First, let`s talk about the substrate thickness: simulations have shown that, the higher the thickness, the lower the impedance. If your impedance is higher than 100 ohms, try to thicken the substrate. However, avoid make it too thick, or else, the impedance will oscilate with frequency variation. That`s what I`ve noticed using CST.
I`m not sure about the equations, but there is indeed a relation between the highest frequency and the inner radius (the same happens with the lowest frequency and the outer radius). Since your lowest frequency is 2 GHz, you don`t need to make the antenna as large as I did, but in the other hand, the inner radius must be much smaller. But remember that you must regard the fabrication process limitations. I mean, you cannot fabricate an antenna with a gap as small as you want. Besides, the inner radius has some influence in the impedance.
I think I have a paper about an spiral antenna covering the range you need, but I`m not home now, so I can`t send you until monday. I hope I was able to help. And I will be glad to send you any useful paper as soon as I get home.