Let me tell how, I would do it.

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Hi, Tom, you will need a minimum of about 12" - 18" fall
on your 20'wide patio,.
ok now you have a size to work from, you know how high the
front will be so now just add 12"/18" to the back where your
roof will fit to the house.
fit/work out where you want the support posts ( +/- 12ft between
you will have to go to the main vertical studs that are apart
of the house screw through the timber,because you will have to
take away all the stucco and insulation, down to where you are
going to fix the ledger board.
now this part of the project is where you pay the big bucks, you
will have to get rolls of lead 10" wide ( dont forget the thicker
it is the more you will have to pay) so go for the mimimum weight.
roll out the lead, and bend it to a slight shape of 4" ( this will be
nailed to the ledger board) the rest will/should hand down.
now turn the lead ( the 6" ) up away from the roof,you will see why
later,