Single-Step Tunable Group Delay Phaser for Real-Time Spectrum Sniffing

0.44 MB·English

by  Tongfeng Guo

1
Single-Step Tunable Group Delay Phaser
for Real-Time Spectrum Sniffing
Tongfeng Guo, Qingfeng Zhang, Yifan Chen, Rui Wang, and Christophe Caloz
Abstract—This paper presents a single-step tunable group
delay phaser for spectrum sniffing. This device may be seen τ
as a “time filter”, where frequencies are suppressed by time
separation rather than by spectral attenuation. Compared to its τN
multiple-stepcounterpart,thisphaserfeatureshigherprocessing
5
1 resolution, greater simplicity, lower loss and better channel τi
equalization, due to the smaller and channel-independentgroup
0
delayswing.Athree-channelexampleisprovidedforillustration.
2 τ2
n Index Terms—Phaser, time filtering, tunability, group delay, τ1
spectrum sniffing, real-time analog signal processing (R-ASP).
a
J ω1 ω2 ωn ωN ω
(a)
3 I. INTRODUCTION τ
2 reconfigurable state
Real-timeanalogsignalprocessing(R-ASP),inspiredbyul- τ1

] trafastopticsandsurfaceacoustics,exhibitsremarkableadvan-
s
tages over digital signal processing in some applications [1],
c
i such as for instance fast and low-cost spectrum analysis [2]–
t ω
p [4], pulse compansion [5] and spectrum sniffing [6]. ω1 ω2 ωn ωN
o Real-time spectrum sniffer, as a typical R-ASP system, (b)
.
s is particularly promising for cognitive radio [7]. The key
c Fig. 1. Comparison of the group delay responses of(a) a stair-case group
componentofthereal-timespectrumsnifferisaphaser,which
i delayphaser[6]and(b)theproposedsingle-steptunablegroupdelayphaser
s exhibitsastair-casegroupdelayresponseversusfrequency[6]. foranN−channelspectrum sniffer.
y
Different temporal frequencies of the multi-tone input pulse
h
p are subsequently separated in time due to the differentdelays
[ they experience. However, the design complexity of the stair- involves challenging phaser design due to increasing group-

casephasergreatlyincreasesasthechannelnumberincreases. delay-bandwidthproductwith increasing numberof channels.
1
v We propose here a single-step tunable group delay phaser Increasing group delay also leads to increasing loss, as loss
0 for enhancedreal-timespectrumsniffing.Thisphaser features is inversely proportional to group delay, and therefore harder
5 lower design complexity and improved system performance channel discrimination due to lower signal-to-noise ratio.
7 compared to [6]. The proposed single-step tunable group delay response,
5
0 showninFig.1(b),overcomestheaforementionedissues.Itis
. II. PRINCIPLE composed of a number of reconfigurablestates corresponding
1
tothenumberofchannels,eachofwhichexhibitsasinglestep
0 Figure 1(a) shows an N-channel stair-case group delay
5 response, where different delays τ1,τ2,...,τN corresponds group delay response centered at frequency ωn and therefore
1 to different channels centered at ω1,ω2,...,ωN. The signals discriminating channel n from the others. In contrast to the
: staircase case, the average group delay is the same for all
v in different channels experience different delays through the
i phaser, and therefore get separated in time. For complete the channels, so that all the channels are on an equal footing
X
from the viewpoint of loss, if one (reasonably) ignores the
separation, the delay step should comply with the uncertainty
ar principle[8]:τn−τn−1 ≥2π/[ωn−ω(n−1)].Themainbenefit loss difference due to frequency-varyingdielectric and ohmic
of stair-case group delay sniffing is its instantaneous channel losses. The single-step tunable response also leads to simpler
phaser design for a given resolution since each single step
discrimination following from the fact that all the chan-
in Fig. 1(a) can easily be designed to provide a larger group
nels are processed simultaneously. However, this approach
delay swing than the individual steps in Fig. 1(a). The only
Manuscriptreceived Jan.23,2015. disadvantageoftheproposedapproachliesinthelimitedspeed
T.Guo,Q.Zhang,Y.ChenandR.WangarewiththeDepartmentofElectri- duetotherequirementofstateswitching;itisthusonlyaquasi
calandElectronic Engineering,SouthUniversityofScienceandTechnology
real-time technique.
ofChina,Shenzhen, Guangdong, China, Email:[email protected].
C. Caloz is with the Department of Electrical Engineering, Poly-Grames The single-step group delay response of a given state in
Research Center, E´cole Polytechnique de Montre´al, Montre´al, QC, Canada
Fig. 1(b) is very similar to the magnitude response of a
H3T 1J4. C. Caloz is also with King Abdulaziz University, Jeddah, Saudi
Arabia. magnitudefilter. However,thetwo devicesoperateina totally
2
ω1,ω2,ω3 |S21| ω2 λ/2 λ/2 λ/2 λ/2
Filter J1 J2 J3 Jn O.C.
t t
ω
ω1 ω2 ω3
InputSignal Device OutputSignal
ω1,ω2,ω3 τ21 ω1,ω3 ω2 (a)
Phaser λ/4 λ/4 λ/4 λ/4 λ/4 λ/4
t t J1 C1 J2 C2 Jn Cn O.C.
ω
ω1 ω2 ω3 C1
C2
Fig. 2. Comparison between theoperation principles ofafilter, essentially Cn
featuringaselectivemagnituderesponse,andtheproposedphaser,essentially
(b)
featuring aselective delayresponse.
Fig. 3. Circuit model and microstrip reflection-type implementation ofthe
proposedphaser:(a)staticcase,(b)tunable case.
different fashion, as illustrated by Fig. 2. The figure uses a
three-tone pulse and bandpass filter example, where pulses of functions
central frequencies ω1,ω2,ω3 are presented to the bandpass λ/4 λ/4 −tan πω
filter; energies centered at ω and ω are attenuated whereas (cid:18)ω0(cid:19)
1 3
that of ω2 is transmitted, as shown in the top part of the Yin J C
2ωC2Z0
figure. In contrast, the phaser delays the unwanted spectral
content by a lower amount than the wanted contents instead
of suppressing it, as shown in the bottom part. The spectrum C2>C1>0
centered at ω is delayed more than the spectra around ω , ω2<ω1<ω0
2 1 2ωC1Z0
leading to time discrimination. The undesired channels may
thenbesuppressedusingdynamicthresholdingortimegating.
ω
0 ω20 ω2 ω1 ω0
III. PHASERDESIGN
Fig. 4. Effect of capacitance variation on the resonant frequency of the
Severaltypesofphasers,includingreflectiontype[9],cross- loadedtransmissionlineresonators inFig.3.
coupled transmission type [10] and all-pass C-section type
[11], can provide the group delay responses in Fig. 1. Here,
we use a reflection-type phaser implemented in microstrip tunable capacitances, which results in tunable resonant fre-
technology, featuring simple architecture and easy tuning quencies. The relation between the inserted capacitance and
compared with cross-coupled and C-section phasers. theresonantfrequency,ω ,iscomputedbyanalyzingtheinput
0
admittance Y of the resonator element in the inset figure of
in
A. Static Case Fig. 4. The resonance occurs when Yin =0, which leads to
Figure 3(a) shows the J-inverter circuit model of a πω
−tan =2ωCZ . (1)
reflection-type phaser, which is a dual circuit of that used (cid:18)ω (cid:19) 0
0
in[9].TheJ-inverterandtheopenendinFig.3(a)correspond
No closed-form solution is available for the above equation.
to the K-inverter and short end in [9], respectively. All the
However, it can be solved graphically by finding the inter-
invertersareconnectedby half-wavelengthtransmissionlines,
ception point of two curves corresponding to the left-hand
which act as resonators. The circuit is implemented by edge-
and right-hand sides of (1), as shown in Fig. 4. Note that as
coupled transmission lines, where edge coupling is modeled
the capacitance increases, the resonance frequency decreases.
bytheJ-inverter[12].Theclosed-formsynthesismethodof[9]
The resonant frequency is thus inversely proportional to the
canbedirectlyappliedtothecircuitinFig.3(a).However,the
capacitance. Also note that the resonant frequency is nonlin-
circuit in Fig. 3(a) is a static circuit, and should therefore be
earlyrelatedtothecapacitance,duetothenonlinearfunctions
slightly modified to achieve tunability.
constituting the left-hand side of (1). This nonlinear effect is
increasingly notable for increasing capacitance.
B. Tunable Case
Thedesignprocedurecomprisesthefollowingsteps.Firstly,
Figure 3(b) shows the circuit model and implementationof one synthesizes the static circuit in Fig. 3(a) for a specified
the tunable version of the phaser, where varactors have been single-step group delay in one channel using the closed-
added to the middle part of the half-wavelength transmission form technique provided in [9]. One subsequently applies
line. These varactors, biased by different voltages, provide the synthesized parameters to Fig. 3(b) with a set of chosen
3
20.31 17.19 19.5 Circuit Full-wave Measured
16.67 16.93
C1 C2 C4 State1 State2 State3
C3
wgaidpt=h0=.02.362 gwaipd=th0=.317.67 gwaipd=th1=.117.67 gap=0.5616.67 1.67 )sn(
Unit:mm width=1.67 length=7.07 ya
le
d
p
Fig.5. Photograph (topview)ofthefabricated prototype. u
o
rG
TABLEI
CAPACITANCESINDIFFERENTSTATES(UNIT:PF). f1 f2 f3
channel channel channel
OperationState C1 C2 C3 C4
state1 51 47 75 10 Frequency (GHz)
state2 4 5 5 6.2
state3 2 2 2 2.2 Fig. 6. Full-wave and measured group delay responses of the proposed
phaser(f1=2.3GHz,f2=2.5GHz,f3=2.7GHz).
capacitances. One may locally tune and optimize the initial f1′,f2′,f3′ f1′ :2.25GHz f3′ :2.65GHz
parametersandthecapacitancestobetterfitthespecifiedgroup v) f2′ :2.45GHz
(
delay response. The same procedure is repeated for all the Vin
channels with the same circuital parameters but different sets Vin PhaserinFig.6 Vout
of capacitances.
Time(ns)
IV. DESIGN EXAMPLE )v f1′ )v f2′ )v f3′
( ( (
To illustrate the proposed system, consider a three-channel Vtuo Vtuo Vtuo
example, with 20 MHz channel bandwidths centered at 2.3, state1 state2 state3
2.5, and 2.7 GHz. For these parameters, the group delay
Time(ns) Time(ns) Time(ns)
step should be larger than 5 ns, according to the uncertainty
principle [8]. For proof of concept, we employ three groups Fig. 7. Responses of the spectrum sniffer based on the fabricated phaser
shown in Fig. 5 and characterized in Fig. 6. A channel frequencies shift of
of static capacitors instead of varactors.
0.05GHzwasintroduced foralignment andcomparisonwithexperiments.
Figure 5 shows the fabricated prototype, where the sub-
strate is Rogers RO4350 (εr = 3.66,tanδ = 0.004) with
thickness 0.762 mm, and the capacitors are GQM18 series [3] J.D.Schwartz,J.Azan˜a,andD.Plant,“Experimentaldemonstrationof
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are listed in Tab. I. The synthesized and measured group
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delay responses are shown in Fig. 6. Note that the measured spectrum analyzer (RTSA)based onthe spectral-spatial decomposition
results are in reasonable agreementwith full-wave and circuit property ofleaky-wave structures,” IEEETrans.Microw. TheoryTech.,
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