Noise Analysis

The LNA is the first stage of the receiver front end. The noise performance is first consideration in design low noise amplifiers. Therefore, the study of noise is very important because it represents a lower limit to the size of electrical signal that can be amplified by a circuit without significant deterioration in signal quality. In this section, the various sources of electronic noise are considered separately. And MOSFET’s noise model will be described here.

2.1.1 Source of Noise Type

In the integrated circuit, there are many kinds of noise sources, such as shot noise, thermal noise and flicker noise (1/f noise).

Shot noise is always associated with a direct current flow and is present in diodes, MOS and bipolar transistors. The origin of shot noise can be seen by considering the diode and the carrier concentrations in the device in the forward-bias region. The

passage of each carrier across the junction, which can be modeled as a random event, is dependent on the carrier having sufficient energy and a velocity directed toward the junction. The shot noise current can be represented as i² =2qI^D∆f , q is the electronic charge (1.6 10 C× ⁻¹⁹ ), ∆ is the bandwidth in hertz. f

Thermal noise is generated from the conventional resistors. It is due to the random thermal motion of the electrons and is unaffected by the presence or absence of direct current, since typical electron drift velocities in a conductor are much less than electron thermal velocities. Since this source of noise is due to the thermal motion of electrons, we expect that it is related to absolute temperature T. The thermal noise can be represented by a series voltage generator v or shunt current generator ² i . These representations are 2 v² =4kTR f∆ ,i² =4kT(1/ )R ∆f where k is Boltzmann’s constant. At room temperature:4kT =1.66 10× ⁻²⁰V− . C

Flicker noise is a type of noise found in all active devices, as well as in some discrete passive elements such as carbon resistor. The origins of flicker noise are varied, but it is caused mainly by traps associated with contamination and crystal defects. These traps capture and release carriers in a random fashion and the time constants associated with the process give rise to a noise signal with energy concentrated at low frequencies. Flicker noise, which is always associated with a flow of direct current, displays a spectral density of the form i² =K I1( /^a f^b)∆f , where

∆ is small bandwidth at frequency f , I is direct current, K1 is constant for a f particular device, a is constant in the range 0.5 to 2, b is constant of about unity. It is apparent that flicker noise is most significant at low frequencies, although in devices exhibiting high flicker noise levels, this noise source may dominate the device noise at frequencies well into the megahertz range.

2.1.2 Noise Model of MOSFET

MOSFET’s noise source mainly comes from gate current noise, drain current noise (channel thermal noise) and flicker noise.

Drain current noise i^d2 (channel thermal noise) is the dominant noise source of MOS devices. Since MOSFETs are essentially voltage-controlled resistors, they exhibit thermal noise. In the triode region of operation particularly, one would expect noise commensurate with the resistance value. Indeed, detailed theoretical considerations lead to the following expression for the drain current noise of FETs.

d2

i =4kT gγ ^d0∆f (2-1) where gd0 is the drain-source conductance at zero VDS. The parameter g has a value of unity at zero VDS and, in long devices, decreases toward a value of 2/3 in saturation. Note that the drain current noise at zero VDS is precisely that of an ordinary conductance of value gd0.

Another kind of thermal noise is gate current noise i^g2. The fluctuating channel potential couples capacitively into the gate terminal, leading to a noisy gate current.

Although this noise is negligible at low frequencies, it can dominate at radio frequencies. The gate current noise may be expressed as

g2

where δis the coefficient of gate noise, classically equal to 4/3 for long-channel devices. Equation (2-2) is valid when the device is operated in saturation.

The gate noise is partially correlated with the drain noise, with a correlation coefficient given by

≡ × ≈

where the value of 0.395j is exact for long-channel devices. The correlation can be treated by expressing the gate noise as the sum of two components, the first of which is fully correlated with the drain noise, and the second of which is uncorrelated with the drain noise. Hence, the gate noise is re-expressed as

g2 2

Because of the correlation, special attention must be paid to the reference polarity of the correlated component. The value of c is positive for the polarity.

In electronic devices, 1/f noise (flicker noise) arises from a number of different mechanisms, and is most prominent in devices that are sensitive to surface phenomena.

Charge trapping phenomena are usually invoked to explain 1/f noise in transistors.

Some types of defects and certain impurities can randomly trap and release charge.

The trapping times are distributed in a way that can lead to a 1/f noise spectrum in both MOS and bipolar transistors. Larger MOSFETs exhibit less 1/f noise because their larger gate capacitance smooths the fluctuation in the channel charge. Here, if good 1/f noise performance is to be obtained from MOSFETs, the largest practical device sizes must be used (for a given gm). The mean-square 1/f drain noise current is given by where A (=WL) is the area of the gate and K is a device-specific constant. Thus, for a fixed transconductance, a larger gate area and a thinner dielectric reduce this noise term.