Chapter 2 Signal Integrity in Broadband Communications 10
2.1.3 Bandwidth
The bandwidth directly improves the capacity in (2.1) and affects the SNR in (2.8).
Bandwidth is useful for limiting noise in the link, but, more recently, data rates in high-speed serial links are restricted by the bandwidth. While the bandwidth in optical communication systems is tailored to maximize (2.8), bandwidth in serial links is fixed by frequency dependent attenuation and reflections in the transmission line and connectors.In
Rnn( )τ No ---2 δ τ( )
=
Snn( )f No ---2
= V2
Hz---
Pnoise No G f( )2df
0
∫
∞ [ ]V2=
SNR Psignal Pnoise
--- Vs2 No ---
2T sin(πfT) ---πfT
⎝ ⎠
⎛ ⎞2 G f( )2df
0
∫
∞G f( )2df
0
∫
∞---
⋅
= =
Figure 2.3, ideal low-pass responses are plotted. The higher-order filters approach the limit of the “brick-wall” filter, ideal for filtering the noise PSD demonstrated in Figure 2.2. Once the signal PSD falls below the noise PSD, the response should attenuate the noise to maintain the SNR. In optical receivers, the bandwidth of the receiver is often chosen to be around 70% of the bit rate [53]. Higher bandwidths become noise-limited, while lower bandwidths reduce the signal energy. In the following sections, bandwidth limitations of high-speed optical and electrical channels are reviewed.
2.1.3.1 High-Speed Serial Links
Currently, data rates in high-speed serial links are impeded by bandwidth-limitation.
High-speed serial links are designed with transmission line channels that connect the input/output (I/O) between different chips. A shielded cable is a simple serial link. In servers and parallel computers, a backplane, shown in Figure 2.4, provides I/O between different boards. Two peripheral boards are connected to the backplane through high-speed connectors. The differential transmission line starts at one chip and is routed through the peripheral boards and backplane. The transmission lines have vias created by fabricating the transmission lines from one layer to another layer. Thus, the backplane link
Figure 2.3 Bandwidth for butterworth filters with different roll-offs.
contains the impedance discontinuities introduced by the vias and connector. Complete shielding is not possible due to the routing density and several serial links run in parallel.
Shielded transmission lines are limited by skin-effect losses and dielectric losses. Skin effect arises from non-uniform electric field in conductors. Consequently, the resistance of the wire increases and is accompanied by an effective internal inductance [51]. The skin loss can be expressed as
, (2.9)
where l is the wire length, µ is the permeability, and σ is the conductivity. The loss is a function of frequency, which is why it is generally referred to as a frequency-dependent loss. The phase shift and amplitude attenuation are identical for skin effect.
Additionally, the dielectric material of the FR4 material causes loss:
, (2.10)
where εr is the dielectric constant and tanδ is the loss tangent of the material. A thorough discussion of the skin and dielectric losses in modern materials is given by Deutsch [52].
Gskin( )f = e–(1+j)l πµσf
Figure 2.4 FR4 backplane with peripheral boards and connectors for serial communication.
Gdielectic( )f e
l εrtanδ ---c f –
=
The via stubs and connectors cause signal reflections at gigahertz frequencies. These reflections also cause dispersion and, consequently, intersymbol interference in the link. In Figure 2.5, the FR-4 frequency response features bumps that are attributable to these reflections. Finally, the connectors and parallel transmission lines in the backplane can generate crosstalk between neighboring lines. The crosstalk also limits the bandwidth.
For modern backplanes, these loss and dispersion mechanisms limit the bandwidth of interconnects to around 3GHz. Consequently, the bandwidth is fixed, and the challenge for circuit designers is to reach higher data rates through equalization, different modulation schemes, and coding.
2.1.3.2 Optical Links
Optical fiber represents broadband channel that may replace electrical interconnects.
The loss of fiber is low over a wide range of optical frequencies. At the 1.55µm wavelength, the loss of 0.2dB/km extends over 10THz. In principle, this window could support a data capacity of 4 Tb/s [54]. However, in long-haul fiber-optic communication dispersion limits the modulation frequency and the optical bandwidth is split into 10Gb/s
Figure 2.5 Signal attenuation for a commercial FR4 material and for a shielded cable.
channels using wavelength-division-multiplexing (WDM). Reaching 40Gb/s is possible if fiber dispersion is controlled.
The origins of dispersion depend on the fiber [55]. Initially, fibers were designed with large fiber diameters (50-100µm). As light propagates down the fiber, it reflects off the fiber walls randomly. The different path lengths cause modal dispersion given by the range of arrival time for the optical signal, ∆T:
, (2.11)
where L is the fiber length, c is the speed of light, and ncore and nclad are the index of refraction of the cladding and the core. Over 1km of fiber, this dispersion is greater than 100ps. In response, fiber manufacturers developed single mode fiber with a narrower core (8-10µm).
Next, the modulated signal suffers from a group-velocity dispersion, characterized by the variation in the group velocity variation, D. The amount of dispersion depends on the modulation bandwidth and, hence, the data rate. Group velocity dispersion is given by
, (2.12)
where the modulation bandwidth is the range of wavelengths, ∆λ.
Finally, optical bandwidth is limited by polarization mode dispersion. The modulated light is composed of two polarizations that propagate at different speeds. This causes a statistical spread in the arrival time due to the time-varying coupling between modes:
, (2.13)
where Dpmd is the polarization mode dispersion.
Tremendous optical bandwidth exists, but the design of optical transceivers above 10Gb/s must consider the use of electronic as well as photonic equalization techniques for lightwave communication [56].
∆T ncore–nclad 8c n⋅ core ---
⎝ ⎠
⎜ ⎟
⎛ ⎞2
L
=
∆T = D ⋅∆λ⋅L
∆T = Dpmd L