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I ran a long USB extension cable from my pc to a WiFi adapter. The cable was too long and the gauge was too thin. So the resistance made the voltage drop to ~3V under load, making the WiFi adapter disconnect. To overcome the voltage drop, I devised this:

I snapped the USB extension cord's power cables (the data cables were kept intact) and ran them through a 0.9-4.5 to 5V boost converter capable of handling 1 Amp at input (the WiFi adapter takes 300mAmp max at 5V as measured by USB doctor.)

Now one would think that this setup would work. Kind of like voltage stabilizers that step up low.voltages of household. But it didn't work. I can't find out why. Whenever the WiFi adapter kicks in, the input voltage drops to 1.5V and the booster can't keep up with the power demand. Why is this happening? The same principle is used for stabilizers of households where the voltage is low. So why don't stabilizers trip like this USB booster is doing?

You have discovered the negative resistance feature that occurs with switch mode regulators.

This is a very simplified explanation of what is going on. For all intents and purposes and assuming a fixed load, you can consider the regulator to be a constant-power device. If the input voltage increases, the input current decreases. The opposite occurs when the input voltage decreases - the input current increases.

Now consider what happens when the load current increases. The input current has to increase to handle increased load current. But: the resistance of the USB cable means that the input voltage decreases. Recall that I mentioned that the input current has to Increase when the input voltage drops.

This is a vicious cycle and results with the voltage input to the regulator dropping to a very low value.

There are a couple of ways to fix the problem.

1) Add a pair of heavy wires in parallel with the power conductors of the USB cable.

2) Use a boost converter at the source end of the USB cable, followed by a buck converter at the load end. In other words, feed the power input of the USB cable with a voltage that is high enough to overcome the wire resistance.

A voltage-output boost converter also boosts input current by as much the voltage ratio that it is capable of boosting to support the power rating. Normally, the boost draws current then flyback a higher voltage at a variable frequency depending on load. However the charge current could have a crest factor of >5x that is normally dampened by a low ESR input bulk cap. However if the USB source impedance added to the cable resistance does not permit the boost current to rise fast enough, the output fails to achieve regulation.

I would add a large bulk input storage cap sized according to potential PTC poly resistor fuses such that they do not trip if using heavier DC cable does not fix it.

You should read the USB standards, which states that 2 meters is the maximum cable length (with present standards). It has nothing to do with power so much as power supplies made now days can boost the voltage as high as 27 volts, and there is talk of a 48 volt version.

Adding a boost converter is dangerous as the device must request a specific voltage from the more advanced power supplies. If you just want a long distance charge ability then just bypass the existing power/ground wires in the USB cable with much heavier gauge wire. 10 Awg should be good enough.

USB packet timing is 1 millisecond apart. If an endpoint device cannot respond to queries within 1 ms its connection is terminated as if it had been unplugged. Unlike Ethernet, USB does not have the complex speed management algorithms or a "push back" function to slow down the data stream or adjust packet size and timing.

A USB cable has a higher capacitance per meter than Cat-5 Ethernet, so even at 2 meters it has severe speed and current limits. USB-C works around this with 4 pairs of data channels instead of 1 plus higher voltage options. One ms seems like a long time to CAT-5 cable, but for current standard USB cables 4 meters would be a problem. USB-C proves that there is an effort to get past power and speed limits, but current cable designs put a severe limit on length, even at the lowest standard speed.

Making a USB cable 4 meters long can violate this nitpicky timing rule. It may be ok for charging purposes though some power loss will occur.

Why doesn't a boost converter help overcome USB cable resistance?

I ran a long USB extension cable from my PC to a WiFi adapter.

Note that not all PC USB ports are specced to deliver a full 2A or special charging voltages over USB. In data mode, the highest(usb 3.x) current specified is 900mA. I use Rampage Extreme motherboards, which are relatively top of the line for a desktop, and even on these a few extra steps have to be taken to enable it's full USB function. Even with this function enabled, note that USB port power is likely ganged together onto rails, in which case spreading high power usb devices across rails may be necessary. It's probably not a bad idea to measure the resistance of your cable and make sure that your voltage drop can be accounted for. If you're losing 2v at 300mA, you should have about 6.66 ohms.

The cable was too long and the gauge was too thin. So the resistance made the voltage drop to ~3V under load, making the WiFi adapter disconnect.

This is probably the best place to attack the problem. Use better (larger power wire) cable, possibly make your own. If you really want premade, shielding would help, and for store bought cable, a single cable of a given length is more likely to have lower impedance than 2 or more connected in series, because it was intended to be that length. Your cable has already been cut, so you can guess at how much this will help by splicing larger wires in parallel to the power wires.

You appear to be trying to use existing equipment, either to save money or to use in combination with something like a laptop with limited port selection.

If you'd like to save money and you don't mind a solder/heatshrink/electrical tape solution, this is probably cheapest, especially if you can get some cheap larger guage wire to test with, as parasitic inductance and capacitance on data lines will likely be the limiting factor and determine whether you need an inline signal boost.

The maximum power a wire can transfer at a given voltage occurs when voltage drop accounts for half of original voltage, as mentioned by Ben Voigt, if you're losing 2V, you're operating close to this limit already.

If simply using a better cable is not good enough, or the size of wire you'll need to reduce volt drop to say 10% is larger than you want, you may be able to convert to a higher voltage at the start of the cable and back to 5V at the other end of the cable to reduce losses, but bear in mind that you will use power in both voltage conversions.

For example: If you find a 24v to 5v buck converter that is 95% efficient when operating at 24v in and 300mA out, it will need 66mA in at 24v. If your cable resistance stays roughly at 6.66 ohms, your volt drop will be 0.43v, only 1.8% instead of 40%. If you can find a 5v to 24v boost converter that is 95% efficient at 5V in and 66mA out, you will only be drawing 340mA at 5V and have a solid 5V output. Total end to end loss is reduced to 12% instead of 40%. This is how voltage conversion to reduce line loss works. It is crucial to take efficiency at intended load into account. If both voltage converters are 90% efficient instead of 95% efficent, end loss increases to 20%, still better than the original, but far from ideal. Look at these from a converter manufacturer I'm familiar with:

These are from the same datasheet and marked "efficiency up to 91%" in product information, but as you can see, if you have 24V input and 5V out, your efficiency maxes out at 85%. It appears they've used different switching methods for the two output voltage versions. The first one I'm guessing is pulse frequency driven, so switching time compared to on time for a pulse remains the same across the load spectrum and at very low currents decrease in conduction losses appears to allow increased efficiency. The 5vdc version appears to be using PWM type switching, which increases losses as load decreases because the switching time remains the same as on time decreases. Both converters also suffer higher losses at higher output voltages for this reason. The higher the voltage, the more ON time must decrease while switching speed stays the same and the more resistive losses there will be on the primary side of the circuit. I'm just speculating on the nature of these converters based on their efficiency curves, but the point is, you have to take this step to confirm the efficiency at the intended worst case load and input voltage for that specific device. If you were using the 5VDC converter in the right hand graph, you'd be operating at 70% or worse efficiency. You might still have your 5V output, but you'd be drawing 628mA @5V on one end of the cable to give yourself 300mA @5V on the other end, and your overall efficency would only be 47.8%, worse than the efficiency of the original volt drop problem. Note that even in this case, actual line loss is only using 2.5% of the power. The higher transmission voltage is still helping, just the conversion losses dominate.

You can see that the device doesn't just have to correct voltage, but also efficiency loss as well, especially because as a design principle, if you make such a device it should follow the rules for usb loads itself, draw no more than 500mA for USB 2 and 900mA for USB 3. This means if you can find 5V->24V->5V voltage converters that are about 95% efficient at the right load levels and you use a 6.5 ohm cable, you can output about 438mA max with an input of 500mA at 5V.

To overcome the voltage drop, I devised this:

I snapped the USB extension cord's power cables (the data cables were kept intact) and ran them through a 0.9-4.5 to 5V boost converter capable of handling 1 Amp at input (the WiFi adapter takes 300mAmp max at 5V as measured by USB doctor.)

Edit: the following paragraph was not appreciated on principle, so I've added some clarification rather than removing it, because while this paragraph states that the method may be possible, as it is with a voltage stabilizer, it is meant to dissuade from incorrect application in an informative way. Because OP is so close to the hard limit of power the cable can carry at 5V, it will not be possible to use just an inline boost converter.

Well, it was worth a shot, and you still may be able to pull it off, however, show us specs for the boost converter you chose. Lots of switching converters' efficiencies decreases at lower loads, so at 300mA @ 5V @ .7 efficiency will require 2.14 VA, so 714mA at 3V(The USB output on the other end of the wires will still have to put out 714mA at 5V). One other thing to note is that a boost converter combined with an inadequate source will keep pulling more current at lower voltage(due to the line drop and load regulation of the source) to support it's output, so if load regulation is a problem in the first place, the boost converter will aggravate it.

Now one would think that this setup would work. Kind of like voltage stabilizers that step up low.voltages of household. But it didn't work. I can't find out why. Whenever the WiFi adapter kicks in, the input voltage drops to 1.5V and the booster can't keep up with the power demand. Why is this happening?

Yep, that sounds like a load regulation problem. The voltage source in your computer is just unable to output enough total power to support the actual load plus line losses(aggravated by the boost converter) plus the losses of the converter itself. You can think of the resistance of the USB cable as resistors on the output of the power supply, which is exactly what they are, and the more resistance, the worse load regulation will be, even if the power supply itself maintains full 5v output right up to it's cutoff point. Judging by brownout my keyboard sometimes causes at max brightness when on the same bus as another high power device, I suspect voltage can actually sag significantly before cutoff, and it can definitely support a significant near-short load (short circuit or shoot through from an aliexpress USB device was sufficient to melt plastic casing of the device before I disconnected it, and I suspect more than 10w were involved just from the speed of the incident).

The same principle is used for stabilizers of households where the voltage is low.

All wires in a house are (if installed correctly) adequately sized and also current protected, and line voltage from the power company generally has good regulation, so giving a small voltage updoot would not be a big problem, however, normal practice for large voltage drops is to go to higher voltage and/or larger wire to reduce losses.

The voltage regulator in question deals with a specific problem, inadequate voltage at destination, and these are used in locations where electrical networks are inadequate or equipment connected to them distorts the signal too much. or particularly clean power is needed. In order to do it's job, it uses power, increasing line losses on it's input lines.

So why don't stabilizers trip like this USB booster is doing?

The stabilizer is being used so much as a signal booster and as an active filter. It has an adequate power source, or in cases where it doesn't, it will also be unable to maintain output. The root cause of the problem in some countries is inadequacy of the electrical network in the first place, which could include both the distribution lines and the sources, but in these cases, the AC stabilizers would basically increase the share of the total power that it's output received and use more power in the process. This means when the source is inadequate, that all of the lines with a stabilizer on them would be aggravating brownout on all of the lines without a stabilizer, same as a boost converter is aggravating the problem in your circuit.

Thanks to Ben Voigt for useful usb info.