Noise is a critical and important factor in achieving high-performance integrated circuits. To design analog circuits, at least a basic understanding of noise is required.
Noise exists because electrical charge is not continuous but carried in discrete amounts equal to the charge of an electron, known as electronvolt (eV). The current is a quantized behaviour.
Analog designers have to deal with noise because it can’t be deleted or removed and it compromises relevant aspects of a circuit such as speed, linearity or power dissipation.
Noise is present in any real circuit, independent of the circuit architecture or technology
Noise handling is not a straightforward problem that can be solved. Circuits must coexist with noise. Although a proper understanding of the problem can help mitigate the effect of noise in circuits.
Noise is not a deterministic phenomenon, but a random process, so the instantaneous value cannot be predicted at any time, even if the past values are known.
Noise is often the limiting factor in many circuit designs, especially those pushing the boundaries of the technology, for example:
- The lowest amplitude of an input signal to be amplified. Signal-to-noise SNR ratio.
- The usable gain of an amplifier (upper limit)
For example, a good SNR value is important when designing high-definition (high number of bits) ADCs. Also, the sensitivity of communication systems is limited by noise.
In this article, we are going to review the main sources of noise in CMOS analog circuits such as thermal noise, flicker noise and shot noise to have a better understanding of the problem.
Thermal noise is in every ohmic conduction or wire. It is produced by the thermal agitation of charge in the conductor.
Thermal noise is often referred as “white noise” because it is constant in the frequency domain, although this is not exactly correct, as explained in . Thermal noise has a flat frequency spectrum and a Gaussian amplitude distribution.
From the “Fluctuation dissipation theorem“, thermal noise is produced whenever there is dissipation of energy (energy loss). Following this theorem, the components which have thermal noise are thoose with energy loss. I.e. a resistor dissipates energy (heat), but an ideal resistor does not.
There are not many things we can do to reduce the thermal noise in resistors. The only way is by decreasing the temperature or reducing the bandwidth.
Also, pure reactive components like inductors or capacitances don’t generate any thermal noise, although real world devices always have a resistive component due to non-idealities.
It is important to notice that thermal noise is not related to a current. That means that in the absence of current, thermal noise is evenly generated.
Thermal Noise in Resistors
Every physical resistor generates noise (pure ohmic resistors). This is also known as “Johnson–Nyquist noise“.
The thermal noise in resistors is easily modeled with a series-connected voltage source, but also may be replaced by its Norton equivalent current source in parallel. The voltage or current sources do not have polarity, i.e. the noise is generated randomly in both directions; therefore, the current source symbol is drawn with a double arrow.
To have an idea a 1kOhm resistor at room temperature with a bandwidth of 1Hz generates a noise of 4nV (rms).
The noise of different resistors in a circuit are uncorrelated.
- Carbon resistors are affected by thermal noise (always) and Flicker noise (only in presence of current).
- Monolithic and thin-film resistors only exhibit thermal noise and not flicker noise.
Although the capacitors, ideally, are noiseless devices, but when combining capacitors and resistors in the classic “RC circuits”, a different noise equivalence is generated.
Interestingly, the mean-square and RMS noise voltage has no dependance with R, but it includes the capacitance
We can extrapolate to inductor and resistor noise to:
i^2 = k·T /C
This is because, every system in thermal equilibrium, the energy is shared equally between each state of the system. Translated to this case, the thermal energy of the resistor is shared with the energy stored in the capacitor, which means mathematically:
From the previous equation, we can derive the v^2 formula.
Thermal Noise in FET Transistors
In the end, MOSFETs devices are a kind of voltage-controlled resistors.
Thermal noise in MOSFET devices is modelled as a current source in parallel with the drain-source.
γ is a coefficient that depends on the channel length.
As a general rule of thumb: less transconductance gm = less noise.
For relatively wide transistors, gate resistance noise is noticeable and not the source-drain resistance.
The gate resistance can be reduced a lot with a nice layout adding contacts to both sides of the transistor.
Flicker noise is also referred to as “1/f noise”, as it decreases with frequency. As with many other noise sources, it can not be easily predicted.
The origin of flicker noise is not 100% clear, and there are still some other believed mechanisms that generate flicker noise. It is produced by the contact of Silicon Oxide and the substrate. The traps in the silicon crystal are associated with crystal defects. These traps capture and release carriers in a random manner, generating the flicker noise.
The amount of flicker noise depends on contamination and crystal imperfections, which are a random process and vary from wafer to wafer in IC circuits.
Flicker noise introduces noise only when a dc current is passing, for example, in the drain current of a MOSFET. Unlike thermal noise, no current means no flicker noise.
The device area must be large. Flicker noise is inversely proportional to W*L. If we augment the device area, the random signals generated due to the impurities of the silicon oxide are averaged along the full area. So when the gate area is large, the random signals produced in all the surface tend statistically to be partially compensated and therefore reducing the overall output noise.
PMOS devices have less flicker noise than NMOS.
The Corner frequency
Flicker noise dominates the noise in devices in the low-frequency range, up to entering the MHz range. On the other side, the thermal or white noise is dominant.
The “Corner frequency” is defined as the frequency where the flicker and thermal noise equalize.
Any dc current flowing through a diode generates the so-called “shot noise” due to the random nature of the hole and electron transitions across the pn junction.
Shot noise is not relevant in CMOS devices since it is only present in bipolar transistors and junction diodes.
The origin of the Shot noise is derived from the fact that electrical charge is carried in discrete amounts, and equal to 1eV, current is not totally a continuous phenomenon. 1 eV = 1.6x10e-19C
In general terms, any current consists of current pulses of 1eV every X seconds.
Shot noise is associated with a direct current flow of a pn-junction, and it is independent of the temperature .
where q is the charge of an electron and Δf is the bandwidth in Hertz.
Other Noise Types
Further noise sources can be found sometimes, but they are not as relevant as the previous discussed:
- The burst noise is a low-frequency noise producing pulses at a few kilohertz range. It can be listened if connected to a speaker and therefore has the nickname of “popcorn noise”.
- The 50Hz-noise is proceeding from secondary and artificial sources instead of physical effects. The origin is the power-line at 50Hz in Europe and 60Hz in the States.
- The avalanche noise is produced by a breakdown avalanche in a pn-junction producing a series of large noise spikes. We have to consider when Zener diodes are used in the circuit.
: Design of Analog CMOS Integrated Circuits. Behzad Razavi. Chapter 7.
: Analysis and Design of Analog Integrated Circuits. Gray Meyer. Chapter 11.
: CMOS Analog Circuit Design. Allen and Holberg. Sections 2.5 and 7.5.
: The Design of CMOS Radio Frequency Integrated Circuits. Thomas H. Lee. Chapter 11.