Introduction to Low-Noise Electronic Design

Many electronic products have performance requirements that are degraded by noise. As technology is pushed to the limits of precision, repeatability, and speed, the effects of electronic noise bound product performance. For example, high-seed data communications physical-layer performance is bound by the communications channel signal-to-noise ratio (SNR). Examples of noise-limited measurement applications include all sensors and transducers (temperature, position, field, force, sound, etc). The sensor or transducer signal fidelity and information are obscured by noise, limiting the signal quality and ultimate utility of the information.  The understanding of noise sources, types of noise, noise characteristics, noise mathematical relationships, noise modeling and system performance prediction are paramount to successful high-technology product development.

Noise sources are either extrinsic or intrinsic to an electronic product or circuit. Extrinsic noise sources will radiate noise that is unintentionally received by susceptible circuitry. Extrinsic noise sources include electro-magnetic (E-M) field noise known generally as Electromagnetic Interference (EMI). EMI can be further classified as near-field or far-field E-M noise dependent upon the distance from the noise source to the noise receiver. The significance will be explained in a moment.  First, near field is defined as a source-receiver distance of less than λ/(2π), whereas a far field is defined as a source-receiver distance of greater than λ/(2π).
 

Near-field E-M has wave impedance that is characteristic of the source; electric field (E) or magnetic field (H). Electric field dominated waves in the near field have impedance > 377 ohms.  Magnetic field dominated waves in the near field have impedance < 377 ohms.  The so called, uniform plane waves are far-field transverse E-M waves where the impedance converges to 377 ohms (the intrinsic impedance of free space). Knowledge of the noise source impedance and distance to the noise source suggest noise mitigation techniques. For example, magnetic field noise sources are high-current loops. These loop areas must be closed and/or the circulating current reduced to reduce the noise source power. Electric field noise sources are typically dipole antennas – so mitigation relies on decreasing the antenna radiation effectiveness and/or voltage.

Noise can also be extrinsically coupled into susceptible circuits via cable crosstalk.  Here, the electric-field crosstalk component is coupled from aggressor cables to victim cables by distributed capacitance. The magnetic-field crosstalk component is coupled from aggressor cables to victim cables by distributed mutual inductance.  Near-end crosstalk (also known as backwards crosstalk) is related to the sum of the electric-field and magnetic field coupling components, whereas far-end crosstalk (forward crosstalk) is proportional to the electric field component minus the magnetic field component. Intrinsic (also known as inherent) noise in electronic circuits arises from random signals due to fundamental properties of circuits, and generated by resistors and semiconductors.  Examples of intrinsic noise are thermal (or Johnson, white) noise in resistors and semiconductors, shot noise and flicker noise (also known as 1/f noise) in semiconductors.

Noise can be characterized by its spectral shape.  White noise is flat or constant over frequency.  Noise with 1/f spectral shape is also shown in the NSD plots below:

Two noise voltages in series or two noise currents in parallel add according to,

;

C is the correlation coefficient

When noises are random in nature, and not correlated to other signals, the correlation coefficient, C = 0 and the noise sum of the individual noise contributors is equal to,

;

This is valid for flat noise spectral density (NSD) across the frequency band of interest.  If the NSD is not flat over frequency, then the noise sum is obtained by squaring the summing the individual NSDs over the frequency band of interest. NSD is the average normalized noise power over a 1 Hz bandwidth.  For voltage noise sources, Vn is in units of V²/√Hz.   For current noise sources, In is in units of A²/√Hz.  Either voltage noise or current noise can be expressed in relative dB, referred to as dBm.  (The m designation refers to measured (in this case calculated) with respect to a reference)

;

Common 0 dBm reference voltages are,

A few interesting noise summations are shown in the following table:

Two signals are perfectly correlated if they are sine waves of the same frequency with relative phase 0° (C = +1) or relative phase 180° (C = -1).  For C = +1, the two sinusoidal signals add linearly in voltage. For C = -1, the two sinusoidal signals subtract linearly in voltage.

Noise Bandwidth and Noise Power

Noise power is dependant upon the noise source spectrum and the noise bandwidth. Sinusoidal noise sources have noise power concentrated at the sinusoidal frequency, ideally with zero bandwidth.  Random noise sources have power spectrum spread across the frequency band, as was shown above for white and 1/f noise.

The Vrms noise power over a frequency band, f₁ to f₂ is,

 

The Irms noise power over a frequency band f₁ to f₂ is,

 

System performance can often be improved by careful noise band shaping and band limiting in general. The simple RC low-pass filter has a signal bandwidth of,

 

yet, this same filter has a noise bandwidth of,

This noise bandwidth is the bandwidth of an equivalent brick-wall low-pass filter applied to a white noise source. 

A white-noise source measured with low-pass noise filter with corner frequency, fc_noise, yields a Vrms noise power of,

Also note, in terms of spectral density, band limiting is simply the NSD multiplied by the noise bandwidth, 

Total noise power can be easily calculated in dBm for flat NSD (or nearly flat NSD) without integration by noting,

;

The above tools can be used to perform noise modeling and predict noise-limited system performance. An example from an actual product design is shown below. This is a receive path for a high-performance signal-processing device. The noise performance for each block and the noise interactions between blocks is modeled to predict overall product performance.  In some blocks, digitally programmable gain could be enabled, so the optimum gain selection is desired for overall performance.  The signal processing chain begins with a summing amplifier, then proceeds to High-Pass Filter stage 1 (HPF1), then proceeds to High-Pass Filter stage 2 (HPF2), then proceeds to the Equalizer (EQ), and finally digitized by a 14-bit ADC.