IEEE Solid-States Circuits Magazine - Fall 2020 - 24

in the electrical domain, it is related
to propagation constant b , represented as [43]

The loss of passive channels forms the
fundamental limit to maximum communication
distances and the supportable bandwidths for
relatively long distances.
and a hollow-plastic-cable-based
link with 3.3 Gb/s across 7.6 m [34].
To facilitate integrated solutions for
small factors and high bandwidth
densities, silicon-compatible and
integrated packaging-based low-loss
silicon dielectric waveguide (DWG)
schemes have also been developed
[35]-[40]. We have devised the first
high-resistivity, silicon-based DWG
with a loss of <0.014 dB/mm and a
3-dB bandwidth across 50 GHz [40].
This performance relieves the system link budget by more than 60 dB
for a 1-m communication distance,
compared to both wireless and conventional wireline counterparts. Therefore, the energy efficiency based on
the low-loss DWG can be significantly
boosted; for example, our first integrated sub-THz interconnect systems to support both single channels
and orthomode channels, shown

Transmitter

2

in Figure 4, have demonstrated an
energy efficiency of 0.32 and 0.64
pJ/b, respectively [41], [92].

Dispersion: The Ultimate
Devil for Loss-Low Channels
Up to the Meter Reach
Low-loss media extend communication
distances for wide-bandwidth wireline
applications. However, for commu-
nication distances shorter than a few
meters, the interconnect bandwidth is
instead constrained by the dispersion.
One key component that causes dispersion is the channel, which triggers
waveguide and material dispersion
that leads to a frequency-dependent
dielectric constant or a reflective
index [42]. Channel dispersion is
quantified by dispersion coefficient
D, with the unit of ps/ ^km $ nmh. In
the optical domain, dispersion coefficient D is related to reflective index n;

Sub-THz Channel

2
2rc 0 d b
D = - m d n2 or D = c 0 dm
m 2 d~ 2
	
2
2
d b
=- ~
,
(2)
2rc 0 d~ 2

where c 0 is the speed of light in the
vacuum and m and ~ are the corresponding signal wavelength and
radian frequency, respectively. These
two representations are the same but
have different formats suitable in the
corresponding fields.
Dispersion causes group delay
variation (GDV), meaning different
frequency signals traveling at different speeds, thus resulting in wideband signal spreading in the time
domain and causing intersymbol
interference. The GDV, ∆t g , is proportional to dispersion coefficient
D, communication distance L, and
signal bandwidth ∆m or ∆f , formulated as
d2 b
	Tt g = DLTm or Tt g = 2r
LTf.
d~ 2
(3)

Receiver

(a)
Receiver

670 µm

Buffer
Det

in1

on1

220 µm

in2
760 µm
(b)

OMT
With Baluns

Top p1
View
p2
Bottom
View

8 mm
Trench
Reflector

p4
p3

5 mm

op1

1,400 µm

on2

350 µm

op2

180 µm
Oscillator
Modulator

110 µm

810 µm

Transmitter

16 mm

FIGURE 4: (a) A single-channel sub-THz link based on a near-field-coupling silicon DWG [92]. (b) A dual sub-THz channel through the same
physical link based on an orthomode silicon DWG [41]. OMT: orthomode transducer. in1: first transmitter data input; in2: second transmitter
data input; op1 and on1: first receiver output differential data; op2 and on2: second receiver output differential data.

24	

FA L L 2 0 2 0	

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IEEE Solid-States Circuits Magazine - Fall 2020

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