Why do I need an isolator
Reread my first message. I wrote,
"If you need your Teensy to have a different ground potential than the computer (USB GND pin potential), you do need to use an USB isolator."
It is critical that you understand that "1 V" describes
a difference of one volt. In Teensies and other microcontrollers, all voltages are referenced to ground. Thus, in a single electrical circuit, there can only be one "ground" or zero-volt reference, to which all other voltages are measured against. Otherwise, some of the signal levels will be wrong, and can even damage the Teensy or other components.
(There is sometimes a
safety ground, which is not a reference voltage, but actually connected via grounded sockets' ground pin to the physical ground. Humans are hurt or killed when they become a part of an electrical circuit with sufficient current and voltage, typically via their hands to their feet to a wet puddle or similar to physical ground.
Safety ground is intended to be a better conductor, so that instead of through the human, the current flows through the safety ground instead, hopefully saving the human. It isn't foolproof, of course, especially when someone grabs one thing with one hand and another thing with the other hand, causing them to become part of the electrical circuit without any ground connection. All that depends on what path the current takes through the body: many have survived lightning strikes, but 12V from say a car battery is sufficient to kill in certain circumstances.)
Isolators are devices that "translate" signals from one reference potential side to another. Most of them are
galvanic isolators, which means they do not pass any current over the barrier, only the signal in some form. Isolated DC-DC supplies pass current over the barrier, typically at around 80% efficiency: to provide say 5V 200mA = 1 W on the "downstream" side, they draw 1.25 W (for example, 5V 250mA) from the "upstream" side.
Safe USB wall warts are actually isolated AC-DC supplies. The positive output is typically 4.75V to 5.25V above the negative output, but the pair is "floating", not referenced to any specific potential. (There may be a
class Y capacitor from the output to the input to keep down the electromagnetic noise generated by the supply, which can cause a "tingle" if you touch either the positive or the negative output, for example the connector on a cable with the other end connected to the supply, because the input is alternating current so the capacitor can pass a tiny amount of current. I prefer so called
class II MOPP-rated (Means Of Patient Protection, i.e. "medical grade") supplies myself, without such a capacitor.) Technically, the negative output is the "ground" side, except it is not tied to any specific potential, it "floats".
Thus, if I want to create a self-powered –– as opposed to USB-powered –– Teensy project, all I need to do is either cut the VUSB trace on the Teensy, or replace it with a (Schottky) diode with sufficiently high current capability, and power it using one of my safe USB wall warts. In that case, the ground potential is set by whatever is connected to the USB ground, including both my Teensy project and even the wall wart!
I sometimes use my Teensies to examine the operation of my routers and single board computers (SBCs), streaming data to my host computer. The ones I know are powered from isolated AC-DC supplies, I can connect directly, because then my host computer sets the ground potential all the way including the router or single board device. This is the majority of cases, especially with legitimate (and safe) products.
For the others, I can either use a laptop (which is not connected ot mains) so the target device ground sets the ground potential all the way including my host laptop; or, I can use an USB isolator, making a ground barrier at the USB connection. The cheap ~ USD $10 USB isolators off eBay and elsewhere, based on ADuM3160/4160, work just fine with Teensies, although you do need to check which isolated DC-DC converter they use: everything except the DC-DC converter providing power over the isolation barrier is straight off the datasheet, but the amount of current and other properties vary among DC-DC converters quite a bit.
(There are now Analog Devices' ADuM3165/3166/4165/4166 and TI ISOUSB211 chips, that are only slightly more complicated, that provide isolation for USB 2.0 low speed, full speed,
plus high speed (480 Mbit/s), i.e. all that Teensies themselves support, that require about USD $20 in parts or so when bought from Digikey/Mouser in singles. Unfortunately, these haven't become common yet, and those that exist, seem to have pretty "dumb" isolated DC-DC supply circuits. Many users would prefer one completely without.)
One of my favourite isolation schemes with Teensies, however, is when I want to connect my host computer to the serial port on a router or SBC I'm investigating and not sure yet: TI ISO6721 digital isolator. On the Teensy side, it is connected to 3.3V, RX, TX, and GND. On the other side, it is connected to VCC (1.8V or 2.25V – 5.5V), TX, RX, and GND. (On both sides, you also need a 0.1µF X7R bypass capacitor between the supply and GND. See
here for my break-out board design for this.) In this case, the digital isolator is the barrier. It does need to be powered from both sides, but it doesn't need much current. On the router/SBC side, the supply also sets the RX and TX signaling levels. This way, even if the router/SBC is somehow grounded to a specific potential, everything is referenced to a single ground potential, with the ISO6721 as an isolation barrier; and it all works safely.
Whenever two points at different voltage potentials are connected with a conductor, current will flow until the voltage difference vanishes. When you have a circuit where two ground points are somehow tied to a specific but different potential, you get a
ground loop. Depending on the voltage and current, this can be irrelevant, annoying (causing noise), troublesome (causing problems), or even damage your circuits. If you follow the rule of only tying the ground to a specific potential at a single point, this will not happen.
I suspect the confusion stems from a misunderstanding; not realizing that voltage is always a
relative measurement. You physically cannot say or measure that a point in a circuit is at
X volts, without either explicitly or implicitly specifying
a point or potential it is measured relative to. This is why multimeters have
two connectors: one is for the reference potential ("ground"), and the other is for the point or thing you want to measure the voltage at/of.
In digital circuits and many analog circuits, the signals are defined by the voltage levels. For USB, this is the USB ground. For Teensies, this is the USB ground, or if not connected to USB, the power supply ground (negative side). When connected to both,
they must have the same ground potential.
Because all safe USB wall warts are isolated AC-DC supplies, whose positive output is about +5V with respect to their negative output, but the pair can float (within limitations, of course!), powering Teensy from such while connected to USB
typically only requires one to cut the VUSB trace or add a couple of diodes (two, so that neither USB nor the external supply will try to power the other, or "backfeed" the other; only power the Teensy). In my part of the world, all legal/safe DC wall warts are similarly isolated, so diodes will suffice for normal self-powered projects.
(LED lighting supplies are a typical example of
non-isolated, mains-referenced DC supplies. They may or may not be legal in your jurisdiction, so do not just blindly assume everything should be isolated. Similarly, cheap eBay/AliExpress/Temu USB wall warts may be mains-referenced, no matter how dangerous or illegal that might be.)
There are other scenarios, however, especially connecting two separately powered devices (like a desktop computer connected to mains, and a router or single-board computer connected to mains, for example) where isolation can be desired or needed. To determine for yourself, you must check if any (and how many) points tie your ground to a specific potential.