It depends on dungeon structure - unless you enforce a completely linear structure then you don't know how many of your planned encounters the party will defeat before finding a way to the next level. And it also depends on what encounter difficulties you want (easy versus deadly) and what other sources of XP you have, if any (awards for social encounters, milestone XP awards, etc). There are ways to conceal a linear structure ("you need to find the green key to unlock the green door to reach the stairs, but it's guarded by a dragon who wants you to recover the treasure from the bottom of the well, which is guarded by a water weird", etc) if you're sure that's what you want.
So assuming you're happy to enforce a linear structure this is fairly simple to calculate using the XP per level tables and the XP per encounter recommendations. The Old Guy Gaming blog did a breakdown of this (6 'typical' encounters to get to level 2, 5.33 more to get to level 3, 10.29 to get to level 4...) and so did the Angry DM. I'd recommend the second as it explores encounter heterogeneity in more detail.
Personally, if you really want to tie dungeon level to player level I'd focus on making individual encounters interesting and use milestone XP for either finding the stairs or overcoming particular factions (slaying the lizard king, helping the kobolds defeat the goblin boss, etc). Or you can make the players aware that things will get more dangerous as you get deeper, and they'll work out their own balance between risk and reward.