Dear 

by matlab

a=0.256;

w=2*pi*20*10^(6);

m=4*pi*10^(-7);

D=5030*10^(-6);

h=30*10^(-6);

b=30*10^(-6);

P=1.72*10^(-8);

p=10*10^(-6);

x=(w*m*D*h*b*(1-a))/(4*pi*P*p);

y=log((1+a)/(1-a));

z=0.2235*((1-a)/(1+a));

Q=(x)*(y+z+0.726)

Q= 340.0829

Thank You Saif,,,I just wonder for planar spiral coil (The entire coil is embedded in silicon substrate) the permeability suppose air or silicon?

Dear Norliana,

After revising the paper, your answer and Saif answer, i came that the mistake is the value of the distance between two adjacent copper paths p. You took the value of p equal to the value of the gap between the two paths. But the distance between the two paths must be measured from the center of the path to the path of the adjacent center. Since the the width of the path is 30 um and the gap is 10um , this gives 30+10=40 um =P. Accordingly your value must be scaled by down by 4 which gives a value for Q= 84.75 which is very near from the that given in the paper. 

On the other side the authors gave values for the resistance of the coil R= 11.58 ohm and L=7.62 uH. Then according to these values Q= wL/R= 82.69, which is more approaching the value calculated by the given formula.

Best wishes

Thank You Abdelhalim Zekry for the answer.