Parameters

5.9.2 Return Loss

5.10 RF Techniques Glossary

5.11 References and Bibliography

Chapter

RF Techniques

This chapter is a compendium

of material from ARRL publications

and other sources. It assumes the

reader is familiar with the concepts

introduced in the

Electrical

Fundamentals

and

Analog Basics

chapters. The topics and techniques

discussed here are associated

with the special demands of circuit

design in the HF and VHF ranges.

The material is collected from

previous editions of this book

written by Leonard Kay, K1NU;

Introduction to Radio Frequency

Design

by Wes Hayward, W7ZOI;

and

Experimental Methods in RF

Design

by Wes Hayward, W7ZOI,

Rick Campbell, KK7B, and Bob

Larkin, W7PUA. Material on ferrites

is drawn from publications by Jim

Brown, K9YC. The section on Noise

was written by Paul Wade, W1GHZ,

with contributions from Joe Taylor,

K1JT. The editor was Ward Silver,

NØAX.

5.1 Introduction

When is an inductor not an inductor? When it’s a capacitor! This statement may seem

odd, but it suggests the main message of this chapter. In the earlier chapter,

Electrical

Fundamentals,

the basic components of electronic circuits were introduced. As you may

know from experience, those simple component pictures are ideal. That is, an ideal compo-

nent (or element) by definition behaves exactly like the mathematical equations that describe

it, and only in that fashion. For example, the current through an ideal capacitor is equal to

the capacitance times the rate of change of the voltage across it without consideration of the

materials or techniques by which a real capacitor is manufactured.

It is often said that, “Parasitics are anything you don’t want,” meaning that the component is

exhibiting some behavior that detracts from or compromises its intended use. Real components

only approximate ideal components, although sometimes quite closely. Any deviation from

ideal behavior a component exhibits is called

non-ideal

parasitic.

The important thing to

realize is that

every

component has parasitic aspects that become significant when it is used

in certain ways. This chapter deals with parasitic effects that are commonly encountered at

radio frequencies.

Knowing to what extent and under what conditions real components cease to behave like

their ideal counterparts, and what can be done to account for these behaviors, allows the

circuit designer or technician to work with circuits at radio frequencies. We will explore how

and why the real components behave differently from ideal components, how we can account

for those differences when analyzing circuits and how to select components to minimize, or

exploit, non-ideal behaviors.

5.2 Lumped-Element versus

Distributed Characteristics

Chapter 5 —

CD-ROM Content

Supplemental Articles

•

“Reflections on the Smith Chart” by

Wes Hayward, W7ZOI

•

Tuned Networks

•

“Simplified Design of Impedance-

Matching Networks,” Parts I through

III by George Grammer, W1DF (SK)

•

LTSpice

simulation files for

Section 5.3, Effects of Parasitic

Characteristics

Most electronic circuits that we use every day are inherently and mathematically considered

to be composed of

lumped elements.

That is, we assume each component acts at a single point

in space, and the wires that connect these lumped elements are assumed to be perfect conduc-

tors (with zero resistance and insignificant length). This concept is illustrated in

Fig 5.1.

These

assumptions are perfectly reasonable for many applications, but they have limits. Lumped

element models break down when:

•

Circuit impedance is so low that the small, but non-zero, resistance in the wires is important.

(A significant portion of the circuit power may be lost to heat in the conductors.)

•

Operating frequency is high enough that the length of the connecting wires is a significant

fraction (>0.1) of the wavelength causing the propagation delay along the conductor or

radiation from it to affect the circuit in which it is used.

•

Transmission lines are used as conductors. (Their characteristic impedance is usually sig-

nificant, and impedances connected to them are transformed as a function of the line length.

See the

Transmission Lines

chapter for more information.)

Effects such as these are called

distributed,

and we talk of

distributed elements

or effects

to contrast them to lumped elements.

RF Techniques

5.1

Fig 5.3 — The effects of distributed

resistance on the phase of a sinusoidal

current. There is no phase delay between

ends of a lumped element.

Fig 5.1 — The lumped element concept.

Ideally, the circuit at A is assumed to be

as shown at B, where the components

are isolated points connected by per-

fect conductors. Many components

exhibit nonideal behavior when these

assumptions no longer hold.

To illustrate the differences between

lumped and distributed elements, consider

the two resistors in

Fig 5.2,

which are both 12

inches long. The resistor at A is a uniform rod

of carbon. The second “resistor” B is made of

two 6-inch pieces of silver rod (or other highly

conductive material), with a small resistor

soldered between them. Now imagine con-

necting the two probes of an ohmmeter to each

of the two resistors, as in the figure. Starting

with the probes at the far ends, as we slide the

probes toward the center, the carbon rod will

display a constantly decreasing resistance on

the ohmmeter. This represents a distributed

resistance. On the other hand, the ohmmeter

connected to the other 12-inch “resistor” will

display a constant resistance as long as one

probe remains on each side of the small resis-

tance and as long as we neglect the resistance

of the silver rods! This represents a lumped

resistance connected by perfect conductors.

Lumped elements also have the very desir-

able property that they introduce no phase shift

Fig 5.2 — Distributed (A) and lumped (B)

resistances. See text for discussion.

resulting from propagation delay through the

element. (Although combinations of lumped

elements can produce phase shifts by virtue

of their R, L and C properties.) Consider a

lumped element that is carrying a sinusoidal

current, as in

Fig 5.3A.

Since the element

has negligible length, there is no phase dif-

ference in the current between the two sides

of the element —

no matter how high the

frequency

— precisely

because

the element

length is negligible. If the physical length of

the element were long, say 0.25 wavelength

(0.25

λ)

as shown in Fig 5.3B, the current

phase would

not

be the same from end to

end. In this instance, the current is delayed

by 90 electrical degrees as it moves along

the element. The amount of phase difference

depends on the circuit’s electrical length.

Because the relationship between the

physical size of a circuit and the wavelength

of an ac current present in the circuit will

vary as the frequency of the ac signal varies,

the ideas of lumped and distributed effects

actually occupy two ends of a spectrum. At

HF (30 MHz and below), where

λ ≥

10 m,

the lumped element concept is almost always

valid. In the UHF and microwave region

(300 MHz and above), where

λ ≤

1 m and

physical component size can represent a sig-

nificant fraction of a wavelength, nearly all

components and wiring exhibits distributed

effects to one degree or another. From roughly

30 to 300 MHz, whether the distributed ef-

fects are significant must be considered on a

case-by-case basis.

Of course, if we could make resistors, ca-

pacitors, inductors and so on, very small, we

could treat them as lumped elements at much

higher frequencies. For example, surface-

mount components, which are manufactured

in very small, leadless packages, can be used

at much higher frequencies than leaded com-

ponents and with fewer non-ideal effects.

It is for these reasons that circuits and

equipment are often specified to work within

specific frequency ranges. Outside of these

ranges the designer’s assumptions about the

physical characteristics of the components

and the methods and materials of the circuit’s

assembly become increasingly invalid. At

frequencies sufficiently removed from the

design range, circuit behavior often changes

in unpredictable ways.

5.2

Chapter 5

5.3 Effects of Parasitic Characteristics

At HF and above (where we do much of

our circuit design) several other considerations

become very important, in some cases domi-

nant, in the models we use to describe our

components. To understand what happens to

circuits at RF we turn to a brief discussion

of some electromagnetic and microwave the-

ory concepts.

Parasitic effects due to component leads,

packaging, leakage and so on are relatively

common to all components. When work-

ing at frequencies where many or all of the

parasitics become important, a complex but

completely general model such as that in

Fig 5.4

can be used for just about any compo-

nent, with the actual component placed in the

box marked *. Parasitic capacitance, C

, and

leakage conductance, G

, appear in parallel

across the device, while series resistance, R

and parasitic inductance, L

, appear in series

with it. Package capacitance, C

pkg

, appears

as an additional capacitance in parallel across

the whole device.

These small parasitics can significantly

affect frequency responses of RF circuits.

Either take steps to minimize or eliminate

them, or use simple circuit theory to predict

and anticipate changes. This maze of effects

may seem overwhelming, but remember that

it is very seldom necessary to consider all

parasitics at all frequencies and for all ap-

plications. The

Computer-Aided Circuit

Design

chapter shows how to incorporate

the effect of multiple parasitics into circuit

design and performance modeling. Files for

the

LTSpice

simulation package that include

parasitic characteristics for a resistor, capaci-

tor and inductor are provided on the CD-

ROM that comes with this

Handbook.

Fig 5.4 — A general model for electrical

components at VHF frequencies and

above. The box marked * represents the

component itself. See text for discussion.

Fig 5.5 — Inductive consequences of

Maxwell’s equations. At A, any wire

carrying a changing current develops a

voltage difference along it. This can be

mathematically described as an effective

inductance. B adds parasitic inductance

to a generic component model.

5.3.1 Parasitic Inductance

Maxwell’s equations — the basic laws of

electromagnetism that govern the propaga-

tion of electromagnetic waves and the opera-

tion of all electronic components — tell us

that any wire carrying a current that changes

with time (one example is a sine wave) devel-

ops a changing magnetic field around it. This

changing magnetic field in turn induces an

opposing voltage, or

back EMF,

on the wire.

The back EMF is proportional to how fast the

current changes (see

Fig 5.5).

We exploit this phenomenon when we

make an inductor. The reason we typically

form inductors in the shape of a coil is to con-

centrate the magnetic field and thereby maxi-

mize the inductance for a given physical size.

However,

all

wires carrying varying currents

have these inductive properties. This includes

the wires we use to connect our circuits, and

even the

leads

of capacitors, resistors and

so on. The inductance of a straight, round,

Fig 5.6 — A plot of inductance vs length for straight conductors in several wire sizes.

RF Techniques

5.3

nonmagnetic wire in free space is given by:

 





(1)

0.00508 b



  −

0.75











where

L = inductance, in µH

a = wire radius, in inches

b = wire length, in inches

ln = natural logarithm (2.303 × log

)

Skin effect (discussed below) changes this

formula slightly at VHF and above. As the

frequency approaches infinity, the value 0.75

in the above equation increases to approach

1. This effect usually causes a change of no

more than a few percent.

As an example, let’s find the inductance of

a typical #18 wire (diameter = 0.0403 inch

and a = 0.0201) that is 4 inches long (b = 4):

 





0.00508 (4)





 −

0.75



 

0.0201





Good design and construction practice is to

minimize the effects of lead inductance by

using surface-mount components or trimming

the leads to be as short as possible.

The impact of reactance due to parasitic

inductance is usually very small; at AF or LF,

parasitic inductive reactance of most compo-

nents is practically zero. To use this example,

the reactance of a 0.106 µH inductor even at

10 MHz is only 6.6

Ω.

Fig 5.6

shows a graph

of the inductance for wires of various gauges

(radii) as a function of length. Whether the

reactance is significant or not depends on the

application and the frequency of use.

We can represent parasitic inductance in

component models by adding an inductor of

appropriate value in series with the compo-

nent since the wire leads are in series with the

element. This (among other reasons) is why

minimizing lead lengths and interconnecting

wires becomes very important when design-

ing circuits for VHF and above.

PARASITIC INDUCTANCE IN

RESISTORS

The basic construction of common resistor

types is shown in

Fig 5.7.

The primary para-

sitic effect associated with resistors is parasitic

inductance. (Some parasitic capacitance exists

between the leads or electrodes due to pack-

aging.)

Fig 5.8

shows some more accurate

circuit models for resistors at low to medium

frequencies. The type of resistor with the most

parasitic inductance are wire-wound resistors,

essentially inductors used as resistors. Their

use is therefore limited to dc or low-frequency

ac applications where their reactance is negli-

gible. Remember that this inductance will also

affect switching transient waveforms, even at

dc, because the component will act as an RL

circuit. The inductive effects of wire-wound

resistors begin to become significant in the

audio range above a few kHz.

As an example, consider a 1-Ω wire-wound

resistor formed from 300 turns of #24 wire

closely-wound in a single layer 6.3 inches

long on a 0.5-inch diameter form. What is

its approximate inductance? From the in-

ductance formula for air-wound coils in the

Electrical Fundamentals

chapter:

0.5

300

18d

40l (18

0.5)

(40

6.3)

0.0203

[

5.98

−

0.75

]

0.106

Wire of this diameter has an inductance

of about 25 nH per inch of length. In circuits

operating at VHF and higher frequencies,

including high-speed digital circuits, the in-

ductance of component leads can become sig-

nificant. (The #24 AWG wire typically used

for component leads has an inductance on the

order of 20 nH per inch.) At these frequencies,

lead inductance can affect circuit behavior,

making the circuit hard to reproduce or repair.

If we want the inductive reactance to be

less than 10% of the resistor value, then this

resistor cannot be used above f = 0.1 / (2π ×

86 µH) = 185 Hz! Real wire-wound resistors

have multiple windings layered over each other

to minimize both size and parasitic inductance

(by winding each layer in opposite directions,

much of the inductance is canceled). If we as-

sume a five-layer winding, the length is reduced

to 1.8 inches and the inductance to approxi-

mately 17 µH, so the resistor can then be used

below 937 Hz. (This has the effect of increasing

the resistor’s parasitic capacitance, however.)

The resistance of certain types of tubular

film resistors is controlled by inscribing a

spiral path through the film on the inside of

the tube. This creates a small inductance that

may be significant at and above the higher

audio frequencies.

NON-INDUCTIVE RESISTORS

The resistors with the least amount of para-

sitic inductance are the bulk resistors, such

as carbon-composition, metal-oxide, and ce-

ramic resistors. These resistors are made from

a single linear cylinder, tube or block of resis-

Fig 5.7 — The electrical characteristics of different resistor types are strongly affected

by their construction. Reactance from parasitic inductance and capacitance strongly

impacts the resistor’s behavior at RF.

Fig 5.8 — Circuit models for resistors. The

wire-wound model with associated induc-

tance is shown at C. B includes the effect of

temperature (T). For designs at VHF and

higher frequencies, the model at C could be

used with L representing lead inductance.

5.4

Chapter 5

Plik z chomika:

umts

Inne pliki z tego folderu:

01.pdf (9117 KB)
02.pdf (6826 KB)
07.pdf (7909 KB)
03.pdf (4816 KB)
05.pdf (4808 KB)

Inne foldery tego chomika:

ARRL 2017 Handbook Supplemental Files