Signal Processing for High-Speed Links - Signal Processing Systems - page 314

where f c is the carrier frequency of the optical source, typically around 193 THz
for 1,550 nm wavelength . 1 Note that the transmit signal spectrum for an NRZ
transmitter has finite bandwidth. The optical signal is hard to attenuate completely
at such high data rates. Thus, one measure of the quality of the laser is the extinction
ratio E r (see Fig. 2 )

10 log 10 P 1
P 0

E r = (2)

where P 1 and P 0 are the powers in a transmitted one and zero , respectively.
Extinction ratios of 8 dB are typical for directly modulated lasers employed in
short reach, while long-haul applications employ externally modulated lasers using
Mach-Zehnder modulators [ 18 ] with an extinction ratio of around 15 dB. Unlike
back-plane links where higher signal to noise ratio ( SNR ) usually implies a higher
quality signal and a lower bit-error rate BER , for optical communications, a higher
optical signal-to-noise ratio ( OSNR ) may not provide a lower BER , if the extinction
ratio is poor. The power in the “signal” component of the OSNR includes that in
both the ones and the zeros , while the BER of an optical link will be a function of
the difference in these optical powers.

2.2 The Channel

Channel modeling is a critical first step in developing transmitter and receiver
algorithms, architectures and circuits. Back-plane channel models tend to be simpler
than those for fiber due to the presence of non-linearities in the latter. This
subsection describes the back-plane and fiber channel models.

2.2.1 Back-Plane Channel Model

A complete back-plane channel begins at the output node of the transmit driver,
and ends at the input node of the receive amplifier. Starting from the transmitter, a
simplified channel model (see Fig. 3 a ) includes the transmit side pad capacitance C T ,
bond wire inductance L T , a transmission line model of the FR-4 trace, impedance
Z T representing discontinuities due to vias and unterminated stubs, and ending with
coupling capacitor C C (in some cases) at the receiver, receive termination resistor
R T (either off-chip or on-chip), bond wire inductance L R , and receive side pad
capacitance C R . The transmission line model for the FR-4 trace can be described
by Telegrapher's equations shown below, which in turn can be derived via the
application of KCL and KVL to the RLGC circuit in Fig. 3 b , as follows:

1 The center frequency is 228 THz for 1,310 nm wavelength, which can be obtained using the
relationship f λ = c .