Effects of unearthed PSU and shielding on audio 50Hz hum

Question

I am trying to get a good understanding on sources of 50 Hz “ground hum” interference in audio equipment and good practices for shielding and grounding by making hum on purpose and taking steps to remove it.

I have been doing some experiments using a EMU 0404 external soundcard with 1 Mohm ¼” jack unbalanced line inputs. I am using it as a pre-amp/ headphone amplifier (not attached to a computer).

Here are my observations:

1. The EMU has an unearthed 5V dc ”wall wart” power supply. I noticed that there is a stable 100V ac (50Hz) and 0.2V dc potential difference between the 0V connection and earth. However, if I touch 0V and earth at the same time, I do not receive an electric shock. Why is there this large (presumably high impedance) common mode voltage? Why is it stable, if it is a “floating” power supply?

2. If I connect an unterminated 2 meter unbalanced ¼” jack cable to one of the inputs, I can hear lots of 50 Hz hum on the output. This is not surprising as the cable is acting as an antenna and the 0404 has high input impedance. However, when I connect the sleeve part of the jack to earth, most of the hum disappears. I can still increase the hum significantly by touching the tip of the jack with my finger.

3. If I remove the earth connection and insert the jack into a shielded but unearthed box, I can no longer detect the hum with my ears.

Can someone explain these observations, in particular the effect of the large common mode potential difference to earth on 50Hz hum?

My thoughts:

So I was surprised about the behaviour of the power supply and also that it would be used for audio equipment. Presumably the common mode voltage is stable because neutral is attached to earth in the uk. Could someone point me to a schematic of a switched mode power supply which behaves like this?

What I conclude from 2. Is that most of the hum is caused by the large common mode ac voltage of the sleeve/shield (which is connected to signal ground), which I find surprising. Surely the tip connection also has this common mode voltage at the input stage of the soundcard, so overall it should not make any difference?

When I touch the tip, I am turning the cable into a better dipole antenna, so this increased hum does not surprise me.

Observation 3. tells me that when everything is fully shielded, the common mode voltage no longer seems to matter.

Answer 1

I don't know what "earth" you've used for the first experiment, so I'll [mostly] punt on that (for now). I suspect you have a SMPS with an Y-rated capacitor connecting its isolated side with the primary. This is permitted provided that leakage current is kept under control. It's done to reduce EMI from the power supply. You can look at this paper for example. Diagram from a better quality article

The tradeoff is that

In general, the larger the value of the Y-capacitor, the lower the magnitude of the EMI that the supply generates. Conversely, the larger the value of the Y-capacitor, the higher will be the leakage current that flows across the isolation barrier.

Now onto your question:

If I connect an unterminated 2 meter unbalanced ¼” jack cable to one of the inputs, I can hear lots of 50 Hz hum on the output. This is not surprising as the cable is acting as an antenna and the 0404 has high input impedance. However, when I connect the sleeve part of the jack to earth, most of the hum disappears. I can still increase the hum significantly by touching the tip of the jack with my finger.

Yes, the shielding does what it's supposed to on the cable itself. The 50Hz hum signal is low frequency, so it gets coupled into the shield and shorted to signal ground. This is electrostatic shielding i.e. negates capacitively coupled signals by shorting them back their source:

But you are not shielded and you are also capacitively coupled to the mains... as hard as that may seem to believe. (I'll add some youtube videos links about this once I find them. There sure must be some. N.B. Here's one: https://www.youtube.com/watch?v=c3SRuX9lW58) So you negate the effect of the cable shield when you touch the tip of the jack.

If I remove the earth connection and insert the jack into a shielded but unearthed box, I can no longer detect the hum with my ears.

You need to clarify this experiment as well. How can you insert just the jack in a box? Do you mean the whole 0404 USB? Add a photo you can. Shielding without a ground (i.e. sans current return) connection is effective against electromagnetic (but not against electrostatic) interference/noise. I doubt however that simply shielding the jack can have the effect you describe, especially against low frequency noise like the mains frequency. I suggest this app note for more in-depth treatment of shielding (both electrostatic and electromagnetic). See also this answer and yet another app note that says not to bother much with anti-electromagnetic cable shielding as it's hard to achieve (instead simpler things like twisted cable pairs are more effective at negating that).