Estimation of IQ vector components of RF field - Theory and implementation M. Grecki, T. Jeżyński,...

Estimation of IQ vector components of RF field - Theory

and implementation

M. Grecki, T. Jeżyński, A. Brandt

Agenda

• Introduction - LLRF system

• Downconversion and IQ estimation

• VHDL implementation of IQ estimator

• Sources of incorrectness

• Simulation and optimization of IQ estimation parameters (IF, SF)

• Conclusion

FPGA

FT PZT

Klystron

AD

C

AD

CA

DC

DA

C

DA

C

DA

C

Digital feedback

~ ~ ~waveguidetunerHV

cav.1

RF power waveguide

AD

C

rf switch

~ AincAreftiming

DOOCS server

VM

E

beam

I Q

wectormodulator

Control panel

FT PZT

AD

C

AD

CA

DC

DA

C

~waveguidetuner

cav.n

AD

C

~ AincAref

....

LO - LocalOscillator

FPGA computational algorithm

[aij]

ab

ba+

Feedforwardtable

Gaintable

Setpointtable

[bij]

[zij]

...

cav A

cav B

cav Z

+

LLRF control system

Agenda






• Conclusion

Problem:• signal downconversion

• I and Q estimation

xif=xrf·xloxrf

xlo

xif

lo

F()

rf rf- lo rf+ lo

tQtI

tAtx

ifif

if

cossin

sin

lorfif

lolololo

rfrfrf

tAtx

tttAtx

sin

)(sin

]cos

2[sin

21

)(

lolorf

loiflorfif

tt

ttAtAtx

)2sin(21 loiflorfif ttAtAtx

Sampling of downconverted signal

tQtI

tAtx

ifif

if

cossin

sin

System migration

Future:IF = 81MHz ?SF = 36MHz ?TS = 1usmany samples per TSaveraging possible (noise reduction)

Now:IF = 250kHzSF = 1MHzTS = 1us4 samples / IF signal periodprediction needed

AD Conversion parameters

• Constant SF (time uniform sampling)

• M·IF=N·SF (M,N –integer numbers)

• TS=1s, IF >= 1MHz

• SF >= 3MHz, limited by ADC parameters

• SF - averaging => noise reduction

• SF - ADC accuracy drops down

• IF - ADC accuracy drops down

Agenda






• Conclusion

IQ estimation

ixM

Q

ixM

I

SFIF

M

ii

M

ii

1

0

1

0

cos2

sin2

2

IF=81MHz, SF=36MHz

entity IQestim is port (I : buffer BREG; -- I output Q : buffer BREG; -- Q output iqr : out bit; -- IQ output ready S : in BREG; -- sample input sr : in bit; -- sample ready input clk : in bit; reset : in bit);end;

I

resetclk

sr

iqrQ

S

Numerical algorithm

sin cos

xi

18x18

14b int

14b int

24b int

>>8 >>8

>>5

32b int

*int(218/M)>>17

I Q14b int

>>5*int(218/M)

>>17

28b int

-213 < xi < 213-1

-213 < sin, cos < 213-1

%0122.0422.12113 e

The computation algorithm assures ~14bits accuracy of results

VHDL implementationDesign Summary--------------Target Device : x2v4000Target Package : ff1152Target Speed : -6Logic Utilization: Total Number Slice Registers: 64 out of 46,080 1% Number used as Flip Flops: 62 Number used as Latches: 2 Number of 4 input LUTs: 55 out of 46,080 1%Logic Distribution: Number of occupied Slices: 43 out of 23,040 1% Number of Slices containing only related logic: 43 out of 43 100% Number of Slices containing unrelated logic: 0 out of 43 0% *See NOTES below for an explanation of the effects of unrelated logicTotal Number 4 input LUTs: 80 out of 46,080 1% Number used as logic: 55 Number used as a route-thru: 25 Number of bonded IOBs: 46 out of 824 5% IOB Flip Flops: 29 Number of MULT18X18s: 4 out of 120 3% Number of GCLKs: 2 out of 16 12%

--------------Design statistics: Minimum period: 11.224ns (Maximum frequency: 89.095MHz)

Agenda






• Conclusion

Accuracy of ADC - AD6645 (1)

bitsdB 1590 bitsdB 1485

Accuracy of ADC - AD6645 (2)

Frank Ludwig / 03.12.04

Agenda






• Conclusion

IF=81MHzSF=36MHzVn=0.5mVjit=5ps

IF=81MHzSF=72MHzVn=0.5mVjit=5ps

Aerr(mean,std,min,max)=-0.0055 / 0.0238 / -0.0977 / 0.0669 PHI(mean,std,min,max)=0.0003 / 0.0223 / -0.0845 / 0.0821 deg.

Aerr(mean,std,min,max)=-0.0024 / 0.0430 / -0.1525 / 0.1629 PHI(mean,std,min,max)=-0.0008 / 0.0263 / -0.1065 / 0.0976 deg.

IF=81MHz, Vn=0.5mV, jit=5ps

IF=9MHz, Vn=0.5mV, jit=5ps

Error vs SF

SF=36MHz, Vn=0.5mV, jit=5ps

SF=72MHz, Vn=0.5mV, jit=5ps

Error vs IF

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

1 10 100 1000

INL[bits]

Aerr[%]

-2.5

-2

-1.5

-1

-0.5

0

0.5

1 10 100 1000

INL[bits]

Aerr[%]

S shapeU shape

Nonlinearity of ADC

Nonlinearity does hardly influence phase

Agenda




• Source of incorrectness


• Conclusion

Conclusion

• Algorithm of IQ calculation is straightforward • Its implementation in FPGA is simple and uses few

resources• The results of IQ calculation by Matlab script and

VHDL model is identical• the IF frequency should be chosen low (e.g. 9MHz)• the SF frequency should be chosen high, limited by

ADC SNR raise (e.g. 72MHz)• all the noise sources and jitters should be identified and

their influence on IQ estimation error investigated

Thank you for your attention.

Questions?

Some maths....

sincos QIx

when we sample x(t) we can say that we measure real part of complex RF vector in rotating coordinate system

RF

MMM QIx

QIx

QIx

sincos

......

sincos

sincos

222

111

x

from this equations I and Q have to be calculated

I

Q

Some more maths....

0

......

0

0

222

111

MMM xQbIa

xQbIa

xQbIa

0

0

2

2

iii

ii

iii

iii

iii

ii

xbbQbaI

xabaQaI

LS

22212

11211

sQaIa

sQaIa

ia

iiaa

ia

M

i

M

i

M

i

1

0

222

1

02112

1

0

211

cos

cossin

sin

ixs

ixs

M

ii

M

ii

1

02

1

01

cos

sin

where

where

that isconstantfor givenconversion scheme

that needscalculation samplesbetween

advance phase

Some math tricks...

2

cossin

0cossin

1

0

222

1

0

211

1

02112

Miaia

iiaa

M

i

M

i

M

i

Ms

Q

Ms

I

2

1

2

2

ixs

ixs

M

ii

M

ii

1

02

1

01

cos

sin

that is true if M=k*360deg

ixM

Q

ixM

I

M

ii

M

ii

1

0

1

0

cos2

sin2

Estimation of IQ vector components of RF field - Theory and implementation M. Grecki, T. Jeżyński,...

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