Programme

Examiner: Magnus Isaksson

Supervisor: Christian Fager

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DEPARTMENT OF TECHNOLOGY AND BUILT ENVIRONMENT

Pulse Modulated Transmitter Architectures

Carrier bursting

Jessica A. Chani Cahuana

Master’s Thesis in Electronics/Telecommunications

1

Abstract

The study of the possibility of implementing a novel Envelope Pulse Modulated power amplifier that integrates a narrow bandwidth reconstruction filter at the output network of a single ended amplifier is presented. In order to achieve the integration, a detailed analysis of the effects of the interaction of the amplifier and the filter is performed. With the purpose to counteract the undesired effects such integration may imply on the amplifier operation, the switched resonator concept is explored in detail and further extended to higher order filters. Moreover, a different method to predict the filter response based on static measurements is derived, and used to establish the specification of the filter to be fulfilled to minimize the effects of the interaction. The integration hypothesis was tested with a Class B power amplifier operating at 1GHz and different kinds of reconstruction filters. The simulation results showed inconsistency with the initial hypothesis due to incompatibility between the output network of the amplifier requirements and the reconstruction filter input characteristics. This indicates that further investigation is needed to find a power amplifier topology that works properly with the input characteristics presented by the reconstruction filter.

Keywords

Switched Resonator, Envelope Pulse Modulation, Carrier Bursting, Power Amplifier

2

Contents

Abstract ......................................................................................................................................1

Contents .....................................................................................................................................2

Glossary .....................................................................................................................................4

Chapter 1 Introduction ........................................................................................................... 5

1.1 Power amplification problems and efficiency enhancement methods ................... 7

1.2 Pulse Modulated Transmitter architectures............................................................ 8

1.3 Envelope pulse modulation - Carrier bursting ....................................................... 8

1.4 Carrier bursting technical issues .......................................................................... 10

1.5 Thesis Goal .......................................................................................................... 11

1.6 Thesis outline ....................................................................................................... 11

Chapter 2 Power amplifiers basics ....................................................................................... 12

2.1 Basic RF power amplifier characteristics ............................................................ 12

2.2 The load line of the amplifier ............................................................................... 13

2.3 Figures of merit .................................................................................................... 15

2.4 Classes of amplifier: from Class A to Class C ..................................................... 16

2.5 Dynamic load modulation concept ...................................................................... 19

2.6 Simulation tools ................................................................................................... 19

Chapter 3 Reconstruction Filter ........................................................................................... 22

3.1 Response of a filter driven with a carrier bursting signal .................................... 23

3.2 Effective impedance of high order filters............................................................. 27

3.3 Mathematical analysis of the effective impedance of high Q filters .................... 31

3.4 Reconstruction filter discussion ........................................................................... 37

3.5 Reconstruction filter implementation issues ........................................................ 40

Chapter 4 Integration of the reconstruction filter in a Class B amplifier mode ................... 43

4.1 Integration of a high Q reconstruction filter guidelines ....................................... 43

4.2 Integration of a high Q reconstruction filter-simulation results ........................... 44

3

Chapter 5 Discussion and future work ................................................................................. 55

5.1 Future work .......................................................................................................... 56

References ................................................................................................................................57

4

Glossary

3G Third Generation

4G Fourth Generation

BPF Band Pass Filter

BB Base Band

BW Bandwidth

CB Carrier Bursting

DC Direct Current

DLM Dynamic Load Modulation

EPM Envelope Pulse Modulation

LTE Long Term Evolution

PA Power Amplifier

PLM Pulse Load Modulation

RBS Radio Base Station

RF Radio Frequency

SDR Software Design Radio

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Chapter 1

Introduction

In the last decades, we have been witnesses of the evolution of wireless communications and how the introduction of these technologies has progressively changed our lives, in particular, the way we communicate. A good example of this are mobile communications which have taken us from the first-generation (1G) analogue systems that could handle only voice calls, to the sophisticated services offered by 3GPP Long Term Evolution (LTE) systems which include mobile internet, video calls and mobile TV. Now, projecting to the fourth-generation (4G) systems, which promise to offer more and better services at higher data rates. But the fast growing demand for wireless services besides of producing a big impact on the lifestyle of hundreds of millions of people has also started to produce a profound environmental impact due to the large amounts of energy that wireless networks consume. In 2007, studies revealed that the telecom industry consumed around 164 TWh, quantity that represents 1 percent of the global energy of the planet and also equates to the CO2 emission of 29 million cars [1]. These alarming results of environmental pollution, together with the interest of the network operators to reduce their electrical expenses has lead to the development of strategies to reduce the energy consumption in different areas [1].

Major contributors to the energy consumption in wireless networks certainly are radio base station (RBS), whose consumption represents 90 percent of the wireless network energy, most of which wasted due to inefficiencies presented in the operation of radio equipment and power amplifiers (PA). Energy saving strategies are interested in improving the energy efficiency of power amplifiers as well as in the optimization of the structure of the radio equipment, which in turn, is very much related to the power amplification part [1]. But before explaining why, it is important to understand what is a power amplifier and what is the role they play in a RBS.

A power amplifier is an important element of a radio transmitter because it is responsible of converting a low-power radio frequency signal into a larger signal of significant power for driving the antenna of the transmitter. Important requirements of power amplifiers are: power efficiency, linearity and output power. But most of the times, it is the power efficiency which is the main character in the design of power amplifiers. Another important fact about power amplifiers is that they generate not only RF power but also a big amount of heat generated

6

RF Conversion

&Power

Signal Processing

& Control

DC Power

System

Cooling

AC

Feeder

Radio Base Station

Antenna

Fig. 1.1 Block diagram of a radio base station unit. [1]

RF Conversion

&Power

Signal Processing

& Control

DC Power

System

Cooling

AC

Radio Base Station

Antenna

Optical

Fiber

Remote Radio Unit

Fig. 1.2 RBS Remote Radio Block Diagram [1]

due to inefficient operation. In order to maintain the reliability of the system, power amplifiers require a cooling system that in turn increases the total energy consumption of the system. Thus, power efficiency of power amplifiers plays an important role in the power reduction of RBS. But, they are also an essential key in the optimization of the radio equipment. In order to understand this, let us explain a little more about the topology of a typical RBS unit, illustrated in Fig. 1.1.

As seen in Fig. 1.1, a RBS is composed by many elements including DC power system, cooling system, signal processing and control and finally RF conversion and power. The interesting part of this structure is that after performing the common functions of modulation, up conversion and power amplifications, a typical RBS unit delivers the power to the antenna through a feeder cable whose losses are generally of 3 dB. This means that half of the energy produced by a RBS is wasted on the way to the antenna. In order to overcome this problem, radio equipment optimization strategies propose to reduce the size of the radio unit and move it, from the base station to the top of the tower, as illustrated in Fig. 1.2 [1]. This scenario would obviously reduce the large power drop due to the antenna feeder cable, but at the same time requires of high efficient operation of power amplifiers in order to relax their cooling requirements that most of the times add volume to the radio unit [1].

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Therefore, whether to reduce the environmental pollution or decrease the electrical expenses of the network operators, reducing the energy consumption of wireless networks is an important issue of today’s society. As described before, there is much to gain by improving the power efficiency of power amplifiers in RBS. Unfortunately, different factors related to the operation of traditional power amplifiers and modulation schemes used by modern wireless communication systems make this task not so easy.

1.1 Power amplification problems and efficiency enhancement methods

Improving the efficiency of power amplifiers has always been a very controversial issue of the RF design world. Over the years researchers have studied and introduced different methods aiming to achieve this desired goal. However, as might be expected, until this date none of them have been able to obtain completely satisfactory results because of different problems and contradictions encountered in the operation of power amplifiers. This section treats some of the existent problems in the design of power amplifiers and the most typical methods used to overcome these problems.

The first problem is that the envelope of the modulating signals can be distorted to some degree, if the power device is used at its full rated RF power level [2]. Solutions to this problem are termed as “linearization techniques”. Among some of the most suggested linearization families are: feedback [3], feedforward [4] and predistortion [5,6]. These techniques however have some limitations generally in the form of lower efficiency and baseband frequency limitations. Nevertheless, they are widely used and indispensable in applications where linearization is a primary goal. Therefore, they are left out from the purpose of this work.

A second problem and perhaps the most significant is that conventional power amplifier designs can only offer maximum efficiency at a single power level, which is generally near the maximum rated power for the device. As the driven signal is backed-off from that level the power efficiency drops sharply [2]. This situation, combined with the high peak to average power ratios signals used by modern modulation schemes, produces a mean efficiency performance much lower than efficiency at the maximum power level. Solutions to this problem, generally termed as “efficiency enhancement techniques”, have been widely studied since the early era of radio broadcasting. Among the most important are: the Doherty amplifier [7], the Chireix outphasing amplifier [8], dynamic load modulation [9], envelope tracking (ET) [10] and envelope elimination and restoration (EER) [11]. The improvement offered by those techniques do however come at the price of circuit complexity and add physical footprint to the transmitter.

Naturally, as the wireless communications revolution progresses and the modulation schemes becomes every time more and more unfriendly to the amplification process, PA designers will continue coming with new alternatives to overcome the power efficiency problems in PAs. Among some of the emerging techniques currently drawing the attention of the PA community are pulsed modulated transmitter architectures [11]. These architectures are treated in the next Section.

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1.2 Pulse Modulated Transmitter architectures

Pulse modulated transmitter architectures are architectures that address the power efficiency problem in a different way. Since the main dilemma in the power amplification is that the full-capability of the power amplifier is used only at the peaks of the signal envelope and is wasted when the envelope dips to lower amplitudes. These architectures propose to achieve high power efficiency by using the power amplifier only in its most power efficient regions [12].

The fundamental idea behind its operation relies then on the signal used to drive the amplifier. Instead of using an envelope varying modulated signal, pulse modulated architectures encode the communication signal into a binary pulse train. In this way, as the communication signal is represented by only two discrete points, pulse modulated transmitter architectures can ensure high efficiency operation, since the amplifier will use its full capability during the on-state (pulse duration) of the signal and dissipate very little power in the off-state.

A drawback of these architectures is however the generation of a large amount of quantization noise as a result of representing the communication signal by two discrete points. In order to recover the desired signal, that noise needs to be handled by means of a reconstruction filter [12].

Depending on the quantization method they use, pulse modulated transmitter architectures can be divided in two categories: RF-level pulse modulation, that perform the quantization process at the RF level, and baseband (BB) level pulse modulation, that do it on the baseband signal. Commonly suggested architectures to the first category are: RF Band-pass Delta-Sigma modulation (RF-BP∆Σ) [13] and RF-Pulse width modulation (RF-PWM) [14,15], while most representative of the second are envelope pulse modulation and Cartesian modulation. A major discussion about these architectures has been presented in literature [12, 13]. The work presented in this master thesis will be focused on envelope pulse modulation.

1.3 Envelope pulse modulation - Carrier bursting

Envelope pulse modulation (EPM), also known as carrier bursting (CB), is a very promising method that in the same way that other pulse modulated transmitter architectures drives the power amplifier in its most efficient states. The particularity of carrier bursting is that, it performs the 1-bit quantization on the envelope of the baseband signal. Carrier bursting thereby encodes particular characteristics of the envelope component of the communication signal onto a pulse train using quantization rates much lower than the RF carrier. Thereafter it recombines the quantized envelope with the phase component of the baseband signal, to be then up-converted to the RF level and later drive a high efficient power amplifier [12]. An illustration of this process is depicted in Fig. 1.3.

To gain a better understanding of the main idea behind carrier bursting systems, let us present a simple example of a carrier bursting signal using PWM modulation as quantization technique. For the sake of simplicity, instead of using an envelope varying signal, let us consider the communication signal to be a fixed-amplitude,

[ ] 5.0nS = (1.1)

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Fig. 1.3 A carrier bursting system, here illustrated with a Σ∆-modulator for encoding the amplitude

component. Modified from [12]

0 T 2T 3T 4T

-V

0.5V

0

0.5V

V

t

CB

in

pu

t sig

na

l (V

)

D

Ts

Fig. 1.4 CB signal. Note that the information is carried in the duty cycle of the envelope of a CB.

Assuming the maximum amplitude of the modulator to be 1, the carrier bursting signal generated at the output of the modulator is as shown in Fig. 1.4. As observed, from a time domain viewpoint carrier bursting is seen as periodical pulse train up converted to RF, where the duty cycle (D) of the envelope of each pulse is proportional to the instantaneous amplitude of the communication signal. In this way, as the information is not longer carried in the amplitude of the modulated signal but in the duty cycle of the pulse train, carrier bursting provides a suitable driving signal for a power amplifier to keep its high efficiency performance, since the amplifier will work on bursts of phase modulated RF carrier.

A major drawback of carrier bursting is that, the magnified version of the carrier bursting signal at the output of the amplifier contains a large amount of quantization noise. (See Fig. 1.5). Due to different wireless communication systems regulations, that quantization noise cannot be transmitted. Therefore, it must be eliminated by means of a reconstruction filter. Unfortunately for carrier bursting systems that is not an easy task. As observed in Fig. 1.5, due to the low quantization rates carrier bursting uses, the quantization noise is generated

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0.95 0.975 1 1.025 1.05-120

-95

-70

-45

-20

5

CB

Sp

ectr

um

D5

0 (

dB

m)

0.95 0.975 1 1.025 1.05-50

-40

-30

-20

-10

0

Filte

r a

tte

nu

atio

n (

dB

)

f (GHz)

fs

fs

Fig. 1.5 Frequency domain representation of a carrier bursting signal, quantization noise generated ath frequencies fsnfc ⋅± , and the role of the reconstruction filter (in read).

at frequencies nearby the desired signal and should be handled by means of a high Q narrow-band filter. As it is known that kind of filters are also associated to large insertion losses, which will imply a reduction of the power delivered to the load and consequently to a reduction of the overall power efficiency of the system. Nevertheless, its capability to drive the amplifier at only two RF drive levels and to control the output power by a single bit drive signal has made of carrier bursting a very attractive area of study for both the industry and academia.

1.4 Carrier bursting technical issues

There exist three major constraints in designing a EPM transmitter architecture: The selection of the quantization pulse rate, the insertion loss introduced by the reconstruction filter, and the interaction of the reconstruction filter with the power amplifier.

The first two are typical to all kinds of pulse modulated transmitter architectures, in fact in order to minimize their impact different solutions based on noise shaped coding have been suggested in [12] with good results. Yet, the third one is of major concern for many researchers, who in order to avoid undesired effects in the amplifier performance have usually opted for using an isolator in between the amplifier and reconstruction filter. However such interaction should not always imply bad effects in the amplifier performance. Precedent work presented by Liao et al. [16] used the amplifier-filter interaction as an advantage to the development of a novel transmitter architecture called pulsed load modulation (PLM). In that work they connected a balanced amplifier configuration to a narrow bandwidth filter and used the amplifier-filter interaction to modulate the load impedance of the amplifier in a digital fashion. This fact makes us to believe that the amplifier-filter interaction, if properly handled, can be also implemented in single ended power amplifiers, producing positive effects in the performance of an EPM transmitter architecture.

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Fig. 1.6 Block diagram of the EPM power amplifier proposed in this thesis.

1.5 Thesis Goal

For the aforementioned reasons, the design of a high efficiency single-ended EPM power amplifier demonstrator that integrates a narrow bandwidth reconstruction filter in its output network is to be accomplished.

The key objective is then to investigate how a high efficiency power amplifier and reconstruction filter should be co-designed to ensure high efficiency operation. The amplifier mode designated for this thesis work was a conventional high efficiency amplifier. The specifications for the amplifier or reconstruction filter are not given in the task description, since the feasibility of the concept in general has to be analyzed. An illustration of the proposed amplifier configuration is depicted in Fig. 1.6

1.6 Thesis outline

This thesis is organized as follow. In Chapter 2, a brief overview of the basic theory of power amplifiers is presented. Chapter 3 is dedicated to the last stage of the proposed architecture that is the reconstruction filter. In this chapter we will study in detail the behavior a reconstruction filter presents when it is driven with a carrier bursting signal, paying special attention on finding out the causes of that response and of how to minimize its effects on the power amplifier performance. Thereafter in Chapter 4 we will use the theory learnt in Chapter 3 to proceed with the integration of the narrow bandwidth reconstruction filter into the output network of a Class B power amplifier. There, we will analyze the amplifier performance using different kinds of reconstruction filters. And finally in Chapter 5, the final conclusions are presented.

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Chapter 2

Power amplifiers basics

This chapter is thought to give a short introduction into the theory of RF power amplifiers. Among some of the subjects discussed in this chapter are: the basic structure of a single ended power amplifier, conventional high efficiency power amplifiers, dynamic load modulation technique and simulation tools used along this work.

2.1 Basic RF power amplifier characteristics

A power amplifier is an important element of a radio transmitter. Its purpose is to convert a low-power radio frequency signal into a larger signal of significant power for driving the antenna of the transmitter. Important considerations for power amplifiers are power efficiency, linearity and output power.

In order to start to a description of a RF power amplifier, a general configuration of a single-stage RF amplifier is presented in Fig. 2.1. From the figure, a power amplifier comprises three important blocks: an input network, the active device and an output network.

Needless to say the key element in an amplifier is the active device. Its role is to amplify the signal input power via multiplying the voltage or current by an amplification factor. The amplifier requirements of output power, linearity and operating frequency will be determined by the choice of the active device.

The input and output networks are responsible to provide the adequate conditions to the active device for the amplifier to have optimal performance according to a specific goal. While small signal objectives are typically to design the output matching network for complex conjugate match, the output network of power amplifiers is designed to extract the maximum power out of the device. The output network is critical to high-power designs, because the output is where the voltage and current swings of the device are high, and where these need to swing in such a way to minimize distortion and maximize power efficiency[17]. Among other general roles of these networks are:

• To provide a proper bias insertion point for the RF device. The bias of the transistor determines the class of operation and therefore figures of efficiency, linearity and gain.

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LR

SR

AC

Fig. 2.1 Simplified diagram of a single stage power amplifier

• To transform the impedance levels at the ports of the active device to a desired interface level.

• To provide the adequate harmonic terminations to the RF device, so that the amplifier can operate in a determined mode.

• To ensure and maintain the stability of the amplifier for determined load and source impedances.

2.2 The load line of the amplifier

The load line is considered an important and very useful tool in the design of power amplifier. The load line represents the trajectory of all the instantaneous values of current ( Di ) and

voltage ( DSv ) of the RF device when this one is operated under a specific load and at a given

bias point.

The load line is rich in information. It is centered around the bias point of the device. Its length indicates the level of signal swing while its slope the load impedance. The load line traverses different regions of the device I-V curves, and close examination can reveal the device operation regions, its instantaneous output power, where distortion arises and even the efficiency of the amplifier [17].

To better illustrate the concept of load line, consider the basic amplifier schematic shown in Fig. 2.2. The RF device is biased through a RF choke with a quiescent bias voltage DDV

and drain bias current DQI . The output blocking capacitor 0C is used to maintain the voltage

DDV during the entire cycle. From the schematic, the following equations can be established:

0DDDS vVv += (2.1)

0DQD iIi −= (2.2) where DSv and Di correspond to the sum of the DC and AC components of voltage and

current, respectively.

The load impedance can be used to relate 0v and 0i ,

0

0L

i

vZ =

(2.3)

14

Fig. 2.2 Basic amplifier schematic for calculating the load line

Combining the previous equations, the relation between Di and DSv can be established by,

L

DDDSDQD

Z

VvIi

−−=

(2.4) This last equation defines the load line of a device given the bias point ( DQI , DDV ) and a

load impedance LZ . If LZ is a real resistance LR , the slope of the load line will equal LR/1−

and its length will be determined by the amplitudes of current and voltage swings at the drain [17].

There are four constraints that limit the excursion of the load line. The knee voltage kV ,

the breakdown voltage BRV , the minimum drain conduction current into the device which

cannot go negative, and the device maximum current .Imax It is important to remember that

exceeding these constraints can be catastrophic for the device. So a designer should ensure that the actual load seen at the output of the device should maintain the load line excursion within the limit previous mentioned, any faulty output connection or unusual load may potentially cause the load line to be different and lead to failure of the device.

Fig. 2.3 illustrates the load line using three different load resistor values. The three curves pass through the device bias point which is set to ( DDV , DQI ).

The case when OLL RR = corresponds to the optimal load resistance. Note that for this

case the current and voltage swings are the maximum attainable for the device, resulting in maximum output power and power efficiency. This load line is typical of a Class A amplifier, in which the device is always conducting and the load line remains within the active region of the device. The output resistance OLR can be calculated from the slope of the load line, giving

max

kDDOL

I

)VV(2R

−=

(2.5) The case when OLL RR < have a steeper slope than the optimum case. Note that the

current swings between 0 and .Imax However because the load resistor is too small, the output

voltage swing is not as large as in the optimum case. This results in a reduction of output power and power efficiency. This circuit is said to be current limited because the maximum current swings limits the output power [17].

15

Fig. 2.3 Load line plotted with three different load resistors

For the case when OLL RR > , the voltage swing is the maximum possible for the device.

However, the current swing is not as large as before. This is because the load resistor is too large and the output current cannot swing between its potential peak values. This circuit is said to be voltage limited because the bias voltage limits the voltage swing that can be obtained for the chosen load resistor [17].

2.3 Figures of merit

Before describing the two basic figures of merit of power amplifier, let us to define some of the power components presented in the amplifier operation.

• Input power ( inP ) defined as the power flowing into the amplifier input, over a

determined frequency range. Generally, for initial design purposes the input power is considered to be concentrated in a single frequency component also known as fundamental.

• Output power ( outP ) defined as the power flowing out from the amplifier, over a

determined frequency range. If the input contains only one harmonic, the output power corresponds to the power measured at the fundamental.

• DC power ( dcP ) defined as the power drawn from the power supply during the amplifier

operation.

• Dissipated power ( dissP ) defined as the power dissipated in the device as a heat. This

power waste is undesired and has to be minimized.

Given these definitions the figures of merit of an amplifier are:

Drain efficiency

The drain efficiency (η ) is defined as the efficiency of converting DC power into RF power

at the fundamental frequency,

dc

out

P

P=η (2.6)

This figure of merit is useful when different amplifier types are compared in theory because it does not include the driving requirements. The drain efficiency does not account

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for the power required to drive the transistor and might therefore be misleading as an efficiency figure for a full amplifier system.

Power added efficiency

The power added efficiency (PAE) is defined as the ratio of the power added to the RF signal to the DC power consumed by the amplifier,

dc

inout

P

PPPAE

−= (2.7)

This figure of merit is more useful to make fair comparisons and evaluation of amplifier systems, because the required input drive power to the amplifier is also taken into account.

2.4 Classes of amplifier: from Class A to Class C

In this section a short summary of the classic modes of amplifier operation is presented. Detailed information of this subject can be found in literature [2,17]

2.4.1 Class A amplifier

Class A amplifier is the most basic power amplifier configuration. This amplifier mode is characterized for setting the bias voltage in the middle between the cutoff voltage and the saturation voltage. For pure class A operation, the voltage swing must never reach saturation or cutoff region. This means that the RF device is always in conduction, which makes of this amplifier mode the more linear amplifier class available.

The main drawback of Class A operation is its poor drain efficiency. In theory, the maximum efficiency achieved by this amplifier mode is only 50%. This amplifier mode is always drawing a constant DC power, independent of the level of the output power.

2.4.2 Reduced conduction angle- Class AB, Class B and Class C

Reduced conduction angle, high efficiency power amplifier are amplifier modes that were used since the early days of vacuum tubes as an alternative to improve the power efficiency of the traditional Class A amplifier. A general schematic of these configurations is illustrated in Fig. 2.4.

The fundamental idea these amplifier modes share is to achieve higher efficiency by biasing the active device to a quiescent point ( qV ) lower than the Class A condition and

keeping the same maximum current and voltage excursion. As a result, the RF device conducts only during a reduced portion of RF cycle, also known as conduction angle (α). The output current waveforms take the form of asymmetrically truncated sine waves. (See Fig. 2.5).

Depending on the conduction angle value, the Class AB, Class B and Class C are defined as indicated in Table 2.1. The conduction angle is determined by the quiescent gate voltage ( qV ), which is a function of the cut off voltage ( tV ) and built in voltage ( biV ).

17

DDV

0f

LR

inV

+

=,...f3,f2@0

f@0jRZ

00

0L

L

DSv

1i 432 i,i,i

Di

outV

Fig. 2.4 General schematic of reduced conduction angle power amplifier modes

0 π π2 π3 π42α

Fig. 2.5 Reduced conduction angle current waveforms [2]

Table 2.1 Classical reduced conduction angle modes

Mod

e Bias point )V( q Quiescent

current

Conduction

Angle

A Vt+0.5·(Vbi-Vt) 0.5Imax 2π

AB Vt+(0→0.5)· (Vbi-Vt) 0→0.5Imax π-2π

B Vt 0 π

C <Vt 0 0-π

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Harmonics

Returning to the current waveforms in Fig. 2.5 , it is clear they have harmonic content. In order to prevent any harmonic voltage from being generated at the load, they must be properly terminated by means of a harmonic short block. The main role of this block is to provide short circuit to all the harmonics except the fundamental, so that the impedance seen from the output of the RF device is,

+

=,...f3,f2@0

)f@0jRZ

00

0opt

L (2.8)

In principle, the harmonic short could be realized using a parallel shunt resonator tuned at the fundamental frequency. In practice due to limitations of availability of good quality passive components for microwave ranges, the requirement for a short circuit termination at all harmonics must be solved using simple solutions in the form of resonant transmission line stubs.

Efficiency- Output power

Some simple Fourier analysis of the current waveforms [2] demonstrates the maximum efficiency increases sharply as the quiescent level is reduced (See Fig. 2.6). This improvement does not only apply at the maximum drive level but also at back-off condition, which increases specially in relation to Class A configuration. From Fig. 2.6 some important remarks can be made:

• For Class AB operation, the fundamental RF output power is approximately constant.

• Class B condition delivers the same power as Class A, but with a DC supply reduced by a factor of π/2 compared to Class A operation. This gives an ideal efficiency of 78.5 %.

• Class C condition shows an ever-increasing efficiency as the conduction angle is reduced. However, this efficiency improvement comes at the price of substantially reduced output power.

Fig. 2.6 RF output power and efficiency as a function of the conduction angle [2]

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Table 2.2 Efficiency and linearity for Class A to C amplifiers

Linearity

The reduction of the conduction angle has also effects in the linearity of the amplifier. This is due to the fact that at reduced conduction angles the device will have smaller excursion in the linear region. The highest linearity is obtained in Class A operation while less linearity is seen in Class C operation. A good tradeoff between linearity and efficiency is obtained using Class AB condition. Table 2.2 summarizes the most important information for Class A to Class C operation.

2.5 Dynamic load modulation concept

The dynamic load modulation is a technique used to improve the drain efficiency of a power amplifier by changing the effective impedance seen by the RF device when the input drive level dips to lower levels.

The main idea of this technique is that when a conventional power amplifier operates at back off condition the optimal resistance is too low to allow a full rail-to-rail voltage swing. So if by some means the load resistance can be made to change its value dynamically as the drive level is backed-off a full voltage swing can be obtained and high efficiency can be maintained.

In principle the load modulation concept could solve the efficiency drop problem of conventional power amplifiers. In practice however, the problem is quite complicated. The main concern is the way how to dynamically transform the load impedance at the output of the RF device on the same timescale as the amplitude modulated carrier.

Important efficiency enhancement methods that use this concept are: the Doherty amplifier [7] which changes the load resistor value using a configuration of two separate amplifiers. And, varactor based load modulation [9] which in turn uses an electronically tuned output filter.

2.6 Simulation tools

Agilent EEsof Advance Design System (ADS) is used in the development of this work. This section describes briefly some of features and limitations of the simulation tools used along this work.

2.6.1 Transient analysis

The transient analysis is performed entirely in the time domain. Transient analysis presents poor performance when it is necessary to resolve relatively low modulating frequencies in the presence of high carrier frequency and also when there are distributed transmission lines present in the design [18, 19].

Mode Conduction angle Theoretical Efficiency Linearity

A 2π 50% high

AB π-2π 50%-78.5% between class A and B

B π 78.5% moderate

C 0-π 78.5%-100% poor

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2.6.2 Harmonic balance analysis

The harmonic balance is a highly accurate frequency domain technique suitable to analyze the steady state solution of nonlinear circuits and systems that are most naturally handled in the frequency domain [20, 21].

Harmonic balance can handle mild non-linearity and lossy distributed transmission lines. Since harmonic balance performs only the steady state analysis, it is not suitable to represent the continuous spectrum of a transient signal or non periodic digitally modulated signal, which is the case in all commercial wireless communication systems [19].

2.6.3 Envelope transient analysis

Envelope transient analysis is a technique that has the capability to predict the response of a circuit when it is driven with a complex digital modulation signal, without excessive computational overhead. This technique considers a modulated signal as a combination of a low frequency dynamic (envelope of the carrier or modulation) and a high frequency dynamic (carrier). It combines harmonic balance analysis of the high frequency signal with the transient analysis of the low frequency signal, providing a fast and complete analysis of the complex digital modulation input signal [22].

Envelope transient analysis is considered the best suited and only practical simulation technique, used in conjunction with harmonic balance and linear RF simulation, for present and future wireless communication designs [19]. The envelope transient technique is useful in analyzing long term behavior of certain RF circuits. For example it is used in the analysis of the turn-on behavior of oscillators, in the IMD analysis of power amplifiers with realistic input signals, etc.

Envelope transient analysis is nowadays implemented in most commercial CAE tools. Due to the time varying envelope characteristic of carrier bursting signals, this technique will be the simulation tool chosen by default, and will be referred along this thesis as envelope simulation.

It is also important to highlight that due to the wide spectrum carrier bursting signals present, special attention should be taken in the simulator frequency domain parameters. In particular the maximum allowed bandwidth, which should be much higher than the modulation frequency of the CB signal. The wrong selection of this value can lead to inaccurate results, as it is shown in Fig. 2.7. There envelope simulations where carried on a narrow bandwidth filter using a carrier bursting excitation. Note that the measured input current and filter effective impedance for the three settings differs entirely from each other. This is not desired especially when the simulator results are used as a comparison point to theoretical analysis. The results in Fig. 2.7 will be better understood in the following chapter. There we will continue with the analysis of different aspects of the last stage of the proposed architecture. That is the reconstruction filter.

21

9.8 9.85 9.9 9.95 109.0

9.2

9.4

9.6

9.8

10

10.2

Ifilt (m

A)

time (µs)

BW 25fm

BW 50fm

BW 100fm

(a) Filter input current

9.8 9.85 9.9 9.95 1090

95

100

105

110

Rfilt (

Ω)

time (µs)

BW 25fm

BW 50fm

BW 100fm

(b) Effective resistance

Fig. 2.7 Effect of varying the simulation maximum allowed bandwidth (a) current measured at the input of a high Q filter when driven with a CB signal. (b) Effective impedance measured at the input of the filter.

22

Chapter 3

Reconstruction Filter

A reconstruction filter is an important element in pulse modulated transmitter architectures, because it eliminates the undesired quantization noise generated at the output of the amplifier, generating a smooth modulated signal ideal to transmit without violating the spectral mask. The specifications of this filter vary from architecture to architecture. In RF level pulsed modulated transmitter architectures for instance, due to the high frequency quantization rates used, the quantization noise occurs in the vicinity of the carrier harmonics and can be handled by a low Q, low loss reconstruction filter. Therefore the design and integration of the filter into the amplifier does not represent a major problem.

In carrier bursting systems however, due to the comparably low quantization rates used, the requirements of the filter become more stringent. A reconstruction filter for carrier bursting systems must fulfill three important requirements: narrow bandwidth, low insertion loss in the passband and sufficient stop band suppression. However, there is another factor in the design that has usually been omitted and therefore very little work has been reported on it. That is the integration of the reconstruction filter into the amplifier. The reason of this is generally to avoid undesired effects in the amplifier performance due to interaction of the narrow bandwidth filter with the carrier bursting signal. Nevertheless, based on previous research work presented in [16, 23] it is believed that such interaction, if properly handled, may be achieved and bring good effects in the power efficiency of a single ended power amplifier.

Understanding the reasons of the CB signal-filter interaction and finding the way to use them for our benefit is the key in the development of the proposed amplifier design. Therefore, this chapter presents a more intensive study of those matters. In the first section, a discussion about the response a narrow bandwidth filter exhibits when is driven with a CB signal is presented. As first point, it treats an innovative concept that represents the foundation of this work. That is switched resonators. In Section 3.2, this concept is extended to higher order filters and based on simulations try to explain some effects of the filter-CB signal interaction. However it will be seen that there is a missing link that limits our understanding. Therefore, in Section 2.3 a different method to analyze the reasons and effects of the integration is presented. That method is used in Section 3.4 to define some

23

considerations to take into account in the design of the filter. And finally, Section 3.5 deals with the practical implementations of the reconstruction filter.

3.1 Response of a filter driven with a carrier bursting signal

This section analyses the behavior shown at the input of the reconstruction filter when the filter is driven with a carrier bursting excitation as a separate stage. The purpose of this study is to provide understanding on the effects the reconstruction filter may cause when it is later integrated in the amplifier network. A logical starting point to this discussion is to talk about switched RF resonators whose general behavior presents some similarities to the proposed configuration, carrier bursting signal-narrow bandwidth band pass filter.

3.1.1 Switched RF resonators

First introduced by Kim et al. [23], a switched resonator is defined as a resonator whose RF energy storage behavior is controlled by one or more switches. An illustration of a simple switched resonator is shown in Fig. 3.1.

Simple in their structure, switched resonators take advantage of the energy storage behavior that resonators exhibit when they are exposed to a strategically controlled charging and discharging process. In this way, switched resonators are able to dynamically control the equivalent impedance characteristics of the resonator. To gain a better understanding of the general behavior of switched resonators, let us first explain more about the transient characteristics of a resonator.

Transient characteristics of a resonator

The switched resonator discussed in this section is shown in Fig. 3.1. The circuit comprises four important elements: a resonator, a load resistor, a controllable switch and a RF source. In order to analyze the energy storage behavior of the resonator, in this part the case when the switch is connected to the RF source is considered. The analysis presented here is accurate based on the following assumptions: The resonator is used to store the energy of the RF signal i.e. the RF signal is tuned at the resonator resonant frequency. The operating bandwidth of the resonator is much smaller than its resonant frequency. And, the resonator presents a decent quality factor (Q) value.

outv

itcosV oω

0f

CLD

R

v

Fig. 3.1 Series LC switched resonator example.

24

0 1 2 3 4 5

-20

-10

0

10

20

t (us)

Cu

rre

nt (m

A)

Fig. 3.2 Current waveform measured at the input of the resonator when the RF signal is applied to the circuit.

Fig. 3.2 shows the current response of the resonator when the RF source is connected to the resonator. As observed, due to the energy storage capabilities the resonator exhibits, the current does not change instantaneously, but starts increasing from zero to a value that is determined by the load resistor. The current response during this settling period is called the transient response of the filter. The interesting part is that due to the increasing current behavior the resonator exhibits while the input voltage is kept constant, the resonator does not only present an energy storage behavior but also behaves like a time-varying impedance. In order to demonstrate that particular characteristic, the instant equivalent impedance of the resonator can be solved analytically.

Because the resonator consists of a series RLC circuit, the current (i) across the resonator follow the solution to the equation,

( ) )tcos(ViRdiC

1

dt

diL 0

t

ωττ ⋅=⋅+⋅+⋅ ∫ ∞− (3.1)

Therefore, the expression of the current across the resonator can be expressed by,

( )

)/(tan

)tcos(R

V)tcos(Ce)t(i

01

001t

ωαφ

ωφωα

−

−

=

⋅++⋅=

(3.2)

where α is the damping attenuation constant ( )L2/(R ⋅=α ), 0ω is the resonant frequency and

1C is determined by the initial conditions of the resonator.

As the resonator presents high Q, i.e. αω ⋅>> 20 and it is initially uncharged, the current

expression reduces to,

( )t0 e1)tcos(

R

V)t(i αω −−⋅⋅= (3.3)

Moreover, as the voltage across the resonator is expressed by,

tcosV)t(v 0ω⋅= (3.4)

25

the instantaneous equivalent impedance measured at the input of the resonator at any time instant can be written by,

tine1

R)t(Z α−−

= (3.5)

As observed in expression (3.5), during the transient time the equivalent input impedance of the resonator varies from open circuit (when the resonator is uncharged) to a value equal to the load resistor (when the resonator is fully charged and reaches its steady state). As the variable impedance behavior appears only during the energy storage phase, a natural assumption is that such behavior is related to the amount of energy stored in the resonator at any time instant. Consequently, by controlling that amount of energy it will be also possible to control the equivalent impedance of the resonator.

Effective impedance of a switched resonator

A way to take advantage of the variable impedance behavior of resonator is to keep the resonator working at the vicinity of a certain stored energy level. Switched resonators then exposed the filter to a periodical charging a discharged process by time switching the RF source [23]. If the switching action is made in a time frame shorter than the resonator settling time but longer than the carrier period, after some charging/discharging process the resonator will not complete the energy storage but will reach certain level at which it will settle. Because of the periodic nature of the switching action, the energy settled in the resonator and consequently its effective impedance will be determined by the ratio between the charge and discharge time. That is the duty cycle (D).

In order to demonstrate the previous formulation, according to [16] the effective resistance ( effR ) observed at input of the resonator can be solved analytically. Assuming the resonator

offers enough suppression of the switching harmonics, it can be said that the voltage delivered to the load would be approximately proportional to the duty cycle of the switching action i.e. DVV maxout ⋅= , as it is shown in Fig. 3.3.

0T 1T 2T 3T 4T 5T

0.1

0.3

0.5

0.7

0.9

1

Vo

ut (V

)

t

D=0.1

D=0.3

D=0.5

D=0.7

D=0.9

Fig. 3.3 Voltage measured at the output of the switched resonator circuit shown in Fig. 3.1.

26

Due to the series configuration of the circuit elements, the current flowing into the resonator equals the current through the load resistor, therefore it can be defined as,

R

DVI

R

VI

maxin

outin

⋅=

=

(3.6)

As the envelope of the input voltage can be expressed by,

<<⋅⋅≤<

=TttD0

tDt0VV

max

in (3.7)

The effective resistance, defined as ratio of the input voltage ( inV ) to the input current

( inI ), is given by,

<<⋅

⋅≤<=

TttD0

tDt0D

R

Reff (3.8)

Observing the expression in Equation (3.8), the effective impedance of the resonator appears to be a function of the duty cycle of the switching action. To better illustrate that behavior, the foregoing derivations were verified for different duty cycles using envelope simulations. The results are shown in Fig. 3.4. As expected, the effective impedance exhibit by the resonator changes its value in inverse proportion to the duty cycle. However, it is interesting to note that the results also show a non-constant response when the switch is connected to the RF source. That variation, although small for this resonator example, is obviously caused by the non-ideal attenuation characteristic of the resonator. Therefore, its magnitude should increase for resonators that offer less attenuation in the suppression band, as it shown in Fig. 3.5.

From (3.8), it is important to note that the signal generated by switching action of the RF source and ground is not more than a carrier bursting signal. Where, the period and duty cycle of the switching action will define the modulation frequency and duty cycle of the CB signal, respectively. And, the RF source represents the carrier frequency of the CB signal. Consequently, in future sections this signal will be referred as CB signal.

0T 0.2T 0.4T 0.6T 0.8T 1T0

100

200

300

400

500

Rfilt (

Ω)

t

D=0.1

D=0.3

D=0.5D=0.7

D=0.9

Fig. 3.4 Variable impedance behavior of the switched resonator shown in Fig. 3.1. The effective impedance is inversely related to the duty cycle of the CB signal.

27

0.98 0.99 1 1.01 1.020

10

20

30

40A

tte

nu

atio

n (

dB

)

f (GHz)

RLC1

RLC2

RLC3

(a)

0T 0.2T 0.4T 0.6T 0.8T 1T0

80

160

240

320

400

Rfilt (

Ω)

t

D=0.3

RLC1

RLC2

RLC3

(b) 50% duty cycle

0T 0.2T 0.4T 0.6T 0.8T 1T0

50

100

150

200

Rfilt (

Ω)

t

D=0.5

RLC1

RLC2

RLC3

(c) 50% duty cycle

0T 0.2T 0.4T 0.6T 0.8T 1T0

25

50

75

100

125

Rfilt (

Ω)

t

D=0.7

RLC1

RLC2

RLC3

(d)70% duty cycle

Fig. 3.5 Effects of the attenuation response on the effective impedance of the a series LC resonator. (a) Attenuation response for series LC resonator with different quality factor

3.2 Effective impedance of high order filters

The necessity to use a high Q filter instead of a resonator as reconstruction filter relies on practical implementation. Although a resonator is also a bandpass filter and may fulfill the requirements of attenuation to the quantization noise, it does not fulfill the insertion loss requirements in-band or at least not to all the frequencies. Carrier bursting, in practice, encodes communication signals with finite bandwidth. Therefore in order not to attenuate important information, it is necessary to use a filter that provides certain passband. This section continues with the analysis of the filter response to a carrier bursting signal but using filters whose frequency characteristics fulfill the requirements of the reconstruction filter intended in this work. The main purpose of this analysis is to identify the parameters that optimize the performance of the filter as reconstruction filter but most important as variable impedance.

The filters investigated in this section were 2nd and 3rd order Butterworth and 0.5 dB Ripple Chebyshev lumped bandpass filters. The filters were designed to have 5 MHz bandwidth and 1 GHz central frequency (f0). The attenuation characteristics of the filters are shown in Fig. 3.6. The simulations were performed using the carrier bursting parameters stated in Table 3.1. The results are shown in Fig. 3.7. For comparative purposes, the

28

effective impedance response of the switched resonator studied in Section (3.1.1) is also shown in the simulation results (Fig. 3.7).

The results show that compared with the resonator case, the effective impedance exhibit by the higher order high Q filters presents significant variation on the on-state of the CB signal. The magnitude of the variation changes for different duty cycles, becoming more significant for small duty cycle values. Moreover, the effective impedance does not seem to show any improvement when using filters with steeper transition bands and larger suppression to the quantization noise. The impedance variations either do not present major improvement, as the case of the Chebyshev filter, or get even more significant, as in the Butterworth case. This goes contrary to the assumption that a filter with better attenuation response would fit better as variable impedance, as it occurred in the resonator case (Section 3.1.1).

Table 3.1 Carrier bursting signal parameters

Symbol Specification Value

f0 Carrier frequency 1 GHz

fs Switching frequency 10 MHz

D Duty cycle 30%, 50%, 70%

0.98 0.99 1 1.01 1.020

20

40

60

80

f (GHz)

Atte

nu

atio

n (

dB

)

3rd

2nd

RLC

Buttw

Cheb

Fig. 3.6 Attenuation characteristics of the filters considered in Section 3.2.

29

0T 0.2T 0.4T 0.6T 0.8T 1T0

80

160

240

320

400

Rfilt (

Ω)

t

D=0.3

RLC

2nd But

3rd But

(a)

0T 0.2T 0.4T 0.6T 0.8T 1T0

50

100

150

200

Rfilt (

Ω)

t

D=0.5

RLC

2nd But

3rd But

(c)

0T 0.2T 0.4T 0.6T 0.8T 1T0

25

50

75

100

125

Rfilt (

Ω)

t

D=0.7

RLC

2nd But

3rd But

(e)

0T 0.2T 0.4T 0.6T 0.8T 1T0

80

160

240

320

400

Rfilt (

Ω)

t

D=0.3

RLC

2nd Chb

3rd Chb

(b)

0T 0.2T 0.4T 0.6T 0.8T 1T0

50

100

150

200

Rfilt (

Ω)

t

D=0.5

RLC

2nd Chb

3rd Chb

(d)

0T 0.2T 0.4T 0.6T 0.8T 1T0

25

50

75

100

125

Rfilt (

Ω)

t

D=0.7

RLC

2nd Chb

3rd Chb

(f)

Fig. 3.7 Simulated variable impedance response of high Q filters when driven with a CB signal. Note that the effective impedance exhibited by Butterworth and Chebyshev filters present significant variation in comparison to the resonator case. The Butterworth filters present the largest variations for each duty cycle.

30

3.2.1 Effective impedance of a shunt LC resonator

Other important results worthwhile to mention were observed using the shunt LC switched resonator configuration shown in Fig. 3.8. That circuit presents an attenuation response similar to the switched resonator studied in previous sections. However, its effective resistance differs entirely from the effective impedance measured on the series LC resonator. As observed in Fig. 3.9, the effective impedance of a shunt LC switched resonator varies in direct proportion to the duty cycle in the on-state of CB signal and behaves as an open circuit during the off-state.

<<⋅∞⋅≤<⋅

=TttD

tDt0DRReff (3.9)

These results confirmed the wrong idea that the variable impedance behavior of the filter

can be directly associated to the usual reconstruction filter design parameters. i.e. attenuation response. Clearly others are the parameters that influence in the variable impedance response.

outi

0f

CL

D

R

outv

tcosV oω

v

i

Fig. 3.8 Switched shunt LC resonator example

0T 0.2T 0.4T 0.6T 0.8T 1T0

10

20

30

40

50

Rfilt (

Ω)

t

D=0.1

D=0.3

D=0.5

D=0.7

D=0.9

Fig. 3.9 Effective input impedance of the Shunt LC switched resonator in Fig. 3.8. The effective

impedance of this circuit is directly related to the the duty cycle of the CB excitation.

31

3.3 Mathematical analysis of the effective impedance of high Q filters

In order to exploit the particular variable impedance behavior of resonators and use it for the development of more sophisticated applications, it is very important to find out the characteristics of the resonator/filter that determine or influence more in their variable impedance response. Unfortunately, the method used in [16] although useful for understanding the relation between the effective resistance and duty cycle, does not give any hint in that regard. As noticed in the simulation results, the relation duty cycle-effective resistance changes drastically for other filter arrangements. The measured effective impedance presented a non-constant response during the CB burst on state, which makes more difficult the prediction of the effective resistance for certain duty cycle.

After further investigation, it was discovered that the variable impedance response is not directly related to the attenuation response of the filter, but can be better associated to the input impedance/admittance response of the filter over certain bandwidth. In order to probe this formulation, in this section a different method to analyze the variable impedance behavior of filters is presented. This method is based on the impedance concept but analyzed from a different perspective. For the sake of simplicity, in this analysis only the steady state behavior is considered.

Let us start this analysis by recalling the impedance concept. Consider a 1-port linear time invariant (LTI) network which may be a portion of a larger network as shown in Fig. 3.10.

Suppose that voltage v across the LTI network is a sinusoidal of the form,

)tcos(Vv φω += (3.10)

Therefore, in the steady state it can be said that the current through the network would also be a sinusoidal of the same frequency but with a different phase produced by the interaction with the LTI network, that is

)tcos(Ii θω += (3.11)

v

+

−

i

inz

Fig. 3.10 Impedance concept

32

According to basic circuit theory, the input impedance of this network is defined as the ratio of the phasor representation of the voltage across the network to the phasor representation of the current through the network, i.e.

I

V

Ie

VeZ

tj

tj

in == ω

ω (3.12)

whereV and I are complex numbers φjeV and θjeII = , respectively. Once refreshed the

basic knowledge in circuit theory, let us extend this concept to the carrier bursting case.

A carrier bursting signal, as discussed before, is a periodical pulse train signal up converted to RF, where the width of each pulse is proportional to the instantaneous amplitude of the signal that CB encodes. Although, the switching frequencies used by carrier bursting systems are generally lower than the RF carrier, they are also much higher than the maximum frequency of the signal to be encoded. Therefore the duty cycle of a CB signal can be considered to be constant over a long time period or to vary slowly. Hence, in this analysis a CB signal with static duty cycle will be considered.

The simplest mathematical expression of a CB signal is then given by,

<<≤<⋅

=ss

s0

TtT.D0

T.Dt0)tcos(A)t(v

ω (3.13)

where, A , 0ω , D and sT are the amplitude, carrier frequency, duty cycle and switching period of

the CB signal, respectively.

Using the Fourier series representation, a carrier bursting signal can be expressed by,

⋅= ∑

∞

−∞=k

tjkwk0

sea)tcos()t(v ω (3.14)

where sω represent the CB switching frequency and ka is defined by,

)kD(sinceDAa Djkk ⋅⋅⋅= − π (3.15)

Simplifying even more, a CB signal can be expressed by,

= ∑

∞

−∞=

+

k

t)k(jk

s0eaRe)t(v ωω (3.16)

Now, let us see what happen when this signal is applied to the one-port LTI network whose input impedance or admittance is a function of frequency.

)(j

inin e)(Y)(Y ωφωω ⋅= (3.17)

As the voltage signal is a linear combination of different complex exponentials, from superposition property the output response to the sum (in this case input current) is the sum of the response shown by the LTI system at each complex exponential frequency separately, that is,

33

( ) ( )

( ) ( )( ) ( )( ) ( )

( ) ( ))tk(js0ink

)tkww(jk

)t(js0in1

)tww(j1

j0in0

jw0

)t(js0in1

)tww(j1

)tk(js0ink

)tkww(jk

s0s0

s0s0

00

s0s0

s0s0

e)k(YaReeaRe

e)(YaReeaRe

e)(YaReeaRe

e)(YaReeaRe

e)k(YaReeaRe

)t(i)t(v

ωω

ωω

ω

ωω

ωω

ωω

ωω

ω

ωω

ωω

++

++

++

++

−−

−−

−−

−−

+→

+→

→

−→

−→

→

MM

MM

(3.18)

Thus, the input current flowing into the LTI network can be expressed by,

⋅+⋅⋅⋅⋅=

⋅+⋅=

∑

∑∞

−∞=

+−

∞

−∞=

+

k

t)k(js0in

Djk

k

t)k(js0ink

s0

s0

e)k(Y)kD(sinceDARe)t(i

e)k(YaRe)t(i

ωωπ

ωω

ωω

ωω

(3.19)

Observing the expression in Eq. (3.19), the input current appears to be a function not only of the network impedance at the carrier frequency, but it is also influenced by the input admittance of the network at the quantization noise frequencies.

Once having found the expression of voltage and current, the effective impedance of the LTI network can be found by dividing the phasor representation of voltage and current.

According to simple mathematical theory, a phasor refers to an expression that encodes the amplitude and phase of a sinusoid at certain frequency. In other words, given a signal of the form,

tjj

)t(j

eeARe

eARe)tcos(Aωθ

θωθω

⋅⋅=

⋅=+⋅ +

(3.20)

The phasor of the signal is given by the complex constant, θjeA ⋅ , where A and θ represent the amplitude and phase of the sine wave, respectively. Thus, by simple comparison with Eq. (3.16) and Eq. (3.19) , the voltage phasor (v~ ) and current phasor ( i

~) are given by,

∑∞

−∞=

−⋅⋅⋅=k

)Dktkw(j se)kD(csinDAv~ π (3.21)

∑∞

−∞=

+−⋅+⋅⋅⋅=k

)Dktkw(js0in

kse)kww(Y)kD(sincDAi~ φπ (3.22)

where )k( s0k ωωφφ += .

Dividing both expressions, the effective impedance of the LTI network is finally given by,

∑

∑∞

−∞=

+−

∞

−∞=

−

+=

k

)Dktkw(js0in

k

)Dktkw(j

ks

s

e.)kww(Y.)kD(sinc

e)kD(sinc

z~φπ

π

(3.23)

34

As observed in Eq. (3.23), the effective impedance of the network is not only a function of the duty cycle (D) of the CB signal but also of the admittance response of the LTI network at the quantization noise frequencies.

To better illustrate the fundamental idea behind the foregoing derivations, let use those equation to analyze the effective impedance of the switched resonator discussed in Section 3.1.1. The resonator’s resonant frequency was set to 1GHz with an inductor and capacitor of 25.3µH and 1fF, respectively. The carrier bursting signal considered in this example presents 50 % duty cycle, 10 MHz switching frequency and 1V amplitude (A).

Because the switched resonator consists of a RLC circuit, its transfer input admittance can be easily derived and is given by,

Cj

1jwLR

1)(Yin

ω

ω++

= (3.24)

Using the expression in Eq. (3.16) and Eq. (3.19) , the spectral components of the CB signal and input current are as illustrated in Fig. 3.11 and Fig. 3.13, respectively.

From Fig. 3.11, as expected the CB spectral component at the carrier frequency is proportional to the duty cycle of the CB signal, i.e. DAv 0 ⋅=ω .

Because the admittance of the resonator is frequency dependent, when the CB signal is applied to it, each voltage spectral component is affected in a different extent (See Fig. 3.13). Since the input admittance is R/1)(Y 0in =ω at the fundamental and very small to other

frequencies, the resulting input current is mostly influenced by the current component at the fundamental. Which translated to time domain terms would be a sine wave with amplitude approximately equal to R/DA ⋅ . (See Fig. 3.14)

Finally, because the CB signal in time domain terms is seen as bursts of sine wave with constant amplitude ( A ) and the input current is duty cycle dependent, the input impedance appears to change its effective value becoming duty cycle dependent as well.

0.9 0.95 1 1.05 1.1

0

0.25

0.5

vk(

V)

f(GHz)

(a) Magnitude

0.9 0.95 1 1.05 1.1

-180

-90

0

90

180

∠v k

(d

eg

ree

)

f(GHz)

(b) Phase

Fig. 3.11 Fourier coefficients of a CB signal with 50% duty cycle and 10 MHz switching frequency and 1V amplitude.

35

0.9 0.95 1 1.05 1.10

0.005

0.01

0.015

0.02

0.025

Yin

(S

)

f(GHz)

(a) Magnitude

0.9 0.95 1 1.05 1.1

-90

-45

0

45

90

∠Y

in (

de

gre

e)

f(GHz)

(b) Phase

Fig. 3.12 Input admittance of the RLC circuit shown in Fig. 3.1

0.9 0.95 1 1.05 1.1

0

5

10

ik

(mA

)

f(GHz)

(a) Magnitude

0.9 0.95 1 1.05 1.1

-180

-90

0

90

180

∠i k

(d

eg

ree

)

f(GHz)

(b) Phase

Fig. 3.13 Fourier coefficients of the input current of the RLC circuit

0 0.2 0.4 0.6 0.8 1-2

-1

0

1

2

t (ns)

v(t

) (V

)

(a)

0 0.2 0.4 0.6 0.8 1-20

-10

0

10

20

t (ns)

i(t)

(m

A)

(b)

Fig. 3.14 Time domain representation of (a) CB signal with 50% duty cycle (b) input current.

36

In a similar way, this analysis method can be used to determine the input impedance for the shunt resonator switched resonator,

∑

∑∞

−∞=

−

∞

−∞=

+−+=

k

)Dktkw(j

k

)Dktkw(js0in

s

ks

e)kD(sinc

e.)kww(Z.)kD(sinc

z~π

φπ

(2.23)

To demonstrate the validity of this analysis method, the effective impedance described by the foregoing derivations was verified for different filter arrangements using envelope and transient simulations. The results showed good agreement among them, as it is illustrated in Fig. 3.15, Fig. 3.16, Fig. 3.17 and Fig. 3.18.

0 0.25T 0.5T 0.75T 1.0T9

9.5

10

10.5

11

Ifilt (m

A)

Analytical

ADS Env

(a)

0 0.25T 0.5T 0.75T 1T0

25

50

75

100

125

Rfilt (

Ω)

t (µs)

Analytical

ADS Env

(b)

Fig. 3.15 Comparison between Analytical method and ADS Circuit envelope simulator (a) Input current (b) Effective resistance, Series RLC resonator

2.4 2.425 2.45 2.475 2.55

10

15

20

25

Ifilt (m

A)

t (µs)

Analytical

ADS Env

ADS Tran

(a)

2.4 2.425 2.45 2.475 2.50

50

100

150

200

Rfilt (

Ω)

t (µs)

Analytical

ADS Env

(b)

Fig. 3.16 Comparison of Analytical and simulation methods (a) Input current (b) Effective resistance, 5MHz bandwidth Butterworth 3rd bandpass filter

37

2.4 2.425 2.45 2.475 2.55

10

15

20

25Ifilt (m

A)

t (µs)

Analytical

ADS Env

ADS Tran

(a)

2.4 2.425 2.45 2.475 2.50

50

100

150

200

Rfilt (

Ω)

t (µs)

Analytical

ADS Env

(b)

Fig. 3.17 Comparison of Analytical and simulation methods (a) Input current (b) Effective resistance, 5MHz BW Chebyshev 3rd BPF

0 0.25 0.5 0.75 1 00

25

50

75

100

t

Rfilt (

Ω)

Analytical

ADS Env

(a)

0 0.25 0.5 0.75 1 00

25

50

75

100

t

Rfilt (

Ω)

Analytical

ADS Env

(b)

Fig. 3.18 Comparison of Analytical and simulation methods (a) Input current (b) Effective resistance, Shunt LC resonator treated in Section 3.2

3.4 Reconstruction filter discussion

The switched resonator concept introduced by Kim, et al. [23 ] demonstrates the possibility to use the transient characteristics of resonator for the implementation of novel RF envelope signal processing functions. Although that behavior is obviously caused by the charging and discharging process the filter is subject of, in our work a detailed analysis of the parameters that influence in the variable has been performed. It was discovered that the variable impedance behavior can be also analyzed using the input impedance/admittance response the filter presents over certain bandwidth. The simplicity of evaluation offered by the proposed method does not only facilitate the analysis in computational terms, but also allows us to determine the effective input impedance behavior of filters whose input admittance/impedance cannot be derived analytically for the complexity of its structure, e.g. microstrip filters, dielectric filters, etc. In which case, the admittance/impedance can be derived experimentally from S-parameter measurements. Based on that ground, the next conclusions can be drawn:

38

Kind of variable impedance behavior

Depending on the input impedance/admittance response the resonator presents, two kind of variable impedance behavior can be achieved.

A variable impedance whose value varies in direct proportion to the duty cycle of the CB signal.

D.R)D(Reff = (3.25)

This behavior will be presented by filters whose input impedance response offers short impedance in the suppression band of the filter (see Fig. 3.19).

A variable impedance whose value varies in inverse proportion to the duty cycle of the CB signal,

D/R)D(Reff = (3.26)

This behavior will be presented by filters whose input impedance response offers open impedance in the suppression band of the filter (see Fig. 3.20).

0.9 0.95 1 1.05 1.10

10

20

30

40

50

Zin

(S

)

f(GHz)

(a) Magnitude

0.9 0.95 1 1.05 1.1

-90

-45

0

45

90

∠Z

in (

de

gre

e)

f(GHz)

(b) Phase

Fig. 3.19 Ideal impedance frequency response for a filter to vary in direct proportion to the duty cycle

0.9 0.95 1 1.05 1.10

0.005

0.01

0.015

0.02

0.025

Yin

(S

)

f(GHz)

(c) Magnitude

0.9 0.95 1 1.05 1.1

-90

-45

0

45

90

∠Y

in (

de

gre

e)

f(GHz)

(d) Phase

Fig. 3.20 Ideal admittance frequency response for a filter to vary in inverse proportion to the duty cycle

39

Variable impedance behavior in higher order filters

The variable impedance controlled by the duty cycle of a CB signal concept can be also extended to high order filters. However, the effective input impedance exhibit by higher order filters will present some variation during the CB on-state. This is because the different input impedance characteristics higher order filter present at frequencies near the central frequency (See Fig. 3.21). The magnitude of the variation will be influenced by the impedance/admittance response of the filter at the quantization noise frequencies. Therefore, especial attention should be taken in the impedance/admittance response at frequencies when selecting/designing a reconstruction filter.

Effective impedance variation

The magnitude of the variation can be controlled either by selecting a filter whose impedance/admittance response is well behave or by selecting a higher switching frequency (See Fig. 3.22).

0.98 0.99 1 1.01 1.020

0.02

0.04

0.06

Yin

(S

)

f(GHz)

RLC

3rdBut

3rdChb

(a) Magnitude

0.98 0.99 1 1.01 1.02-100

-50

0

50

100∠

Yin

(S

)

f(GHz)

RLC

3rdBut

3rdChb

(b) Phase

Fig. 3.21 Comparison input admittance RLC, 3rd order Butterworth and 3rd order Chebyshev bandpass filter

0T 0.2T 0.4T 0.6T 0.8T T0

50

100

150

Rfilt (

Ω)

t

fs/BW=1

fs/BW=2

fs/BW=4

Fig. 3.22 Effects of the increase of switching frequency , 3rd order Chebyshev filter.

40

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

100

200

300

400

500

D

Reff

( Ω)-

op

en

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

Reff

( Ω)-

sh

ort

Fig. 3.23 Effective resistance vs. duty cycle

An illustration of the ideal effective impedance to be achieved with both of the filters described before is illustrated in Fig. 3.23. It is important to remark that relations in expressions (3.25) and (3.26) are valid for filters that can provide the described impedance/admittance. The relation effective impedance-duty cycle may present different behavior when using filters that do not provide the described impedance/admittance response.

3.5 Reconstruction filter implementation issues

Another factor worthwhile to discuss is the design of a reconstruction filter that it can actually work as variable impedance. According to the thesis proposal, it was desired to embed the filter into the amplifier board. So the reconstruction filter was initially planned to be realized using microstrip technology. For that purpose, different kinds of microstrip filters were analyzed, however the results were not satisfactory.

Fig. 3.24 shows the effective input impedance measured on a 50MHz bandwidth Coupled Line filter using a CB switching frequency of 50MHz and 50% duty cycle. As observed, the effective impedance clearly shows a distorted response during the CB on state. That distorted response is due to the existence of spurious bands close in frequency to the desired band as shown in Fig. 3.25. Further investigation of the coupled line structures revealed that the spurious bands in the admittance response of the filter cannot be eliminated. The spurious bands are inherent to the use of distributed element in the design of the filter and to the interaction of the coupled line structures.

Similar input admittance behavior was also observed in other narrow bandwidth microstrip filter structures, such as Zig-Zag filter (Fig. 3.26), stepped impedance resonator (Fig. 3.27) and Hairpin filter (Fig. 3.28).

Even when those filter structures can fulfill the attenuation characteristics required by the reconstruction filter, lumped element networks have certain properties that cannot be replicated using distributed elements. Microstrip filters do not exhibit suitable admittance/impedance response to be used as variable impedance. In order to successfully use the switched resonator concept in the proposed amplifier design, other filter technologies should be taken into consideration. Possible target technologies are dielectric filters. This subject is still pending and should be object of further investigation.

41

560 570 580 590 6000

40

80

120

160

200

Rfilt(S

)

t (ns)

Fig. 3.24 Coupled Line Filter Effective impedance for 50% duty cycle CB signal

0.7 0.85 1 1.15 1.30

0.05

0.1

0.15

0.2

0.25

Yin

(S

)

f (GHz)

(a) Magnitude

0.7 0.85 1 1.15 1.3-120

-60

0

60

120

∠Y

in (

de

gre

e)

f (GHz)

(b) Phase

Fig. 3.25 Admittance response of a Coupled line filter

0.5 0.75 1 1.25 1.50

0.015

0.03

0.045

0.06

Yin

(S

)

f (GHz)

(a) Magnitude

0.5 0.75 1 1.25 1.5-120

-60

0

60

120

∠Y

in (

de

gre

e)

f (GHz)

(b) Phase

Fig. 3.26 Ad Admittance and impedance response of a Zig-Zag Filter BPF

42

0.5 0.75 1 1.25 1.50

0.015

0.03

0.045

0.06Y

in(

S)

f (GHz)

(a) Magnitude

0.5 0.75 1 1.25 1.5-120

-60

0

60

120

∠Y

in (

de

gre

e)

f (GHz)

(b) Phase

Fig. 3.27 Admittance and impedance response of a Stepped impedance resonator BPF

0.5 0.75 1 1.25 1.50

0.015

0.03

0.045

0.06

Yin

(S

)

f (GHz)

(a) Magnitude

0.5 0.75 1 1.25 1.5-120

-60

0

60

120

∠Y

in (

de

gre

e)

f (GHz)

(b) Phase

Fig. 3.28 Admittance and impedance response of a Hairpin BPF

43

Chapter 4

Integration of the reconstruction filter in a

Class B amplifier mode

In this Chapter, the idea of incorporating the reconstruction filter into the output network of a single-ended Class B amplifier is analyzed. The reasons for the selection of a Class B amplifier mode were its simplicity of design, its capability to not dissipate power when there is no signal presented and its capability to handle the load modulation concept. This chapter is organized as follows. In the first section some guidelines for a proper integration are stated. Thereafter in Section 4.2 the results of the integration of the reconstruction filter into the output network of the amplifier using different filters are presented.

4.1 Integration of a high Q reconstruction filter guidelines

From the analysis in previous chapters a few guidelines for the integration can be made:

In order to allow a proper operation of the amplifier, the output network should provide the proper harmonic terminations at the output of the RF device. For a Class B amplifier that is,

+

=,...f3,f2@0

f@0jRZ

00

0opt

L (4.1)

Assuming that the filter will present the variable impedance behavior described in Chapter 3, the effective impedance at any moment should be larger than the optimal impedance at the maximum drive level of the amplifier. This is because any load impedance smaller than the optimal would not allow a full rail-to-rail drain voltage, which will produce a reduction of the drain efficiency.

In order to counteract the effects of the load modulation, it might be also necessary to vary the amplitude of the input drive signal.

Last and most important, since the effective change in load impedance must be on the intrinsic drain of the transistor, the input impedance of the whole output network should fulfill the required input impedance response described in Section 3.4. This means that one must ensure that the other components of the output network do not degrade the input impedance of the filter at least at frequencies near the fundamental carrier.

44

4.2 Integration of a high Q reconstruction filter-simulation results

This section presents the simulation results of the integration of the filter with a Class B power amplifier. For illustrative purposes of the concept of using the reconstruction filter as variable impedance, filters with open and short impedance in suppression band were considered. The transistor used in the designs was an in house model transistor optimized for switch mode operation [24].

4.2.1 Filter integration- short impedance response in the suppression band of the filter

The integration of the filter was analyzed on an ideal Class B power amplifier operating at 1GHz. The peak efficiency of the amplifier is 68% with and optimal load of 40Ω. The filters used in the analysis of the integration were: a shunt LC resonator tuned at 1GHz and a Chebyshev bandpass filter with 1 GHz central frequency and 6 MHz bandwidth. The attenuation and impedance responses of both filters are shown in Fig. 4.1.

Fig. 4.2 shows the schematic diagram of the amplifier. The gate and drain biasing was realized through quarter wave stubs TL1 and TL2. TL2 also provides short circuit of the second harmonic. Because this kind of filters presents short impedance in the suppression band, the filter was directly integrated in the output network of the amplifier.

Fig. 4.3 shows the effective impedance measured at the reference plane (A) indicated in Fig. 4.2. The figure shows a slight variation in the input impedance compared to the input impedance of the filter by itself. This was due to the interaction of the other components of the output network with the reconstruction filter. Nevertheless, this variation is minimal and does not influence much in the results.

0.982 0.988 0.994 1 1.006 1.012 1.0180

15

30

45

60

Atte

nu

atio

n (

dB

)

f (GHz)

RLC

Cheb

(a) Attenuation

0.982 0.988 0.994 1 1.006 1.012 1.0180

20

40

60

80

Zin

(Ω

)

f (GHz)

RLC

Cheb

(b) Input impedance

Fig. 4.1 Attenuation (a) and input impedance (b) characteristics of the filters considered in the analysis

45

Fig. 4.2 Schematic diagram of integration of a reconstruction filter that present short impedance response in the suppression band

0.982 0.988 0.994 1 1.006 1.012 1.0180

20

40

60

80

Zin

( Ω)

f (GHz)

RLC

Cheb

Fig. 4.3 Input impedance measured at the input of the output network of the amplifier shown in Fig. 4.2

Simulations

The simulations were performed using ADS envelope transient simulator. The simulations were carried using CB signals with 1 GHz carrier frequency, 6 MHz switching frequency and different duty cycles.

Waveforms

Due to the envelope time varying behavior of the CB excitation, the current and voltage waveform results are divided in two parts: results during the CB on state and results during the CB off state. Fig. 4.4 and Fig. 4.5 show the results during CB off state for the LC and Chebyshev filter, respectively. The figures clearly show that during the off state the amplifier does not consume significant power.

Fig. 4.6 and Fig. 4.7 show the results during the CB on state using the LC and Chebyshev filter respectively. From Fig. 4.6(d) and Fig. 4.7(d), the direction of the movement of the load line while decreasing the duty cycle indicates a reduction of the impedance at the output of the transistor. That impedance reduction does not allow the voltage to swing over the full range.

46

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)

(a) 70% duty cycle

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)

(b) 50% duty cycle

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)

(c) 30% duty cycle

0 10 20 30 400

0.25

0.5

0.75

1

1.25

Drain Voltage(V)D

rain

Cu

rre

nt (A

)

D=0.9D=0.7D=0.5D=0.3

(d) Loadline behavior

Fig. 4.4 Results of the integration of a LC series resonator in the output network of a Class B amplifier, voltage and current waveforms in the CB off state

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)

(a) 70% duty cycle

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)

(b) 50% duty cycle

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)

(c) 30% duty cycle

0 10 20 30 400

0.25

0.5

0.75

1

1.25

Drain Voltage(V)

Dra

in C

urr

en

t (A

)

D=0.9D=0.7D=0.5D=0.3

(d) Load line

Fig. 4.5 Results of the integration of a 6MHz BPF in the output network of the Class B power amplifier, voltage and current waveforms in the CB off state

47

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)

(a) 70% duty cycle

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)

(b) 50% duty cycle

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)

(c) 30% duty cycle

0 10 20 30 400

0.25

0.5

0.75

1

1.25

Drain Voltage(V)D

rain

Cu

rre

nt (A

)

D=0.9D=0.7D=0.5D=0.3

(d) Loadline behavior

Fig. 4.6 Results of the integration of a 6MHz RLC in the output network of the Class B power amplifier . Voltage and current waveforms measured in the CB-on state for (a) 70% (b) 90% (c) 30 % duty cycle. (d) Loadline behavior.

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)

(a) 70% duty cycle

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)(b) 50% duty cycle

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)

(c) 30% duty cycle

0 10 20 30 400

0.25

0.5

0.75

1

1.25

Drain Voltage(V)

Dra

in C

urr

en

t (A

)

D=0.9D=0.7D=0.5D=0.3

(d) Load line

Fig. 4.7 Results of the integration of a 6MHz BPF in the output network of the Class B power amplifier. Voltage and current waveforms measured in the CB-on state for (a) 70% (b) 90% (c) 30 % duty cycle. (d) Loadline behavior.

48

Drain efficiency

Fig. 4.8 show the drain efficiency for the LC resonator and Chebyshev filter respectively. The results indicate a reduction of efficiency as the duty cycle of the CB is decreased.

0T 0.2T 0.4T 0.6T 0.8T 1T0

20

40

60

80

100

Eff (

%)

t

D=0.1D=0.3

D=0.5

D=0.7

D=0.9

D=1

(a) RLC

0T 0.2T 0.4T 0.6T 0.8T 1T0

20

40

60

80

100

Eff (

%)

t

D=0.1D=0.3

D=0.5

D=0.7

D=0.9

D=1

(b) Chebyshev

Fig. 4.8 Drain efficiency results (a) LC series resonator (b) 6 MHz Chebyshev bandpass filter.

Effective input impedance

Fig. 4.9 shows the simulated results of the effective impedance measured at the output of the amplifier for both filters. As expected, the effective impedance for this kind of filter varies in direct proportion to the reduction of the duty cycle. These results are in agreement with theory developed in Chapter 3. Unfortunately this kind of effective impedance behavior is not advisable for a Class B power amplifier, since it produces a reduction in the power efficiency of the amplifier. From Fig. 4.9 (a) and Fig. 4.9 (b), it can also be noticed that the effective impedance using the Chebyshev filter presented a large variation compared to the effective impedance of the LC resonator. This was due to the difference on input impedance at frequencies near the fundamental carrier.

0T 0.2T 0.4T 0.6T 0.8T 1T0

10

20

30

40

Rfilt (

Ω)

t

D=0.1

D=0.3

D=0.5

D=0.7

D=0.9

(a) RLC

0T 0.2T 0.4T 0.6T 0.8T 1T0

10

20

30

40

Rfilt (

Ω)

t

D=0.1

D=0.3

D=0.5

D=0.7

D=0.9

(b) Chebyshev

Fig. 4.9 Effective input impedance measured for different duty cycles (a) LC series resonator, (b) 6MHz Chebyshev bandpass filter.

49

4.2.2 Filter with a open impedance response out-of-band

The integration of this kind of filters was analyzed on an ideal Class B power amplifier operating at 1 GHz. The reconstruction filters used in the analysis were: a series LC resonator and a 6 MHz Chebyshev filter. The filters were designed to have a characteristic impedance of 50Ω. The attenuation and impedance responses of both filters are shown in Fig. 4.10. Because of the open impedance that the reconstruction filters exhibits in the suppression band, the integration process was not straightforward. In order to allow a proper operation of the amplifier, an extra interconnection network was necessary. Fig. 4.11 shows the schematic diagram of the amplifier.

0.982 0.988 0.994 1 1.006 1.012 1.0180

15

30

45

60

Atte

nu

atio

n (

dB

)

f (GHz)

RLC

Cheb

(a) Attenuation

0.982 0.988 0.994 1 1.006 1.012 1.0180

0.01

0.02

0.03

0.04

0.05

Yin

(S

)

f (GHz)

RLC

Cheb

(b) Input impedance

Fig. 4.10 Attenuation (a) and input impedance (b) characteristics of the filters considered in the analysis

In Fig. 4.11, the gate and drain biasing are accomplished through quarter wave stubs TL1 and TL2. The quarter wave stubs TL2 also provides a short-circuit termination of the second harmonic at the device output. The optimal resistance for Class B operation is 40Ω.

The fundamental output matching is achieved through a quarter wave transformer TL10. This matching method was selected for its capability to not degrade the input impedance of the reconstruction filter at frequencies near the fundamental.

The open stubs TL9 and TL7 provide short-circuit termination of the third and fifth harmonics, respectively. Short circuited stubs TL6 and TL8 are used to compensate the imaginary admittance that TL9 and TL7 introduce at the fundamental frequency. The electrical length of TL3 is adjusted to maintain the short circuit termination of the fifth harmonic at the reference plane (A), i.e. length of TL3 equals 180° at the fifth harmonic. In the same way, the sum of the electrical lengths of TL3 and TL4 are adjusted to maintain the short circuit termination of the third harmonic at the reference plane (A).

In order to not degrade the input impedance of the filter the sum of electrical length of TL3, TL4, TL5 and TL10 is adjusted to 180° at the fundamental. The input admittance of the output network seen at the reference plane (A) is as shown in Fig. 4.12.

The amplifier presented a drain efficiency of 62.78% using a continuous wave with an input voltage level of 2V. Fig. 4.13 shows the voltage and current waveforms at the maximum drive level.

50

Fig. 4.11 Schematic diagram of a Class-B power amplifier with a narrow bandwidth filter with open

impedance in the suppression band

0.96 0.98 1 1.02 1.040

0.01

0.02

0.03

0.04

0.05

Yin

(S

)

f (GHz)

RLC

Cheb

Fig. 4.12 Input admittance simulated at the input of the output network of the amplifier shown in Fig. 4.11

0 0.5 1 1.5 20

20

40

60

t (ns)

Dra

in V

olta

ge

(V

)

0 0.5 1 1.5 20

0.25

0.5

0.75

1

1.25

Dra

in C

urr

en

t (A

)

Fig. 4.13 Voltage and current waveforms using a continuous wave

Simulations-Series LC resonator

The simulations for the series LC resonator were carried using CB signals with 1 GHz carrier frequency, 6 MHz switching frequency and different duty cycles. The results were not satisfactory.

The amplifier presented a random response for duty cycles lower than 85%. The effective impedance at those duty cycle levels increased substantially reaching very high values. For example, Fig. 4.14 shows the results using a CB signal with 50% duty cycle. The input

51

voltage level of the CB excitation was reduced to 0.5 V. This reduction was necessary in order to allow the simulator to work. The results clearly show a poor performance of the amplifier. The effective impedance reached very high values and presented a large variation during the CB on state. The drain efficiency was reduced to values lower than 10% during the CB on state.

The results for duty cycles higher than 85% presented a more comprehensive behavior, however the performance of the amplifier was still degraded compared to the efficiency obtained using a continuous wave.

Fig. 4.15, Fig. 4.16 and Fig. 4.17 show the results using CB signals with 85%, 90% and 95%, respectively. The CB input voltage level for each duty cycle was chosen to maximize the efficiency performance. The selected values were 1.3 V, 1.6 V and 1.8 V, for 85%, 90% and 95% duty cycle respectively. The maximum drain efficiency achieved for each duty cycle during the CB on state was lower than the efficiency using a continuous wave. The efficiency response during the CB off state indicates that the amplifier draws power even when a zero level signal is applied to the amplifier.

0 1 2 30

2000

4000

6000

Rfilt (

Ω)

t (µs)

(a) Effective impedance as a function of time

0T 0.2T 0.4T 0.6T 0.8T 1T0

2000

4000

6000

Rfilt (

Ω)

t

(b) Effective impedance during one CB period

0 1 2 30

25

50

75

100

Eff (

%)

t (µs)

(c) Drain efficiency as a function of time

0T 0.2T 0.4T 0.6T 0.8T 1T0

25

50

75

100

Eff (

%)

t

(d) Drain efficiency during one CB period Fig. 4.14 Simulation results using a series LC resonator as reconstruction filter and a CB signal with

50% duty cycle.

52

0 1 2 30

50

100

150

200R

filt (

Ω)

t (µs)

(a) Effective impedance as a function of time

0T 0.2T 0.4T 0.6T 0.8T 1T0

50

100

150

200

Rfilt (

Ω)

t

(b) Effective impedance during one CB period

0 1 2 30

25

50

75

100

Eff (

%)

t (µs)

(c) Drain efficiency as a function of time

0T 0.2T 0.4T 0.6T 0.8T 1T0

25

50

75

100

Eff (

%)

t

(d) Drain efficiency during one CB period

Fig. 4.15 Simulation results using a series LC resonator as reconstruction filter and a CB signal with 85% duty cycle.

0 1 2 30

50

100

150

200

Rfilt (

Ω)

t (µs)

(a) Effective impedance as a function of time

0T 0.2T 0.4T 0.6T 0.8T 1T0

25

50

75

100

Rfilt (

Ω)

t

(b) Effective impedance during one CB period

0 1 2 30

25

50

75

100

Eff (

%)

t (µs)

(c) Drain efficiency as a function of time

0T 0.2T 0.4T 0.6T 0.8T 1T0

25

50

75

100

Eff (

%)

t

(d) Drain efficiency during one CB period Fig. 4.16 Simulation results using a series LC resonator as reconstruction filter and a CB signal with 90% duty cycle.

53

0 1 2 30

50

100

150

200R

filt (

Ω)

t (µs)

(a) Effective impedance as a function of time

0T 0.2T 0.4T 0.6T 0.8T 1T0

25

50

75

100

Rfilt (

Ω)

t

(b) Effective impedance during one CB period

0 1 2 30

25

50

75

100

Eff (

%)

t (µs)

(c) Drain efficiency as a function of time

0T 0.2T 0.4T 0.6T 0.8T 1T0

25

50

75

100

Eff (

%)

t

(d) Drain efficiency during one CB period

Fig. 4.17 Simulation results using a series LC resonator as reconstruction filter and a CB signal with 95% duty cycle.

Simulations-6MHz bandpass Chebyshev filter

The simulations carried with the 6MHz Bandpass Chebyshev filter were also not satisfactory. The effective impedance measured at the output of the transistor varied in a random way. It was not possible to obtain acceptable results for switching frequencies lower than 15 MHz. The simulation presented here were performed using CB signal with a switching frequency of 18 MHz.

For duty cycles lower than 80% the effective impedance increased substantially which lead to poor efficiency performance. Fig. 4.18 show the results obtained using a CB with 50% duty cycle and voltage level of 0.5 V. The efficiency performance fluctuates in a unpredictable way during various CB periods. The efficiency results also indicate the amplifier draws power even during the CB off state.

0T 1T 2T 3T 4T 5T0

2000

4000

Rfilt (

Ω)

t

(a) Effective impedance

0T 1T 2T 3T 4T 5T0

25

50

75

100

Eff (

%)

t

(b) Drain efficiency Fig. 4.18 Simulation results using a 6MHz Chebyshev filter as reconstruction filter and a

CB signal with 50% duty cycle.

54

Fig. 4.19, Fig. 4.20, Fig. 4.21 show the effective impedance and drain efficiency simulated results using CB signals with 85%, 90% and 95%, respectively. The CB voltages used in the simulations were 1.7 V, 1.8 V and 1.9 V for duty cycles of 85%, 90% and 95%, respectively. The results show the effective impedance increased as the duty cycle was reduced, however the relation duty cycle effective impedance increased faster than expected. For this reason, the amplifier presents poor efficiency performance for duty cycle lower than 90%.

It is also important to highlight that the simulations carried with this amplifier were unpredictable and very sensitive to the voltage level of the CB signal and the switching frequency. The wrong selection of the voltage level at certain duty cycle caused malfunctioning of the simulator. For the aforementioned reasons, the idea of integrating this kind of filter with a Class B power amplifier could not be demonstrated.

0T 1T 2T 3T 4T 5T0

50

100

150

200

Rfilt (

Ω)

t

(a) Effective impedance

0T 1T 2T 3T 4T 5T0

25

50

75

100

Eff (

%)

t

(b) Effective impedance Fig. 4.19 Simulation results using a 6MHz Chebyshev filter as reconstruction filter and a

CB signal with 80% duty cycle.

0T 1T 2T 3T 4T 5T0

25

50

75

100

Rfilt (

Ω)

t

(a) Effective impedance

0T 1T 2T 3T 4T 5T0

25

50

75

100

Eff (

%)

t

(b) Effective impedance Fig. 4.20 Simulation results using a 6MHz Chebyshev filter as reconstruction filter and a

CB signal with 90% duty cycle.

0T 1T 2T 3T 4T 5T0

25

50

75

100

Rfilt (

Ω)

t

(a) Effective impedance

0T 1T 2T 3T 4T 5T0

25

50

75

100

Eff (

%)

t

(b) Effective impedance Fig. 4.21 Simulation results using a 6MHz Chebyshev filter as reconstruction filter and a

CB signal with 95% duty cycle.

55

Chapter 5

Discussion and future work

This work has presented the study of the feasibility of implementing a new type of envelope pulse modulated power amplifier that incorporates the narrow bandwidth reconstruction filter into the output network of a single ended Class B power amplifier.

In order to understand the challenges such integration may involve, a detailed analysis of the behavior the filter exhibits when it is driven with a CB excitation as a separate stage was performed. The results indicated the possibility to use the effects of the CB signal-filter interaction in a controlled way.

It was found that if the reconstruction filter is designed to have determined input impedance response over certain bandwidth (more specifically at frequencies were quantization noise occurs), the filter will present a variable impedance behavior whose value will be controlled by the duty cycle of the CB signal used to drive the filter. However, it was also discovered that the applicability of this concept will be limited by the implementation of practical filter designs that can meet the input impedance requirements.

Because the attempts to design a reconstruction filter that satisfied the desired requirements failed, the integration of the narrow bandwidth filter concept was only analyzed using different lumped filters. Filters with two kind of input impedance response were used in the analysis: filter that offer short circuit termination in the suppression band and filters with open impedance termination in the suppression band.

The results for the first kind of filters were in agreement with the theory develop in Chapter 3. The effective impedance measured at the output device was reduced from the optimal resistance as the duty cycle was reduced. Although this kind of impedance behavior is not advisable for a Class B power amplifier because it causes efficiency reduction, the results demonstrate the possibility to control the effects of the amplifier-reconstruction filter interaction.

The results obtained with the filter with open impedance termination were not satisfactory. The effective impedance measured at the output of the device increased with a ratio larger than expected. This may be attributed to incompatibility of this kind of filter to the harmonic requirements of a Class B amplifier, which led to the need of extra components in the output network which in turn distorted the input impedance of the filter at frequencies

56

near the fundamental carrier. Consequently, the power amplifier showed acceptable results only for duty cycles larger than 80%.

Finally, for the aforementioned reasons until the end of this work it was not possible to demonstrate the proper operation of the proposed amplifier topology. Therefore, no power amplifier hardware was implemented. However, the results have helped us to identify some very serious practical problems relating the hardware implementation of carrier bursting, which indicates that the potential of carrier bursting for practical high efficiency transmitter may be limited.

5.1 Future work

Although the concept of integrating the reconstruction filter was not successful for a Class B power amplifier, it does not discard the possibility to work in other amplifier modes. It is still believed that if the physical challenge of finding/designing a reconstruction filter that can provide the desired input impedance is met, the integration will be feasible in other amplifier modes.

The limiting factor to the operation of the power amplifier topology presented in this work was that the efficiency performance in a Class B amplifier depends very much on the fundamental impedance measured at the device output. Nevertheless, this concept may present better performance when it is applied to an amplifier mode where the figure of efficiency depends on other parameters.

57

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