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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Modulation and Demodulation
Techniques for FPGAs
Ray Andraka P.E., president,
A
ndraka
C
onsulting
G
roup,
I
nc.
the
16 Arcadia Drive
•
North Kingstown, RI 02852-1666
•
USA
401/884-7930 FAX 401/884-7950
2
copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
You can do Math
in them things???
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Overview
• Introduction
• Digital demodulation for FPGAs
• Filtering in FPGAs
• Comparison to other technologies

cos(
ω
c
t)-
j
sin(
ω
c
t
)
Decimate
by R
Video
Bandpass
Filter
2
f
(t) cos(
ω
c
t)
Phase
Split
ω
c
-ω
c
-ω
c
ω

(t)
I
Q
Decimate
by R
ω
c
-ω
c
-2ω
c
00
-2ω
c
0
e
-j
ω
ct
Re-arranged Demodulator
*
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Complex Mixer
Re[A
k
]
Im[A
k
]

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Frequency
Synthesizer
Phase Angle
to Wave
Shape
Conversion
Waveform
Out
Phase Angle
Modulation
Waveform Synthesis (NCOs)
• Various Methods
– Look up table (LUT)
– Partial products
– Interpolation
– Algorithmic
• Most methods use a
frequency synthesizer
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
∆ Phase
(phase increment)
Sample Clock
Phase Accumulator Design
• “Direct Digital Synthesis”
• Essentially integrates phase increment
• Increment value may be modulated
– Frequency and PSK modulation
• Binary Angular Measure (BAMs)

++
Q1 Sin
LUT
Q1 Sin
LUT
Q
MSB
MSB-1
remaining
bits
I
Phase MSB’s
Count
sequence
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Waveform Synthesizer plus Multiplier
• Obvious Solution
• Separate into functional
parts
• Treat each part
independently
Numerically
Controlled Oscillator
sin(ω
c
t)
cos
(ω
c

A[3:2]
6-LUT
A[5:4]
6-LUT
A[7:6]
<<2
<<2
<<4
Phase[3:0]
n+8
Partial Products Modulator
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
6-LUT
I[0]
6-LUT
I[1]
6-LUT
I[2]
6-LUT
I[3]
<<1
<<1
<<2
Phase[3:0]
n+8
Q[1]
Q[2]
Q[3]
Q[0]

CORDIC Modulator
I
out
= I
in
cosφ - Q
in
sinφ
Q
out
= Q
in
* cosφ + I
in
sinφ
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
CORDIC Algorithm Explained
• Coordinate rotation in a plane:
x’ = xcos(φ) - ysin(φ)
y’ = ycos(φ) + xsin(φ)
• Rearranges to:
x’ = cos(φ) [x - ytan(φ)]
y’ = cos(φ) [y + xtan(φ)]
cosφ
sinφ
φ
I
Q
21

±± ±
>>4 const
sign
CORDIC Structure
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Digital Filtering
y[k]=Σx[k-i]•C
i
Z
-1
Z
-1
C
0
C
1
C
i-2
C
i-1
Z
-1
x[k]
• Many Constant
Multipliers
• Delay Queues
• Products Summed
• Advantages
– No tolerance drift

1
+ C
2
+ C
3
1111 C
0
+ C
1
+ C
2
+ C
3
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Take Advantage of Symmetry
SREG
X[k]
SREG
SREG
• Real filters are
symmetric
• Add bits with
like coef’s before
filtering
• Uses Serial
Adders
• Halves taps
SREG
SREG

k-4
C
4
+…
Y
n+4
= a
k+4
C
0
+a
k+3
C
1
+a
k+2
C
2
+a
k+1
C
3
+a
k
C
4
+…
Y
n+8
=a