IEEE Solid-States Circuits Magazine - Fall 2020 - 25

Df =

Df =

1
or
SNR
d2 b
20
L
2r
10
d~ 2

1
Hz.
SNR
D m 2 L10 20
c0

(5)

Using a silicon DWG as an example, with f = 11.7, Figure 5 displays
the supportable bandwidth versus communication length due to
attenuation and dispersion, with the
assumption that D = 1ps/ ^km $ nm h,
a = 10 dB/m, and the carrier frequency is f0 = 300 GHz; the former
electronic system performances are
also supposed. Also, within a distance of less than 1 m, the supportable bandwidth constrained by the
attenuation is higher than 100 GHz.
The supportable bandwidth drops
exponentially by one order of magnitude per meter. For example, the
supportable bandwidth is >10 GHz
at a distance of up to 5 m. When
the distance is longer than 8 m,
the supportable bandwidth drops
below 100 MHz. The distance and
bandwidth product is one important
FOM to quantify link performance.
The FOM is determined by four factors: transmitter output power S,
receiver noise floor density N, target SNR, and channel medium loss
quantified by attenuation constant
a. The maximum transmitter output
power is governed by the semiconductor device capabilities, including the unit current gain frequency
(f T), maximum oscillation frequency
(fmax), breakdown voltages, and operating frequency.

100

80

60

Supportable
Bandwidth (GHz)

1
SNR
∆f
tb
=
= 10 20 and
∆t g
d2 b
2r
L∆f
	

d~ 2
2
2rc 0 d b
D =ps/ ^km $ nmh, (4)
m 2 d~ 2

The output power drops with the
rate by roughly 20 dB/decade versus the frequency increase [44].
Besides, due to parasitic effects and
stray power consumption, the output power also faces a tradeoff with
efficiency, further constraining the
efficient transmitter output power
delivery capability. The receiver noise
density is proportional to the NF.
Novel noise cancelation ideas have
greatly reduced the NF at lower-gigahertz frequency ranges [45], [46], but
it is challenging to achieve a <10-dB
NF for amplifiers at frequencies that
are >200 GHz. The two classical RFIC
texts show that the NFs of fundamental frequency amplifiers drop with
the rate to roughly 20 dB/decade
when the NF is much larger than one
[47], [48].
The SNR requirement is set by the
system demands, such as the BER.
To achieve a BER better than 10 −12,
the binary phase-shift keying signal
should have an SNR >15 dB to avoid
power-hungry and ultrahigh-speed
signal processing and equalization.
Figure 5 shows that, to support gigahertz-level bandwidth, existing electronics systems can transmit up to a
few meters, a distance known as the
EI reach limit. Beyond this, electronics systems are not suitable for wideband links because the supportable

Supportable Bandwidth (GHz)

To quantify the signal degradation
due to dispersion, time-domain signal SNR is adopted and defined as
the ratio of the single bit duration
t b versus the time spreading Tt g
due to GDV. For binary modulation
schemes, t b = 1/∆f . Therefore,

signal bandwidth drops exponentially. However, at a relatively short
distance, bounded by the " EI reach
limit, " the supportable signal bandwidth is ultimately constrained by
the dispersion.

Causes of Dispersion
Besides material innate dispersion
[49]-[51], waveguide dispersion is
the key factor for DWG channels
[52]-[54]. Figure 6(a) presents the
simulated dielectric constant versus the operating frequency of one
silicon DWG, obtained using the
High-Frequency Structure Simulator
electromagnetic simulation tool. The
simulated material is high-resistivity
silicon with a dielectric constant
of 11.7. This is consistent with the
DWG propagation constant theoretical formula [55], [56]
	

b = k1

1 -`

~ c j2
,(6)
~

where b is the propagation constant, k1 is the wave vector, ~ c is
the waveguide cutoff frequency, and
~ is the operating frequency. Due to
waveguide dispersion, the dielectric
constant increases with frequency,
with a larger changing rate at a lower
frequency.
For example, the dielectric constant grows from 4.12 to 6.92 when

40
35
30
25
20
15
10
5
0

1 2 3 4 5 6 7 8 9 10
Communication Distance (m)

40

20

0
10-1

Channel Attenuation
Channel Dispersion
100
Communication Distance (m)

101

FIGURE 5: Signal bandwidth versus communication distance, under the constraints of signal
attenuation and dispersion.

	 IEEE SOLID-STATE CIRCUITS MAGAZINE	

FA L L 2 0 2 0	

25
IEEE Solid-States Circuits Magazine - Fall 2020

Table of Contents for the Digital Edition of IEEE Solid-States Circuits Magazine - Fall 2020
