Noise

Introduction

One man's signal is another man's noise

Noise is inherent to electronic circuits and shows itself as irregular, seemingly random, voltage fluctuations superimposed on the signal voltages in the circuit. Where current is flowing, noise is present. Noise is composed of harmonics that extend all over the frequency spectrum.
Internal noise is the noise that is generated within the circuit itself. External noise is noise that is picked up by the circuit from external sources.

The internal noise of a circuit has various causes related to:

• temperature

• variations in the number of charge carriers crossing a semiconductor PN-junction in a diode or transistor

• irregularities in conduction paths or bias currents

• imperfections in semiconductor material, etc …

External noise sources can couple into the electronic circuit via the power supply (conducted interference) or via the air (radiated interference, radio waves or capacitive/inductive coupling) and add up to the internal noise.
It is impossible for a signal to have an infinite signal-to-noise ratio, because noise is never 0 and is always present.

Most important kinds of internal noise

• Thermal noise (aka Johnson or Nyquist noise):
  This kind of noise is proportional to temperature and is a result of the thermal agitation of atoms f.e. when current is flowing through a resistance causing heat dissipation. Only when a circuit is operating at absolute zero (0K or -273 degrees Celsius) there is no thermal noise. Because thermal noise has a constant power spectral density over a wide range of frequencies, so the energy is distributed uniformly over the whole frequency spectrum, it is considered (Gaussian) 'white' noise.

• Shot noise (aka Poisson noise):
  This kind of noise is produced by f.e. diodes, photodetectors, and microwave circuits and is caused by the statistical fluctuations in the arrival of electrons at the terminals of a conductor when the electrons pass across a barrier. Shot noise is more pronounced at low currents and depends on the amount of current flowing through the device. Shot noise is also a form of Gaussian white noise.

• Flicker noise (1/f or excess noise):
  Besides thermal and shot noise, flicker noise is also always present. It is not fully understood what causes it, but the construction of the components influence it.  The power spectral density of flicker noise decreases with increasing frequency, making it more significant at lower frequencies.

Noise flavors

• White noise (constant over f):
  It has a constant power spectral density over the frequency spectrum because the magnitude is equal over the frequency spectrum. It can be filtered to get other noise types, like pink noise.

• Pink noise (proportional to 1/f):
  The amplitude of pink noise falls down with increasing frequency at a rate of 3dB per octave (=-10dB/decade). Pink noise is used to test audio amplifiers because it matches the way humans perceive audio, with higher perception levels at low frequency than at high frequencies.

• Red noise (aka brown aka Brownian noise, proportional to 1/(f^2)):
  The amplitude of red noise falls down with increasing frequency at a rate of 6db per octave. It matches the signal handling capacity of a delta modulator, but is also used for calibration and testing of audio equipment.

• Blue noise (proportional to f):
  The amplitude of red noise rises with increasing frequency at a rate of 6db per octave. Blue noise is used for f.e. dithering in image or audio processing.

• Violet noise (proportional to f^2)

Components and their major noise sources

• Resistors:  thermal noise.

• Diodes: shot noise

• Bipolar junction transistors (BJT):  thermal noise and shot noise, low flicker noise.

• JFETs have less shot noise and flicker noise than BJT transistors.

• MOSFET transistors: thermal noise and flicker noise (1/f). MOSFETs have no shot noise.

• OPAMPs: which noise type is prevalent, depends on if the OPAMP input stage consists of bipolar, JFET or MOSFET transistors.

• Capacitors and inductors: don't generate noise, but can pick up noise.

How to design a circuit for minimal internal and external noise?

Minimize internal noise:

• Use metal film resistors instead of carbon film resistors. Metal film resistors cause lower thermal noise.

• Use wire wound resistors when low value resistance is required because they have a lower thermal noise.

• Use low value resistors where possible, especially in feedback and input paths of amplifiers.
  Low value resistors cause lower thermal noise, since thermal noise is proportional to the resistance value.

• Use capacitors with a low leakage current.

• Place filtering capacitors as close as possible to power pins of a chip, so the connection is a short as possible. Connect the other terminal of the capacitor directly to a ground plane. Don't use several via's in one of the connections, because via's introduce both extra resistance and inductance, which compromise the filtering effect of the filtering capacitance.

• Use a parallel combination of low value and high value capacitors for power supply filtering. Low value capacitors have better high frequency characteristics than high value capacitors. By combining them, you get a better filtering.

• Use low noise bipolar transistors in amplifiers.

• Don't use MOSFETs in low noise applications, because they introduce flicker noise.

• Separate analog and digital circuits, so the analog part of the circuit does not pick up noise from the high frequency switching digital circuits. Also separate their ground planes and connect them at 1 point only.

• Reduce resistance and inductance in your layout by using a proper width of copper tracks to carry the current and keep the tracks a short as possible. 

• Use a multilayer PCB with ground planes. Prevent cutouts in the ground planes. Minimize perforation by via's that would restrict current paths in the ground planes.

• Use ground pouring in your PCB layout because it helps to reduce the inductance of track loops that you might have in your layout. It also forms a lower resistance/inductance ground path for return currents.

• Use star grounding when you can use ground planes, so all return currents come together in one "clean" point.  When you use multiple grounding points in your layout, you will accumulate noise.

• Use shielded inductors to minimize the influence of the electromagnetic field of the inductor on other components, on inductive loops in the PCB layout …

• Pay special attention to the PCB layout around switching DC/DC converters to minimize noise due to the high dI/dt involved. Keep inductance of the related tracks as low as possible by keeping them short and wide.

• Add a low resistance (f.e. 22 to 33 Ohms) damping resistor in series with digital signals (TTL), to reduce the slope of the leading or trailing edges. This also reduces possible over- and undershoot and the ringing period.  Use low resistance values, so signal integrity is not affected by creating too much delay. 

• In general, restrict bandwidth where possible to reduce the power spectral density of the signal over the frequency spectrum. Less bandwidth is less noise.

• In audio systems, paralleling amplifiers instead of using one amplifier is a way to reduce noise.

• Use OPAMPs with a high common mode rejection, so noise that is present on both the inverting and the non-inverting input is cancelled out and does not appear on the output.

Minimize external noise:

• Use thick enough leads when using an external power supply to reduce inductance and resistance.

• Use differential inputs (analog, LVDS) to eliminate noise that got picked up by the wiring.

• Use shielded twisted pair wiring for differential inputs to reduce inductive pickup of noise from external sources and also reduces the magnetic field created by the wires.
  Non-twisted wiring can create a loop that picks up noise by induction. The extra shielding prevents capacitive pickup and also prevents the wire from radiating electromagnetic fields.

• Use coax cables for single ended high frequency signals. The shielding reduces capacitive pickup and prevents radiating the signal.

• Use proper shielding and grounding to reduce capacitive pickup of noise from external sources.
  Pay attention that you don't create ground loops.

• If you use a DC/DC converter in your power supply, then use an isolated DC/DC converter, so the incoming power supply lines are floating. The reference ground for your application is isolated from the power supply return. This decoupling prevents making a ground loops that introduce noise in the circuit via the power supply wiring.

• Use opto-coupler inputs because they electrically isolate signals and reject common mode currents and noise coming from an external source.

• Use a common mode choke at the power supply input to prevent common mode currents from entering or leaving the device. Common mode currents are caused by currents that don't return to the power supply, but instead are radiated by the circuit or are picked up from external sources. Because they have to come from somewhere or have to go somewhere, they either enter or leave a device via the power supply connections.

• Use a multilayer PCB layout in which the outer planes are ground planes that function as a shield for the tracks on the inner layer.

• Use shielded cables and flat cables.

• Use a metal enclosure that functions as a cage of Faraday.

How to generate noise?

There are many ways to deliberately generate noise.

• A conducting diode, zener diode or the reversed biased emitter-base junction of a transistor that behaves as a zener diode (of ca. 7V), is probably the easiest way to generate broadband white noise. This noise source can be amplified by a transistor or OPAMP amplifier to get the desired amplitude level.

• Current flow through a large resistor causes thermal white noise.

• A voltage regulator or voltage reference (f.e. TL431) can also be used as a noise source.

• Noise can also be mimicked by digital circuits generating pseudo-random patterns using f.e. a chain of D-flip-flops forming a shift register and feeding some outputs back to the input after combining them with digital logic ports.

The noise can be shaped to f.e. obtain pink noise from white noise, by adding a low pass filter and adjusting the gain of the filter to achieve a 3dB/octave slope.

How to measure noise?

• Split core and closed core current transformers offer an elegant way to measure noise without grounding issues due to the measuring probe. Split core have less gain and are more noisy than closed core transformers.

• A spectrum analyzer is used to check the power spectral density of the noise over the frequency spectrum.

• An oscilloscope can be used to get an idea about the peak to peak value of the noise voltage. Use a very short grounding connection for the scope ground because the wire of a grounding clip and the probe create a loop that picks up external noise by induction.

• A LISN (Line Impedance Stabilization Network) together with a spectrum analyzer can be used to measure the noise generated by a device.

How to amplify small signals without burying them in noise?

When dealing with very small signals, the signal-to-noise ratio (SNR) becomes small, and it becomes difficult to separate the signal from the noise. Simply amplifying the signal will also amplify the noise, so we need to use other methods to amplify the signal and get rid of the noise.

• When dealing with a slow varying DC signal in the presence of noise, a low pass filter (integrator) can be enough to filter out the high frequency noise. The filter will reduce the high frequency content of the noise.

• In digital systems, the signal can be sampled with a high frequency (oversampling), after which the samples are averaged or decimated to reduce noise and increase the signal-to-noise ratio. 

• Chopper stabilization can be used to modulate the input signal using a higher carrier frequency, after which it is amplified and then demodulated back to baseband. This prevents that amplification adds extra 1/f noise.

• Lock-in amplifiers are primarily designed for AC signals (not for slow varying DC signals). They work as a very narrow bandpass filter for frequencies other than the reference frequency, thereby rejecting noise at those frequencies. They can detect signals down to the nanovolt level, even in the presence of noise that is a thousand times bigger.
  A reference signal is generated that is locked to the frequency of the signal, so it has the same frequency as the signal (f.e. by using a PLL=Phase Locked Loop). The signal is then multiplied (mixed) with the reference signal, resulting in a signal that contains the sum and difference of both frequencies. This signal is then low pass filtered to remove the frequency sum together with the high frequency noise, leaving only the frequency difference. Because the reference frequency is locked to the input signal frequency, the difference will have a frequency of 0, in other words, DC. This resulting DC signal is proportional to the component of the signal that matches the reference frequency and phase. 
  The principle that the lock-in amplifier uses is that when you multiply 2 sine waves of different frequency (regardless of phase delay), the result will be a signal that is symmetrical around the x-axis. So when averaging (filtering) this signal over time, you end up with 0. But when multiplying 2 sine waves with the same frequency and phase, the result will be a sine wave that is not symmetrical around the x-axis, but is always positive. Averaging that signal over time will result in a positive DC signal.
  This is called orthogonality. See image below:

• A lock-in amplifier can also be used with slow varying DC signals after modulating this DC signal with a carrier frequency. The lock-in amplifier will then lock to this carrier frequency. Modulating the DC signal with a high frequency carrier helps to avoid the 1/f noise that would be added to the signal when amplifying the signal without modulation. 1/f noise has a higher amplitude at low frequencies, so "moving" to a higher frequency by modulating it, moves it away from the frequencies where the 1/f noise is dominating.
  
  Below, the frequency spectrum of a very small signal, after being amplified  (f.e. a low noise OPAMP), is shown. The low noise amplifier mainly adds pink 1/f noise (flicker noise), that is dominant in the low frequency range, where also the signal is present. The result is that the signal gets buried in the noise:

When we use a lock-in amplifier, the signal is first modulated so it is re-located to a higher frequency, before it is amplified. Because the signal is moved to a higher frequency by the modulation, it will not get buried in the 1/f noise that is added by the amplifier. Noise that was already present in the signal can not be removed, but the principle of modulation allows amplifying without adding extra noise.

See the image below for how a small signal is manipulated in a way that it can be amplified without getting buried in noise:

• Synchronous detectors aka synchronous demodulator aka synchronous rectifier aka phase sensitive rectifier use the same principle as the lock-in amplifier, but at a lower level of performance. For synchronous detectors, an external reference signal is used to modulate the input signal and at the same time functions as the reference signal that is multiplied with the signal. A square wave reference signal can be used, but they give less noise reduction due to the harmonic content containing multiples of the reference frequency. CMOS switches can be used for demodulation (multiplying).
  See picture below for a principle diagram of a simple synchronous detector: