3-mixer_nco

Institute for Communication Networks and Satellite Communications

Professor Horst Cerjak, 19.12.2005Wolfgang Kogler Software Defined Radio Digital mixer and numerical oscillators

Software Defined Radio

Digital mixer and numerical controlled

oscillators


Professor Horst Cerjak, 19.12.2005

2

Wolfgang Kogler Software Defined Radio Digital mixer and numerical oscillators

Block diagram



3


Complex mixer

( ) ( ) ( )

( ) ( )ttinjtt

tjtjej tj

ωωωω

ωωω

cosImsResinImcosRe

sincosIm ReIm Re

⋅+⋅+⋅−⋅=

+⋅+=⋅+



4


Spectrum



5


Real up mixer

( )( ) ( ) ( )( )

tt

tjtjej tj

ωω

ωωω

sinImcosRe

sincosIm ReRealIm ReReal

⋅−⋅=

+⋅+=⋅+



6


Spectrum



7


Real down mixer

( )

tinjt

tjte tj

ωω

ωωω

s RecosRe

sincosReRe

⋅+⋅=

+⋅=⋅



8


Spectrum



9


Hardware implementation

• FPGA state of the art– Multiplier are available in silicon structure (DSP blocks)

– Memory are available in silicon structures (true dual port memories)

• Needed components for complex mixer– Multiplier

– Look up table for sine / cosine

– Address counter



10


The Numerical controlled Oscillator (NCO)

• Advantages– Frequency, Phase, and Amplitude can be manipulated precisely

– Changes are phase continuous

– No settling time after changes

– Extremely fine frequency resolution

– No thermal drift

– No aging

– No influence of parameter variations of analog components



11


Principles of the NCO

Main blocks

– Phase Accumulator

– Phase to Amplitude converter

– D/A converter

– Antialiasing filter

( )tfts ⋅⋅= c2sin)( π



12


Phase Accumulator



13


Frequency Resolution

• High Frequency resolution requires high number of bits

in the phase accumulator

• High number of bits in the phase accumulator requires a

giant LUT

• Truncation is necessary → Spurious

HZ0,046612

MHz200

12

2

32c_res

m

clkc_res

m

clkc

=⋅=

⋅=

⋅=

f

ff

Mf

f



14


Phase to Amplitude Convertera) 2

m

0

b) 2m

0

2P

2P



15


Digital Direct Synthesizer (DDS)

Phase

accumulator

Phase-to-

amplitude

converter

DA converter

Reference

clock

fclock

m P P

Tuning word M

Digital representation of the signals Approximated

sine wave

Digital direct sequence DDS

( ) M2

MN

;2N

;2sin)(m

clockclockNCOm

clockclockNCONCO outmin

fff

ffftfts ====⋅⋅= π



16


Truncation error

F1

F3

F2

F4

M

I

Q

m

P m-P

MSB LSB

X XX X X X0

000 (0)0011 (3)00011000 (24)

010 (2)0010 (2)00010010 (18)

100 (4)0001 (1)00001100 (12)

110 (6) 0000 (0)00000110 (6)

000 (0)0000 (0)00000000 (0)

Phase error e

bin (dec)

Phase word p

bin (dec)

Accumulator m

bin (dec)



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Spur ratio

( )

P

Pm

m

error

Pm

PmPmPmPm

Pm

error

PmPmPm

Pm

error

SPR

t

ttFP

tFPtfts

MifMt

MifMt

+

−−

−

−

−−−−−

−

−−−−

−

===

⋅=

−⋅⋅=

>−=

≤=

1

2

1

NCO

1

1

22

2

amplitudeSpur

amplitudeCarrier

2)(

)(2sin)(

2)2mod( )2mod(2

2

2)2mod(

)2mod(

2

π



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Sources of NCO spurious

Digital domain– Truncation of the phase accumulator word

– Finite precision of the sine values in the LUT

Analog domain– DA converter errors:

• Differential non linearity

• Integral non linearity

• Missing codes

– Anti aliasing filter

– Phase noise of the clock source

Please note, that a frequency offset of the clock does not

introduce spurious, but an corresponding frequency error!


Professor Horst Cerjak, 19.12.2005Wolfgang Kogler Software Defined Radio Digital mixer and numerical oscillators

Thank you for your attention

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