Low-Noise Power Supply Design for Audio Devices: What You Need to Know

0 Members and 1 Guest are viewing this topic.

BjornKarl

• Newbie
• Posts: 2
• Country:

Low noise 5VDC power supply design

« on: September 08, , 08:25:04 am » Hi,
I’m not good at circuit design but I can use a soldering iron. I have a high-end audio device which is currently operating with 2 Li-Ion batteries. I constantly forget to charge the batteries si I’m looking to replace them with a line operated DC supply. The output from this supply shall be 5VDC with a current output of about 100mA. But, the output must have ultra low audible noise, approaching that what I get from using the battery. It must also be well filtered to eliminate hum. Can anyone point me in a direction where I could possibly find a circuit diagram with appropriate component values for this use?

I have looke all over to find a ready made board for this but can’t find anything other than cheap stuff from China which of course have no specifications to support the claims. I’m grateful for any advice I can get on this.

rooppoorali

• Regular Contributor
• Posts: 100
• Country:

Re: Low noise 5VDC power supply design

« Reply #1 on: September 08, , 09:43:21 am » Have you tested this circuit ever? https://www.theengineeringprojects.com//04/how-to-design-a-dc-power-supply-in-proteus.html

Among the ready-made ones, this one has good reviews: https://allo.com/sparky/shanti.html

There are 2 options here. 5V,3A and 5V,1A. 5V,1A means, it can output Maxium 1A current. If your requirement is less, you can still use this power supply. The following users thanked this post: BjornKarl

Vovk_Z

• Super Contributor
• Posts:
• Country:

Re: Low noise 5VDC power supply design

« Reply #2 on: September 08, , 10:07:12 am »

But, the output must have ultra low audible noise, approaching that what I get from using the battery. It must also be well filtered to eliminate hum. Can anyone point me in a direction where I could possibly find a circuit diagram with appropriate component values for this use?

I'm not sure there is a circuit diagram which may give 'ultra low noise' itself without some additional knowledge how to make an ultra low noise devices.
I would recommend to study some book about how to achieve low noise, for example, 'Noise Reduction Techniques in Electronic Systems by Henry W OTT, and 'High Speed Digital Design: A Handbook of Black Magic', and similar. Somewhere there was a topic about literature on this topic.
eevblog.com Book about noise? « Last Edit: September 08, , 10:12:34 am by Vovk_Z » The following users thanked this post: BjornKarl

Terry Bites

• Super Contributor
• Posts:
• Country:
• Recovering Electrical Engineer

Re: Low noise 5VDC power supply design

« Reply #3 on: September 08, , 10:24:36 am » Low noise design requires careful layout/ wiring and good filtering on the input and output. Adding an LDO after the ouput will reduce ripple and noise.
You will probably need a shielded box or can to stop radiated fileds coupling into your deleicate circuit. It will not be easy to get right without the electical know-how.

See this example problem solving https://recom-power.com/en/rec-n-very-low-noise-filter-for-isolated-dc!sdc-converters-46.html?0

Here is a deep dive into issues and solutions www.ti.com/lit/pdf/slyp709?keyMatch=SLYP709 The following users thanked this post: spostma, helpmerepair777

mariush

• Super Contributor
• Posts:
• Country:
• .

Re: Low noise 5VDC power supply design

« Reply #4 on: September 08, , 11:09:10 am » You could just go old school with an AC linear power supply

They make small transformers that you can mount on a prototyping board .. add a fuse, a bridge rectifier,a smoothing capacitor and a linear regulator to regulate to 5v and a small capacitor on output of this regulator (or capacitor - inductor - capacitor as a pi filter) and you have a linear power supply.

Pick a transformer that outputs 8..12v AC  because after rectification using a bridge rectifier, you'll have a DC voltage with a peak equal to Vdc peak = Vac x 1.414 - 2  x (voltage drop on diode inside bridge rectifier)
So for example, for a 9v AC output transformer, you'll have Vdc peak = 9vx1.414 - 2 x 0.8v  = 11v
If you use a plain linear regulator, such regulators usually require that the input voltage must always be above the output voltage by at least 1 - 1.5v so let's make sure it will by adding a capacitor after the bridge rectifier.
You say you need around 0.1A so let's calculate things for a maximum of 0.25A of current.

This formula approximates how much capacitance would be the minimum to use to always have the voltage above some threshold :

C = Current / [ 2  x AC Frequency x (Vdc peak - Vdc min) ]

With the 9v transformer example above we can put the values in formula C = 0.25A / 2 x 60 Hz x (11v - 7v)   = 0.25 /  120*4 = 5.20e-4  Farads or around 520uF  so to guarantee at least 7v before the regulator even if your circuit consumes 0.25A, you would need at least 560uF.
Considering you're estimating 0.1A, you can probably go with a standard value of 470uF (should be rated for at least 25v).

For the actual linear regulator, it won't really matter ... a would work... and have a small 100uF 10v (or higher) rated capacitor on the output of this regulator. The following users thanked this post: BjornKarl

Peabody

• Super Contributor
• Posts:
• Country:

Re: Low noise 5VDC power supply design

« Reply #5 on: September 08, , 03:03:21 pm » For an audio device, I wonder if a switching supply might be a better choice.  If it oscillates at 500KHz or more, perhaps the remaining ripple would just be at a much higher frequency than you  could hear.  But I'm no expert.  Maybe it doesn't work that way.  It just seems that with a linear regulator it's hard to get rid of mains hum, which you defintely can hear.


The following users thanked this post: BjornKarl

tooki

• Super Contributor
• Posts:
• Country:

Re: Low noise 5VDC power supply design

« Reply #6 on: September 08, , 06:27:45 pm »

For an audio device, I wonder if a switching supply might be a better choice.  If it oscillates at 500KHz or more, perhaps the remaining ripple would just be at a much higher frequency than you  could hear.  But I'm no expert.  Maybe it doesn't work that way.  It just seems that with a linear regulator it's hard to get rid of mains hum, which you defintely can hear.

I'd say you've got it precisely backwards. It's easy for a linear regulator to get rid of hum. Trivially easy. If you're getting audible hum, it's not because of the regulator, but a ground loop.

Switching supplies can be OK, but they are often very noisy. It's rarely that they switch at an audible frequency, but rather that there are audible-frequency harmonics that can get spewed out into your circuit (both in ripple and as electromagnetic interference induced into nearby circuits). And they can still cause ground loops.

And finally, any amplifier worth its salt is fairly impervious to power supply ripple. In the past, it was actually quite common to use unregulated power supplies for the power amplifier stages. Just rectified and smoothed with big caps.

BjornKarl

• Newbie
• Posts: 2
• Country:

Re: Low noise 5VDC power supply design

« Reply #7 on: September 09, , 04:26:27 pm » Thank you for your inout. I’m already very familiar with the ALLO Shanti and it is a very good one. But the supply also has a 5V/3A included which I do not need. Also, the Shanti is a complete standalone unit which takes up a lot of space. I’m looking for a circuit that I can incorporate together with  a streamer and a DAC in my own enclosure. And I already have 9VAC available.

TimFox

• Super Contributor
• Posts:
• Country:
• Retired, now restoring antique test equipment

Re: Low noise 5VDC power supply design

« Reply #8 on: September 09, , 05:15:59 pm » If you decide to go the old-fashioned transformer-rectifier-filter power supply route, I highly recommend PSUD II freeware from Duncan to design the rectifier section.
Note that the software models the transformer by no-load voltage and equivalent secondary resistance, but manufacturers specify them by loaded voltage at specified load current.
https://groups.io/g/duncanampspsud

BILLPOD

• Frequent Contributor
• Posts: 477
• Country:

Re: Low noise 5VDC power supply design

« Reply #9 on: September 09, , 05:32:42 pm » Any USB charger would work for this, and you must have several, as everyone must have.  Cut off the USB plug and strip back the wires a bit.
Attach whatever connectors you need to power your audio device to the red and black wires.

beatman

• Regular Contributor
• Posts: 76
• Country:

Re: Low noise 5VDC power supply design

« Reply #10 on: September 11, , 01:01:57 pm » i have the same problem about.i want to replace the two stock switch mode psu,s from two motu devices.i just by one 18v -3a linear laboratory power supply with just 0.5 millivolt ripple .i replace the caps inside with good quality lock the knob to 15.2v and power the two units ecxelent solution.better sound overal The following users thanked this post: BILLPOD

MathWizard

• Super Contributor
• Posts:
• Country:

Re: Low noise 5VDC power supply design

« Reply #11 on: September 13, , 04:32:39 pm » Yeah I have a stereo with an unregulated 18V from a transformer, it feeds all the op-amps, etc, and a for a reference voltage. I guess it's all common mode-noise to the op-amps, and mostly cancels out at the output.

The only real amount of 120Hz hum it ever has is when I had a ground loop by connecting the return path of 1 PCB to the wrong gnd point, it should be a star-gnd.

jc101

• Frequent Contributor
• Posts: 757
• Country:

Re: Low noise 5VDC power supply design

« Reply #12 on: September 13, , 08:42:00 pm »

I have a high-end audio device which is currently operating with 2 Li-Ion batteries. I constantly forget to charge the batteries

Get a second set of batteries, keep one set charged and swap them over as needed - so there is always a charged set to hand?

radiolistener

• Super Contributor
• Posts:
• Country:

Re: Low noise 5VDC power supply design

« Reply #13 on: September 15, , 06:30:32 pm » you can use usual linear regulator IC. For example, you can use some popular LDO from ST or other manufacturer.

But it's not clear what is your noise level expectations?
If you're needs ultra low noise, there are also more expensive ultra low noise linear regulators, for example LT.

What is your noise level requirements?

radiolistener

• Super Contributor
• Posts:
• Country:

Re: Low noise 5VDC power supply design

« Reply #14 on: September 15, , 11:06:09 pm »

But, the output must have ultra low audible noise, approaching that what I get from using the battery.

If it's for a hi-end audio DAC, I think LT solution will be good enough.

But such design also require proper shielding and ground layout, otherwise bad PCB design can kill profit from a good regulator IC performance due to RFI and near field coupling. « Last Edit: September 16, , 05:19:21 am by radiolistener »

tooki

• Super Contributor
• Posts:
• Country:

Re: Low noise 5VDC power supply design

« Reply #15 on: September 16, , 05:57:47 pm » I very much doubt LT levels of performance are necessary, and given that the OP isn’t that experienced in electronics, the PCB layout requirements of the LT to achieve its full performance are likely out of reach.

Besides, we don’t even know if the device needs unusually clean power, or if it’s just a phoney-baloney “audiophile” “requirement” rooted only in superstition.

Introduction

When evaluating an amplifier’s performance for a low noise application, both internal and external noise sources must be considered. This application note briefly discusses the fundamentals of both internal and external noise and identifies the tradeoffs associated in selecting the optimal amplifier for low noise design.

External Noise Sources

External noise includes any type of external influences, such as external components and electrical/electromagnetic interference. Interference is defined as any unwanted signals arriving as either voltage or current, at any of the amplifier’s terminals or induced in its associated circuitry. It can appear as spikes, steps, sine waves, or random noise. Interference can come from anywhere: machinery, nearby power lines, RF transmitters or receivers, computers, or even circuitry within the same equipment (that is, digital circuits or switching-type power supplies). If all interference is eliminated by careful design and/or layout of the board, there can still be random noise associated with the amplifier and its circuit components.

Noise from surrounding circuit components must be accounted for. At temperatures above absolute zero, all resistances act as noise sources due to thermal movement of charge carriers called Johnson noise or thermal noise. This noise increases with resistance, temperature, and bandwidth. Voltage noise is shown in Equation 1.

where:
Vn is voltage noise.
k is Boltzmann’s constant (1.38 × 10−23 J/K).
T is the temperature in Kelvin (K).
B is the bandwidth in hertz (Hz).
R is the resistance in ohms (Ω).

Current noise (noise associated with current flow) is shown in Equation 2

where:
In is current noise.
k is Boltzmann’s constant (1.38 × 10−23 J/K).
T is the temperature in Kelvin (K).
B is the bandwidth in hertz (Hz).
R is the resistance in ohms (Ω).

Resistors

For the purposes of this application note, the resistor noise is limited to thermal (Johnson) noise. To keep a low level of this type of noise, resistance values should be as low as possible because RMS voltage of thermal (Johnson) noise is proportional to the square root of the resistor value. For example, a 1 kΩ resistor has a thermal noise of ~4 nV/√Hz at room temperature.

For an in-depth analysis and low noise designs, other types of resistor noise should be accounted for, such as contact noise and shot noise. A few practical notes follow and they should be considered when selecting a resistor.

• Choose the largest practical wattage resistors, as the contact noise is decreased with a larger volume of material.
• Choose low noise resistive element material
  
  
  • Resistive elements composed of pure metals and/or metal alloys in bulk exhibits low noise characteristics. Such as Vishay Bulk Metal® foil technology resistors (such as, S102C, Z201)
  • Wirewound technology resistors composed of metal alloys have similar noise characteristics as Bulk Metal foil technology, but are much more inductive.
  • Metal film technology resistors as thin film are noisier than Bulk Metal foil or wirewound technology resistors because of significant noise contributions from occlusions, surface imperfections, and nonuniform depositions.
  • Thick film and carbon composition resistors are the nosiest resistors.

Reactances

Reactances, such as capacitors and inductors, do not generate noise, but the noise current through reactances develops noise voltage as well as the associated parasitic.

Practical Tips

Output noise from a circuit can be reduced by lowering the total component resistance or by limiting the circuit bandwidth. Temperature reduction is generally not very helpful unless a resistor can be made very cold, because noise power is proportional to the absolute temperature,

All resistors in a circuit generate noise. The effect of generated noise must always be considered. In practice, only resistors in the input and feedback paths (typically in high gain configurations) are likely to have an appreciable effect on total circuit noise. The noise can be considered as coming from either current sources or voltage sources (whichever is more convenient in a given circuit).

Internal Noise Sources

Noise appearing at the amplifier’s output is usually measured as a voltage. However, it is generated by both voltage and current sources. All internal sources are generally referred to the input, that is, treated as uncorrelated or independent random noise generators in series or in parallel with the inputs of an ideal noise-free amplifier (see 1). Because these noise sources are considered random and/or exhibit Gaussian distribution behavior, it is important to take proper care when summing the noise sources as discussed in the Summing the Noise Sources section.

If the same noise appears at two or more points in a circuit (that is, input bias current cancellation circuitry), the two noise sources are correlated noise sources and a correlation coefficient factor should be included in the noise analysis. Further analysis of correlated noise is limited in this application note as typical correlation noise sources are less than 10% to 15% and they can usually be disregarded.

Internal amplifier noise falls into four categories:

• Input-referred voltage noise
• Input-referred current noise
• Flicker noise
• Popcorn noise

Input-referred voltage noise and input-referred current noise are the most common specifications used for amplifier noise analysis. They are often specified as an input-referred spectral density function or the rms noise contained in Δf bandwidth and usually given in terms of nV/√Hz (for voltage noise) or pA/√Hz (for current noise). The /√Hz is needed because the noise power adds with (is cumulative over) bandwidth (Hz) or the voltage and current noise density adds with square root of the bandwidth (√Hz) (see Equation 1 and Equation 2).

Input-Referred Voltage Noise

Input-referred voltage noise (en) is typically viewed as a noise voltage source.

Voltage noise is the noise specification that is usually emphasized; however, if input impedance levels are high, current noise is often the limiting factor in system noise performance. It is analogous to offsets, where the input offset voltage often bears the blame for output offset, when in reality the bias current causes the output offset where input impedances are high.

Note the following points about input-referred voltage noise:

• Op amp voltage noise can be lower than 1 nV/√Hz for the highest performance amplifiers.
• Although bipolar op amps traditionally have less voltage noise than FET op amps, they also have substantially greater current noise.
• Bipolar amplifier noise characteristics are dependent on the quiescent current.
• Present day FET op amps are capable of obtaining both low current noise and voltage noise similar to bipolar amplifier performance, though not as low as the best bipolar input amplifiers.

Input-Referred Current Noise

Input-referred current noise (in) is typically seen as two noise current sources pumping currents through the two differential input terminals.

Shot noise (sometimes called Schottky noise) is current noise due to random distribution of charge carriers in the current flow through a potential barrier, such as a PN junction. The shot noise current, in, is obtained from the formula

where:
IB is the bias current in ampere (A).
q is the electron charge in coulomb (1.6 × 10−19 C).
B is the bandwidth in hertz (Hz).

The current noise of a simple bipolar and JFET op amp is typically within 1 dB or 2 dB of the shot noise of the input bias current. This specification is not always listed on data sheets.

Note the following points regarding input-referred noise:

• The current noise of typical bipolar transistor op amps, such as the OP27, is about 400 fA/√Hz, where IB is 10 nA, and does not vary much with temperature except for bias, current-compensated amplifiers.
• The current noise of JFET input op amps (such as the AD: 5 fA/√Hz at IB = 10 pA) while lower, doubles for every 20°C chip temperature increase, because JFET op amp bias currents double for every 10°C increase.
• Traditional voltage feedback op amps with balanced inputs usually have equal (correlated and uncorrelated) current noise on both their inverting and noninverting inputs.
• Many amplifiers, especially those amps with input bias current cancellation circuits, have considerably larger correlated than uncorrelated noise components. Overall, noise can be improved by adding an impedance-balancing resistor (matching impedances on both positive and negative input pins).

Flicker Noise

The noise of op amps is Gaussian with constant spectral density (white noise), over a wide range of frequencies. As frequency decreases, the spectral density starts to rise because of the fabrication process, the IC device layout, and the device type at a rate of about 3 dB per octave for CMOS amplifiers, 3.5 dB to 4.5 dB per octave for bipolar amplifiers, or up to 5 dB per octave for JFET amplifiers.

This low frequency noise characteristic is known as flicker noise or 1/f noise because the noise power spectral density goes inversely with frequency (1/f). It has a −1 slope on a log plot. The frequency at which an extrapolated −3 dB per octave (for a CMOS-type amplifier) spectral density line intersects the broadband constant spectral density value is known as the 1/f corner frequency and is a of merit for the amplifier (see 2). Bipolar and JFET amplifiers typically have lower 1/f corner frequency than CMOS amplifiers.

Popcorn Noise

Popcorn noise (not specified or advertised) is an abrupt shift in offset voltage or current lasting for several milliseconds with amplitude from several microvolts to hundreds of microvolts. This burst or pop is random. Low temperatures and high source resistances usually produce the most favorable conditions for popcorn noise. Although the root cause of popcorn noise is not absolute, both metallic contamination and internal or surface defects in the silicon lattice can cause popcorn noise in ICs. Although considerable work has been done to reduce the sources of popcorn noise in modern wafer fabrication, it cannot be eliminated. Further analysis of popcorn noise is beyond the scope of this application note.

Summing the Noise Sources

If the noise sources are uncorrelated (that is, one noise signal cannot be transformed into the other), the resulting noise is not their arithmetic sum, but the square root of the sum of their squares.

where:
Vni, TOTAL is the total noise referred-to-input (RTI).
en is input-referred voltage noise.
in is input-referred current noise.
RS is an equivalent source or input resistance to the amplifier.
Vn (REX) is voltage noise from external circuitry.

Note the following:

• Any resistance in the noninverting input has Johnson noise and converts current noise to a voltage noise.
• Johnson noise in feedback resistors can be significant in high resistance circuits.

3 visually shows the Equation 5 as the summation of vectors by using the Pythagorean Theorem.

Noise Gain

The noises previously discussed can be grouped into referred-to-input (RTI) noise of the amplifier circuit. To calculate the total output noise of the amplifier circuit, the total combined noise on the input must be multiplied by the amplifier circuit’s noise gain. Noise gain is the gain of the amplifier’s circuit for referred-to-input noise and it is typically used to determine the stability of the amplifier circuit.

To simplify the noise gain calculation, the noise sources in the simple amplifier circuit in 1 can be reduced to a single total RTI noise source (Vni, TOTAL), as shown in 4. It is a common practice to lump the total combined RTI noise to the noninverting input of the amplifier.

where:
Vno, TOTAL is the total referred-to-output (RTO) noise.
Vni, TOTAL is the total referred-to-input (RTI) noise

where:
GN is the noise gain.
R1 is the feedback equivalent impedance.
R2 is the gain setting equivalent impedance.

In some cases, the noise gain and the signal gain are not equivalent (see 5). Note that the closed-loop bandwidth is determined by dividing the gain bandwidth product (or unity gain frequency) by the noise gain of the amplifier circuit.

Case 1: In a noninverting configuration, both the signal gain and the noise gain are equal to 1 + R1/R2.

Case 2: In an inverting configuration, signal gain is equal to −(R1/R2), but the noise gain is still equal to 1 + R1/R2.

Selecting Low Noise Op Amp

If an op amp is driven with a source resistance, the equivalent noise input becomes the square root of the sum of the squares of the amplifier’s voltage noise, the voltage generated by the source resistance, and the voltage caused by the amplifiers current noise flowing through the source impedance.

For very low source resistances, the noise generated by the source resistance and amplifier current noise contribute insignificantly to the total. In this case, the noise at the input is effectively only the voltage noise of the op amp.

If the source resistance is high, the Johnson noise of the source resistance may dominate both the op amp voltage noise and the voltage due to the current noise. However, note that, because the Johnson noise only increases with the square root of the resistance, while the noise voltage due to the current noise is directly proportional to the input impedance, the amplifier’s current noise always dominates for a high enough value of input impedance. When an amplifier’s voltage and current noise are high enough, there may be no value of input resistance for which Johnson noise dominates.

An amplifier can be selected where its noise contribution is negligible compared to the source resistance by using a of merit, RS, OP, of an op amp. It can be calculated by using an amplifier’s noise specification.

where:
en is input-referred voltage noise.
in is input-referred current noise.

6 shows a comparison of the voltage noise density of a number of high voltage (up to 44 V) op amps from Analog Devices, Inc., vs. RS, OP at 1 kHz. The diagonal line plots the Johnson noise associated with resistance.

Similar types of graph can be constructed for a chosen frequency from the data in the op amp data sheet (see 8). For example, the AD has an input-referred voltage noise of 1.07 nV/√Hz and an input-referred current noise of 2.3 pA/√Hz at 1 kHz. The RS, OP is about ~465 Ω at 1 kHz. In addition, note the following:

• The Johnson noise associated with this device is equivalent to a source resistor of about 69.6 Ω (see 6).
• For a source resistance above ~465 Ω, the noise voltage produced by the amplifier’s current noise exceeds that contributed by the source resistance; the amplifier’s current noise becomes the dominant noise source.

To use the graph (see 7), follow Step 1 through Step 4.

1. Typically, the source resistances are known (such as sensor impedances). If the resistances are not known, calculate them from the surrounding or preceding circuit components.
2. Locate the given source resistance, such as 1 kΩ, on the Johnson noise line.
3. Create a horizontal line from the point located in Step 2 to the right of the plot.
4. Create a line down and to the left from the point located in Step 2) by decreasing one decade of voltage noise per one decade of resistance.

Any amplifiers below and to the right of the lines are good low noise op amps for the design as highlighted in the shade of gray in 7.

For the example shown in 7, the following devices are good candidates for the design: AD, AD, AD797, ADA-2, ADA, OP270, OP27/OP37, AD743/AD745, and OP184.

Conclusion

Consider all potential noise sources when evaluating an amplifier’s noise performance for low noise design.

The key noise contribution of an op amp is dependent on source resistance as follows:

• RS >> RS, OP; input-referred current noise dominates.
• RS = RS, OP; amplifier noise and resistor noise are equal
• RS << RS, OP; input-referred voltage noise dominates.

In summary, reduce or eliminate interference signals by

• Proper layout techniques to reduce parasitics.
• Proper ground techniques, such as isolating digital and analog ground.
• Proper shielding.

For resistive noise sources, use the following rules:

• Restrict bandwidth to only what is necessary.
• Reduce resistor value where possible.
• Use low noise resistors, such as bulk metal foil, wirewound, and metal film technology resistors.
• Reduce the number of resistive noise sources where possible.
• Use 8 and 9 to assist with the selection of an Analog Devices low noise amplifier using the criteria described in this application note.

For more information on noise, see the article, “Noise Optimization in Sensor Signal Conditioning Circuit” available at http://www.analog.com/noiseoptimization.

References

Analog Devices, Inc., AN-280 Application Note Mixed Signal Circuit Techniques.

Barrow, J., and Paul Brokaw. . “Grounding for Low- and High-Frequency Circuits.” Analog Dialogue. Analog Devices, Inc. (23-3).

Bennett, W. R. . Electrical Noise. New York: McGraw-Hill.

Bowers, Derek F. . “Minimizing Noise in Analog Bipolar Circuit Design.” IEEE Press.

Brockman, Don and Arnold Williams. AN-214 Application Note Ground Rules for High-Speed Circuits. Analog Devices, Inc.

Brokaw, Paul. . AN-202 Application Note An IC Amplifier User’s Guide to Decoupling, Grounding, and Making Things Go Right for a Change. Analog Devices, Inc. (February).

Brokaw, Paul and Jeff Barrow. AN-345 Application Note Grounding for Low- and High-Frequency Circuits. Analog Devices, Inc.

Bryant, James Bryant and Lew Counts. . “Op Amp Issues–Noise ” Analog Dialogue. Analog Devices Inc. (24–2).

Freeman, J. J. . Principles of Noise. New York: John Wiley & Sons, Inc.

Gupta, Madhu S., ed., . Electrical Noise: Fundamentals & Sources. New York: IEEE Press. Collection of classical reprints.

Hernik, Yuval and Belman, Michael. Linearity and Noise Capabilities of Ultra High Precision Bulk Metal® Foil Resistors. Vishay Intertechnology, Inc. (February ).

Johnson, J. B. . “Thermal Agitation of Electricity in Conductors” (Physical Review 32): 97–109.

Motchenbacher, C. D., and J. A. Connelly. . Low-Noise Electronic Design. New York: John Wiley & Sons, Inc.

Nyquist, H. . “Thermal Agitation of Electric Charge in Conductors” (Physical Review 32): 110–113.

Rice, S.O. . “Math Analysis for Random Noise” Bell System Technical Journal (July): 282–332.

Rich, Alan. . “Understanding Interference-Type Noise.” Analog Dialogue. Analog Devices Inc., (16–3).

Rich, Alan. . “Shielding and Guarding.” Analog Dialogue. Analog Devices Inc. (17–1).

Ryan, Al and Tim Scranton. . “DC Amplifier Noise Revisited.” Analog Dialogue. Analog Devices, Inc., (18–1).

Schottky, W. . “Small-Shot Effect and Flicker Effect.” (Phys. Rev. 28): 74–103.

Van Der Ziel, A. . Noise. Englewood Cliffs, NJ: Prentice-Hall, Inc.