BLIND CORRECTION OF GAIN AND TIMING MISMATCHES
FOR A TWO-CHANNEL TIME-INTERLEAVED
ANALOG-TO-DIGITAL CONVERTER
1 inch
1cm
Munkyo Seo, Mark Rodwell, Upamanyu Madhow
Department of ECE, University of California, Santa Barbara, CA 93106
Email: {mkseo, rodwell, madhow}@ece.ucsb.edu
1cm
analog
input
digital
output
ADC 1
How to MEASURE
Mismatches?
Challenge: Mismatches
Why Time-Interleaving?
1 Samples@ t= 1, 2, 3,…
2 Samples@ t=0.8,1.8,2.8,…
1 Gain= 1.0
2 Gain= 1.2
(1) Training method
(off-line)
G=?
∆t=?
ADC 2
Training signals
1
2
1
2
1
2
1
2
Sampling Rate = Nchannel (Unit Sampling Rate)
(2) Blind method
(online)
Analog
Circuitry
1
2
Drift, process variation 
1
1
2
2
(2) Digital post-correction
1
No interruption 
System interruption 
Calibration detuning 
Good accuracy 
Mismatches creates distortion.
Must correct these!!
(1) Analog pre-correction
?? Unknown input ??
1 2 1 2 1 2 1 2
1 2 1 2 1 2 1 2
How to CORRECT
Mismatches?
Digital
Filter
2
Tracks time-varying error 
Reliable, flexible, scalable 
Compromised accuracy 
1cm
1
2/1
2
(∆G0, ∆t0)
2/1
Parameterized
Filter Bank
(∆G, ∆t)
(∆G0, ∆t0)
Find (∆G, ∆t) such that output auto-correlation
is shift-independent.
It can be shown, NO FALSE CORRECTION
(i.e., such (∆G, ∆t) is unique)
10
10
10
10
10
10
10
10
10
10
∆G= ±10%
14-b A/D boards
Signal
∆t= ±5%
Nsample=102~106
100 MSPS
ADC chip
Filter
Summary
Logic Blind Mismatch
analyzer Correction
√
Clock
0
Filter
 G (uncorrect ed)
-1

~

 G G , ' WIDE'
-2
-3


~
 G G , ' SINE'
-4
-5
10
10
Experimental Result
2
10
3
0
10
4
10
Nsample
5
10
6
Amplitude (dB)
Normalization
10
Standard deviation
Assume Wide-Sense Stationary (WSS) input.
Let’s restore output WSS
30 Monte-Carlo runs
Input: ‘SINE’, and ‘WIDE’
Standard deviation
Mismatch yields “uneven” output
Simulation Result
 G (uncorrect ed)
-1

~

-3

~

 G G , ' SINE'
-4
-20
-20
-40
_X
O
2
4
6
Z
-100
-120
0
-40
20
40
5
7
3
-80
Y
8
60
-100
80
100
-120
0
2
10
3
10
Nsample
4
10
√ Proposed blind method
Generality
Unified framework
_X 2
4
6
Z
20
40
5
7
3
Y
8
60
O
80
100
√ First Uniqueness proof
(for M=2)
√ Simulation / Experiment
80
60
1 2 1 2 1 2
40
-5
10
2
-60
-60
-80
0
After cal.
After Blind
Calibration
1
100
 G G , ' WIDE'
-2
0
Before cal.
Before Blind
Calibration
1
1
SFDR
SFDR (dB)
Proposed Blind Algorithm
1cm
5
10
6
20
0
0.1
0.2
0.3
0.4
0.5
WSS assumption invalid
Algorithm fails