In communications, one of the most well-known equations is the Friis transmissio

ID: 2075945 • Letter: I

Question

In communications, one of the most well-known equations is the Friis transmission formula. It takes characteristics of a transmitting antenna, and a receiving antenna, and calculates what the predicted receive power may be for a given wave being transmitted. It can be defined as: P_R = P_TG_TG_R lambda^2/(4 pi r)^2 definitions: P_R - power received at receiving antenna G_R - gain (linear, no units) of receiving antenna P_T - power transmitted (in Watts) of transmitting antenna G_T - gain (linear, no units) of transmitting antenna lambda - wavelength of the wave being transmitted r - distance between the two antennas Cellphones operate in the United States between 800e6 and 1900e6 (MHz). Their wavelength lambda are computed from c/frequency, where c is the speed of light 3e8 m/s. Create a frequency vector in this range with a stepsize of 10e6. Then create a matching wavelength vector. Make a function called frissFormula() that will compute the received power given the input definitions above. You need to calculate the received power across the wavelength vector you computed in step (1). Assume a transmit power of 10 (Watts), a transmit gain of 1.5. and receiver gain of 1. Do this for 3 different distances (r): 5e3. 10e3.30e3 (km) Make a single figure showing the received power in decibals vs frequency for each distance. You calculate decibal power by 10*np.logl0(power). In other words, have one line plot for 5km. one for 10km. and one for 30km. I'd like you to reverse the problem you calculated in steps (1-4). Imagine the transmitter is now a cellphone with a transmit power of 1 (Watt), and the receiver is the tower. Use the same gains as before and calculate the receive power at the tower across the wavelengths for the same three distances. Make a single figure showing all 3 plots like you did for step (4).

Explanation / Answer

I am going to solve this question using MATLAB.

I will give code for questions and explain the script with comments in code.

Of course I will give snapshot for the outputs.

1)Ans:

% To create a wavelength vector.
frequency=800e6:10e6:1900e6;%United States Cellphones operation frequency.
c = 3e8;%The speed of light.
lambda = c./frequency;%The wavelength lambda are computed from formula lambda = (c/frequency).

2)Ans:

% This function will compute the received power given
%Definitions
%P_R -power received at receiving antenna
%G_R -gain(linear,no units) of receiving antenna
%G_T -gain(linear,no units) of transmitting antenna
%P_T -power transmitted(in Watts) of transmitting antenna
%lambda - wavelength of the wave being trasmitted
%r - distance beween the two antennas.
function P_R =frissFormula(G_R,G_T,P_T,lambda,r)%Function fto compute the received power with input parameters as definitions above.

Numarator = (P_T*G_T*G_R*(lambda)^2);%The numarator value of P_R

Denominator = ((4*pi*r)^2);%The demominator value of P_R

P_R = (Numarator/Denominator);

end

3)Ans:

%Given P_T = 10 Watts
% G_T = 1.5;
% G_R = 1;
%For three different distances r=5e3,10e3,30e3 km
P_T = 10;
G_T = 1.5;
G_R = 1;
P_R = zeros([3 111]);
r=[5e3 10e3 30e3];
for i=1:3
    for j=1:length(lambda)
        P_R(i,j)=frissFormula(G_T,G_R,P_T,lambda(j),r(i));
    end
end

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