> db.coll.update({}, {$set: {a: {$ref: "c", $db: "test"}}})
WriteResult({
	"nMatched" : 0,
	"nUpserted" : 0,
	"nModified" : 0,
	"writeError" : {
		"code" : 55,
		"errmsg" : "The DBRef $ref field must be following by a $id field"
	}
})

> db.coll.insert({a: {$ref: "c", $id: 0, $db: "test"}})
WriteResult({ "nInserted" : 1 })
> db.coll.update({}, {$unset: {"a.$id": true}})
WriteResult({ "nMatched" : 1, "nUpserted" : 0, "nModified" : 1 })
> db.coll.find()
{ "_id" : ObjectId("594d2381ae497a9bea475a71"), "a" : { "$ref" : "c", "$db" : "test" } }