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Broadband Microwave Negative Group Delay Transmission Line Phase Shifters
Sinan KeserM.A.Sc. Thesis Defense
October 1, 2012
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Outline
• Introduction
• Background
• Loaded Transmission Lines
• Negative Group Delay (NGD) Phase Shifter Design
• Simulation & Experimental Results
• Conclusions
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Phase shifters Basics
phase 𝜙 = arg 𝑆21
phase delay 𝜏𝑝 = −𝜙
𝜔
group delay 𝜏𝑔 = −𝜕𝜙
𝜕𝜔
phase BW Δ𝜔 ≈𝜙𝑡𝑜𝑙
𝜏𝑔 𝜔0
Transmission-type phase shifter
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Motivation
• Design a NGD network to cascade with an equivalently matched phase shifter with an equal but positive group delay to achieve a flat phase response (zero group delay).
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Background – NGD Circuits
NGD feedback Amplifier
Kandic, et al. (2011)
NGD & NRI Loaded TL Unit Cell
Mojahedi, et al. (2004)
Microwave NGD FET Amplifier
Ravelo, et al. (2007)
X Non reciprocal
X Narrowband
X High Return & Insertion Loss / Poor Efficiency
X Combining Gain and NGD into one stage is not beneficial
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Background – Metamaterial TLs
Negative Refractive Index
Transmission Line (NRI-TL)
Eleftheriades, et al.
Composite Right/Left-Handed
Transmission Line (CRLH-TL)
Caloz, et al.
Passive
Broadband
Low Return loss
Low Insertion loss
Positive or Negative Phase Delay
… But Always Positive Group Delay
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Proposal
• Design a broadband impedance matched loaded TL with a specified negative group delay, and:
– Determine relationship between NGD, Insertion Loss and NGD Bandwidth. (trade-offs)
– Minimize the frequency variation of both group delay and gain.
• Given the specifications of a phase shifter:
– Select either positive or negative phase delay on the basis of group delay minimization, and
– Combine with NGD unit cell to produce a zero group delay phase over a wideband.
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Loaded TL Unit Cell
𝑍
𝑍0=
𝑌
𝑌0≪ 1
Metamaterial-TL (MTM-TL)
𝜃𝑇𝐿 ≪ 1
𝐿𝑇𝐿 = 𝑗𝑍0𝜃𝑇𝐿
𝐶𝑇𝐿 = 𝑗𝑌0𝜃𝑇𝐿
Host TL Loading Elements
Small host TL
Balanced Condition
𝑆 𝑀𝑇𝑀 ≈ 𝑒−𝑗𝜃𝑇𝐿 0 𝑒−𝑍 𝑍0
𝑒−𝑍 𝑍0 0
Impedance matched
and Reciprocal
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MTM-TL Characteristics
ln 𝑆21 = −1
𝑍0
𝑅1 + 𝑅2 + ⋯+ 𝑅𝑛
𝜙21 = −1
𝑍0
𝑋1 + 𝑋2 + ⋯+ 𝑋𝑛
𝜏𝑔 =1
𝑍0 𝜕𝑋1
𝜕𝜔 +
𝜕𝑋2
𝜕𝜔 + ⋯+
𝜕𝑋𝑛
𝜕𝜔
• Insertion Losses add
• Phases add
• Group delays add
𝛾 =1
𝑍0
𝑍𝑛
𝑛
Equivalent TL
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Lossless MTM-TL & Group Delay
• Lossless unit cells always have a positive group delay proportional to the stored energy Wav (in reactive elements)
Use 1st order MTM-TLs to minimize group delay
𝜏𝑔 =𝑊𝑎𝑣
𝑎 2 =
1
𝑍0
𝜕𝑋
𝜕𝜔> 0
𝜔𝑐 =1
𝐿𝐶, 𝑍0 = 𝐿/𝐶
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Low-Pass & High-Pass S21 Responses
• The balanced NRI-TL is the combination of both low-pass and high-pass unit
cells (band-pass).
• To minimize its group delay, the host TL length should be minimized.
low loss
𝜙𝐿𝑃 ≈ −𝜔/𝜔𝑐
𝜙𝐻𝑃 ≈ 𝜔𝑐/𝜔
𝜔 ↑ 𝜔 ≫ 1
𝜔 ≪ 1
S21 Polar Plot
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Proposed NGD Unit Cell
𝛾 =𝑍
𝑍0=
𝑌
𝑌0=
𝐴
1 + 𝑗𝑄 𝜔𝜔0
−𝜔0𝜔
𝐴 =𝑅𝑧
𝑍0=
𝑍0
𝑅𝑦 , 𝑄 =
1
𝑅𝑧
𝐿𝑧𝐶𝑧
= 𝑅𝑦 𝐶𝑦𝐿𝑦
, 𝜔0 =1
𝐿𝑧𝐶𝑧=
1
𝐿𝑦𝐶𝑦
NGD
S21 Polar Plot
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NGD Unit Cell Phase and Magnitude Response
𝜏𝑔 ,𝑚𝑎𝑥 = 2𝐼𝐿𝑚𝑎𝑥
Δ𝜔𝑁𝐺𝐷
Δ𝜙𝑝𝑝 = ILmax = 𝐴
Δ𝜔𝑁𝐺𝐷 =𝜔0
𝑄
𝜏𝑛𝑔𝑑 ,𝑚𝑎𝑥 =2𝐴𝑄
𝜔0
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Constant NGD with varying Insertion Loss
A=3dB
A=1dB
A=5dB
A=5dB
A=3dB
A=1dB
For a constant NGD, Bandwidth increases with increasing Insertion Loss
BW1
BW3
BW5
𝐼𝐿𝑚𝑎𝑥
Δ𝜔𝑁𝐺𝐷= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
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Maximum Return Loss per NGD unit cell
Max. Return Loss vs. Max. Insertion LossReturn Loss vs. Frequency
• Return loss increases as Insertion loss increases
• For a low return loss, the insertion loss (and thus bandwidth-
NGD product) per unit cell must be kept sufficiently low.
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ADS Ideal Microstrip Simulation Setup
• NGD unit cell component values are determined by specifying the phase shifters 1. centre frequency, 2. characteristic impedance, 3. NGD (to produce zero group delay) and 4. maximum Insertion Loss.
TL lengths determine
phase delay
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Simulated -300 NGD TL Phase Shifter
±20 phase bandwidth
Unloaded TL:105 MHz
NGD: 550 MHz
• Return loss < 40dB
• Insertion Loss < 3dB
NGD
Unloaded TL
NGD
Unloaded TL
NGD
Unloaded TL
NGD Return Loss
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Simulated -900 (two-cells) NGD TL Phase Shifter
±50 phase bandwidth
Unloaded TL: 87 MHz
NGD: 650 MHz
• Return loss < 37dB
• Insertion Loss < 8dB
NGD
Unloaded TL
NGD
Unloaded TL
NGD
Unloaded TLNGD Return Loss
NGD
unit cell
NGD
unit cell
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-450 Two-Cell Stagger Tuned NGD Phase Shifter
±20 phase bandwidth
Unloaded TL: 105 MHz
NGD: 905 MHz
two-cell NGD unit cell 1 unit cell 2 Unloaded TL
• Return loss < 33dB
• Insertion Loss < 4dB
• Low IL ripple
input port
output port
NGD
unit cell 1
NGD
unit cell 2
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Hybrid NRI-NGD 00 Phase Shifter
• Combination of NRI (high-pass) and NGD (lossy
resonator) into one non-symmetric unit cell.
• Low return loss (< 20 dB) & Insertion Loss (< 2.5 dB)
• Reduced size & number of components
±2o Phase bandwidth
NRI only: 79MHz
NGD-NRI: 553MHz
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Beam Squint for a Linear Series-Fed Antenna Array
to remove beam squint :
1) m=0 main lobe NRI-TL
2) equal phase and group delay NGD
𝐴𝑟𝑟𝑎𝑦 𝐹𝑎𝑐𝑡𝑜𝑟 𝐵𝑒𝑎𝑚 𝑆𝑞𝑢𝑖𝑛𝑡
𝜕𝜃
𝜕𝜔=
𝜏𝑔 − 𝜏𝑝 +2𝑚𝜋𝜔
𝜔𝑑𝐸𝑐
cos𝜃
Phase Shifter±50 beam angle
Bandwidth
-3600 Unloaded TL 27 MHz
00 NRI –TL 122 MHz
Hybrid 00 NGD NRI-TL 607 MHz
𝜕𝜃
𝜕𝜔= 0
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Experimental Setup
Rogers RT Duroid 5880 substrate (εr=2.2)
– 50Ω Microstrip TLs
RF surface mount components (0402, 0603)
– Coilcraft ceramic inductors
– Murata ceramic capacitors
– Vishay thick film resistors
Modelithics component models
– Empirical data models
– Substrate scalable, pad dimension scalable
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-300 NGD TL Phase Shifter (3dB loss)
½ Z Y
R 8 Ω 156 Ω
L 1.5 nH 20 nH
C 16 pF 1.2 pF
component values
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-300 NGD TL Phase Shifter (3dB loss)
Summary• ±20 phase bandwidth: 610MHz – 1240MHz (63%)
450% increase over unloaded TL (14%)• Measured Insertion Loss < 3.1dB• Measured Return loss < 20dB
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-300 NGD TL Phase Shifter (2dB loss)
½ Z Y
R 5.9 Ω 210 Ω
L 1 nH 33 nH
C 14 pF 0.8 pF
component values
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-300 NGD TL Phase Shifter (2dB loss)
Summary• ±20 phase bandwidth: 680MHz – 1160MHz (51%)
364% increase over unloaded TL (14%)• Measured Insertion Loss < 2.12 dB• Measured Return Loss < 20dB• Less Ins. Loss but also less NGD bandwidth
Inse
rtio
n L
oss [d
B]
Ph
ase
[d
eg
]
Re
turn
Lo
ss [d
B]
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00 NGD NRI-TL Phase Shifter
½ Z Y NRI
R 10 Ω 100 Ω -
L 3.6 nH 30 nH 56 nH
C 11 pF 2.7 pF 27 pF
component values
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00 NGD NRI-TL Phase Shifter
Measured NGD NRI-TL
phase error (700MHz)
= +3.60
±20 phase bandwidth
NRI-TL: 71 MHz
NGD NRI-TL: 188 MHz
Measured
• Return loss < 14 dB
• Insertion Loss < 3.37 dB
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Conclusions
• Passive Broadband NGD Unit Cell Proposed– Frequency, Impedance and NGD scalable
– Quasi-linear phase at centre frequency
– NGD, Insertion Loss and Bandwidth trade-off identified
• NGD combined with lossless phase shifters to significantly increase phase bandwidth
• Beam Squint may only be removed entirely with NGD phase shifters.
• Experimentally verified microstrip NGD phase shifters with both positive and negative phase delays at 0.5GHz – 1.2GHz.