Engineering Math - Quick Reference                                 Home : www.sharetechnote.com Hill Function   It is very usefull function to approximate various degree of Hard Limitor (Similar to Step function) just by changing Ka, A, n in the following equation. This is very widely used in BioChemistry.   Example 1 >  When n > = 0     n = 2; A = 0.5; Ka = 1.0; L = 0:0.1:10;   Theta = A ./((Ka ./ L).^n .+ 1); plot(L,Theta); xlim([L(1),L(length(L))]); ylim([0,1.25 .* max(Theta)]);xlabel('L');ylabel('Theta');   Example 2 >   When n > = 0     A = 0.5; Ka = 1.0; L = 0:0.1:10;   for n=0:1.0:10     Theta = A ./((Ka ./ L).^n .+ 1);     plot(L,Theta); xlim([L(1),L(length(L))]); ylim([0,1.25 .* max(Theta)]);xlabel('L');ylabel('Theta');     hold on; end;   Example 3 >   When n < = 0     n = -2; A = 0.5; Ka = 1.0; L = 0:0.1:10;   Theta = A ./((Ka ./ L).^n .+ 1); plot(L,Theta); xlim([L(1),L(length(L))]); ylim([0,1.25 .* max(Theta)]);xlabel('L');ylabel('Theta');   Example 4 >   When n < = 0     A = 0.5; Ka = 1.0; L = 0:0.1:10;   for n=0:-1.0:-10     Theta = A ./((Ka ./ L).^n .+ 1);     plot(L,Theta); xlim([L(1),L(length(L))]); ylim([0,1.25 .* max(Theta)]);xlabel('L');ylabel('Theta');     hold on; end;