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
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
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
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
Notas do Editor
simplify
animate
Introduce the concept of butterworth filter and other filter types, IPM/constant-k
Show a unit cell and the energy that its stored and also show these on aFosters reactance theoremEnergy delay
Add linear filter conceptAdd bode plot and polar plotExplain the tp/tp ratio.Sinh(f) still trueN=3 Butterworth n=2, bessel filter, all linearTransmission line = n=infinity LP filter with infinite bandwidthIntroduce the time constants soonerSum of time constantsMatching condition is for matching, and to prevent stopbandsNRI-TL length reduction and Q
Add legend, use colorAnimate
labels
Show design equations
Label bandwidth, show networkslegnds
Label bandwidthsShow network
Label bandwidthsShow the cascade of two ngd unit cells