# Mains Hum

© 2006-2012, Kevan Hashemi, Open Source Instruments Inc.

By mains hum we mean AC power hum, which is 50 Hz in Europe, and 60 Hz in North America. The following figure shows the mains hum we pick up with a 10-MΩ oscilloscope probe resting upon a wooden table in our laboratory in Boston. The amplitude of the signal is 10 mV rms (root mean square), 15 mV in amplitude (average to peak), or 30 mV p-p (peak to peak).

Figure: Mains Hum. Scale is 5 mV per division in the vertical direction and 5 ms per division in the horizontal.

Our Subcutaneous Transmitters have a 10-MΩ input impedance, and they likewise pick up tens of millivolts of mains hum when we set them on a table. Biometric potentials such as EEG have baseline amplitudes measured in tens of microvolts. Here we study the sources of mains hum and present ways we can reduce its amplitude to a few microvolts.

We start by assuming that the source of mains hum in any circuit can be modeled by an alternating-current (AC) voltage source, V, in series with an impedance, Z, which we call the source impedance. We are going to measure mains hum with an oscilloscope. We define our ground potential as the ground terminal of the oscilloscope probe. The voltage V induced on the probe will be a voltage with respect to ground.

We place the tip of our probe upon the metal frame beneath a wood-topped table. We do not connect the probe's ground terminal to the frame. Instead we clip the ground terminal to the insulation of the probe cable, so as to keep it isolated from the probe tip. With this arrangement, we see mains hum of amplitude 1 V (2 V p-p).

Now we unclip the ground lead from the probe cable and touch it to the metal frame of the table, which is the same frame we are touching with the probe tip. The mains hum disappears. Its amplitude is less than 10 mV. When we touch the ground clip to the table, we are connecting Z directly to ground with a 0-Ω resistor, and all of V is dropped across Z. None is left for our probe to measure. When we do not touch the ground clip to the table, V is connected to Z in series with the impedance of our probe, which is 10-MΩ. With 10 MΩ loading our source of mains hum, we are still left with around 1 V amplitude.

These two measurement alone do not allow us to estimate the amplitude of V nor the magnitude of Z. But if we connect the ground clip through a variety of resistors, we get to see how Z shares V with each resistance, and so we can deduce both Z and V. In the following table we show how the probe voltage, Vp, varies with with the load resistance, R. Note that R is the 10 MΩ probe impedance in parallel with the resistance we place deliberately in series with the ground clip.

R (MΩ)Vp (mV AC)
101100
5900
2400
0.120
0.01<10
Table: Table Frame Mains Hum with Ground Resistance. We give the probe voltage in mV amplitude.

From these measurements, we conclude that Z is of order 10 MΩ. It may be capacitive or inductive, but we doubt it is purely resistive. We now performed the same experiment with the author's tongue in place of the table. We press the probe tip on the tongue and the end of a resistor as well. The other end of the resistor is connected to the probe ground. We observe a slight direct current (DC) voltage as well as our mains hum, which we include in the table. From these measurements, we conclude that Z for mains hum on a human tongue with respect to the oscilloscope ground is of order 1 MΩ.

R (MΩ)Vp (mV AC)Vp (mV DC)
1050-500
550-500
240-250
0.110-100
0.01<10<10
Table: Table Frame Mains Hum with Ground Resistance. We give the probe voltage in mV amplitude.

There are two ways that mains hum can be induced in a conducting object such as the metal frame of a table. They can pick up magnetic fields from AC currents flowing nearby, or they can pick up electric fields from AC voltages nearby. When they pick up magnetic fields, they are acting like the secondary coil of a transformer, while the current-carrying wires are the primeary coil. When they pick up electric fields, they are acting like one plate of a capacitor, while the voltage-carrying wires are the other plate. If the mains hum we see in our laboratory is magneticaly-induced, then we will be able to pick up a large amplitude with a coil of wire, but not with a copper plate. If the mains hum is electrostatically induced, the converse will be true.

We made a loop of wire 15 cm in diameter and connected it to our oscilloscope probe. One end we connected to ground and the other to the probe tip. The 15-cm loop picked up 4 mV of mains hum right next to a power supply, but ≤ 1 mV elsewhere. This is very much less than our probe picked up when disconnected. We made a 3-m diameter loop of wire. It picked up no more than the 15-cm loop. We see that the effect of connecting the loop to the probe is the same as connecting the probe ground and tip together. There is no significant magnetic pick-up of mains hum by a loop of wire.

When we attach our probe tip to a large plate, however, we pick up thousands of milivolts of mains hum. We verified this on our metal table-tops and table-frames, as well as metal cabinets.

The Subcutaneous Transmitter (A3013 or A3019) presents a 10-MΩ input impedance across its two electrode leads. We can measure the mains hum by taking the fourier transform of the signal over a period of several seconds, and looking for the component at 60 Hz. Resting on a wooden table, they pick up of order ten millivolts. Within one of our Faraday Enclosures, however, they pick up no more than a few microvolts of mains hum.

Figure: Faraday Enclosure with Steel Fabric Walls. This enclosure will not block magnetic fields, but does block electrostatic fields.

Because our faraday enclosure is made of steel fabric, it is too thin to block magnetic fields. But it does block electrostatic fields, such as those that would carry mains hum through body capacitance. We have never seen mains hum inside a faraday enclosure, which means that the mains hum we experience is electrostatic.

We conclude that the mains hum on bodies in our laboratory is due entirely to capacitive coupling between conducting bodies and the AC power lines. Of course, in our laboratory we do not have large currents flowing, such as one might have near welding stations on a factory floor. But we suspect that neurscience laboratories are similar to ours in this regard: they have AC voltage all over the place, but not hundreds of amps of current.

One way to estimate the capacitive connection between an object and the power lines is to assume that the the body is in free space, surrounded by a large sphere at voltage V. In that case, the connection between the body and V is the free-space capacitance of the body. The free-space capacitance of a spherical conducting body is 4πεa, where ε is the capacitance of free space and a is the body's radius.

Figure: Capacitive Component of Impedance for Spherical Conductor in an Infinite Resistive Medium.

Let us model the human body as a sphere of radius 0.5 m, within a much larger spherical shell with 110 V rms at 60 Hz to represent the power wires in the walls. The capacitance between the two is roughly 60 pF. At 60 Hz, the impedance of 60 pF is 50 MΩ. Thus we have our mains voltage connected through a 50 MΩ impedance to our human body. From this calculation we expect the source impedance of laboratory mains hum to be tens of megaohms.

The wires in our laboratory wall will not, however, present a uniform 110 V alternating voltage to an object's body capacitance. There are opposite phases of this voltage in the cables, and accompanying neutral and ground wires. Thus we expect a very much smaller signal to be induced by capacitance on our body, and this is what we observe.

Now suppose we want to measure the voltage between two points in an animal, and we want to do so without interference from mains hum. If possible, we must connect one of these points through a low impedance to ground. This eliminates the mains hum at the point we connect to ground, and by the conduction of the body fluids, the same connection greatly reduces the mains hum at other points in the animal. The other point we want to monitor we can can connect to a high-impedance amplifier. We now measure the potential generated by local voltage source between these two points, and we load these local voltage sources only with the high impedance of our amplifire.

If, on the other hand, we connect both points to the high-impedance inputs of a differential amplifier, we will have up to 1 V of mains hum on both lines. Even with the very best of twisted and shielded cables, we will still end up with 1% of that 1V, which is 10 mV as a differential signal on our input. There is a time and a place for high-impedance, differential amplifiers, or instrumentation amplifiers. Whenever you use an instrumentation amplifier, you must to add a third low-impedance connection from the body of your signal source to the ground potential of the amplifier, or else all benefit of your differential inputs will be lost.

We conclude that mains hum originates in power cables and propagates capacitively through the air to all objects in the room. These objects in turn propagate the mains hum to one another. We expect to observe mains hum source impedances anywhere up to 10 MΩ, and voltages up to 1 V.