masters thesis defense - broadband negative group delay phase shifters

1. Broadband Microwave Negative Group Delay
Transmission Line Phase Shifters
Sinan Keser
M.A.Sc. Thesis Defense
October 1, 2012

2. Outline
• Introduction
• Background
• Loaded Transmission Lines
• Negative Group Delay (NGD) Phase Shifter Design
• Simulation & Experimental Results
• Conclusions
2

3. Phase shifters Basics
Transmission-type phase shifter
phase 𝜙 = arg 𝑆21
𝜙
phase delay 𝜏 𝑝 = −
𝜔
𝜕𝜙
group delay 𝜏 𝑔 = −
𝜕𝜔
𝜙 𝑡𝑜𝑙
phase BW Δ𝜔 ≈
𝜏 𝑔 𝜔0
3

4. 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).
4

5. Background – NGD Circuits
NGD & NRI Loaded TL Unit Cell NGD feedback Amplifier Microwave NGD FET Amplifier
Mojahedi, et al. (2004) Kandic, et al. (2011) 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
5

6. Background – Metamaterial TLs
Negative Refractive Index Composite Right/Left-Handed
Transmission Line (NRI-TL) Transmission Line (CRLH-TL)
Eleftheriades, et al. Caloz, et al.
 Passive
 Broadband
 Low Return loss
 Low Insertion loss
 Positive or Negative Phase Delay
… But Always Positive Group Delay
6

7. 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.
7

8. Loaded TL Unit Cell
Small host TL
𝜃 𝑇𝐿 ≪ 1
𝐿 𝑇𝐿 = 𝑗𝑍0 𝜃 𝑇𝐿
𝐶 𝑇𝐿 = 𝑗𝑌0 𝜃 𝑇𝐿
Balanced Condition
Metamaterial-TL (MTM-TL)
𝑍 𝑌
= ≪1
𝑍0 𝑌0 Loading Elements Host TL
0 𝑒 −𝑍 𝑍0
𝑆 𝑀𝑇𝑀 ≈ 𝑒 −𝑗 𝜃 𝑇𝐿
𝑒 −𝑍 𝑍0
0
Impedance matched
and Reciprocal
8

9. MTM-TL Characteristics
Equivalent TL
1
𝛾= 𝑍𝑛
𝑍0
𝑛
1
ln 𝑆21 = − 𝑅 + 𝑅2 + ⋯ + 𝑅 𝑛 • Insertion Losses add
𝑍0 1
1
𝜙21 = − 𝑋 + 𝑋2 + ⋯ + 𝑋 𝑛 • Phases add
𝑍0 1
1 𝜕𝑋1 𝜕𝑋2 𝜕𝑋 𝑛
𝜏𝑔 = + +⋯+ • Group delays add
𝑍0 𝜕𝜔 𝜕𝜔 𝜕𝜔
9

10. Lossless MTM-TL & Group Delay
• Lossless unit cells always have a positive group delay
proportional to the stored energy Wav (in reactive elements)
𝑊𝑎𝑣 1 𝜕𝑋
𝜏𝑔 = = >0
𝑎2 𝑍0 𝜕𝜔
Use 1st order MTM-TLs to minimize group delay
1
𝜔𝑐 = , 𝑍0 = 𝐿/𝐶
𝐿𝐶
10

11. Low-Pass & High-Pass S21 Responses
low loss
S21 Polar Plot
𝜔≫1
𝜙 𝐿𝑃 ≈ −𝜔/𝜔 𝑐 𝜔↑
𝜙 𝐻𝑃 ≈ 𝜔 𝑐 /𝜔 𝜔≪1
• 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.
11

12. Proposed NGD Unit Cell
S21 Polar Plot
NGD
𝑍 𝑌 𝐴
𝛾= = =
𝑍0 𝑌0 1 + 𝑗𝑄 𝜔 − 𝜔0
𝜔0 𝜔
𝑅𝑧 𝑍0 1 𝐿𝑧 𝐶𝑦 1 1
𝐴= = , 𝑄= = 𝑅𝑦 , 𝜔0 = =
𝑍0 𝑅𝑦 𝑅𝑧 𝐶𝑧 𝐿𝑦 𝐿 𝑧 𝐶𝑧 𝐿 𝑦 𝐶𝑦
12

13. NGD Unit Cell Phase and Magnitude Response
Δ𝜙 𝑝𝑝 = ILmax = 𝐴
𝜔0 𝐼𝐿 𝑚𝑎𝑥
Δ𝜔 𝑁𝐺𝐷 =
𝑄
𝜏 𝑔,𝑚𝑎𝑥 =2
Δ𝜔 𝑁𝐺𝐷
2𝐴𝑄
𝜏 𝑛𝑔𝑑 ,𝑚𝑎𝑥 =
𝜔0
13

14. Constant NGD with varying Insertion Loss
BW5
A=5dB
BW3
A=1dB
BW1 A=3dB
A=1dB
A=3dB
A=5dB
For a constant NGD, Bandwidth increases with increasing Insertion Loss
𝐼𝐿 𝑚𝑎𝑥
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Δ𝜔 𝑁𝐺𝐷
14

15. Maximum Return Loss per NGD unit cell
Return Loss vs. Frequency Max. Return Loss vs. Max. Insertion Loss
• 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.
15

16. 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
16

17. Simulated -300 NGD TL Phase Shifter
±20 phase bandwidth
Unloaded TL:105 MHz
NGD: 550 MHz
NGD NGD
Unloaded TL Unloaded TL
NGD Return Loss
• Return loss < 40dB
• Insertion Loss < 3dB
NGD
Unloaded TL
17

18. Simulated -900 (two-cells) NGD TL Phase Shifter
NGD NGD
unit cell unit cell
NGD NGD
Unloaded TL Unloaded TL
±50 phase bandwidth
Unloaded TL: 87 MHz
NGD: 650 MHz
NGD
Unloaded TL
NGD Return Loss
• Return loss < 37dB
• Insertion Loss < 8dB
18

19. -450 Two-Cell Stagger Tuned NGD Phase Shifter
NGD NGD
unit cell 1 unit cell 2
two-cell NGD unit cell 1 unit cell 2 Unloaded TL
±20 phase bandwidth
Unloaded TL: 105 MHz
NGD: 905 MHz
input port
output port
• Return loss < 33dB
• Insertion Loss < 4dB
• Low IL ripple
19

20. Hybrid NRI-NGD 00 Phase Shifter
±2o Phase bandwidth
NRI only: 79MHz
NGD-NRI: 553MHz
• 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
20

21. Beam Squint for a Linear Series-Fed Antenna Array
𝐴𝑟𝑟𝑎𝑦 𝐹𝑎𝑐𝑡𝑜𝑟 𝐵𝑒𝑎𝑚 𝑆𝑞𝑢𝑖𝑛𝑡
2𝑚𝜋
𝜕𝜃 𝜏𝑔 − 𝜏𝑝 +
= 𝜔
𝜕𝜔 𝜔𝑑 𝐸
𝑐 cos 𝜃
𝜕𝜃
to remove beam squint =0 :
𝜕𝜔
1) m=0 main lobe  NRI-TL
2) equal phase and group delay  NGD
±50 beam angle
Phase Shifter
Bandwidth
-3600 Unloaded TL 27 MHz
00 NRI –TL 122 MHz
Hybrid 00 NGD NRI-TL 607 MHz
21

22. 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
22

23. -300 NGD TL Phase Shifter (3dB loss)
component values
½Z Y
R 8Ω 156 Ω
L 1.5 nH 20 nH
C 16 pF 1.2 pF
23

24. -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
24

25. -300 NGD TL Phase Shifter (2dB loss)
component values
½Z Y
R 5.9 Ω 210 Ω
L 1 nH 33 nH
C 14 pF 0.8 pF
25

26. -300 NGD TL Phase Shifter (2dB loss)
Insertion Loss [dB]
Phase [deg]
Return Loss [dB]
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
26

27. 00 NGD NRI-TL Phase Shifter
component values
½Z Y NRI
R 10 Ω 100 Ω -
L 3.6 nH 30 nH 56 nH
C 11 pF 2.7 pF 27 pF
27

28. 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
28

29. 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.
29