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i have a 28mAh power brick capable of charging my laptop when charged. I bought a 28W solar panel which outputs 5V over usb capable of charging ipads etc, however when i connected it to power brick's input it couldnt charge it (or at least charging light didnt come on) Its only then i realised power brick is running off 15-19V 2A mains charger. Is it possible to step up my solar panel to this voltage and trickle charge the power brick at all?

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    \$\begingroup\$ Details of the output circuit of the brick charger would be ideal else it's guesswork. \$\endgroup\$ – Andy aka Jul 17 '16 at 11:47
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    \$\begingroup\$ 28mAh is very small. \$\endgroup\$ – immibis Jul 17 '16 at 12:34
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    \$\begingroup\$ Welcome to EE.SE! While yes, it's physically possible to step up a voltage using a switching power supply, you haven't provided enough details to gauge the possibility of charging. Please provide more information about the solar panel, power brick, and mains charger: model number and datasheet or product specifications page. A picture of the device label may help if online details aren't available. \$\endgroup\$ – user2943160 Jul 17 '16 at 12:54
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You didn't provide enough details so I can't say for sure but it's possible to step up the voltage but it will not help you that you for a simple reason:

your device runs on 15-19 volts 2 amps which means it runs on 30-38 watts but the solar panels output is 28 watts , so if your power brick doesn't work on less than 2 amps or a voltage below 15 volts then it won't work again.

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Yes, it is possible. You need a boost or step-up converter. A step-up converter can increase the voltage (but the power VI is constant.)

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