Thermal Noise Floor and Increasing Signal-to-Noise Ratio
Low frequency noise and thermal noise can be significantly amplified in some systems
Noise can’t be avoided in your electronic systems. Smart design choices can help make your system relatively immune to some noise sources, but there is one source of noise that you can’t avoid: thermal noise. In systems for gathering sensitive measurements and other communication systems, the thermal noise floor sets the minimum noise level you can hope to achieve.
There are other intrinsic noise sources in electronic components that are unavoidable and will appear alongside thermal noise. This creates a complicated noise environment that can be difficult to analyze, especially when other noise sources are present in an electronic system. Here’s how the thermal noise floor determines the minimum level of noise on can hope to see in an electronic system and what you can expect to measure in a real PCB.
What Determines the Thermal Noise Floor?
Simply put, the temperature of the system determines the thermal noise floor. When the temperature of the system is higher, the thermal noise floor will be higher. When we say noise floor, we are referring to the same idea as a general noise floor. In the absence of any broadband noise sources, 1/f noise, or Brownian noise, the minimum noise level you can hope to measure in an electronic system is the thermal noise floor.
Analyzing noise, in general, can be difficult as there are a variety of intrinsic noise sources, and these intrinsic noise sources are unique to different systems. Perhaps the most important aspect is describing the behavior of 1/f noise and Brownian noise at low frequencies. Development of stochastic models that describe the general statistical nature of 1/f noise and Brownian noise has been an active area of research for nearly a century. These models have been used to describe noise behavior in electronics, optics, finance, economics, biology, and other areas.
In an electronic system, the thermal noise floor will manifest at a sufficiently high frequency when a voltage is measured across a reference resistor. At low frequency, 1/f noise and Brownian noise will dominate, and these noise sources will be unique to the particular system being studied. At sufficiently high currents to avoid shot noise, the 3 primary intrinsic noise sources that might be measured are thermal noise, 1/f noise, and Brownian noise. The temporal waveforms and power spectral densities of these sources are shown below.
Types of noise in electronic circuits and their power spectral densities
When Does the Thermal Noise Floor Dominate?
As 1/f noise and Brownian noise fall off with increasing frequency, eventually the noise floor will converge to the thermal noise floor. Any noise source that is more intense than thermal noise floor will sit above the thermal noise floor and can be easily seen in a spectrum analyzer measurement.
If you look at the formula for the thermal noise bandwidth, you’ll find that thermal noise fluctuations are proportional to the square root of temperature. Voltage fluctuations are proportional to the Thevenin resistance of the system being examined, but the thermal noise power spectral density is a constant that is directly proportional to temperature (in Kelvins). Stated another way, increasing the temperature of the system by 20% increases these fluctuations by 20%.
If you look at datasheets for components, thermal noise values are generally on the order of nV/√Hz. The thermal noise floor you measure will depend on the bandwidth of your instrument. The thermal noise floor only dominates for frequencies greater than some corner frequency. This is the frequency at which 1/f noise becomes approximately equal to the thermal noise floor. Because 1/f noise depends heavily on the construction of a particular electronic system, there are no universal, closed-form solutions for calculating this corner frequency.
Simple example showing the transition from 1/f noise to thermal noise (a.k.a. white noise).
Can You Reduce the Thermal Noise Floor?
The simple answer is yes, but not by much. The minimum noise floor in the absence of all other noise sources will always be the thermal noise floor, which can only be reduced by decreasing the temperature of your components. If you take a look at component datasheets, the noise floor in your system will be generally specified over a broad range of temperatures that span beyond the recommended operating temperature.
The thermal noise floor and its bandwidth are extremely important in RF front-end receiver circuits, precision optical sensors, and other sensors that output at very low voltage (less than mV ). However, in most systems that run at mV levels, you probably won’t notice thermal noise. For a 1 mV signal with 100 nV of RMS thermal noise, the SNR value will be 40 dB, which is sufficient for many applications.
If you want to examine the effect of amplification and filtration stages in a signal chain, you need to use some basic simulation tools. Noise will be low enough that any components will operate in the linear regime, making it quite easy to simulate the behavior of broadband noise as it traverses a signal chain. Noise should always be simulated in an electronic system with amplifiers in order to determine the maximum gain that should be used in a signal chain.
When it comes time to simulate the thermal behavior of your system and examine how the thermal noise floor affects signal behavior in your PCB, you need to use the right PCB design and analysis software. The design tools in Allegro PCB Designer from Cadence integrate with a full suite of analysis tools, giving you the power to examine signal integrity and simulate thermal behavior in a single platform. These tools are ideal for designing and simulating all aspects of your board’s functionality.
If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.