That is a hard question to answer because it depends on where you want to operate relative to the frequency of its resonance.  Let's say a metamaterial has a dimension of 1 cm and it has its resonance at 4 GHz.  This is roughly 1/10 of a wavelength, however, you may be interested in its electromagnetic properties away from its resonance.  My group is working on nonresonant metamaterials where we operate far below the resonance.  In this case our period can be a billionth of a wavelength and it would still work just fine.  If you are looking for negative values for mu/eps then you will be working pretty close to the resonance.  Other times you may be interested in values less than one which will put you at some other range of frequencies away from the resonance.  Other times you will be more interested in the slope of the effective properties vs frequency (dispersion) and will operate at whatever range of frequencies you need.

You can also load your unit cells with dielectric (or magnetics) to "shrink" their size.

I hope this helps explain why it is a difficult question to answer.  More information is needed about how you will be using the metamaterial.

I am of the opinion what Raymond wrote. Many follow the effective permittivity method only.

Best wishes Shweta

The period P of unit cell of metamaterial needs to meet the conditions P(1+sin(theta))

It is convenient to have one cell into a period and you can have one or more split ring in one cel.....it depends on your structure to study and your goal.

How to calculate the dimensions of the unit cell, Mr. Zhang Cheng Li gave a valid explanation.

Thankyou all for the help 

can you guide me what should be the dimensions of air box while testing unit cell.

I would not worry about the dimensions. You can always just scale the size of your unit cell to shift the response to whatever frequency you want. Just pick a dimension, simulate it, find the behavior you want, determine the frequency where that happens, determine the frequency where you want it to happen, and scale your design. I don't even see dimensions or frequencies anymore.

This concept is called scalability. Say you design a metamaterials with dimension 1 cm along each side and it does something magical at 4.0 GHz. If you scale all of the physical dimensions so that each side becomes 2 cm, the metamaterial will behave the exact same way, but at 2.0 GHz.

@Shweta, What is the simulator you are using ? I think In general, you should follow the far field rule as (2d^2/lambda), where d is largest dimension and lambda is operating wavelength.

i am using CST

This is the program.The value of airbox d has to be mentoned.My substrate is of 1.6mm

%NOTE: When saving data in CST save the data as follows: the magnitude of

%s11 as s11.txt, the magnitude of s21 as s21.txt, the phase of s11 as

%s11_arg.txt,and the phase of s21 as s21_arg.txt.

clc;

s11_mag=dlmread('C:\Users\Admin\Documents\MATLAB\s11.txt','',2,0);

format long;

s21_mag=dlmread('C:\Users\Admin\Documents\MATLAB\s21.txt','',2,0);

s11_arg=-1.*dlmread('C:\Users\Admin\Documents\MATLAB\s11_arg.txt','',2,0);

s21_arg=-1.*dlmread('C:\Users\Admin\Documents\MATLAB\s21_arg.txt','',2,0);

%convert magnitude and phase of s11 and s21 into a complex number

s11= s11_mag(:,2).*(cosd(s11_arg(:,2))+1i*sind(s11_arg(:,2)));

s21= s21_mag(:,2).*(cosd(s21_arg(:,2))+1i*sind(s21_arg(:,2)));

%impedance has a both positive and negative answer

z_pos = ((((1+s11).^2-s21.^2)./((1-s11).^2-s21.^2)).^.5);

z_neg = -1.*z_pos;

% used to determine the values for the imaginary part of the refractive

% index.

z=zeros(length(z_pos),1);

for i=1:length(z_pos)

if real(z_pos(i))>=0

z(i)=z_pos(i);

else

z(i)=z_neg(i);

end

end

z_real=real(z);

e_inkd_pos=(s21./(1-s11.*((z_pos-1)./(z_pos+1))));

e_inkd_neg=(s21./(1-s11.*((z_neg-1)./(z_neg+1))));

e_inkd=zeros(length(e_inkd_pos),1);

d=0.0024;

f=(10^9).*s11_mag(:,1);

vp=3E8;

lamda=vp./f;

k=(2*pi)./lamda;

n_pos=(imag(log(e_inkd_pos))-1i.*real(log(e_inkd_pos)))./(k.*d);

n_neg=(imag(log(e_inkd_neg))-1i.*real(log(e_inkd_neg)))./(k.*d);

n=zeros(length(n_pos),1);

for i=1:length(n)

if imag(n_pos(i))>=0

n(i)=n_pos(i);

z(i)=z_pos(i);

e_inkd(i)=e_inkd_pos(i);

else

n(i)=n_neg(i);

z(i)=z_neg(i);

e_inkd(i)=e_inkd_neg(i);

end

end

z_imag=imag(z);

epsilon=n./z;

mue=n.*z;

% the plot of the imaginary part of the refractive index.

figure(1)

hold on

plot(f,s11_mag(:,2),'g');

plot(f,s21_mag(:,2),'r');

axis([8E9 14E9 8 60]); % note [ - - - -] here 1st dash is lower limit of x-axis and 2nd one is higher range we can change as per our frequency range

legend('s11','s21');

title('s-parameters vs frequency');

xlabel('frequency');

ylabel('Magnitude of S');

hold off

figure(2)

hold on

plot(f,(pi/180).*s11_arg(:,2),'g');

plot(f,(pi/180).*s21_arg(:,2),'r');

axis([8E9 14E9 -200 200]); % note [ - - - -] here 1st dash is lower limit of x-axis and 2nd one is higher range we can change as per our frequency range

legend('s11','s21');

title('Phase of S vs frequency');

xlabel('frequency');

ylabel('Phase of S(radians)');

hold off

figure(3)

hold on

plot(f,real(n),'g');

plot(f,imag(n),'r');

axis([8E9 14E9 -100 100]); % note [ - - - -] here 1st dash is lower limit of x-axis and 2nd one is higher range we can change as per our frequency range

legend('Re(n)','Im(n)');

title('refractive index vs frequency');

xlabel('frequency');

ylabel('refractive index');

hold off

figure(4)

hold on

axis([8E9 14E9 -200 200]); % note [ - - - -] here 1st dash is lower limit of x-axis and 2nd one is higher range we can change as per our frequency range

plot(f,z_real,'g');

plot(f,z_imag,'r');

legend('Re(z)','Im(z)');

title('impedance vs frequency');

xlabel('frequency');

ylabel('impedance(z)');

hold off

figure(5)

hold on

axis([8E9 14E9 -100 100]); % note [ - - - -] here 1st dash is lower limit of x-axis and 2nd one is higher range we can change as per our frequency range

plot(f,real(epsilon),'g');

plot(f,imag(epsilon),'r');

legend('Re(epsilon)','Im(epsilon)');

title('permittivity vs frequency');

xlabel('frequency');

ylabel('permittivity');

hold off

figure(6)

hold on

axis([8E9 14E9 -100 100]); % note [ - - - -]here 1st dash is lower limit of x-axis and 2nd one is higher range and we can change as per our frequency range

plot(f,real(mue),'g');

plot(f,imag(mue),'r');

legend('Re(mue)','Im(mue)');

title('permeability vs frequency');

xlabel('frequency');

ylabel('permeability');

hold off ]

% the programe ends here %

The size of cells should be less than 0.1 wavelength.

Conference Paper Metamaterials on antenna solutions

Conference Paper Parametric Synthesis of 3D Structure of SRR Element of the M...

The quantity of SRR inside cells can be any