MODELING AND BUDGETING OF TIMING JITTER AND NOISE - Advanced Signal Integrity for High-Speed Digital Design - page 573

Shot noise arises from the quantization of device current to individual device
carriers and has a current spectral density i 2 of

A 2 / √ Hz i 2

= 2 qi (13-31)

10 − 19 C) and i is the current through

×

where q is the charge of an electron (1 . 6

the device.
Shot noise arises from current fluctuations caused by quantization of current
to individual charges. The RMS voltage due to shot noise generated by a device
with current i flowing through an effective resistance R over a bandwidth f

is

= 2 qifR σ shot volts (13-32)

Since thermal noise and shot noise are Gaussian in nature, we must treat them in
a probabilistic fashion when creating a noise budget. Gaussian noise sources are
described by the normal probability density function (PDF), which has the form

1

√ 2 πσ noise e − v 2 / 2 σ noise P(v) = (13-33)

Equation (13-33) yields the probability of having noise of a given value. The
probability that the noise does not exceed a given amount is

− e − v 2 / 2 σ noise P(v noise <v)< 1 (13-34)

Example 13-5 Estimation of Thermal and Shot Noise We have a 2.5-V 50-
transmitter driving a 50- transmission line at 10 Gb/s (5 GHz fundamental
frequency). The circuit operates at room temperature (300 K). From load-line
analysis we can show that the output current is

2 . 5V
50 +

i Tx =

50 =

25 mA

2.5 V

50 Ω 50 Ω

Figure 13-17 Circuit for Example 13-5.