无线通信射频功率放大器第2版：技术指南与实用程序

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《RF功率放大器 for 无线通信,第二版》是一本专注于射频功率放大器技术的专业书籍，专为无线通信领域的专业人士精心编撰。该书旨在提供详尽的技术描述、操作程序和计算机程序，帮助读者理解和应用这些技术在各种无线通信系统中。书中所述的内容是经过作者在广泛的实践中验证和优化的，对于理解射频功率放大器的工作原理、设计方法以及优化策略具有重要的参考价值。本书强调技术描述的严谨性和实用性，旨在确保读者能够掌握关键概念和技术细节。然而，作者和编辑明确表示，书中提供的所有内容，包括公式、程序和步骤，并无任何形式的明示或默示保证。这意味着，尽管技术内容经过了仔细校验，但用户必须自行承担可能存在的错误或不一致性风险，因为使用书中信息来解决特定问题可能导致个人伤害或财产损失。读者在使用书中的程序和操作时，需认识到这可能不适合所有应用场景，而且可能存在尚未发现的问题。因此，任何依赖于书中的解决方案的行为都应由使用者自行负责。编辑、作者和出版商对此类使用产生的后果概不负责。《RF功率放大器 for 无线通信,第二版》是一本极具实践指导意义的参考资料，适合无线通信工程师、系统设计师和研究者在进行射频功率放大器的设计、分析和优化时参考，但使用者必须清楚地了解其局限性并谨慎运用。通过深入学习和理解本书内容，读者可以提升在无线通信领域的工作能力，同时也要注意遵循最佳实践和安全措施。

CHAPTER 1

Introduction

1.1 Introduction

A logical starting point for a book on RF power amplifier design would be to define

what a power amplifier (PA) actually is. A technical definition might be an amplifier

which is designed to deliver the maximum power output for a given selection of

active device. Such a definition is useful in that it emphasizes that many of the tech

niques described in this book will be of interest to “small signal” amplifier design

ers. For example, the problem of obtaining low noise performance and also

maximum dynamic range from an amplifier used in the front end of a receiver could

be considered to be a PA design problem, and the techniques described in Chapter 2

would be applicable.

But in practice, by a “PA,” we really mean an amplifier that can do damage to

something. We are talking about a world of uncharacteristically high excitement in

the RF lab, where attenuators and terminations get hot, and the life expectancy of

expensive test equipment is greatly reduced. This means we are talking about RF

outputs anywhere from the 1 watt level upwards. Above this level, we start to “feel”

our amplifier RF output, even when safely dissipated in an attenuator. PAs are

amplifiers whose outputs either directly or indirectly make an impact on the human

sensory system.

Pyrotechnics notwithstanding, many power amplifier designs are simple exten-

sions or modifications of linear designs. In the first place it will therefore pay to look

at amplifiers in general, and to recall some of the classical results of linear RF ampli-

fier theory. PAs do however usually operate withtheactivedevicedisplayingsome,or

maybe gross, nonlinear behavior, and we run straight into the problems of nonlinear

modeling and characterization. This is a big subject and has been the focus of hun

dreds of papers and several books in recent years. The focus in this book is the devel

opment of useful, practical aprioridesign methods, and we will focus on developing

such methods using some very basic models, which will be used throughout this book.

These models will be introduced in Sections 1.3 and 1.4 of this chapter, where the

important distinction between weak and strong nonlinear behavior will be defined.

One of the principal differences between linear RF amplifier design and PA

design is that for optimum power, the output of the device is not presented with the

impedance required for a linear conjugate match. This causes much consternation

and has been the subject of an extended debate about the meaning and nature of

conjugate matching. It is therefore necessary to swallow this apparently unpalatable

result as early as possible (Section 1.6), before going on to give it more extended

interpretation and analysis in Chapter 2.

1.2 Linear RF Amplifier Theory

The basic results of matched two-port linear RF amplifiers were derived originally

by Mason [1] and Rollett [2], although most microwave engineers first encounter

these results in a famous application note (“AN-95”) written by Bodway under the

old Hewlett Packard label and still available from Agilent [3]. There are also many

books on basic RF design techniques which cover this material in greater detail [4].

The key results can be illustrated by examining the schematic shown in

Figure 1.1. A transistor is represented as a two-port s-parameter matrix. The input

and output impedance, or reflection coefficient, presented to the transistor, can be

adjusted using conceptual tuning devices; since these tuners are realized using pas

sive circuitry (e.g., transmission lines and shunt capacitive slugs or stubs), the reflec

tion coefficients Γ

and Γ

at the input and output device reference planes are

restricted to the range of 0 < |Γ

S, L

| < 1 in magnitude.

The use of tuners as a necessary means for obtaining useful gain from a micro

wave device is often an immediate source of puzzlement for “analog” electronic

designers who have learned their trade at much lower frequencies. Much the same

could also be said for the statutory microwave assumption of 50Ω terminations in

Figure 1.1. This, more than anything else, is the target for much factionalism between

the microwave and analog camps. At microwave frequencies, active devices will typi-

cally give little useful gain due to the domination of their parasitic reactances. Much

attention needs to be paid to resonating these out in order that useful voltage levels

can be established at the device active nodes. As the size and power capability of a

microwave device increases, this problem becomes more acute.

The reasons for the 50Ω standard are sound and well proven, and concern the

parasitic effects of the interconnecting wires between devices themselves, and also

between devices and test instruments. At GHz frequencies, any interconnecting wire

will have a significant electrical length in comparison to a wavelength at the applica-

tion frequency, so that “connections” can no longer be assumed to display the same

voltage at each end. Thus the interconnections have to be regarded as part of the cir

cuit design, and some form of physical uniformity needs to be introduced. Uniform

transmission lines, in their various physical forms, provide a solution to this require

ment, and the selection of a standard characteristic impedance is necessary. It is a

matter of the fundamental physical constants in our universe that transmission lines

which have characteristic impedances below about 20Ω, and above about 100Ω, are

2 Introduction

[]

Input tuner Output tunerActive device

Figure 1.1 Schematic for 2-port gain and stability analysis.

difficult to manufacture. Very low, or very high, characteristic impedance transmis

sion lines have either very narrow or very wide spacing of the two conductors. Just

about anywhere in between these limits would therefore be an acceptable choice,

and in the pre–World War II pioneering days of microwave engineering, both 40Ω

and 80Ω were used. It was the emergence of a microwave test equipment industry

that really sealed the 50Ω standard, with companies such as General Radio and

Hewlett Packard then calling most of the shots. For better or for worse, the micro

wave world revolves around the 50Ω standard, and there seems no end in sight.

Take a transistor, match its input and output to 50Ω, and, presto, you are a micro

wave designer. But there are some hazards on the way, which largely stem from the

fact transistors are not entirely unilateral; there is reverse, as well as forward,

transmission.

Returning to Figure 1.1, much of the complexity of the behavior of this system

is characterized by the relative magnitude of the reverse transmission parameter s

;

however, a more concise parameter emerges after some extensive analysis, and this

is called k, or Rollett’s stability factor. The key equations are quite straightforward,

and represent the change in the input reflection

′

, due to the output plane

being presented with the output load reflection Γ

Input match:

′= +

⋅⋅

−⋅

11 11

21 12

(1.1)

Output match:

′= +

⋅⋅

−⋅

22 22

21 12

(1.2)

So for a conjugate match, one can set

′=s

L22

Γ *

and

′=s

S11

Γ *

giving two equations which, in principle, can be solved for Γ

and Γ

It should now be noted that in general, this solution always exists; however,

there is an additional constraint that the magnitudes of Γ

and Γ

must be less than

unity for the solution to be realizable using passive external circuitry. This is where

the k-factor makes its appearance. After some lengthy but admirable manipulations

of complex algebra, Rollett et al. showed that the 0 < |Γ

S, L

| < 1 condition corre

sponds to a parameter known as the “k-factor” being greater than unity, where

ssD

−−+

⋅⋅

21 12

and

Ds s s s=⋅−⋅

11 22 12 21

1.2 Linear RF Amplifier Theory 3

So in practical terms, if k > 1 the device will never display an input or output

reflection coefficient magnitude which is greater than unity, no matter what passive

matching may be placed at its input or output. This condition therefore makes an

additional statement about the stability of the device. Unfortunately, formulating

the problem as a 2-port introduces some restrictions which are not general enough

for some applications, and there has been an ongoing quest in the literature to find a

“best and final” set of conditions for absolute stability under all conditions [5, 6].

But the simple k >1 condition is undoubtedly a good practical guideline to follow.

It should not, however, be stretched too far. In the world of PA design, one is

often struggling to obtain adequate signal gain, as well as extracting optimum

power from a device. This is an inevitable consequence of cost-driven designs; large

periphery transistors have lower gain and one is usually constrained to use the low

est cost technology. We will see later how, when the signal gain drops below 10 dB,

the extra RF drive power required will often cancel out any efficiency advantage that

had been carefully designed. The upshot of this is that one is often looking for an

optimum situation where the k-factor is greater than unity, but not too much

greater. Devices with high k-factors also tend to have low gain, and some extra gain

can be retrieved by allowing positive feedback around the device, while keeping the

k-factor above unity. This trick is often used, albeit sometimes inadvertently, by the

microwave ECM and mm-wave amplifier community; and was a mainstay of the

pre–World War II tube radio industry, “reaction” controls and all.

If k > 1, expressions can be found in the literature for the conjugate match and

corresponding “maximum available gain” (MAG). These expressions are well

known and are not repeated here [3, 4]. But there are a few ramifications which are

worth noting:

1. Any device which has a k-factor greater than, but not much greater than,

unity displays a more aggressive gain/match characteristic than a theoretical

unilateral device. In particular, the final MAG may be considerably higher,

in a nearly matched condition, than a simple voltage standing wave ratio

(VSWR) mismatch calculation would indicate. For example, such a device

displaying a 10 dB return loss may show more than the calculated 0.7 dB

increase in gain when finally matched to −20 dB return loss.

2. Circuit losses can play havoc with the k-factor, and especially the frequency

where it crosses unity. In practice, devices can be safely used some way below

the unity k-factor point if the k-factor is based on fully de-embedded

s-parameter measurements.

3. The circuit environment in which a transistor is placed can modify

significantly its effective s-parameters, and especially the critical reverse

transmission parameter, s

. This is probably the main cause of unexpected,

or unsimulatable, stability problems.

4. k-factor analysis, as presented here in its classical form, is only applicable to a

single stage amplifier. In a multistage environment, the condition 0 < |Γ

S, L

| < 1

no longer applies, because the input and/or output planes of an intermediate

stage are terminated with active networks. So taking a multistage amplifier as

a single two-port and analyzing its k-factor is a necessary, but by no means

sufficient, condition for overall stability. This problem is often bypassed in

4 Introduction

multistage RF amplifier designs by the use of some form of isolation between

stages, although multistage stability analysis and design strategies have been

published [7].

1.3 Weakly Nonlinear Effects: Power and Volterra Series

The possibility, or reality, of nonlinear effects in linear amplifiers are usually first

introduced in the form of a power series expression, as shown in Figure 1.2.

The amplifier symbol here represents a transistor with its associated input and

output matching circuitry, and the lower case voltages are the small RF signal varia

tions about the transistor operating point. The amplifier output consists of an infi

nite series of nonlinear products which are added on to the linear gain represented

by the first term:

vavavavav

ii i i

=++++

K (etc.)

(1.3)

This “power series” is trotted out in many elementary textbooks as a general

ized formulation for nonlinear behavior; yet it clearly has limitations. Most notably,

there is no allowance for the timing of the various output components. We know,

for sure, that even if the contents of the amplifier icon in Figure 1.2 were a passive

R-C network, the output voltage would show both amplitude and time, or phase,

changes from the input signal. A much stronger formulation of the power series,

called the Volterra series, includes phase effects.

The power series is, nevertheless,

useful for characterizing the behavior of nonlinear products in a small operation

zone in the immediate vicinity of the DC operating point. This usefulness is limited,

additionally, by the problem that the a

coefficients are very sensitive to changes in

the input and output tuning, and also the bias levels at input and output.

Such a formulation, with some enhancements, is useful for analyzing the

“weakly nonlinear” properties of an amplifier or device. Weak nonlinearities may,

1.3 Weakly Nonlinear Effects: Power and Volterra Series 5

(t)

Weakly nonlinear

device

v t av t av t av t av t

oiiii

( ) = ( ) + ( ) + ( ) + ( ) + ................. (etc.)

234

Figure 1.2 Weakly nonlinear device, and power series.

1. The Volterra series in this book is regarded as a power series with complex coefficients; however, the formu

lation is much more general than this.

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