Transcript Single Frequency SAW Tag Example

Passive, Wireless, Orthogonal
Frequency Coded SAW Sensors
and Tags – Design and System
D.C. Malocha, D. Puccio, and N. Lobo
School of Electrical Engineering & Computer Science
University of Central Florida
Orlando, Fl 32816-2450
Acknowledgements: Funding has been provided through the NASA STTR
grants program with industry partners of MSA and ASRD, and through the
NASA Graduate Student Research Program.
Orthogonal Frequency Coded
(OFC) SAWs
• Multiple access operation
• Improved range due to enhanced
processing gain
• Increased sensitivity resulting from
reduced compressed pulse time ambiguity
• Fractional bandwidth can meet ultrawideband (UWB) specifications
• Inherent security using spread spectrum
OFC/PN Background:
Spreading and Coding a Signal
• Given a signal bit length = τB
• To code a bit, divide the bit into N chips, such that,
τB = N·τC
• For a pseudo noise PN sequence, there is a single
carrier frequency but the phase within a chip
changes.
• For OFC-PN, the chip carrier frequency is a
variable and the chip phase is also a variable.
Background:
Orthogonal Frequency Theory
Consider the time-limited nonzero function defined by
t
h(t )   an  n (t )  rect   where
 
n 0

1,
 n t 
n (t )  cos 
,
rect(
x
)



  

0,
N
The members of the basis set, n , are orthogonal if

Kn ,
 n (t ) m (t ) dt  0,

2
1
2
otherwise
x
nm
nm
2
Two functional forms are obtained
 2n   t 
t
h1 (t )   an  cos 

rect

 
  
 
n 0
N
 (2m  1)   t 
t
h2 (t )   bm  cos 

rect

 



 
m0
M
Brief Background
• Single frequency tag
• OFC tag
Single Frequency SAW Tag
Example
• N single frequency bits implemented with N inline reflectors
• Bit locations and phases indicate identification and/or sensor
information
• Impulse response is series of decaying pulses
• All reflectors have same reflection coefficient
• Multiple reflections ignored in analysis
• Optimal chip reflection
coefficient maximizes
power received from last
chip
• Optimal chip reflection
coefficient defined as
Power received from last bit, Plast (%)
Single Frequency SAW Tag Optimal Reflection Coefficient
N=8
N = 12
N = 16
2.5
2
1.5
1
0.5
0
0
10
20
30
40
50
60
70
80
90
100
Reflection coefficient, R (%)
-8
Ropt ( N )  (2N 1)1
-10
-12
Power received
from last bit (dB)
• Power received from last
chip decreases as chip
count is increased given
Ropt
3
-14
-16
-18
-20
-22
-24
0
5
10
15
Bit count, N
20
25
30
Magnitude (Linear)
Schematic
OFC
ID Tag
Example:of
OFC
BitSAW
– 7chips/bit
0.8
0.6
f1
f4
f2
f6
f0
f5
f3
0.4
0.2
0
0
0.2
0.4
Piezoelectric Substrate
0.6
0.8
1
1.2
Normalized Frequency
1.4
1.6
1.8
1
Chip length
0.5
0
Bit Length
0.5
1
0
1
2
3
4
Normalized Time (Chip Lengths)
5
6
7
Approach
• Study a methodology to optimize reflective
structures for OFC devices
– Minimize device insertion loss
– Maintain chip orthogonality
– Find optimum values for bit length, chip
length, and strip reflectivity as a function of
device fractional bandwidth
– Maintain processing gain
– Minimize ISI effects
Boundary Conditions for Analysis
• Assume only a single in-line grating
analysis.
• Assumes no weighting within each
reflective region which composes a chip.
• First order assumptions are made to
understand the phenomenon and verified
by COM models and simulation.
• Multiple parallel tracks can be approached
in a similar manner.
SAW OFC Reflector Coding
• SAW device implementation of the ideal OFC code
using a reflective structure assumes that the ideal
chip can be accurately reproduced by a reflector
– Chip frequency response: Sin(x)/x
– Chip time response: Rect(t/chip)
– Uniform amplitude of chips for maximum coding,
processing gain (PG) and correlation output.
• To what degree can all of the above be achieved
versus design parameters
Intra-chip & Inter-chip Reflector
Considerations
• Chip reflector uniformity for OFC coding
• Intersymbol interference (ISI) – the intra
reflections ring longer than c
• Energy rolloff due to propagation through chips
– Processing gain decrease
– Coding diversity loss
– Orthogonality
• Chip processing gain due to reflector response
• Frequency & time domain distortion
OFC Reflector Bank Uniformity
fc *c  Nc
f1
c  constant
f4
f2
f6
f0
f5
f3
OFC Reflector Responses
0
fc=chip
frequency
determined by
orthogonality
Reflection Magnitude (dB)
-5
-10
-15
-20
-25
-30
-35
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
Normalized Frequency
As fc increases, Nc increases and chip
reflectivity increases
Response of Reflector Test Structure
0.5
-10
Measured response
Predicted-fit
Direct SAW
response
-20
0.4
Reflector
response
-30
|R|
dB (s21)
0.3
-40
-50
0.2
-60
0.1
-70
0
64
65
66
67
Frequency ( MHz )
68
69
-80
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (s)
Under proper conditions, a SAW reflector looks similar to a
Sampling function in frequency and a Rect function in time.
Reflectivity is a function of the substrate and reflector
material, reflector film thickness, substrate coupling coefficient
and line-to-width ratio. The reflector width is approximately
the chip length. How approximate is it???
Simulation of a reflector grating frequency response for
1% reflectivity per strip, and 4 different grating lengths.
Ng equals the number of reflective strips in each grating.
0
Ng=25,
Ng=50,
Ng=100,
Ng=200,
Magnitude (dB)
10
Ng*r=0.25
Ng*r=0.5
Ng*r=1.0
Ng*r=2.0
20
30
40
50
0.9
0.93
0.97
1
Normalized Frequency
1.03
1.07
1.1
Plot of magnitude of reflectivity
versus the product of the number of
strips and reflectivity per strip (Ng.r).
For small reflector loss, chip reflectivity, Ng.r,
should be large but for reasonable sin(x)/x
frequency response, Ng.r product should
definitely be less than 2.
OFC Adjacent Frequency Reflection
• OFC yields reduced reflections between
reflectors compared to single frequency
PN due to orthogonality
• Non-synchronous orthogonal frequencies
are partially reflected
• The closer the adjacent frequency chips
the greater the partial reflection
• Must understand non-synchronous
reflectivity for all chips
Adjacent Frequency Reflection
• Assume an RF burst near
fo as interrogation signal
• Very small reflection of
incident adjacent
frequency RF burst from
weak reflector
• Large adjacent frequency
reflection from strong
reflector
• Transmission through the
reflector bank can be
compromised if chip
reflectivity is too large
which causes energy
rolloff for trailing chips.
1
Reflected Pulse Response
Reflector Response
RF Burst Response
0.8
0.6
Small
Reflectivity
0.4
0.2
0
-0.2
-0.4
0.8
0.85
0.9
0.95
1
1.05
Normalized Frequency
1.1
1.15
1.2
1
Large
Reflectivity
0.8
0.6
0.4
0.2
0
-0.2
Reflected Pulse Response
Reflector Response
RF Burst Response
-0.4
-0.6
0.985
0.99
0.995
1
1.005
Normalized Frequency
1.01
1.015
Frequency Transmission vs Reflectivity
as a Function of Frequency Offset
fSAW is the synchronous
reflector of interest
fn
is a prior asynchronous
reflector in bank
High center frequencies
1
0.9
0.9
Transmission coefficient, T
adj
Transmission coefficient, T
adj
Low center frequencies
1
0.8
0.7
0.6
0.5
0.4
0.3
-1
0.2
fref = f0 - 1
0.1
fref = f0 - 2-1
0
0
fref = f0 - 3-1
2
rNg
4
6
For 90%
transmission,
r*Ng<2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
fref = f0 + 1-1
0.1
fref = f0 + 2-1
0
0
fref = f0 + 3-1
2
rNg
4
6
• COM simulations used to determine non-synchronous reflector
transmission coefficient
• Analysis performed for reflector center frequencies 1,2,3 orthogonal
frequencies higher and lower than incident wave
OFC Adjacent Reflectivity
-1st Order Analysis
• Several assumptions made to simplify
analysis
– Use chirp interrogation signal & OFC reflector
– All reflectors have equal reflectivity
– No propagation loss
– Multiple reflections ignored
– Only adjacent frequency reflector
transmission coefficients considered
Adjacent Frequency Reflector
Transmission Example
f7
f6
f5
f4
f3
f2
f1
f3
f6
f4
f7
f1
f5
f2
Reflectors
SAW
Substrate
Interrogation
Frequency
Adjacent
Frequency
Interactions
1
2
3
4
5
6
7
Sum
0
2
0
1
2
0
1
6
Independent of the OFC
frequency code sequence, the
sum of the adjacent frequency
interactions is always equal to
Nf-1, but the interactions for a
given frequency is code
dependent.
Total Reflected OFC Power
Equations defined to relate several OFC
reflector bank parameters
– Ptot= total output Ptot   R0  1  R0 2b2  Tadj4b4  1   N f  1  Tadj2 


power
b 1
– Tadj=adjacent center
frequency
transmission
1.437 tanh 2 0.3771 r  N g  r  N g  2



– Ro=chip reflectivity R0  
1.4
2 
tanh 0.3771 r  N g   r  N g  2

– r= electrode



2
reflectivity
 rN g 


Nf
– Ng= # of reflector
 6.231 
Ng 
Tadj  e
chip electrodes
% BW
– Nf= # of frequencies
B
Example Reflected Power Prediction
-2
Reflected Power (dB)
• 10% bandwidth
• 2% electrode
reflectivity
• No repeated
frequencies
• Predictions compared
with COM simulations
• Large variations
caused by multireflection interference
0
-4
-6
-8
-10
-12
-14
-16
0 (0mm)
Predicted reflection using equation
Predicted reflection using COM simulation
5 (0.44mm)
10 (1.74mm)
15 (3.92mm)
20 (6.98mm)
25 (10.9mm)
Number of Frequencies (1 GHz bank size on YZ lithium niobate)
Approximate analysis and
COM model agree well for
Nf<10. Optimum reflected
power for 10<Nf<15.
Optimal Reflection Coefficient
Reflected Power (%) for BW=10%
30
60
25
50
20
40
15
30
20
10
10
5
0.5
1
1.5
2
2.5
Strip Reflectivity (%)
3
30
Number of Frequencies
Number of Frequencies
Reflected Power (%) for BW=5%
50
25
40
20
30
15
20
10
10
5
0.5
1
1.5
2
2.5
3
Strip Reflectivity (%)
• Reflected power for 5% and 10% fractional bandwidths
• Optimal empirically derived relationship for # of frequencies (Nf), strip
reflectivity (r) and %BWbit:
Nf  2.6 * %BWbit / r
• White line indicates maximum reflected power
• Total reflected power is maximized for R0 ~ 80%
Check for Self-Consistence
•We now have 2 equations for Nf where the first equation is exact and
the second is approximate based on optimization of parameters.
Nf  %BWbit /(2 * %BWchip)
Nf ~ 2.6 * %BWbit / r
•Substitute r=1.4/Ng for 80% reflectivity (%BW=5) and the exact
expression for Nf as a function of fractional bandwidths, which yields:
%BWbit /(%BWchip) ~ 2.6 * %BWbit * Ng / 1.4
• The number of strips in the reflector is given by: Ng=(2*%BWchip)-1
•Solving both sides of the equation yields:
1 ~ 2.6/2.8
The predictive analysis seems reasonable with the
various assumptions made.
Reflector Test Structure Time Response
-10
Direct SAW
response
-20
Reflector
response
dB (s21)
-30
-40
-50
-60
-70
-80
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (s)
How is the time response affected by chip length and
reflectivity. How approximate is the time domain reflector
compared to a Rect function???
Simulation of a SAW grating time response for
1% reflectivity and 4 different grating lengths.
1
Magnitude
Ng=25,
Ng=50,
Ng=100,
Ng=200,
Ng*r=0.25
Ng*r=0.5
Ng*r=1.0
Ng*r=2.0
Time scale is normalized
to reflect the number of
wavelengths at center
frequency
0.5
0
0
0.25
0.5
0.75
1
1.25
Relative time
1.5
1.75
2
2.25
2.5
2.75
3
1. Impulse response
length of reflector
increases beyond desired
chip -ISI
(Normalized to Ng*r)
Magnitude (dB)
0
Ng=25,
Ng=50,
Ng=100,
Ng=200,
As Ng*r increases:
Ng*r=0.25
Ng*r=0.5
Ng*r=1.0
Ng*r=2.0
2. Energy leakage
beyond desired chip
increases- energy loss
20
40
0
0.25
0.5
0.75
1
1.25
Relative time
1.5
1.75
(Normalized to Ng*r)
2
2.25
2.5
2.75
Ng*r=1 appears to be
maximum for minimum ISI
3
Chip Correlation with Synchronous
Interrogator Pulse
Magnitude (dB)
0
Correlation is
greater than
ideal, IR length is
near ideal and
sidelobes are
low.
Correlation for Ng*r=.25
Ideal Correlation
10
20
30
40
50
1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
Relative Tim e (Norm alized to Ng*r)
Magnitude (dB)
0
Correlation is
greater but
sidelobes
apparent due to
intra-chipreflections
Correlation for Ng*r=1.0
Ideal Correlation
10
20
30
40
50
3
2
1
0
1
Relative Tim e (Norm alized to N g*r)
2
3
Chip Correlation with Adjacent Frequency
Asynchronous Interrogator Pulse
Magnitude (dB)
0
Near ideal
response.
Correlation for Ng*r=.25
Ideal Correlation
10
20
30
40
50
1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
Cross correlation
shows null at chip
center, as
expected due to
OFC properties.
Relative Tim e (Norm alized to Ng*r)
Magnitude (dB)
0
Correlation for Ng*r=1.0
Ideal Correlation
10
20
30
40
50
3
2
1
0
1
Relative Tim e (Norm alized to N g*r)
2
3
Cross correlation
shows reduced
null at chip center,
and trailing
correlation
sidelobe
distortion.
Measured Device Example
•
•
•
•
•
•
•
fo= 250 MHz
%BW=28%; BW=69 MHz
YZ LiNbO3, k2=.046, r~3.4%
(# frequencies) = (# chips) =7
# of reflectors at fo = 24
c ~ 98 nsec
Ng*r ~ .72
Chip reflector loss~4dB
COM Simulation versus
Experimental Results
f3
f5
f0
f6
f2
f4
f1

f1
f4
f2
f6
f0
f5
f3

Piezoelectric Substrate
COM predictions
Dual delay OFC
device having two
reflector banks and
7 chips/bank
Experimental Measurement
General Results and Conclusions
• Various OFC chip criteria were investigated to provide
guidance in choosing optimal design criteria.
• The ISI and pulse correlation distortion appear to be a
limiting or controlling factor for maximizing the chip
reflectivity and suggests Ng*r<1.
• For Ng*r=1, chip reflector loss is approximately 2.5 dB.
• Based on reflective power predictions and simulations, the
largest number of chip frequencies should be between 10
and 15, with the precise number of frequencies dependent
on the bit fractional bandwidth and strip reflectivity.