Circuit design for linearizing transmitter

List of Figures 2.1 Basic Circuit Diagram for Power Amplifier 8 2.3 Intermodulation Distortion of Power Amplifier 11 3.1 Implementation of Predistorter at different stage of the Transmit

Circuit Design for Linearizing

Transmitter

Sim Chan Kuen

NATIONAL UNIVERSITY OF SINGAPORE

2003

Circuit Design for Linearizing

Transmitter

Sim Chan Kuen, (B Eng., Nanyang Technological University)

DEPARTMENT OF ELECTRICAL ENGINEERING

A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE

2003

Acknowledgement

I would like to take this opportunity to express my warmest thanks to many people who have contributed towards the production of this thesis

In particular, I thank my supervisors, Dr Michael Chia Y W and Prof Lye Kin Mun

I thank Dr Michael Chia for his guidance and support He spent a tremendous amount

of time teaching me discussing the research problem and checking this thesis

I thank my friends and colleagues in the Transceiver System group of Institute of Infocomm Research (I2R) They advised me throughout the course of work and in completion of this thesis

Lastly, I thank my family for their constant support and care

Chapter 2 Power Amplifier Characteristics and Linearization 7

2.1 Classification of Power amplifier 7

2.5.3 Envelope Elimination and Restoration 21 2.5.4 Linear Amplification with Non-Linear Components 22

4.4 Analog predistortion for Radio Over Fiber System (ROF) 80

List of Figures

2.1 Basic Circuit Diagram for Power Amplifier 8

2.3 Intermodulation Distortion of Power Amplifier 11

3.1 Implementation of Predistorter at different stage of the Transmitter 31 3.2 Block of the 3rd Order Analog Predistorter 35 3.3 A Basic Bipolar implementation of Analog Mulitplier 40 3.4 Two general method of implementing analog multiplier in CMOS 41

3.7 Simulated Result of the multiplier 48 3.8 Simulated distortions in multiplier 49

3.10 Simulated results of the transconductance cell 52

3.12 Output Buffer 54

4.2 A Two Tone Test performed on the power amplifier 63 4.3 Test setup for low-IF predistorter 64 4.4 Before Linearization (Two-tones test at low-IF) 65 4.5 After Linearization (Two-tones test at low-IF) 65 4.6 A two-tones test with varying input power 66 4.7 Multi-Carrier Test(Before Linearization) 68 4.8 Multi-Carrier Test(After Linearization) 69 4.9 Frequency spectrum at the input of the power amplifier

two-tones test (before linearization) 77 4.17 Zooming on the frequency spectrum around the two tones

for baseband predistortion two-tones test (before linearization) 77

4.18 Overall output spectrum for baseband predistortion two-tones

4.19 Zooming on the frequency spectrum around the two tones

for baseband predistortion two-tones test (after linearization) 78 4.20 Test Setup using predistorter in Radio Over Fiber system 80 4.21 Overall output spectrum for ROF predistortion two-tones

4.22 Zooming on the frequency spectrum around the two tones

for ROF predistortion two-tones test (before linearization) 81 4.23 Overall output spectrum for ROF predistortion two-tones

4.24 Zooming on the frequency spectrum around the two tones

for ROF predistortion two-tones test (after linearization) 82

4.26 Multi-Carrier Test for ROF system(Before Linearization) 85 4.27 Multi-Carrier Test for ROF system(After Linearization) 85

List of Tables

4.1 Comparison of two-tone test results performed by different design 67

One of the major enabling device for 3G or future cellular systems is the transceiver

It consists of the two major blocks, the receiver and transmitter The receiver receives information from air Whereas the transmitter transmits information generated by the cellular terminals to the air It is thus front end of cellular communication systems

I

Q

RF Power Amplifier

Antenna

Local Oscillator

90 0 Phase Shifter

DAC

DAC

VGA

The block diagram of the modern transmitter is shown in Fig 1.1 [1] The I and Q channels generated by the baseband is converted into analog signals by the Digital-to-Analog converters (DAC) It will then be low pass filtered and upconverted by the mixers

to radio frequencies The signals are amplified by the variable gain amplifiers (VGA) The final amplification of the signals is by the power amplifier It will drive the antenna and transmitted to the air

1.2 Power Amplifier

One of the major blocks of the transmitter is the power amplifier [2] This component consumes the most power of the transceiver [3] For example, RF MicroDevices’s RF2161 [4] or Raytheon’s RTPA5250-130 [5] consume 0.4W and 0.66W respectively

To achieve higher data rate and be spectrally efficient, communication systems use linear modulation for example QAM (Quadrature Amplitude Modulation) Linear modulation allows more data to be send within a given bandwidth However, linear modulation will have varying envelope at the output of the power amplifier To properly amplify the signal, the power amplifier must be linear But linear power amplifier consumes a lot of power compared to non-linear power amplifier

A non-linear power amplifier will cause undesirable distortions to the transmitted signal This will lead to an increase in the overall error rate of the communications system Not only that, a non-linear power amplifier will exhibit spectral regrowth [1] This will cause distortions to adjacent channels

It is possible to design a class A power amplifier to meet the linearity requirements for modern communication systems But class A power amplifier is highly inefficient in power Theoretically the efficiency of the class A amplifier is 50% [1] But in actual implementation, the efficiency of the power amplifier is much lower than 50%

Power efficiency of the power amplifier will affect the power consumption of the transmitter Being the most power consuming block of the transceiver, any reduction in power consumption will reduce the power consumption of the whole transceiver system

A reduction of power consumption will increase the talk time of the communication equipment This is especially important for cellular mobile phones

Therefore there is a compromise between the efficiency and linearity of the power amplifier Generally, class AB power amplifier is good compromise between linearity and efficiency

1.3 Objective

The objective of this research is to improve the linearity of the Radio Frequency (RF) power amplifier so as to operate the power amplifier near the peak efficiency so as to increase the talk time of the mobile handsets

The thesis is organized as follows:

In chapter 2, the general characteristic of the power amplifier is explained It shows how the power amplifier could be modeled, the distortions it creates and the different metrices

to measure the linearity of the power amplifier In this chapter, the reader will also acquaints himself the general techniques that are used to improve the linearity of the power amplifier namely feedback, feedforward and predistortion

The next chapter, chapter 3, the design of the new analog predistorter is described This shall include the architecture and circuit

In chapter 4, the chip was used to linearise an actual RF power amplifier The chip was tested at IF and baseband Two-tone test was used to test the improvement in the linearity

of the power amplifier Then different linear modulations were injected into predistorter

The use of the predistorter was then extended to a Radio Over Fiber (ROF) system The result for the new usage of the predistorter was also illustrated

Finally, chapter 5 presents a summary of the work done in linearization of the power amplifier

2.1 Classification of Power amplifier

There are different classes or types of power amplifiers namely Class A, B, C, E and F The above different classes could be grouped into two [3] The first group, class A, B and

C, are power amplifiers that use the transistors as current sources The second group, class E and F, use transistors as switches

RFC DC

Vin

Filtering/

MatchingNetwork

RL

Figure 2.1 Basic Circuit Diagram for Power Amplifier

Figure 2.1 shows the basic circuit diagram for all the power amplifiers [1] The radio frequency choke (RFC) feeds the DC power to the drain of the BJT It is to provide low impedance for the bias but high impedance for a.c signals The BJT could also be replaced by other types of transistor e.g NMOS Filters and matching network are connected at the output of the power amplifier The filtering network is to reject all undesired out of band signals The matching network is required to deliver sufficient power to the load, RL

In the first group, class A, B and C, the transistors act as current sources The transistor will either sink or source current to the load The differences between class A, B and C is

in their conduction angles In class A, the power amplifier is biased such that the current will conduct at all times But the conduction angle is 180 degrees and below 180 degrees

for class B and C power amplifiers respectively The linearity for class A power amplifiers is the best followed by B and C But the power efficiency is the lowest for class A and highest for class C A compromise between linearity and power efficiency is met by class AB power amplifiers

Class E [6] and F power amplifiers are non-linear power amplifiers The transistors in Class E power amplifiers act as a switch rather than a current source In an ideal switch, when it is ON, the voltage across the switch is zero and the current will be the maximum When the switch is OFF, the voltage should rise to the maximum while the current is zero Therefore the ideal switching power amplifier has 100% efficiency In Class F amplifier, the filtering/matching network has resonances at one or more harmonic frequencies including the fundamental carrier frequency The filtering/matching network will shape the output collector voltage of the power amplifier to a square wave like waveform [7] Generally, Class E and F power amplifiers are more efficient compared to Class A to C power amplifiers However, they generate more distortions than Class A to

Figure 2.2 compares the ideal response at the output of the power amplifier and the practical amplifier In pratice, there is a limited range where the power amplifier is able

to amplify the signal presented in the input The value of the K, as in (2.1), changes as the input of the power amplifier increases When input power exceeds a certain level, the power amplifier will be saturated The non-linearity of the input and output of the power amplifier is also termed as AM-AM conversion However, the efficiency near the saturation point is the highest

One of the ways to compare the linearity of different amplifiers is find the P1dB point This is the point where the output power of the actual power amplifier is 1dB below the ideal response of a power amplifier

The most serious consequence of the amplitude non-linearity is intermodulation distortion Figure 2.3 illustrates this distortion

Power Amplifier

Frequency

Amplitude

Frequency Amplitude

Figure 2.3 Intermodulation Distortion of Power Amplifier

Ideally when two frequency tones are injected into the power amplifier, the output of the power amplifier will have exactly the same two frequency tones but with amplified amplitude Intermodulation distortion causes the power amplifier to produce extra frequency components other than the two original frequency components These additional frequency components will increase in amplitude as the power amplifier is approaching its saturation point and they cannot be filtered out because it is within the bandwidth of the system Due to intermodulation distortion, there is spectral regrowth at the output of the power amplifier This will cause interference of adjacent channels

Phase Distortion

The other subtle aspect of linear power amplifier is that it should have a linear phase response [7] It meant that the time delay between the input and output of the power amplifier should be the same across its bandwidth If the time delay is different the output

of power amplifier will be distorted

One of the phase distortion caused by the power amplifier is known as AM-PM conversion [7][8] It happens when the input modulated signal caused a phase change in the output of the power amplifier The modulated signal will cause extra frequency components at the output of the power amplifier

The distortions discussed above do not take into account of the memory effects of the power amplifier [9][10] For a memoryless power amplifier, it has the same level of distortions throughout its bandwidth But the actual power amplifier will have different AM-AM and AM-PM distortions at different parts of its bandwidth Generally, using the assumption of memoryless power amplifier, it is possible to model the typical distortions

in the power amplifier

2.3 Modeling of Power Amplifier

The simplest way to model the power amplifier is by using a power series [11] as shown

in (2.2)

( ) ( ) 5( )

5

3 3

( )t

V o and V i( )t are the output and input of the power amplifier respectively a n are the

complex coefficients of the power amplifier These coefficients give you the gain of the various frequency components It is assumed that the power amplifier has a narrow bandwidth compared to the RF frequency that it is being transmitted Therefore even order frequency components do not fall into the bandwidth of the transmitter and could

be filtered out Using the power series, it is able to model the 1db compression point, gain and phase distortion But the distortion caused by the higher order in the power series is very low The most serious distortion is caused by third and maybe the fifth order in the power series Therefore most power amplifier could be modeled adequately by a fifth order power series

There are other models available such as [12] The common methods in power amplifier modeling are given in [7] But these models tend to be more complex than the power series and no comparisons of accuracy of different models are given

2.4 Power Amplifier Testing

In order ascertain the linearity of the power amplifier, it should be measured using two tones test, noise power ratio, adjacent channel power rejection and emission mask These tests give an indication of the non-linearity in power amplifier and could be adapted to test the linearity of wideband signal (i.e WCDMA) and multi-carrier system (i.e OFDM)

2.4.1 Two Tones Test

The two-tone test is the standard test for linearity of the power amplifier Figure 2.6 shows how the two-tone test is performed It is to input two frequency tones to the power amplifier For a narrow band system, the frequency spacing of the two tones is estimated

to be the bandwidth of the transmitter At the output of the power amplifier, other frequency components, caused by the intermodulation distortion, will be measured by a spectrum analyzer As the input power to the power amplifier is increased, the extra frequency components will also increase, normally at a faster rate than fundamental two tones Third order intermodulation distortion (IMD3) is the most serious distortion

The two-tones test is the simplest test to be performed on the power amplifier Also it qualitative of the improvement in linearity before and after linearization is implemented

2.4.2 Noise-Power-Ratio (NPR)

Power Amplifier

Frequency Amplitude

Frequency Amplitude

Figure 2.4 Noise Power Ratio Test

Noise Power Ratio Test [7] is normally used to test the linearity of multi-carriers communication systems The center channel is switched off Non-linearity in the power amplifier will produce distortions hence will fill up the center channel By observing the level of increase at the center channel, it is possible to measure the distortions introduce

by the power amplifier

2.4.3 Adjacent Channel Power Rejection (ACPR)

Adjacent channel power ratio (ACPR) [7][13] is a measure of the degree of spreading to adjacent channel Referring to Figure 2.5, ACPR is defined as the power within a specified bandwidth, shown as B1 in Figure 2.5, divided by the power at the adjacent channel, indicated as B2 in Figure 2.5 It gives us a measure of the spectral regrowth of the power amplifier by comparing the ACPR at the input and output of the power amplifier

Figure 2.6 Emission Mask

In most cellular standards, it defines a relative value to the channel output signal the spurious emissions must be below It could be view as an emission mask at the spectrum analyser shown in Figure 2.6 The output signal from the power amplifier must be below the emission mask It is a simple test for compliance of the power amplifier emissions to the cellular standard But every cellular standard has a different emission mask

2.5 Linearization

Linearization can be used to improve the linearity and efficiency of the power amplifier

In this section, the five methods are discussed on the linearization of the power amplifier They are

a Cartesian Feedback

b Feedforward

c Envelope Elimination and Restoration

d Linear Amplification with Non-Linear Components

distortions significantly because normally RF power amplifier does not have enough gain

at high frequency Also there is a problem of stability at RF frequency

A modified version of the feedback is the Cartesian Feedback [7][15] Figure 2.7 shows the general block diagram

0 90

0 90

Phase Shifter

Figure 2.7 Cartesian Feedback

Part of the output of the power amplifier is sampled and demodulated back into I and Q channel It is feedback to the input to create an error signal This error signal is filtered out and modulated to the RF frequency and input to the power amplifier The gain of the power amplifier will definitely decrease due to the feedback But it might decrease the distortions of the power amplifier drastically

The main problem with Cartesian Feedback is the control of the phase shifter The feedback signal should not be in phase with the input otherwise it would lead to instability In order that the feedback signal to be out of phase with the input, the phase shifter must be adjusted to meet this criteria If the modulation bandwidth of the input signal is wide, the phase changes from one part of the bandwidth to another Therefore the phase shifter must be able to automatically change its phase The control of the phase shifter is troublesome and not easily implemented The other problem is that the feedback path must be linear The power amplifier would amplify any distortions in the feedback path Hence the Cartesian Feedback is currently used in narrowband systems

2.5.2 Feedforward

Time Delay

Time Delay

Main Power Amplifier

Error Amplifier

RFIN

RFOUT

Power Splitter

Coupler

Figure 2.8 Feedforward Linearization

Figure 2.8 shows the general block diagram of the feedfoward linearization [16] The RF input is split into two branches The main power amplifier will amplify the input signal

with all the distortions of the power amplifier present The other branch goes through a time delay A directional coupler will then couple part of the power into the second branch This will cancel out the linear portion of the signal, leaving the distortions to be amplified by the error amplifier At the output of the feedfoward system, the distortions amplified by the error amplifier will cancel the distortions produce by the power amplifier Therefore at its output, it will have a linearized RF signal

One of the problems in the feedfoward linearization is the time delay The power amplifier has to be characterize thoroughly so as to be able determine the time delays of various components It is unable to adapt to the changing environment if it not modified Some research work had been done in this area [17] The other problem is that it requires

an error amplifier This adds to the power consumption of the overall system Also the couplers and splitters used are passive, therefore lossy, components This will also decrease the efficiency of the overall system

Feedforward linearization is an open loop linearization Therefore it has much greater bandwidth compared to feedback linearization It is possible to obtain good linearity performance It is normally used in base stations

2.5.3 Envelope Elimination and Restoration

Figure 2.9 Envelope Elimination and Restoration Modulated signal at the output of the power amplifier could be written as

where v( )t is the output signal, a( )t is the envelope of the modulated signal and φ( )t is the phase of the modulated signal The idea of Envelope Elimination and Restoration (EER)[1] of linearization is to decompose the modulated signal into an envelope signal and phase-modulated signal This could be amplified individually and combined at the end This is shown in the illustration in Figure 2.9 The input signal is split into its envelope signal and phase-modulated signal using an envelope detector and limiter respectively The phase-modulated signal is injected into the input of the switching power amplifier such as Class E amplifier The envelope signal is amplified and is used to drive

the supply line of the switching power amplifier Therefore at the output of the switching power amplifier, the modulated input signal is not only amplified but also its envelope and phase is restored back The advantage of this method is that we could use a non-linear switching power amplifier thereby greatly improving the efficiency of the power amplifier

However, there are a few problems using this method Firstly, to properly restore the modulated signal at the output of the power amplifier, the phase shifts for the envelope signal and the phase-modulated signal must be the same This is difficult to accomplish

as the circuits used in the envelope signal and phase-modulated paths are very different Secondly, using a limiter to extract the phase-modulated signal introduce additional AM-to-PM distortions

2.5.4 Linear Amplification with Non-Linear Components

Figure 2.10 Linear Amplification with Non-Linear Components

The idea for Linear Amplification with Non-Linear Components (LINC)[1][7] linearization is to decompose the modulated signal given in Equation (2.3) into two phase-modulated signals given in (2.4)

E amplifier Finally, the amplified signal is restore by combining the output signal of the non-linear power amplifier together

The disadvantage of this method is that firstly it is difficult to implement the signal separator in analog or RF domain The circuits that had to be implemented are non-linear Secondly the phase delay of the two phase modulated signals must be the same Thirdly, the adder at the end must have high isolation between the two non-linear power amplifiers else it will distort the final output signal

2.5.4 Predistortion

Power Amplifier Predistorter

Figure 2.11 Basic principle of Predistortion

Figure 2.11 shows the basic principle of predistortion A non-linear device, in this case a power amplifier, could generate a linear output, if there is a predistorter that is inserted before it The characteristics of the predistorter must be the inverse of that from the power amplifier This technique is very general and is applicable in lot of applications

The modeling of the non-linear device is crucial so that it is possible to generate a predistorter that eliminate or reduce the distortions As discussed in section 2.3, the power amplifier could be modeled as an odd order power series If it is restricted to a third order power series, it could be written as in (2.5)

Vo = a1Vi + a3Vi 3 -(2.5)

where V o and V i are the output and input of the power amplifier respectively a n are the

coefficients of the power amplifier If the predistorter has a similar third order series as shown in (2.6)

VP = β1V’i + β3V’i 3 -(2.6)

where V P and V’ i are the output and input of the predistorter respectively βn is the

coefficients of the predistorter Since the predistorter is inserted before the power

amplifier, then V i =V P.Therefore the output of the power amplifier is

Vo = a1β1 V’i + [a1β3 + a3β1 3] V’i 3 + 3 a1β1 2β3 V’i 5 + 3 a3β1β3 2V’i 7 + a3β3 3 V’i 9

(2.7)

From (2.7), it is possible to draw some possible implications using predistortion Firstly,

it is possible to reduce the third order distortions by proper selection of the coefficients of the predistorter Theoretically, by choosing the correct coefficients, the third order distortion could be eliminated Secondly, as a third order predistorter, fifth, seventh and ninth order distortion starts to appear This is not present when the power amplifier is used alone It is possible to eliminate these higher order terms using a higher order predistorter But even higher order distortions terms will start to appear In practice, these higher order terms are generally much lower in amplitude compared to the third order distortion The combination of the predistorter and power amplifier will still improve the linearity of the overall power amplifier In an actual power amplifier, it does not behave

exactly in manner described by a power series Therefore the third order predistorter will not eliminate all the third order distortion One of things to take note is that it is quite impossible to linearize the power amplifier if it is operating at the saturation point The power series model is impossible to describe power amplifier near or at the saturation point

The third order distortions generated by the power amplifier is the most serious In order

to maximize the power efficiency of power amplifiers, it will be operating near to its saturation point Performing a two-tone test at the saturation point, the third order distortions would have the highest distortion power levels compared to the rest of the distortions If the RF power amplifier is used in a multi-carrier system, the distortions generated is even predominantly third order [18] The fifth and higher order distortions would also be present but these distortions have lower power levels

The predistortion linearization is an open loop linearization method Therefore it has a wide bandwidth Good linearity is able to obtain from this method The most troublesome problem is to find the correct coefficients for the power amplifier Also the power amplifier characteristics will drift in time, the predistorter should be able to track these changes and modify the coefficients to maximize the linearity of the power amplifier

Chapter 3

The Design of Analog Predistorter

Predistortion is simple and effective method of linearizing the power amplifier Also the power amplifier could be modelled as an odd order power series Simply using this odd order power series model, the predistorter is able reduce the distortion by introducing a similar odd power series before the power amplifier

In this chapter, the power amplifier’s model is slightly modified Using the modified model, an analog predistorter was designed and fabricated to linearize the power amplifier The major blocks of the design and different considerations of the blocks are discussed Finally the simulation, layout and die photo of the chip is presented

3.1 Introduction

The power amplifier model introduced in the previous chapter does not take into the account the phase distortion A more accurate model for the power amplifier is to use complex coefficients so that they are complex values [19] as shown in (3.1)

Po = a1Pi + a3Pi 3 + a5Pi 5 + ……

= (a11 + j a11)P i + (a31 + j a31) Pi 3 + (a51 + j a51) Pi 5 + …… (3.1)

In this modified model, the power series is still an odd order function All the even order distortions would be filtered out at the output of the power amplifier thus the distortion it causes is not as significant as odd order distortions The odd order power series is able to model the intermodulation distortion (IMD) However, the model is still a memoryless model

Since the power amplifier could be more accurately modeled using complex coefficients, the predistorter should also use complex coefficients to improve the linearity of the power amplifier

The third order intermodulation distortion (IMD3) is the most serious distortion generated by the power amplifier If the predistorter is able to reduce the IMD3 of the power amplifier, the linearity of the power amplifier would be greatly improved This

is especially true in multi-carrier systems[18] where the distortions is caused predominantly by IMD3 For example, in [20] 3 carriers were injected to a power amplifier The measured IMD3 was at least 31dB greater than the IMD5 In practical

power amplifier, the coefficientsa5 << a3 If the injected signal has n carriers, the IMD3 products generated, such as w i +w i+1 -w i-2 and 2w i -w i+1 where w i is frequency of

the i th carrier, will be more significant than IMD5

The predistorter could be implemented at several different stages of the transmitter chain Figure 3.1 shows the different sections in the transmitter where the predistorter could be implemented The predistorter could be implemented at the baseband before the digital-to-analog converter (DAC) [21] Most likely the predistorter will be one of the modules at the baseband implemented by a digital signal processor (DSP) The advantage of this approach is its flexiblility To change any part of the predistorter, it

is merely changing the software written into the DSP Also it is quite simple to implement the adaptive algorithm to find the optimum coefficients for the predistorter But by using this approach, a high processing power DSP must be acquired which will increase the power consumption of the transmitter

The predistorter could also be used after the DAC Therefore it is still at baseband but now the predistorter is implemented using analog circuits [19][22] The power consumption in this approach is lower than the digital predistortion One of the problems to take note is the distortion caused by the analog circuit in the predistorter Any unwanted distortion caused by the predistorter does not help to reduce the distortion in the power amplifier Instead, it will be amplified by the power amplifier nullifying the linearizing effect of the predistorter This is true for all analog, IF and

RF predistorter

The predistorter implemented at IF is similar to the one implemented at the analog baseband but the bandwidth of the predistorter increased It is easier to filter out the unwanted even order harmonics of predistorter than at baseband It is impossible to filter these distortions at baseband because these even order harmonic distortion falls right in your bandwidth However, predistorter implemented in IF stage requires a ninety degree phase shifter If implemented in integrated circuit, the phase shifter may occupy a substantial die area

If the predistorter is implemented at RF, the high frequency characteristics of the integrated chip is very diffcult to control Hence RF predistorter [11] has very limited flexibility compared to the rest of the predistorters Normally, it consists of diodes and some passive components It has to be designed individually for each type of power amplifier and is difficult to tune when the power amplifier drifts