How to filter document libraries using CAML query?

In my powershell script, I get all lists, then loop through and filter based on if its a document library and if its a certain content type, but I want to do this through CAML.

This is the loop logic

# get all the lists from the source location
$sourceLists = $sourceWebObj.Lists;

# loop through all lists
foreach ($sourceList in $sourceLists) {

    # check if it's a valid document library and it's content type is what we want
    if($sourceList.BaseType -eq "DocumentLibrary" -and $sourceList.ContentTypes[$DocLibContentType] -ne $null) {

    }
}

How can I do the same thing with CAML?

Thanks