POWER AMPLIFIERS - University of Oulutimor/PAcourse.pdf · · 2005-06-02POWER AMPLIFIERS BY: TIMO...

1

(C) 2005- Timo Rahkonen, University of Oulu, Oulu, Finland

POWER AMPLIFIERS

BY:

TIMO RAHKONEN

ELECTRONICS LABORATORY

DEPARTMENT OF ELECTRCAL ENGINEERING AND INFOTECH OULU

UNIVERSITY OF OULU

PO BOX 4500

90014 OULU

FINLAND

email [email protected]

2


CONTENTS

1. Introduction

Device constraints

Efficiency

Linear and switched amplifiers

2. Linearity requirements

Definitions

Effects on single-carrier and multi-carrier signal

3. Linearisation techniques

Feedback

Cancellation techniques

References:

Cripps: RF Power Amplifiers for Wireless Communications. Artech House 1999

Kennington: High-linearity RF amplifier design. Artech House 2000

Vuolevi: Distortion in RF Power Amplifiers. Artech House 2003

Pedro: Intermodulation distortion in microwave and wireless circuits. Artech House 2003

3


1. INTRODUCTION

Devices

Power matching

Operating classes of linear amplifiers

Switching amplifiers

4


DEVICES

RF power transistors have many difficult requirements:

• high breakdown voltages

• high output power

• low thermal resistance to handle large dissipated

power

Due to the large physical size and requirement for high

breakdown voltages, the RF power transistors tend to

have low ft and low achievable gain. Also their termi-

nal impedances are very low.

For example, in the LDMOS left, the lightly doped

area (LDD) acts as a series JFET that saturates the

drain current to a given value, effectively clipping high

current amplitudes.

p+ subst

S DG

p+ sinker

n+ source n+drain

p

p+ epi

LDD

LDMOS transistor

5


POWER MATCHING

To obtain maximum power transfer, complex conju-

gate matching is commonly used. However, due to the

large output resistance of transistors, conjugate match

easily results in excessive voltage swings.

RF power stages are commonly dimensioned to obtain

a maximum amount of power from a limited supply

voltage and device-limited maximum current. This is

called power match or load line match, and the opti-

mum load resistance seen by a transistor biased in class

A is

Due to inductive drain/collector biasing, Vmax can rise

to 2VDD.

RoptVmaxImax-------------

2VDDImax

---------------VDDIQ

------------≈ ≈=

0 VDD0

Imax

VmaxVDS / V

I DS /

A

Q

VDD

VDD

GND

~ 2VDD

6


Example

Assume a transistor with max AC current of 1A and

output AC resistance of 100ohms (i.e., 1V change in

Vout causes 10mA change in current). Conjugate

matching calls for 100 ohm load resistance, meaning

that 1A current swing causes a voltage swing of 50

volts and needs a supply voltage of 100V.

If the supply voltage is limited e.g. to 5V, then

Compared to complex conjugate match, the load-line

or power match results in higher output power with a

given supply voltage, but usually somewhat smaller

gain and poorer output reflection coefficient.

Ropt5V1A------- 5Ω≈=

Pin / dB

Po

ut

/ d

B

conj. match

power match

1A 100 100

transistor load

7


COPING WITH LOW TERMINALIMPEDANCES

Ropt is the impedance that needs to be seen by the

device current source. Ropt is in parallel with a typi-

cally very large drain capacitance that lowers the

impedance considerably even further, and needs to be

resonated away.

Transistors for powers higher than 1 W often employ

an in-package impedance matching to make the exter-

nal impedance matching easier.

FET

Drain

Gate

V

V

Package

FET

Input

matchOutput

match

+13.5 dB+0 dB -1.5 dB -13 dB +8 dB+4.5 dB

22Vp (4.8W)11.8Vp7.8Vp1Vp3.9Vp4.6Vp (0.21W)

50ohm

50ohm

8


Example: 1.9 GHz amplifier

Based on load-line analysis, a transistor with 23 pF

drain capacitance would like to see Ropt = 12 ohm

resistive load. Because the real part of the desired 12

ohm in parallel to the 23 pF drain capacitance is of the

order of 1 ohm only, an in-package matching is used to

increase the external drain impedance to ca. 7 ohms.

This is achieved by an in-package L-C segment, that is

formed by 0.3+0.2 nH bond wires and a 32.3 pF chip

capacitor. Final 1.6nH+4.3pF LC segment is on the

wiring board.

Note that resistive output impedance of the transistor is

much larger than Ropt. Hence, S22 of the amplifier is

poor.

In some cases, a low-frequency series resonator at

drain is used to ensure low-frequency stability (see

photo on previous page).

0 1 2 3 4 5 6-10

-5

0

5

10

15

20

25

30

35 0

1

2

3

4

5

6

0

1

2

3

4

5

6

0123456

50

dB-o

hm

freq / GHz

Zo = 12 ohm

50 ohm

1 ohm

23 pFpackage boardchip

0.3nH 0.2nH 1.6nH

4.3pF32.3pF

9


outI=id

drain

I=ipower

I=iout

VCCS

vcc

in

I=ic1I=Igm

0 500p 1n 1.5n 2n

-2

-0.5

1

2.5

4

Waveform

APLAC 8.00 User: Oulu University Electronics Laboratory

Id Igm

20 pF

CURRENT GAIN DUE TO RESONATING MATCH

I gmVDSV K

-----------

tanh β VST 1VGS VT 0

–

VST----------------------------

exp+

log⋅ R

⋅ ⋅=

VK 0.1=

β 1=

VST 0.03=

VT 00=

R 0.9=

10


OPERATING CLASSES

RF power amplifiers are classified by the conduction

angle during one RF cycle.

• Class A : the transistor conducts during the entire

cycle. i.e., the conduction angle is 360o)

• Class B : the transistor conducts only during half a

cycle (conduction angle is 180o). The amplifier

amplifies only the positive half cycles

• Class AB : the conduction is between 180 and 360

degrees. The amplifier clips during negative half

cycles. The gain decreases at the signal level where

the clipping begins

• Class C : the transistor conducts less than half the

cycle. Gain has nonlinear behavior: small signals are

not amplified at all.

To obtain the same peak current, class B needs twice

the driving voltage amplitude as class A, and class C

needs even more

Vin

ID

Vin

ID

Vin

ID

Vin

ID

(180/360)*T

<(180/360)*T> (180/360)*T

A:

AB:

B:

C:

11


EFFECT OF I-V CURVES

No transistors conduct with zero voltage across the

device. The knee voltage shown left on the VDS-ID

plot sets a minimum usable drain voltage. If the output

swing is increased further, the drain current dips to

zero (shown with thick dashed line), which quickly

reduces the output power.

Following examples are calculated using the I-V

curves left (these resemble an LDMOS device with

zero threshold voltage) and the following parameters.

Table 1:

A AB B C

VDD / V 4 4 4 4

Imax / A 2 2 2 2

Ro / ohm 3.5 4 6 9

VGSQ / V 1 0.5 0 -0.5

Vin(ampl) / V 1 1.5 2 2.5

0 1 2 3 4 5 6 7 80

1

2

-1 -0.5 0 0.5 1 1.5 20

1

2

A (3.5 ohm)

AB (4 ohm)B (6 ohm)

VDS / V

VGS / V

I D /

AI D

/ A

12


0 500p 1n 1.5n 2n

-2.1

-1

0.1

1.2

2.3

Waveform


Id Igm

0 500p 1n 1.5n 2n

-5

-2.5

0

2.5

5

Waveform


Id Igm

RL = 6 ohm RL = 14 ohm

OVERDRIVING CLASS B:

13


SOME CONCLUSIONS

Class A

• 2nd and 3rd order distortion have the traditional 2x

and 3x slope up to compression point. At compres-

sion especially 3rd-order distortion rises rapidly.

• Class A reaches a peak efficiency of 50% at com-

pression.

Class AB

Class AB has the following important characteristics:

• The efficiency decreases more slowly with reduc-

ing amplitude than in class A.

• The gain is not constant but depends on input

amplitude.

• The plot also shows sweet bias points, where dis-

tortion has local minima. These are very much

device dependent.

Class B

• Class B has nearly linear gain, and the distortion is

set by the rectifying behaviour.

• This results in large and signal-independent second

order distortion.

• Efficiency drops slowly with reducing amplitude.

• Class B amplifiers are often used in push-pull

form: one amplifier amplifies the positive half

cycles and the other one the negative ones.

Class C

Class C is highly nonlinear, but very power effective.

These are used e.g. to amplify constant envelope sig-

nals, and the amplifiers in most LC oscillators oper-

ate in class C.

14


0.1 0.3 1.0

-60

-40

-20

0

20

0

25

50

75

100

CLASS C (VB=-0.5, Ro = 9ohm)APLAC 8.00 Oulu University Electronics Laboratory

VoutdB

Vin/V

Eff/%

fund 2nd

3rd Eff

0.1 0.3 1.0

-60

-40

-20

0

20

0

25

50

75

100

CLASS B (VB=0, Ro = 6ohm)APLAC 8.00 Oulu University Electronics Laboratory

VoutdB

Vin/V

Eff %

fund 2nd

3rd Eff

0.1 0.3 1.0

-60

-40

-20

0

20

0

25

50

75

100

CLASS A (VB=1, Ro = 3.5ohm)APLAC 8.00 Oulu University Electronics Laboratory

VoutdB

Vin/V

Eff/%

fund 2nd

3rd Eff

0.1 0.3 1.0

-60

-40

-20

0

20

0

25

50

75

100

CLASS AB (VB=0.5, Ro = 4ohm)APLAC 8.00 Oulu University Electronics Laboratory

VoutdB

Vin/V

Eff/%

fund 2nd

3rd Eff

2x

3x

15


AM-AM AND AM-PM

The most common way to model the linearity of the

amplifier is to measure its gain and phase shift as func-

tions of the amplitude of a 1-tone input test signal.

Next page shows the AM-AM curves of the amplifier

classes simulated before.

AM-AM and AM-PM models are commonly used as

baseband modelling: signal is presented as complex

envelope (ignoring the RF carrier), and shaped by the

AMAM and AMPM responses:

vin(t) = r(t)*exp(j*φ(t))

vout(t) = AMAM(r(t))*exp(j*(φ(t)+AMPM(r(t)))

Ampl_in / V

Am

pl_

ou

t /

V

Ampl_in / V

Ph

ase

16


0 0.5 1 1.5 2

0.00

1.25

2.50

3.75

5.00

0

25

50

75

100

CLASS A (VB=1, Ro = 3.5ohm)APLAC 8.00 User: Oulu University Electronics Laboratory

Vout

V

Vin/V

Eff/%

fund Eff

0 0.5 1 1.5 2

0.00

1.25

2.50

3.75

5.00

0

25

50

75

100

CLASS AB (VB=0.5, Ro = 4ohm)APLAC 8.00 User: Oulu University Electronics Laboratory

Vout

V

Vin/V

Eff/%

fund Eff

0 0.5 1 1.5 2

0.00

1.25

2.50

3.75

5.00

0

25

50

75

100

CLASS B (VB=0, Ro = 6ohm)APLAC 8.00 User: Oulu University Electronics Laboratory

Vout

V

Vin / V

Eff/%

fund Eff

0 0.5 1 1.5 2

0.00

1.25

2.50

3.75

5.00

0

25

50

75

100

CLASS C (VB=-0.5, Ro = 9ohm)APLAC 8.00 User: Oulu University Electronics Laboratory

Vout

V

Vin/V

Eff/%

fund Eff

compression

half-cycle clipping

compressiontoo smallamplitudeto open

compression

compression

Eff ~ Vin2Eff ~ Vin

17


SWITCHING AMPLIFIERS

Power consumption of a switch is low, especially if a

zero-voltage switching can be arranged. There are two

main types of swithing amplifiers:

• Class D : Complementary switches are used to con-

nect the output to either supply rail

• Class E : Only one transistor is used, and a resonat-

ing circuit to create “blimps” in the output node

Technical issues of class E amplifiers

• L affects modulation BW

• CD dictates maximum fo. For large devices, maxi-

mum carrier frequency may be less than 200 MHz.

• Max. VD rises up to 3 times VDD

• Package affects drain waveform

• Harmonics of Vo are set by shape of VD blimp.

Often, harmonic traps are used in the output filter.

• Losses are caused mainly by Ron of the switch as

well as the value of VD when the switch opens.

VDD

L

time

OFF ONVD

VD

0 T

18


2. EFFECTS OF NONLINEARITIES

Signal statistics

• Digital modulation

Distortion effects

• Spectral regrowth

• Vector error

Multicarrier signals

19


DIGITAL MODULATION

Most digital modulations contain both amplitude r(t)

and phase φ(t) variations. To be modulated by an IQ

modulator, this is often given in inphase I(t) and quad-

rature Q(t) components rectangular form

where

Data is coded into certain I,Q combinations called con-stellation points (QAM-16 modulation shown left). To

limit the signal bandwidth, transition from one constel-

lation point to another is not abrupt put smoothed by

(root) raised cosine filter, resulting in trajectories

shown right.

In time domain I and Q signals are usually shown as

eye diagrams. Due to smooth transition from one sym-

bol to another, the data can be recognised only at the

midpoint of each symbol.

For analysis, it is handy to describe the data as I+j*Q.

r t( ) ωot φ t( )+( )cos I t( ) ωot( )cos Q t( ) ωot( )sin+=

I t( ) r t( ) φ t( )( )cos⋅= Q t( ) r t( )– φ t( )( )sin⋅=

5 10 15 20 25 30

-1

0

1

-1 0 1

-1

0

1

-1 0 1

-1

0

1

I(t)I

Q(t)Q

time

Q

symbol midpoint

symbol length

FIR D/A LPF

90o

+

FIR D/A LPF

fLO

+

I(t)

Q(t)

I(k)

Q(k)

RCOS

20


DIGITAL MODULATION ...

From power amplifier point of view, the following

characteristics are important:

• Required linearity. Nonlinear amplification causes

spectral regrowth, widening the signal spectrum and

causing it to leak to neighbouring channels.

• Accuracy of the received constellation points (called

vector error, EVM)

• Amplitude histogram. This sets the ratio of peak and

average power and dictates the power efficiency.

GSM has designer-friendly GMSK modulation. It has

no amplitude variations, so that it can be amplified by

quite nonlinear power amplifiers. Overall efficiency is

improved further by the time multiplexing: amplifier of

one handset transmits only 1/8 of the time.

Spectral regrowth

neighbouring channels

21


AMPLITUDE HISTOGRAM

Different constellation points may have different

amplitudes, and due to filtering, amplitude distribution

has a continuum of values. This means that the peak

power is typically much larger than the desired average

power. This ratio is called crest factor

and it simply means, that the amplifier needs to be able

to handle large peak powers. Especially in multi-car-

rier signals the crest factor is very large.

Very rare peak amplitudes can be clipped without seri-

ous harm. To find the probability of amplitudes

exceeding certain value, it is customary to plot the

cumulative density function (cpdf), 1-cpdf, or cpdf/(1-

cpdf) on a logarithmic scale.

For comparison, in FM r(t) is constant. In such con-

stant-envelope modulation amplifier nonlinearities do

not cause distortion products around the carrier. Hence,

these can be amplified by high-efficiency but nonlinear

switch-mode amplifiers.

CFPpeakPavg

---------------=

0 0.5 1 1.5 2 2.50

pdf r

(t)

0 0.5 1 1.5 2 2.510

-5

100

105

log

cpdf

r(t

)

r(t) V

r(t) V

r(t) rms

r(t) peak

0.001

0.001

pdf: propability density function

cpdf: cumulative propability density function

log cpdf: log10( cpdf/(1-cpdf) )- from this it is easy to find insignificant

min and max amplitudes

22


EFFECTS OF DISTORTION

The spectrum of the distorted signal is much wider

than the original signal, overlapping also the neigh-

bouring channels. The effects of distortion are

described by two figures of merit:

Adjacent channel power (ACP). This explains what is

the amount of power leaking to the neighbouring chan-

nel, given in dBc, dB’s compared to the carrier power

Vector Error (EVM). This describes how much the in-

band distortion affects the constellation points

0 5 10-80

-60

-40

-20

0

SP

EC

TR

UM

510

Distortion

Signal

Adjacentchannel

Inband distortionAdjacent channel distortion

-1 0 1

-1

0

1

-1 0 1

-1

0

1

23


MEMORY EFFECTS

Here, memory effect simply means that the distortion

is somehow bandwidth dependent. Polynomial models

or plain AM-AM model are memoryless, resulting in

bandwidth-independent distortion. However, AM-AM

may show hysteresis, and a typical symptom is asym-

metry between the upper and lower IMD sidebands.

Memory effects are usually not harmful, but they

become a problem in cancelling linearising systems:

the shape of the cancelling signal needs to match

closely with the actual IMD spectrum. On the example

left, the achieved cancellation is bandwidth dependent,

and better on the upper side band.

Ampl_in / V

Am

pl_

ou

t /

V

distorted signal

cancelling signal (memoryless)

linearised signal

frequency

24


CAUSES OF MEMORY EFFECTS

Typical cause of memory effects is the up or down-

conversion of 2nd order distortion from DC and 2nd

harmonic band. Distortion on these bands is shaped by

frequency-dependent bias and matching impedances,

and hence these components have frequency depend-

ency. Another common cause is self-heating, where the

temperature variations are shaped by the low-pass ther-

mal impedance.

Hence, IM distortion consists of broadband, memory-

less contributions caused e.g. by 3rd and 5th degree

nonlinearities, and up and down-converted products

that may have some frequency dependence (this is

illustrated left as a vector diagram of an IM3 tone).

Especially the up-conversion from DC band and elec-

tro-thermal memory may cause asymmetry, as it

appears at opposite phases in upper and lower IMD

sideband.

v

v2 = iNL2 Z(f)

v3

IM3total

3rd-order

envelope

2nd-harmonic

tone spacing in a 2-tone

test is varied

25


SINGLE-CARRIER VS. MULTI-CARRIER

Left, 1- and 2-carrier signals with the same total power

are driven into the same amplifier model.

In the 1-carrier signal it is seen that the nonlinearity

broadens the spectrum and distorts the constellation

diagram, but different symbols can still be recognised,

as the shift of the constellation points is systematic.

In the 2-carrier signal, the 1.4 times larger peak ampli-

tude clearly starts to compress, rounding the IQ trajec-

tory plot. More seriously, now the shift of the

constellation points is largely caused by the neighbour-

ing channel that has non-correlated signal. This makes

the EVM to look random.

Multi-carrier signals require a more linear amplifier

than single-carrier signals.

-1 0 1

-1

0

1

-1 0 1

-1

0

1

-1 0 1

-1

0

1

0 5 10 15

x 106

-80

-60

-40

-20

0

SP

EC

TR

UM

-1 0 1

-1

0

1

-1 0 1

-1

0

1

-1 0 1

-1

0

1

0 0.5 1 1.5 2 2.5 37

-80

-60

-40

-20

0

SP

EC

TR

UM

26


3. LINEARISATION METHODS

Dimensioning

• Backoff

• Sweet bias points

Feedback

• Cartesian and polar feedback

Feedforward

• Efficiency issues

Predistortion

• BB digital/analog, IF, RF

High efficiency transmitters

• Doherty amplifier

• LINC / CALLUM

• Polar transmitter

27


-40 -30 -20 -10 0-80

-60

-40

-20

0

20

100

10

1

Fundamental

IM3Efficiency

IM3 spec

Po

dB

Pin dB

55 dB

Canc.

Effi

cien

cy %

REQUIRED AMOUNT OF LINEARISATION

28


ACCURACY REQUIREMENTS OFCANCELLING SYSTEMS

One method of reducing distortion is to try to cancel it

with distortion equal in amplitude but opposite in

phase. However, the accuracy requirements for this are

quite tough. Using cosine rule to solve the error vector,

the achievable cancellation is

where δA and ∆φ are amplitude and phase errors, res-

pectively. For example, to achieve 30 dB reduction (1/

30 in amplitude) in distortion, amplitude error must be

less than 0.25 dB (3%) and phase error less than 1

degree. These requirements are similar but tougher

than for SSB upconverters.

CANC 10 1 2 1 dA A⁄+( ) ∆φ( )cos 1 dA A⁄+( )2+–( )log⋅=

0.1 1 10-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

0 dB

0.05 dB

0.1 dB

0.25 dB

0.5 dB

1 dB

2 dB

PHASE ERROR (DEGR)

CA

NC

EL

LA

TIO

N d

B

A (to be cancelled)

A+dA

∆φ

error

err2 A2 A ∆A+( )2 2A A ∆A+( ) ∆φ( )cos–+=

29


BACKOFF

Easiest way to improve linearity is to back off the input

power from the compression level. For linear modula-

tions, backoff equal to the crest factor is usually requi-

red.

Backoff results in serious over-dimensioning. For

example, if a 1W average output power is needed and

the backoff level is 10 dB, the peak power level of the

amplifier needs to be 10W. Unfortunately, 10 dB back-

off results in power efficiency of some percents, only.

-40 -30 -20 -10 0-80

-60

-40

-20

0

20

100

10

1

Fundamental

IM3Efficiency

IM3 spec

Po

dB

Pin dB

55 dB

Canc.

Effi

cie

ncy

%

Backoff

30


SWEET BIAS POINTS

Many devices have certain bias points where the dis-

tortion is lower than could be expected from the 3x

linear trend.

These minima are often due to intra-device cancelling

mechanisms, and the various contributions of the IM3

of the gm element (Ids) and the total drain current (ID,

including also the current through drain capacitance)

are shown left. Some of the cancelling components are

frequnecy dependent, hence also the sweet spot may

depend on signal bandwidth, or center frequency.

Left are shown various contributions of a sweet spot in

an LDMOS transistor. Ids is the gm current source, Id

is the total drain node current, including capacitor cur-

rents. Kxy refers to a nonlinear term

Kxy*Vin^x*Vout^y (K10 is a linear term like Cds or

gm)

(Aikio: MTT-IMS 2005)

-30

-40

-50

-60

-70

-80

Id [

dB

]

genIM3(Ids)

K1(Ids)Vo1

ResultId/HB

K1(Cds)*Vo1

genIM3(Cds)

K1(Cgd)V1

100 200 300 400IDQ [mA]

IDQ for phasorpresentation

-30

-40

-50

-60

-70

Ids [

dB

]

-80

-90

K30Vi3K50Vi5

genIM3(Ids)K20VH2

K40Vi4

K10(Ids)Vi1

ResultIds/HB

K20VENV

K03Vo3

Vi1Vo1 K02Vo2

IM3 magnitude vs. bias current

31


FEEDBACK

Provided that the feedback path is linear, feedback

reduces distortion by the amount of loop gain - e.g. to

reduce distortion by 20 dB, we need loop gain of 20

dB.

• Basic principle by Black in 20’s

• Distortion in the forward branch is reduced by 1/T,

where T is the loop gain of the amplifier feedback

combination. Distortion in the feedback branch

appears directly in the output.

• Fundamental problem of using output that already

exists to correct the input that caused that distortion

-> works well only with periodic signals

• Stability and bandwidth issues

noise,distortion, ...

Vin Vout+

-

+

CA

NC

dB

Lo

op

gain

dB f 3dB f 0dB

foffset

32


CARTESIAN FEEDBACK

At RF frequencies it is difficult to achieve very high

loop gain. One way to circumvent this is to form the

error signal at baseband and use quadrature up and

down conversion in the direct and feedback branches.

Problems:

• delay in mixers and PA reduce the achievable band-

width. Any propagation delay reduces the phase

margin directly by amount of

• needs very linear and low-noise feedback path

• power control needs to be arranged so that the loop

gain remains constant

Cartesian feedback is limited to systems with band-

widths of some tens of kHz. It is standardly used e.g. in

Tetra radios. Commonly, lead-lag or lag-lead compen-

sation is needed to ensure stability.

∆φ jωTD–( )exp=

LO

Baseband

I

Q

deep class AB

1 kHz 10 kHz 10 kHz 1 MHz 10 MHz

0.001

0.01

0.1

1

10

100

131030100300

30 degree limit

TD / ns

Offset frequency

Pha

se la

g de

gr

φ 360 f offs ∆T⋅ ⋅=

33


FEEDFORWARD

Feedforward is actually older invention than feedback

(Black @ Bell Labs, 1928).

• The distortion generated by the main amplifier A1 is

extracted, amplified by an auxiliary error amplifier

A2, and substracted from the output signal

• To achieve good cancellation in node B, the error

amplifier A2 needs to have flat frequency response

• Losses of the power splitters / combiners reduce the

overall efficiency

• Adaptation is tricky, requiring two amplitude and

phase tuning loops + accurate delay matching

Although feedforward is not very easy to adapt, it can

provide broadband linearisation and is suited for multi-

carrier signals.

B

A

A1

A2

34


LOSSES AND EFFICIENCY

The upper picture shows the attenuation of the direct

signal as a function of the coupling in power splitters/

combiners. For example, two -10 dB couplers cause a

loss of 1 dB to the output of the main amplifier in a

feedforward amplifier.

The lower figure shows the total efficiency including

losses after the amplifier. For example, 1 dB losses are

sufficient to reduce original 40% efficiency down to

32%. 3 dB combiner losses would reduce the effi-

ciency to 20%.

Pdirect = Pin - Pcoupled

Efficiency = Pdirect / PDC

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0-5

-4

-3

-2

-1

0

Coupling dB

P d

irect

dB

0 0.5 1 1.5 2 2.5 30

10

20

30

40

50

60

Total losses dB

Tota

l effi

cien

cy %

Pcoupled

Pdirect

35


PREDISTORTION

The basic idea of predistortion is to cancel the distor-

tion in the power amplifier by predistorting the trans-

mitted signal with the inverse function of the amplifier.

I.e. if the amplifier is driven to compression, higher

amplitudes need to be expanded to make the total res-

ponse linear.

This compensating nonlinearity makes the spectrum of

the transmitted signal wider, requiring higher sampling

rates, wider IF filters etc.

Note that any frequency dependence between the pre-

distorter and amplifier makes also the cancellation fre-

quency dependent.

PRED

36


DIGITAL PREDISTORTION

Left is the most common digital predistorter structure.

Signal amplitude |r(t)| information is used to choose a

signal-dependent complex gain value from a look-up-

table (LUT), that is used to scale and rotate the signal

vector. Filter block H can be used to introduce memory

effects into predistortion signal. The LUT is slowly

adapted by a feedback loop that IQ downconverts the

linearised output signal.

Predistortion causes spectral regrowth. Hence, a higher

sampling frequency is needed. Also the frequency

response of all filters between the predistorter and the

amplifier needs to be very flat and linear-phase, or the

effects of these need to be corrected by H as well.

I + j*Q

|r(t)| LUTH

Digital

37


ANALOG PREDISTORTER

The connection left is sometimes used as a predistorter

to create controllable amount of IM3 in the input of the

PA. Both diodes are biased on, and due to the balanced

structure, 2nd order nonlinearity of the diodes is can-

celled. Thus, only IM3 is generated (mismatch in dio-

des creates residual IM2 ).

That kind of simple predistorters have been used e.g. in

satellite transmitters.

V

1

2

v2

iNL2 = K2(-v2)2

iNL3 = K3(-v2)3

iNL2 = K2(+v2)2

iNL3 = K3(+v2)3

PA

cancel

sum up

38


DOHERTY AMPLIFIER

In Doherty amplifier the efficiency of the class AB or

B main amplifier is improved by using λ/4 impedance

transformer and a class C peak amplifier to control the

load resistance seen by the main amplifier: RLmain is

actively tuned so that the main amplifier remains at the

edge of compression for e.g. 1:2 input voltage range.

If Zomain, Zopeak >>, RLmain seen by the main

amplifier is

Inclusion of the output impedances Zomain, Zopeak

complicates this simple analysis.

The 90 degree phase shift in the main branch is com-

pensated by delaying the input of the peak amplifier by

T/4.

RLmain

Zo2

Ro 1I peakImain--------------+

------------------------------------=

Vin

Vout,mainRLmain

Ipeak

MAIN AMP PEAK AMP

Ro

Ζο, λ/4

Vout

Zomain >>

Zopeak >>

RLmain

Imain

Vout,main

(saturates, but themain amp powerstill increases)

39


LINC AND CALLUM TRANSMITTERS

In LINC an amplitude-varying signal is presented as a

vector sum of two constant-envelope signals, that are

phase modulated. Thus, the amplifiers can be e.g.

switched amplifiers.

Problems:

• Needs a low-loss combiner

• Spectral regrowth of v1 and v2 is huge. The

regrowth cancels in the summation, provided that the

branches match accurately

• In CALLUM, feedback is employed to improve the

accuracy of v1 and v2. However, then the signal sep-

aration will have an amplitude-dependent band-

width.

v1(t)

v2(t)

v1(t)

v2(t)

vout(t)

vout(t)

Sig

nal

sep

ara

tio

n

40


POLAR TRANSMITTER

In polar transmitters, a power-effective switching

amplifier is driven by phase modulated constant enve-

lope carrier. The amplitude information as added by

modulating the power supply of the amplifier by a

modulated DC source.

The output distortion is very sensitive to time delay

between the amplitude and phase channels, as well as

sufficiently broad frequency response of the amplitude

channel. The bandwidth of the rectified amplitude

|A(t)| is roughly 3 times the baseband bandwidth, while

the CE phase modulated carrier has 5..6 times the

bandwidth of the original signal.

The same idea is applied in the EER transmitter (enve-

lope elimination and restoration), where RF amplitude

detectors and limiting amplifiers are used to separate

the amplitude and phase signals.

PM

|A(t)|

u t( ) A t( ) 2π f ot φ t( )+( )cos⋅=

|A(t)|

φ(t)

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