First of all I have learned that $K_\mathrm{a} = \frac{[\ce{H+}] [\ce{A-}]} {[\ce{HA}]}$ . Also I have been informed that $K_\mathrm{a}$ value is independent of concentration.
So let us take an example. Suppose 1 mole of acid $\ce{HA}$ dissociates to form 0.9 moles of $\ce{H+}$ ions and 0.9 mole of $\ce{A-}$ ions and 0.1 mole of undissociated $\ce{HA}$. So, the $K_\mathrm{a}$ value will be $K_\mathrm{a} = \frac{[0.9] [0.9]} {[0.1]}=8.1$.
But if we take 2 moles of same acid then, 1.8 moles of H+ ions and 1.8 moles of A- ions will be formed leaving 0.2 moles of undissociated HA. This time $K_\mathrm{a} = \frac{[1.8] [1.8]} {[0.2]}=16.2$.
So we can see that $K_\mathrm{a}$ has increased with increase in concentration. Can you tell me where my assumption is wrong?