# Noise scaling in a current source

I have a bunch of constant current sources in my lab: some are laser diode drivers and some are DC power supply units that have a constant current mode. I've known from prior experience that some of these sources are noisy, so I measured the noise spectrum of each device.

For each device, I set the DC output current to some 'I0' (~20-50 mA), connected a bulk resistor (~ 125 Ohms) across the terminals and measured the AC-coupled (i.e. >5 Hz) voltage on an oscilloscope over several seconds at a sampling rate of about 1 MSa/s. From that data, I was able to compute the power spectral density (PSD).

Here's where I need help: while I am able to measure the PSD, I am a bit stuck on understanding theoretically how the noise PSD should scale with the DC current 'I0'.

1. I know that the PSD of shot noise in an electrical circuit scales linearly with 'I0', and that thermal noise depends on temperature 'T' and not directly on 'I0'. However, is it well known how other common but non-fundamental noise in DC voltage/current sources scales with 'I0'?

2. Are commercially sold DC power supply units typically limited by fundamental noise (thermal, shot noise) or do they have other types of noise resulting from, say, EM interference that don't necessarily have a well-defined scaling with 'I0'?

For reference: For many of my devices, the measured noise PSD seems to remain mostly identical for a few different values of 'I0'. Is it safe for me to assume that these devices are operating well above the thermal/shot noise limits, judging by the lack of dependence on 'I0'?

Any inputs or links to articles/references would be highly appreciated. Thank you!

• The answer depends on whether you are considering the lower 1/f noise region or the upper white noise region Mar 30, 2023 at 18:49
• @tobalt thanks for your response. Do you mean that the 1/f noise region would depend on I0 but not the white noise region, or the other way around? Mar 31, 2023 at 12:57
• Yes 1/f voltage noise of resistor scales with current. As a result most most circuits that use resistors have similar behavior. Total absence of 1/f noise would lead to nonphysical implications, such as infinite measurement precision. Mar 31, 2023 at 14:37

## 2 Answers

1. I know that the PSD of shot noise in an electrical circuit scales linearly with 'I0', and that thermal noise depends on temperature 'T' and not directly on 'I0'. However, is it well known how other common but non-fundamental noise in DC voltage/current sources scales with 'I0'?

No, this is entirely wrong. Electrical circuits don't have shot noise because a DC current $$\I\$$ flows. Such noise source comes from active devices actually, ranging from diodes to transistors and it's due to current fluctuations around the mean value due to granularity of charge.

That is to say, if my supply delivers $$\I_0\$$, will $$\S_{out}=qI_0\$$? Sadly, no.

It's way more more complicated than that: each device (active and passive) will determine the output spectral density. This can be estimated knowing how the circuit is made but it generally is hard, and simulations may only be the way; though, actually not all devices contribute equally througout e.g. different stages so you may get an upper estimated for uncorrelated contributions for the variance.

You can measure output noise of your device -- but it's a different beast. But check your datasheets, there will surely be some figures about output noise.

1. Are commercially sold DC power supply units typically limited by fundamental noise (thermal, shot noise) or do they have other types of noise resulting from, say, EM interference that don't necessarily have a well-defined scaling with 'I0'?

electronic noise is unavoidable as it's built into device physics. It is always traded against power dissipation. Other sources of 'noise', instead, can be avoided.

There's no fundamental limit on how low the noise of a constant current source can get, which means that there is also no scaling law for noise PSD with respect to the source's output current. Any noise that's put out by your current sources is due to non-ideal behavior of their circuits, and whether or not this noise scales with the output current (and in what way) depends exclusively on the circuit topology, which can and will vary widely.

In an ideal resistor, voltage noise is proportional to resistance, while current noise is anti-proportional to it. The better your current source, the higher its output impedance will be, thereby lowering the current noise. The noise generated by a resistor is independent of the current flowing through it (and therefore voltage across it); it only depends on the resistance and temperature.

In fact, it's possible to make the noise of a current source arbitrarily low: Given a current source with a finite resistive output impedance, you can add an inductor in series with its output to "buffer" the output current and attenuate noise in the frequency band of interest, just like you can add a capacitor at the output of a non-ideal voltage source to reduce its noise, which is a very common technique with precision references.

So, TL;DR:

1. That's wrong, there is no (general) scaling with current

2. It's just down to non-ideal circuits.