Chapter 1 Introduction
1.1 Motivation
For portable wireless communication devices has given great push to the development of a next generation of low power radio frequency integrated circuits (RFIC) product. Such as wireless phones, cordless and cellular, global positioning satellite (GPS), pagers, wireless modems, wireless local area network (LAN), and RF ID tags, etc., require more low cost; low noise and high power efficiency solutions to supply the demand for low-price product [1].
In UWB systems, the power level from the UWB transmitter should be low enough not to interfere with the already existing communication systems, for example 802.11a. The low output levels that specified by the Federal Communications Commission (FCC) is less than -41.3 dBm/MHz. Therefore, for a 7 GHz bandwidth, the peak output power is approximately-3 dBm or 500μW. UWB systems need not require large transistors, and greatly lighten the difficult of CMOS technology. The main challenging task becomes to achieve a high gain and good impedance match over the entire frequency band.
The RF integrated circuit used for UWB devices are encounter with various possibilities: CMOS, Bi CMOS, and GaAs MESFET, bipolar (BJT), hetero-junction
bipolar transistor (HBT), and PHEMT, etc,. We just study and discuss on the CMOS technology.
Chapter 2 discusses the basic concepts of power amplifier. Chapter 3 presents the basic power amplifiers design for UWB. Chapter 4 deals with wideband matching network, gain flatness and load-line analysis by using inductor-resistor feedback, presents the UWB proposals, design, implementation of our power amplifiers.
Chapter 5 concludes this research effort with some future directions.
Chapter2
Basic concepts of Power Amplifier
2.0 Introduction
A reasonable start of power amplifier, which is abbreviated as PA, would be to recall some classical results of linear RF amplifier theory because many PA designs are simple extensions or modifications of linear design. We can read the detail results of RF linear amplifier in many books, so we skip those and assume some concepts of RF linear amplifier is well known.
As we discuss about power amplifier, some basic concepts should be motioned.
First, the PA operates at a high out power state; for example, CMOS devices could be saturated, and therefore nonlinear effect become significant. If the output power is 1Watt, and how much power the PA should be dissipated? Ideally, we want all the DC supply power be converted to signal power, but it is impossible in practice. Therefore the efficiency is the important performance of PA. And some issues about optimum output power should be studied including load line match and load-pull technology.
So, this chapter presents the main concepts and challenges of RF power amplifiers.
2.1 Amplifier Parameter Definitions
2.1.1 Weakly Nonlinear Effects: Power Series Analysis
Power series is a generalized formula expressing nonlinear behaviors in many
aspects, but it has some limitations: there is no phase component in the linear output term, letting alone the nonlinear terms. A much stronger formula of the power series, called the Volterra series, would be used including phase effects. Weak nonlinearities may be, for instance, inter-modulation distortion at levels lower than, say, -30dBc.
Unfortunately, the PA operating at or beyond the compression point requires different treatment because the nonlinearities become “strong” and arise through the cutoff and clipping behavior of the transistor; besides, the Power and Volterra series is not sufficiently accurate. The fifth and seventh order terms of Power series usually become significant as the 1dB compression point is approached and can dominate at still higher drive levels.
While plenty of RF amplifiers can be described as a linear model to obtain their response of small signals, nonlinearities often lead to interesting and important phenomena. Generally, the “Power Series” is applied to further analysis. For simplicity, we ignore the higher order terms of the series and assume that
y ( t ) ≈ α
1x ( t ) + α
2x
2( t ) + α
3x
3( t )
(2.1) If a sinusoid is applied to a nonlinear system, the output generally exhibitsfrequency components that are integer powers of the input frequency.
Ifx
(
t) =
Acos
ωt, thenA t
In Eq. (2.3), the term cos tω is called the “fundamental” and the higher-order terms the “harmonics.” The amplitude of the nth harmonic, cosnωt, consists of a term proportional to An.
In (2.3), the gain written as
4 3 3 2
1
α
Aα
+ is therefore a decreasing function of Aifα3<0. In most circuits, the output is a “compressive” or “saturating” function of the input; that is, the gain approached zero for sufficiently high input levels. This effect is quantified by the “1-dB compression point,” defined as the input signal level that causes the small-signal gain to drop by 1 dB. If it’s plotted on a log-log scale as a function of the input level, the output level falls below its ideal value by 1 dB at the 1-dB compression point.
When two signals with different frequencies are applied to a nonlinear system, the output in general exhibits some components that are not harmonics of the input frequencies. Called inter-modulation (IM), this phenomenon arises from
multiplication of the two signals when their sum is raised to a power greater than unity. We assume that
x ( t ) = A
1cos ω
1t + A
2cos ω
2t
(2.4)Expanding the left side and discarding DC terms and harmonics, we obtain the A1=A2=A, and the ratio of the amplitude of the output third-order products to α1A defines the IM distortion. If a weak signal accompanied by two strong interferers experiences third-order nonlinearity, then one of the IM products falls in the band of interest, corrupting the desired component.
Use IP3 to characterize this behavior. Called the “third intercept point” (IP3), this parameter is measured by a two-tone test in which A is chosen to be sufficiently small so that higher-order nonlinear terms are negligible and the gain is relatively constant and equal toα1. The third-order intercept point is defined to be at the intersection of the two lines [2].
2.1.2 Strongly Nonlinear Effects
Strongly nonlinear effects refer to the distortion of the signal waveform that is caused by the limiting behavior of the transistor. The drain current exhibits cutoff, or
pinch-off, when the channel is completely closed by the gate-source voltage and reaches a maximum, or open-channel condition, in which further increase of gate-source voltage results in little or no further increase in drain current.
2.1.3 Nonlinear Device Models for CAD
To devise a comprehensive model for a device, it is necessary to characterize both the weak and the strong nonlinear behavior. Unfortunately, each of the nonlinearity traits in a particular device arises from quite different aspects of the device physics.
The PA designer is much more sensitive to some of the shortcomings of widely used computer-aided design (CAD) models than designers of many other kinds of RF devices. The central issue in modeling RF power transistors is scaling. The detailed modeling and curve fitting are done on a small periphery sample device and may be quite accurate. The PA designer has to take that small cell and scale up it, even hundreds, to “build” a power transistor. Unfortunately, such scaling is not a simple set of electrical nodal connections, and can not be handled easily enough on a modern circuit simulator. The large periphery device will display a range of secondary phenomena that may have been quite negligible in the small periphery device model cell. The low impedance by multiple parallel connections evokes other-effects to come, that would be neglected in normally, including current spreading at bond-wire contacts, electro-acoustic coupling in the semiconductor crystal, and mutual coupling
between bond-wire.
Even a basic I-V measurement can pose serious difficulties for an RF power transistor. Mary I-V curve tracers work at speeds several slower than the RF signal for which the model is require and can be slow enough that transient junction heating effects, which will not occur to any significant extent during an RF cycle, intrude into the measurement. Accurate I-V curve are difficult to obtain for RF power transistors;
that has led many to develop custom-built teat rigs, usually incorporating a pulsed measurement scheme [10]. An alternative approach is to build a curve tracer that sweeps through the I-V characteristics at rates in RF range [9].
Reference [11], [12], [15-17] provides starter bibliography, but the research continues.
2.1.4 Gain Match and Power Match
We can get the maximum gain when input and output of circuits was conjugate match. It is well known by circuit theorem that we can deliver maximum power into load component when load impedance is equal to real part of the generator impedance, and the reactive part should be resonated out. This is the concept of conjugate match or gain match. However, the practical devices have physical limited such as Vmax and Imax, the maximum supply voltage and the maximum generated current. Vmax could be maximum DC supply voltage or breakdown voltage of devices; and Imax could be
saturation current of devices. By referring Figure 2-1, this seen the gain match cannot used the full capacity of transistor. If we want to utilize the maximum current and voltage swing of the transistor, a lower value of load resistance would need to be selected; the value is commonly referred to as the load-line match, Ropt, and in its simplest form simply would be the ratio:
max max
/ I V
R
opt=
(2.8)Where we assume the generator’s resistance is high and is not taken into account. This Ropt is so called the load-line match or power match. The power match represents a real compromise that is necessary to extract the maximum power from RF transistors and at the same time keep the RF voltage swing within specified limits and the available dc supply.
Figure2-1: Conjugate match and load-line match.
2.1.5 Knee voltage effect
The knee voltage (pinch-off voltage) divides the saturation and the linear region of the transistor and can be defined as, for example, Vds at the 95% of Imax point. As shown in Figure 2-2[18]. And the optimum load resistance become
max
max
) /
( V V I
R
opt= −
knee (2.9)For sub-micron CMOS transistors, Vknee is only about 10% to 15% of the supply voltage for typical power transistors, while it can be as high as 50% of the supply for deep sub-micron technologies as shown in Figure 2-2. A large portion of the RF cycle could be in linear region. Accordingly, both saturation and linear region must be considered when determining the optimum of operation [18] or relying on balance simulations of circuits.
Figure2-2: The knee voltage of deep sub-micron CMOS transistor.
2.1.6 Load-Pull Measurement
A load-pull test setup consists of the device under test with some form of calibrated tuning device on its output. A typical block diagram is shown in Figure 2-3.
Figure 2-3: Typical configuration of load-pull.
The input probably also will be tunable, but this is mainly to boots the power gain of the device, and the input match typically be fixed close to a good match at each frequency.
Load-pull measurement can find the practical Ropt of PA, and also the maximum output power.
2.1.7 Input and Output VSWR
VSWR are measured at small-signal conditions as well as at large-signal conditions.
There come some problems with power match, It will cause reflections and VSWR at output, the reflected power is entirely a function of the degree of match between the antenna and the 50-Ohm system. The PA does not present a mismatched reverse
large signal impedance, once a device starts to operate in a significantly nonlinear fashion, the apparent value of the impedance will change, but the whole concept of impedance starts to break down as well, because the waveforms no longer are sinusoidal.
2.1.8 Power gain
The power amplifiers are characterized by transducer power gain defined as the ratio of the power delivered to the load (Po) to the power available from the source (Pin) to the amplifier, i.e.,
Power delivered to the load (Po) is known as the output power, which is a strong function of the input power. The output power when the gain is compressed by 1 dB is defined as P1dB, which is normally used as a figure of merit to characterize nonlinearity in amplifiers.
2.1.10 Power Added Efficiency (PAE), Drain Efficiency (ηd),and Power Utilization Factor
output signal power input signal power Po Pin
PAE dc power Pdc
where ηd is known as the drain efficiency. For high-efficiency amplifiers, single-stage gain is required to be on the order of 10 dB or higher. If the RF power gain is less than 10 dB, the drive power requirement will start to take a serious bite out of output efficiency of a PA stage, and the higher the efficiency, the more serious the effect.
Sometimes, it is just as well to keep gain and output efficiency as separate stage, it is noted that at system level or even multistage PA level they will behave interactively on the overall efficiency.
One of the most importance concepts in comparing different PA configurations is the power utilization factor (PUF). PUF is the ratio of the power it would deliver as a simple class A amplifier.
_ where Plin is known as the output power of class A having the same dc supply voltage and peak RF current.
2.1.11 Spectral Regrowth
In a digitally modulated waveform, for example, QPSK, need a low-pass filter precede the modulator to limit the bandwidth of the signal, there by suppressing spectral leakage into adjacency channels. We expect limiting the bandwidth tends to smooth out the abrupt transitions in the time domain. And after filtering, exhibiting
variation in its envelope as the filter bandwidth decreases. If the power amplifier is to maintain the spectrum to the limited bandwidth, then it must also amplify the envelope variations linearly. However, if the PA exhibits significant nonlinearity, then shape signals, it is not preserved and the spectrum is not limited to the desired bandwidth. This effect is called “spectral regrowth” [19], [20] and can be quantified by the relative adjacent channel power [20]. Generally, nonlinear PA has better efficiency than linear PA. Therefore, digital modulation schemes exhibit a trade-off between spectral efficiency and power efficiency.
Figure2-4: The spectral regrowth due to amplifier nonlinearity.
2.1.12 Adjacent Channel Power Ratio (ACPR) [21]
ACPR is a commonly used figure of merit to evaluate the inter-modulation performance of RF power amplifiers designed for CDMA wireless communication systems, ACPR is a measure of spectral regrowth, appears in the signal sidebands, and
is analogous to IM3/IM5 for an analog RF amplifier.
_ _ _ _ _ _ _1
_ _ _ _ _ _ _ 2 3
power spectral density in the main channel ACPR= power spectral density in the offset channel or
, (2.14) There offset frequencies and measurement bandwidths vary with system application.
2.1.13 Peak-to-Average Ratio (PAR) [22]
All single or multi-carrier (modulated or un-modulated) have a peak-to-average ratio. The ratio between the peak power (Pp) and the average power (Pa) of a signal is called the peak-to-average ratio, i.e.,
,10log ( )
Pp Pp
Pa Pa dB χ =
. (2.15) The peak-to-average ratio ΔPs of an input signal consisting of N carriers, each having a average power Pί is defined as
Here χi is the peak-to-average ratio of the ith carrier. If there are n carriers in a given operating bandwidth, it is easy to see that the theoretical maximum peak-to-average power ratio will be n . Gaussian noise has a peak-to-power ratio of about 9 dB, so very dense multi-carrier systems might require about 6 dB more power back-off to achieve a similar level of IM distortion compared to a two-carrier signal having the same power.
2.1.14 Nonlinearity Effect in Power Amplifier Use Two-tone Analysis There many different ways to measure the nonlinearity behavior of an amplifier.
The simplest method is the measurement of the 1dB compression power level P1dB.
Another method that uses two closely spaced frequencies:
1 2
( ) cos( ) cos( ) Vi t = v ω t + v ω t
(2.17) Vi input to amplifier and measure the output frequencies component, this is so-call the inter-modulation (IM) products. The third-order products are at frequencies 2ω2-ω1 and 2ω1-ω2, and the fifth-order IM products are at frequencies 3ω2-2ω1 and
3ω1-2ω2. The third-order Intercept point (IP3) is a concept that represents the intersection between the extrapolated 1:1 slope of fundamental gain, and the 3:1 slope of the third-order IM (IM3) products. IM3 is given by [23]:
1 2 2 1
Another “softness” of the compression characteristic can be varied by choosing two tangible parameters, PCOMP and PSAT. PCOMP represent, in decibels, the different between the P1dB compression point and the maximum linear power point; PSAT
represent, in decibels, the different between the saturated power point and the maximum linear power point, about this value, the characteristic is defined to be ideally flat, or saturated. The detail discuss of nonlinear effect can be studied at [24].
2.1.15 AM-to-PM Effect
Any amplifier, when driven into a strongly nonlinear condition, will exhibit phase as well as amplitude distortion.
Figure 2-5: The phase-shift distortion with input power increases.
This usually is characterize in terms of AM-to-PM conversion and represents a change in the phase of the transfer characteristic as the drive level is increased toward and beyond the compression. The most common manifestation of AM-to-PM effects is an irritating asymmetrical slewing of the inter-modulation (IM) or spectral regrowth display. The detail discuss of AM-to-PM effect can be studied at [24].
2.2 Class of Power Amplifiers
What determine the class of operation of power amplifier is conduction angle of amplifier, input signal overdrive, and the output load network. Figure 2-6 shows how the PA relates to conduction angle and the input signal over-drive. For a small RF input signal Vin, the amplifier can operate in class A, AB, B, or C depending on the conduction angle (bias voltage relative to the transistor’s threshold voltage).
Figure 2-6: The classification of Power amplifier.
The PA efficiency can be improved by reducing its conduction angle by moving the design into class C operation, but at the expense of lower output power. An alternative approach to increasing efficiency without sacrificing output power is to increase the input over-drive such that the transistor acts as a switch.
2.2.1 Class A, AB, B, and C Power Amplifiers
VO
Iq IMAX
Vt Vq
π 2π 3π
α/2 ωt
id
Vg VO
Iq IMAX
Vt Vq
π 2π 3π
α/2 ωt
id Vg
Figure 2-7: Reduced conduction angle current waveform.
The simple process of reducing the conduction angle is illustrated in Figure 2-7, where Vt is the threshold voltage of Vgs for transistors. The required signal voltage amplitude will be
s
1
qV = − V
(2.19)Where Vq is the normalized quiescent bias point, defined according to Vt=0, Vo=1.
The current in the device has the familiar looking, truncated sine-wave appearance.
The conduction angle, α, indicates the proportion of the RF cycle for which conduction occurs, the current cutoff points point are at ±α/2. So the drain current
waveform can be written as
By Fourier analysis of the waveforms, the results can be written:
/ 2 max
We use the conduction angle to define the class of power amplifier, for class A condition, α=0; for class B condition, α=π; for class AB condition, 0<α<π; and for the condition of class C, α>π. The harmonics amplitude is plotted in Figure 2-8.
Figure 2-8: Fourier component of power amplifier relate to conduction angle.
We can see the odd harmonics be seen to pass through zero at the class B point, but in AB mode, the third harmonic is not negligible.
Then, the RF fundamental output power is given by
Then, the RF fundamental output power is given by