E-TUBE: dielectric waveguide cable for high-speed communication

The demand for advanced interconnects to satisfy market requirements on bandwidth, cost, and power is ever increasing with the expansion of data centers. An interconnect called E-TUBE is presented as a cost-and-power-efficient all-electrical-domain wideband waveguide solution for high-speed high-volume short-reach communication links. The E-TUBE achieves an unprecedented level of throughput-distance product, bending radius, and channel density without requiring complex manufacturing process. The E-TUBE link demonstrates nearly 25 GHz bandwidth at a carrier frequency of 70 GHz and exhibits a frequency-independent insertion loss of 5 dB/m with a frequency-independent group delay of 4 ns/m. Such loss and delay characteristics independent of frequency enabled broadband data transmission over extended reach compared to conventional waveguide links. The E-TUBE link transmits 25 Gbps NRZ data over 3 m distance using a 70 GHz RF CMOS transceiver IC, which is the state-of-the-art throughput-reach product. This new interconnect is expected to overcome the limitations of existing electrical and optical interconnects and to replace them in high throughput links, including but not limited to, 100/400 Gbps board-to-board communications.


Supplementary notes 1. Maximum transferable data rate
Channel capacity, the maximum amount of information that can be transmitted over a given channel, on the basis of Shannon's law is given by where f, S, IL and k denote the frequency, power spectrum, insertion loss of the channel and integration index of target frequency, respectively.
The practical channel capacity of the copper, the optical and E-TUBE links can be estimated by reflecting where denotes the signal amplitude, is the baud duration and is frequency.
The signal amplitude is limited by the power supply voltage, which is typically less than 2V. When the level of modulation is raised to increase the data rate without changing the baud rate, the amount of transmitted information saturates at some point since the signal-to-noise ratio (SNR) drops in inverse proportion to the modulation level. Therefore, there exists an optimum level of modulation in the PAM signaling scheme, which determines the maximum transferable data rate.
The copper links are grouped into two types: passive and active. Supplementary Figure 1 shows the description of such copper links.  In the PAM-N signaling, the data rate increases as the modulation index N increases. The maximum feasible N at a given symbol rate can be estimated by using Shannon's channel capacity. The data rate of PAM-N signal cannot exceed the channel capacity calculated from the PSD of the PAM-N signal in a given channel together with the estimated noise floor. For example, the data rate of PAM-32 signaling at a symbol rate of 14 GHz in a noiseless condition is 70 Gbps. However, the calculated channel capacity of the active copper channel is 38 Gbps when SNR condition is considered, which indicates that the PAM-32 signal at a baud rate of 14 GHz cannot be transmitted over 3 m active copper channel without errors. Likewise, the maximum data rate of PAM-N signaling can be estimated with respect to the symbol rate. Supplementary Fig.3 shows the highest data rate of PAM-N signal with respect to the baud rate.
Supplementary figure 3 | The maximum data rate of the copper cable. The maximum data rate is determined by considering the loss and the noise characteristics of the channel link.
At low frequencies, the maximum data rate of the conductor-based interconnects grows in proportion to the baud rate. However, the maximum data rate saturates at high frequencies since no information can be transferred due  Fig. 5). Therefore, E-TUBE is a promising solution that can support rapidly growing demand for bandwidth of the high-speed short-reach communication links.
Supplementary figure 5 | The maximum data rate of the E-TUBE link. The maximum data rate is estimated by considering the loss and the noise characteristics of the channel link.
The actual maximum achievable data rate in using PAM-N signaling can vary when additional signal processing schemes including frequency/wavelength/polarization division multiplexing are employed. The wave reflects back and forth between two metal boundaries while propagating in Z-direction. The condition for the wave propagation is determined by the superposition of the existing plane wave and the reflected-andreturned plane wave. In case constructive interference between the two waves is satisfied, the resultant wave maintains its appearance and propagate through the waveguide. Such condition is satisfied if the phase difference between two waves is identical or different by an integer multiple of 2π, as given by

Low Group velocity dispersion waveguide
where the separation between the two plates is and is the wavenumber in the direction of .
This principle of the operation can be applied to a fully-enclosed metal waveguide with width and thickness of and , respectively. The condition for the constructive interference in the fully-enclosed metal waveguide is where , are the wavenumbers in the direction of and respectively.
In a single-mode waveguide, only one mode is allowed (m = 0, = 1) and satisfies The propagation constant of the guided wave is According to the Maxwell equation, the rectangular waveguide satisfies ω = ω + where ω is cutoff frequency of the waveguide. By taking derivative of both sides, we get 2 = 2 and the group delay defined by ⁄ is The equation shows that the group delay of the fully-enclosed metal waveguide is inversely proportional to the frequency and the variation increases in the vicinities of the cutoff frequency.
Supplementary Figure 7 | Partially-enclosed metal waveguide. A wave is propagating through the dielectric core placed between the two parallel plate waveguide.
where the phase shift, , occurring at the boundary between the dielectric core and the air satisfies The angles and denote the incident angle from the core to the air and the corresponding critical angle, respectively. As shown in the supplementary figure 7, the incident angle can be identified by using and as sin = , cos = 1 − .
For the partially-enclosed metal waveguide, single-mode wave propagation is ensured when ( = 0, = 1) and the propagation constant of the guided wave is The group delay of the partially enclosed waveguide is

Bending performances
The bending performances of the E-TUBE can be compared with the existing interconnects by using the parameters such as bending radius and group delay variation.
The electrical domain bending performance of the existing metallic interconnects referred to as direct attached cable (DAC) is expected to be excellent as long as the cable maintains its designed geometry. As the covering data-rate increases, the stiffness of a DAC increases to due geometry, which eventually limits its bending performance. The typical maximum bending radius of a 25GbE DAC is around 30mm. Precise electrical domain bending performance beyond the bending limit is not well defined since the degradation varies significantly depending on the type and degree of deformation of the cable.
The optical interconnects relies on the phenomenon of total internal reflection between the dielectric core and the dielectric cladding. If the bending degree increases, the propagating wave leaks out the core and thereby increasing the bending loss. Supplementary Figure 10 shows the measured bending loss of a single mode fiber [4][5][6]. In case of the standard single mode fiber, the minimum bending radius showing the loss of 1dB/turn is about 10mm. And the state-of-the-art paper reported that the nano-engineered fibers can reduce the bending radius down to below 5mm. In addition, the group velocity dispersion of the optical fiber can be negligible for a few meter data transmission even in the bended condition.
The E-TUBE suppresses the bending loss by using the reflection at the boundary between the metal cladding and the dielectric core. Supplementary Figure 11 shows the comparison between the straight E-TUBE and the bended E-TUBE, which shows that the loss from a 5mm single-turn bending is negligible. The measured group delay of a bended E-TUBE exhibits that the frequency-independency is maintained. Consequently, the E-TUBE shows the comparable level of bending performances against the existing interconnects although there are a couple of uncertainties to compare the actual bending performances.