MODELING AND BUDGETING OF TIMING JITTER AND NOISE - Advanced Signal Integrity for High-Speed Digital Design - page 572

Equalizer Quantization Error Discrete linear equalizers typically use D/A con-
verters (DACs) to generate the equalizer coefficients. A DAC has a finite resolu-
tion that is a function of the number of bits, which leads to a minimum step size
(granularity) in setting the tap coefficients. For a current steering DAC used in
transmit equalization of differential signals, we estimate the minimum resolution
of the output current to be limited to the least significant bit (LSB) of the DAC:

i DAC
2 n DAC

i res = ( amperes ) (13-27)

where i DAC is the maximum output current and n DAC is the number of bits in
the DAC.
We treat the limited resolution as a voltage “noise” on an output voltage signal,
whose value is equal to one-half of the resolution:

i DAC
2 n DAC + 1 Z 0

v eq , noise = volts (13-28)

Equation (13-28) is an approximation that does not account for other nonidealities
in DACs. An example is the differential nonlinearity, which is the difference
between the ideal and the measured output responses for successive DAC codes.
A thorough treatment of the sources of nonidealities in DACs is provided by
Razavi [1995].
Example 13-4 Equalizer DAC Noise Estimation A current-mode differential
transmitter with a single postcursor equalization tap is designed to have a maxi-
mum tap coefficient of

0 . 2. The transmitter is a 5-mA transmitter that drives a
differential transmission pair whose differential impedance is 100 . The equal-
izer uses a 4-bit DAC to set the coefficient value. The differential voltage swing
is v swing

−

= ( 5mA )( 100 ) = 0 . 500 V. The noise due to the DAC resolution is

[0 . 2 ( 5mA )/ 2 5 ] ( 100 ) = v eq , noise = 3 . 1 mV, which is 0.6% of the total signal

swing.

Thermal Noise and Shot Noise Thermal and shot noise are random in nature
and so are modeled as Gaussian sources [Gray et al., 2001]. Thermal noise , also
known as Johnson noise , is a result of power dissipation in devices, and has a
root-mean-square (RMS) power spectral density of

V 2 / √ Hz

PSD therm = 4 k B TR (13-29)

10 − 23 J/K), T the temperature (K),
and R the device resistance ( ). Over a given bandwidth, we calculate the RMS
thermal voltage noise with equation (13-3):

where k B is Boltzmann's constant (1 . 38 ×

= 4 k B TRf

σ therm volts (13-30)

where f is the bandwidth over which the noise is measured (Hz).