What I mean is that when I plug my charging brick into the wall it produces 5V DC from 120V AC.
Why can't a charging brick have 5V DC input to it and have it output 120V AC?
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It just doesn't work that way. It's a different operation so different hardware is required.
Like how running an signal backwards through an adder won't make it subtract.
The circuit itself has a defined input and a defined output terminal and you can't just try and shove something into the output and hope it comes out the input.
Another reason is that information can be lost between input and output. An AC-DC converter isn't specifically searching for a specific AC input (i.e. specifically a sinusoid of a specific amplitude of a specific frequency) to convert into DC. It's just sitting there accepting a wide range of signals, rectifies it so any negative parts becomes positive and then smears the peaks together as best as it can to produce DC. The circuit itself doesn't specifically know what it is being given nor does it care.
Reversibility of a process is not a given. And even if the process is reversible, the machine itself might not be. Some processes and their machines are both reversible: You can put electricity into a motor to produce rotation, or you can rotate a motor to produce electricity. Other processes are reversible but their machines are not: You can't rotate a gas engine and produce gas, but it is possible to take energy and combustion products of a gas engine to produce gas, but the engine itself can't do it.
The 120V AC to 5V AC transformer inside your brick works both ways. But that is possible only for AC to AC.
The "problem" is the 5V AC -> 5V DC conversion ("rectification") that happens after the transformer. This one is done by simple diodes and it's that process what's not reversible. You would need to replace the diodes with not-so-simple DC -> AC inverter, to get 5V AC first. Then feeding that to the 5V side of the transformer would yield you the expected 120V.
That was how a simple 80's era 50-60Hz transformer (heavy) brick worked. Modern (light) bricks work bit differently. They first convert 120V AC to 120V DC with a simple rectifier, then run an inverter to make high(sonic)-frequency 120V AC, feed that to a tiny high-frequency transformer, and then rectify again. As you can see, now you get not one, but two unidirectional stages.
Theoretically, one could disassemble, rewire and reorder those stages to get 120V AC from 5V DC. Unfortunately, even if it worked, you would get high-frequency 120V AC, unsuitable for powering 60Hz home appliances. Even more, that works only in theory, as the inverter is designed to work on high (120) voltage and tiny current. If you tried to run it on 5V, the current would have to be proportionally larger and the inverter would most likely burn. That's all considering we're staying in the few watts range that the power brick originally supported.
Most power supplies have a passive filter. The filter reduces (or output rectifier) the frequency from 60Hz (or 50Hz to DC and smooths it out with a loss in energy.) This smoothing for filters happens in either direction so if you switch the load and source in the supply, you still have the same filtering.
The same goes for the rectifier, it's built to turn a sine wave into a rectified sine wave. This process only happens in one direction.
If you want the process to happen in reverse you need an inverter that has switches (inverter bridge) that can turn on and off very fast to generate a sine wave.
Built into most chargers are devices called diodes. They act as one-way electrical valves, like a check-valve in hydraulics. The diodes are necessary to convert the incoming AC into DC. Like a check-valve when the Voltage "pushes" current into the opposite direction the diode conducts in, say from the 5V terminals back to the AC line, the diode stops the current flow.
I'm leaving out other complications like, that to get DC power to flow back into AC mains would require higher voltage and a way to synchronize to the line frequency. Look up inverters for more information on just getting AC from DC.
Why can't a charging brick have 5V DC input to it and have it output 120V AC?
Because then it wouldn't be a 'charging brick'.
But there is a class of device that can both charge a battery from the mains and feed power back into the mains from a battery. It is called a Grid-tie Inverter. They are not simple. They are not cheap. No manufacturer would go to all the trouble of designing and building one just to sell it as a 'charging brick'.
Another type of device that does a similar job is the UPS (Uninterruptible Power Supply). These are generally cheaper than grid-tie inverters because they don't feed power back into the mains, but simply generate a local (isolated) AC output that is close enough to the real AC mains waveform to work with computers etc. Even so, they are much more complex and expensive than a 'charging brick'.
Bottom line:- 'charging bricks' are designed to provide low voltage DC power for charging the battery inside a device such as a cell-phone. Adding the parts to make then generate mains power from the battery inside your phone would be pointless, and raise the cost unnecessarily. So they don't.
Both have a different working mechanism...
Roughly, AC to DC uses....a transformer to step down, a rectifier to convert it to pulsating DC, and a filter to smooth it out
Roughly DC to AC ....uses an oscillator (for the drive signal). This signal is amplified, transistors are used for switching operation, and then it’s given to the transformer...
As you see, the hardware is different and cannot be used.
Spinning a lawnmower blade backwards doesn't reassemble cut grass.
Using the JPEG algorithm backwards can't tell you what the original, uncompressed image was.
Some mechanisms are reversible, and some are not. Pulling up on a see-saw will undo what pushing down on the see-saw did. Uncompressing a ZIP file will get you back to the original file. Those are examples of reversible mechanisms.
A power brick "chops up" alternating current (which is "alternating" between negative and positive many times per second (usually 50 or 60 times per second)) and attempts to give you a smooth-as-possible, constant 5 volts with no negative/positive reversals.
To "make it work in the other direction" you would need to have something that took a smooth, constant 5 volts and change it to the rapidly-switching-back-and-forth pattern of alternating current. This kind of thing is called an "inverter" because it takes positive voltage and "inverts" that to negative voltage at 50 or 60 times per second to give you something close to the alternating current you get from the power company through the wall socket.
Imagine making a lawnmower that worked "in the other direction". It would have to take the cut pieces of grass and graft them back on to the part of the grass blade that is still rooted to the ground. Most people are not interested in a machine that also has that capability, so lawnmower companies save a great deal of money by not adding it. A "reversible power brick" is not as complicated to produce as a reversible lawnmower. But the analogy is valid in the sense that either machine would require completely new mechanisms if they wanted to reverse their current function.
We have these and they form the basis of most small scale UPS offerings. The UPS plugs in and charges/maintains a battery, when power is lost the battery powers an inverter. Choice of voltages could be arbitrary.Feeding back to the grid requires some scaling, but this could be a local closed system.
In electro-mechanical systems it is possible to have an armature that acts as both a motor and an alternator/generator crank for generation or supply current for motive force.