Digital Parts of Receivers and Transmitters

Vilmos Rösner

• Digital Parts of Receivers

• Digital Parts of Transmitters

• Special Application: Bandpass Filter

DEMout

f0

Antenna output: U(t)=A(t)•exp(j•(t•ω(t)+φ(t)))

modulation-> information

Problem: receiver selectivity

Superheterodyne Receiver (Edwin Armstrong 1918)

new problem: image rejection

DEMout

IF

f0f0

Frequency Ranges

DEMIFRF IF BBRF

RF IF BB

radio frequency intermediate frequency baseband

~100MHz... ~GHz ~10MHz ~kHz..MHz

generally: FRF: FIF≈ 10..3

problem with tuning linearity, images...problem with image rejection→solution: multiple conversion (IF)

If it is possible, one of the standard intermediate frequencies should be used.

Digital Output, Position of the ADC

digital IF receiver“software radio”

modem

IF BB BBM/U

BBM/U

digital world

ADCIFRFRF

IFRF IF BBRFADC

IFRF IF BBRFADC

BBM/U

analogue world

Digital IF Receiver Components

• Analog to Digital Converter (ADC)• Digital Mixer (multiplier)• Digital Oscillator (NCO Numerically Controlled

Oscillator)• Digital Filter

DDC

outin

DDC

ADC FILTER

NCO

FTW

PACC

LUT

address

data bus

set f

clk

N

• fout=FTW * fClk / 2^N

• Intersil HSP45102, HSP45116A• optionally complex output• other accessories (sweep, modulation, dither)• NCO+DAC≈ Direct Digital Syntheser (DDS)

Digital Filter / FIR

http://www.digitalfilter.com

FIR Filter Coeffitients, Window Functions

rectangular window: effect of increasing taps (order)

other window

side lobe levelstop band attenuation

main lobe widthroll-off (slope)

http://en.wikipedia.org/wiki/Window_function

FIR Filter Design

windowing method: coefs=(ift of ideal response) * window

Further methods (e.g. Parks-McClellan)

Digital Filter / IIR

•better resource utilization as in FIRs•oscillations may occour→not recommended

http://www.bores.com/courses/intro/iir/

Digital Filter/ CIC (Cascaded Integrator-Comb)

•mentioned as FIR filter, but it has a feedback part•stable•there is not multiplier: easy to realize

http://www.us.design-reuse.com/articles/article10028.html

Decimation

if the signal is in a limited narrow band, we can skip samples without losing information

0 +Fsa/2-Fsa/2

0 +Fsb/2-Fsb/2

t

1/Fsa

ignored samples

t

1/Fsb

limited band

Fs=Fsa

Fs=Fsb=Fsa/2

Decimation

0 +Fsa/2

0 +Fsb/2-Fsb/2

0 +Fsa/2

stop bandpass band

-Fsa/2

CIC(lpf)

FsFsDEC

Fs/DEC

the decimation causes spectrum overlapping, therefore the decimation usually happens at the output of a low

pass filter

using Mth order CIC and M factor decimation (M=4)

Functional Block Diagram of DDCs

in out

f0 FsBB

f0 Fs

f0 Fs

CIC

DDC

FIR

The FIR filter is realized with several (1..16) multiplier→ we can use more taps at larger decimation

Example

in outCIC

DEC=16FIR

TAPS=16

64MHz 4MHz

in outCIC

DEC=32FIR

TAPS=32

64MHz 2MHz

• Two different settings of the same DDC• The decimation plays the similar role as down conversion in the analog techique

DDC FIR Filter Limits

ADC

usually faster ADC -> worse SNR

quantization noise, SDFR

0 Fs/2 Fs

Signal

Spour

0 Fs/2 Fs

SDFRbaseband sampling: if the signal has a large and low frequency part, the overtones are in the used band

IF sampling: the overtones can evade the used band, where filters can attenuate them

http://www.beis.de/Elektronik/DeltaSigma/DeltaSigma.html

Advantages of Digital IF

• easy to reproduce• thermal stability• flexibility• the output signal can be better as at BB sampling• accurate IQ output

(analogue complex sampling)

IF CH IADCCH Q

AAF I AMP I

splitter

AAF Q AMP Q

"sin""cos"

0 +Fs/2

SignalAlias

-Fs/2

0 +Fs/2

Signal

-Fs/2

0 +Fs/2

SignalAlias

-Fs/2

real sampling

ideal complex sampling

unbalanced complex sampling

alias rejection

It is possible sampling the IQ signal on baseband, and there are dual ADCs for IQ sampling applications, but these systems have finite rejection to the fs/2 alias because of the analogue gain and phase differences and crosstalk between the two analogue paths.

Digital Upconverters

f0 FsBB

f0 Fs

0

outinINT

DUC

DAC

fFs

Interpolation

• inverse operation of decimation• zero padding or repeating is applicable• we have to use LPF to remove unwanted overtones

Functional Block Diagram of a DUC

Special Application: Bandpass Filter

ADC CIC PFIRMIX

CH1

CH2

CH3

FPGA

GC5016/DDC

CH0

CICPFIR

CH1

CH2

CH3

GC5016/DUC

CH0

MIX DAC