This document describes a student project to implement Friis transmission formula using MATLAB. The project report includes: 1) An objective to use MATLAB to calculate received power given various antenna parameters. 2) An introduction that describes Friis transmission formula and its ideal assumptions. 3) MATLAB code examples that allow the user to input antenna parameters like transmitted power, gains, wavelength, and distance to calculate received power in different unit systems. 4) Additional MATLAB code to calculate received power for a radar targeting an object by accounting for the object's cross-sectional area. 5) The project aims to predict received power given transmission conditions to aid antenna system design and power adjustment.

1. FRII’S FORMULA USING MATLAB
Project Report submitted to VIT University Chennai Campus in the partial
fulfillment of the Requirements for the completion of course
ANTENNAS AND WAVE PROPAGATION (ECE306)
By
KOTESWARA RAO – 11BEC1015
M.ARAVIND KUMAR –11BEC1032
VIDYANATH – 11BEC1035
HARSHAVARDHAN – 11BEC1074
BHARADWAJ – 11BEC1133
Under the esteemed guidance of
PROF.RAVI PRAKASH
School of Electronics Engineering (SENSE)

2. INDEX
Sl. No Contents Page no.
1 OBJECTIVE 3
2 MOTIVATION 3
3 INTRODUCTION 3
4 IMPORTANCE&LEARNING 5
5 DERIVATION 6
7 MATLAB CODES 9
8 CONCLUSION 16
9 FUTURE SCOPE 16
10 REFERENCES 17

3. OBJECTIVE:
The main objective of our project is to implement frii’s formula using matlab. In the
sense what we are going to do is we input all the parameters and then get the received
power.
MOTIVATION:
Why we are doing this project is because in antennas we see that the received power
is always less than the transmitted power. This is because of the losses that occur
during the propagation. So from our project we can basically know beforehand how
much power we are going to receive and based on that the power transmitted can be
adjusted and thus easing our work.
INTRODUCTION:
In its simplest form, the Friis transmission equation is as follows. Given two
antennas, the ratio of power available at the input of the receiving antenna, , to
output power to the transmitting antenna, , is given by
where and are the antenna gains (with respect to an isotropic radiator) of the
transmitting and receiving antennas respectively, is the wavelength, and is the
distance between the antennas. The inverse of the factor in parentheses is the so-
called free-space path loss. To use the equation as written, the antenna gain
may not be in units of decibels, and the wavelength and distance units must be the
same. If the gain has units of dB, the equation is slightly modified to:

4. (Gain has units of dB, and power
has units of dBm or dBW)
This simple form applies only under the following ideal conditions:
 (Reads as much greater than ). If , then the equation would
give the physically impossible result that the receive power is greater than the
transmit power, a violation of the law of conservation of energy.
 The antennas are in unobstructed free space, with no multipath.
 is understood to be the available power at the receive antenna terminals.
There is loss introduced by both the cable running to the antenna and the
connectors. Furthermore, the power at the output of the antenna will only be
fully delivered into the transmission line if the antenna and transmission line
are conjugate matched.
 is understood to be the power delivered to the transmit antenna. There is
loss introduced by both the cable running to the antenna and the connectors.
Furthermore, the power at the input of the antenna will only be fully delivered
into free space if the antenna and transmission line are conjugate matched.
 The antennas are correctly aligned and polarized.
 The bandwidth is narrow enough that a single value for the wavelength can
be assumed.
The ideal conditions are almost never achieved in ordinary terrestrial
communications, due to obstructions, reflections from buildings, and most
importantly reflections from the ground. One situation where the equation is
reasonably accurate is in satellite communications when there is negligible
atmospheric absorption; another situation is in anechoic chambers specifically
designed to minimize reflections.

5. IMPORTANCE & LEARNING
Transmission Formula of Friis Equation
Equation 1:
Equation [1] shows that more power is lost at higher frequencies. This is a
fundamental result of the Frii’s Transmission Equation. This means that for antennas
with specified gains, the energy transfer will be highest at lower frequencies. The
difference between the power received and the power transmitted is known as path
loss. Said in a different way, Frii’s Transmission Equation says that the path loss is
higher for higher frequencies.
The importance of this result from the Frii’s Transmission Formula cannot be
overstated. This is why mobile phones generally operate at less than 2 GHz. There
may be more frequency spectrum available at higher frequencies, but the associated
path loss will not enable quality reception. As a further consequence of Frii’s
Transmission Equation, suppose you are asked about 60 GHz antennas. Noting that
this frequency is very high, you might state that the path loss will be too high for
long range communication - and you are absolutely correct. At very high frequencies
(60 GHz is sometimes referred to as the mm (millimeter wave) region), the path loss
is very high, so only point-to-point communication is possible. This occurs when the
receiver and transmitter are in the same room, and facing each other.
As a further corollary of Frii’s Transmission Formula, do you think the mobile phone
operators are happy about the new LTE (4G) band that operates at 700MHz? The
answer is yes: this is a lower frequency than antennas traditionally operate at, but
from Equation [1], we note that the path loss will therefore be lower as well. Hence,
they can "cover more ground" with this frequency spectrum, and a Verizon Wireless
executive recently called this "high quality spectrum", precisely for this reason. Side

6. Note: On the other hand, the cell phone makers will have to fit an antenna with a
larger wavelength in a compact device (lower frequency = larger wavelength), so
the antenna designer's job got a little more complicated!
DERIVATION:
1. Let's imagine that there are two antennas, entirely in free space. There is no
Earth or any other object near enough to affect propagation. Let's also assume
that these antennas are far enough apart that the antennas interact only by their
far fields.
2. To start, let's assume that both antennas are isotropic, meaning that they
radiate equally in each direction. If we supply a pulse of energy to such an
antenna, this energy will spread out as a sphere, to infinity, at the speed of
light. It also means that if we supply a constant power to such an antenna, then
for any sized sphere centered on that antenna, the power passing through that
sphere is equal to the power being fed to the antenna.
Assume that Watts of total power are delivered to the transmit antenna.
For the moment, assume that the transmit antenna is omnidirectional, lossless, and
that the receive antenna is in the far field of the transmit antenna. Then the power
density p (in Watts per square meter) of the plane wave incident on the receive
antenna a distance R from the transmit antenna is given by:

7. If the transmit antenna has an antenna gain in the direction of the receive antenna
given by , then the power density equation above becomes:

8. The gain term factors in the directionality and losses of a real antenna. Assume now
that the receive antenna has an effective aperture given by . Then the power
received by this antenna
Since the effective aperture for any antenna can also be expressed as:
The resulting received power can be written as:
This is known as the Friis Transmission Formula. It relates the free space path loss,
antenna gains and wavelength to the received and transmit powers.
• The Frii’s equation for radar is
Pr/Pt=GtGr((λ2
)*S/((4*π)3
*R4
)
S = target area cross section

9. MATLAB CODES:
PROGRAM 1:
For the conversion of values:
h=input('n 1. To convert from watt to db n 2. To convert from watt to dbm
n 3. To convert from db to watt n 4.To convert from dbm to watt n
5frequency to wavelenth ');
if (h==1)
value=input('enter the value to be converted =');
value_converted_db=10*log10(value);
fprintf('the converted value is %d',value_converted_db)
elseif(h==2)
value=input('enter the value to be converted =');
value_converted_dbm=10*log10(value/10^(-3));
fprintf('the converted value is %d',value_converted_dbm)
elseif(h==3)
value=input('enter the value to be converted =');
value_converted_watt=10^(value/10);
fprintf('the converted value is %d',value_converted_watt)
elseif(h==4)
value=input('enter the value to be converted=');
value_converted_watt=(10^(value/10))*10^(-3);
fprintf('the converted value is %d',value_converted_watt)
else
value=input('enter the value to be converted=');
value_converted_freq=(3*10^8)/(value);
fprintf('the converted value is %d',value_converted_freq)
end

10. PROGRAM 2:
MATLAB CODE FOR FRIIS FORMULA:
fprintf('n********************FRIIS TRANSMISSION FORMULA FOR RECEIVER POWER
**********************n ')
%%%%%% FRIIS Equation %%%%%%%%%
% Friis free space propagation model:
% Pt * Gt * Gr * (Wavelength^2)
% Pr = --------------------------
% (4 *pi * d)^2 * L
a=input('enter 1. if the values you are going to give are in decibles n 2.
if the values you are going to give are not in decibles n3. if The values
you are going to give are in dBmn 4.if if frequency is given ');
if(a==1)
P1=input(' enter the value of transmitted power in decibles =');
G1=input('enter the value of transmittor gain in decibles =');
G2=input('enter the value of receiver gain in decibles =');
Wavelength=input ('enter the value of wavelength =');
R=input('enter the distance between transmitter and receiver =');
Pt=10^(P1/10);
Gt=10^(G1/10);
Gr=10^(G2/10);
Pr=(Pt * Gt * Gr * (Wavelength^2))/((4 *pi * R)^2 );
fprintf('n the value of received power is %d n',Pr)
Prdbm=10*(log10(Pr/10^(-3)));
fprintf('n the value of received power in dbm %d n',Prdbm)
elseif(a==2)
Pt=input(' enter the value of transmitted power in watts =');
G1=input('enter the value of transmitter gain in watts=');
G2=input('enter the value of receiver gain in watts=');
Wavelength=input ('enter the value of wavelength=');
R=input('enter the distance between transmitter and receiver =');
Pr=(Pt * Gt * Gr * (Wavelength^2))/((4 *pi * R)^2 );
fprintf('n the value of received power is %d n',Pr)
Prdbm=10*(log10(Pr/10^(-3)));
fprintf('n the value of received power in dbm %d n',Prdbm)
elseif(a==3)
P1=input(' enter the value of transmitted power in dbm =');
G1=input('enter the value of transmittor gain in dbm =');
G2=input('enter the value of received power gain in dbm =');
Wavelength=input ('enter the value of wavelength =');
R=input('enter the distance between transmitter and receiver =');
Pt=(10^(P1/10))*10^(-3);
Gt=(10^(G1/10))*10^(-3);
Gr=(10^(G2/10))*10^(-3);

11. Pr=(Pt * Gt * Gr * (Wavelength^2))/((4 *pi * R)^2 );
fprintf('n the value of received power is %s n',Pr)
Prdbm=10*(log10(Pr/10^(-3)));
fprintf('n the value of received power in dbm %d n',Prdbm)
else
P1=input(' enter the value of transmitted power in watts =');
G1=input('enter the value of transmittor gain in decibles =');
G2=input('enter the value of received power gain in decibles =');
freq=input ('enter the value of freq =');
R=input('enter the distance between transmitter and receiver =');
Pt=P1;
Wavelength=(3*10^8)/(freq);
Gt=10^(G1/10);
Gr=10^(G2/10);
Pr=(Pt * Gt * Gr * (Wavelength^2))/((4 *pi * R)^2 );
fprintf('n the value of received power is %d n',Pr)
Prdbm=10*(log10(Pr/10^(-3)));
fprintf('n the value of received power in dbm %d n',Prdbm)
end

12. PROGRAM 3:
MATLAB CODE FOR FINDING RECEIVED POWER BETWEEN RADAR AND
TARGET
fprintf('n********************FRIIS TRANSMISSION FORMULA FOR RADAR AND
TARGET **********************n ')
a=input('enter 1. if the values you are going to give are in decibles = n 2.
if the values you are going to give are not in decibles = n 3. if the values
you are going to give are in dBm n 4. if frequency is given ');
if(a==1)
P1=input(' enter the value of transmitted power in watts =');
G1=input('enter the value of transmittor gain in decibles =');
G2=input('enter the value of receiver gain in decibles =');
Wavelength=input ('enter the value of wavelength =');
S=input('enter the value of the cross section area =');
R=input('enter the distance between transmitter and receiver =');
Pt=P1;
Gt=10^(G1/10);
Gr=10^(G2/10);
Pr=(Pt * Gt * Gr * (Wavelength^2)*S)/(((4 *pi )^3)* (R)^4 );
fprintf('n the value of received power is %d n',Pr)
Prdbm=10*(log10(Pr/10^(-3)));
fprintf('n the value of received power in dbm %d n',Prdbm)
elseif(a==2)
Pt=input(' enter the value of transmitted power in watts =');
G1=input('enter the value of transmittor gain =');
G2=input('enter the value of receiver gain =');
S=input('enter the value of the cross section area =');
Wavelength=input ('enter the value of wavelength =');
R=input('enter the distance between transmitter and receiver =');
Pr=(Pt * Gt * Gr * (Wavelength^2)*S)/(((4 *pi )^3)* (R)^4 );
fprintf('n the value of received power is %d n',Pr)
Prdbm=10*(log10(Pr/10^(-3)));
fprintf('n the value of received power in dbm %d n',Prdbm)
elseif(a==3)
P1=input(' enter the value of transmitted power in dbm =');
G1=input('enter the value of transmittor gain in dbm =');
G2=input('enter the value of receiver gain in dbm =');
S=input('enter the value of the cross section area =');
Wavelength=input ('enter the value of wavelength =');
R=input('enter the distance between transmitter and receiver =');
Pt=(10^(P1/10))*10^(-3);
Gt=(10^(G1/10))*10^(-3);
Gr=(10^(G2/10))*10^(-3);
Pr=(Pt * Gt * Gr * (Wavelength^2)*S)/(((4 *pi )^3)* (R)^4 );
fprintf('n the value of received power is %s n',Pr)

13. Prdbm=10*(log10(Pr/10^(-3)));
fprintf('n the value of received power in dbm %d n',Prdbm)
else
P1=input(' enter the value of transmitted power in watts =');
G1=input('enter the value of transmittor gain in decibles =');
G2=input('enter the value of receiver gain in decibles =');
freq=input ('enter the value of freq =');
S=input('enter the value of the cross section area =');
R=input('enter the distance between transmitter and receiver =');
Pt=P1;
Wavelength=(3*10^8)/(freq);
Gt=10^(G1/10);
Gr=10^(G2/10);
Pr=(Pt * Gt * Gr * (Wavelength^2)*S)/(((4 *pi )^3)* (R)^4 );
fprintf('n the value of received power is %d n',Pr)
Prdbm=10*(log10(Pr/10^(-3)));
fprintf('n the value of received power in dbm %d n',Prdbm)
end

14. PROGRAM 4:
MATLAB CODE FOR FINDING MAXIMUM DISTANCEBETWEEN RADAR
AND TARGET
fprintf('n********************FRIIS TRANSMISSION FORMULA FOR RADAR AND
TARGET MAXIMUM DISTANCE************************n ')
a=input('enter 1 if the values you are going to give are in decibles n 2 if
the values you are going to give are not in decibles n 3 if the values you
are going to give are in dBm n 4 if frequency is given ');
if(a==1)
P1=input(' enter the value of transmitted power in decibels =');
P2=input('enter the value of received power in decibles =');
G1=input('enter the value of transmittor gain in decibles =');
G2=input('enter the value of receiver gain in decibles =');
Wavelength=input('enter the value of wavelength =');
S=input('enter the value of the cross section area =');
Pt=10^(P1/10);
Gt=10^(G1/10);
Gr=10^(G2/10);
Pr=10^(P2/10);
R=((Pt * Gt * Gr * (Wavelength^2)*S)/(((4 *pi )^3)* Pr ))^0.25;
fprintf('n the distance is %d n',R)
elseif(a==2)
Pt=input(' enter the value of transmitted power in watts =');
Pr=input('enter the value of received power =');
G1=input('enter the value of transmittor gain =');
G2=input('enter the value of receiver gain =');
Wavelength=input ('enter the value of wavelength =');
S=input('enter the value of the cross section area =');
R=((Pt * Gt * Gr * (Wavelength^2)*S)/(((4 *pi )^3)* Pr ))^0.25;
fprintf('n the distance is %d n',R)
elseif(a==3)
P1=input(' enter the value of transmitted power in dbm =');
P2=input('enter the value of received power =');
G1=input('enter the value of transmittor gain in dbm =');
G2=input('enter the value of receiver gain in dbm =');
Wavelength=input ('enter the value of wavelength =');
S=input('enter the value of the cross section area =');
Pt=(10^(P1/10))*10^(-3);
Gt=(10^(G1/10))*10^(-3);
Gr=(10^(G2/10))*10^(-3);
Pr=(10^(P2/10))*10^(-3);
R=((Pt * Gt * Gr * (Wavelength^2)*S)/(((4 *pi )^3)* Pr ))^0.25;
fprintf('n the distance is %d n',R)

15. else
P1=input(' enter the value of transmitted power in watts =');
P2=input('enter the value of received power =');
G1=input('enter the value of transmittor gain in decibles =');
G2=input('enter the value of receiver gain in decibles =');
freq=input ('enter the value of freq =');
S=input('enter the value of the cross section area =');
Pt=P1;
Pr=P2;
Wavelength=(3*10^8)/(freq);
Gt=10^(G1/10);
Gr=10^(G2/10);
R=((Pt * Gt * Gr * (Wavelength^2)*S)/(((4 *pi )^3)* Pr ))^0.25;
fprintf('n the distance is %d n',R)
end

16. CONCLUSION:
With the help of matlab we successfully implemented frii’s transmission formula
FUTURE SCOPE:
The formula we implemented is the basic friis equation our future scope is to
implement the frii’s equation which was modified which includes effects of
mismatch, antenna pointing, polarization and absorption.

17. REFERENCES:
http://en.wikipedia.org/wiki/Friis_transmission_equation
http://www.random-science-tools.com/electronics/friis.htm
http://www.antennatheory.com
https://u.osu.edu/
www.mathworks.in/
Antenna Theory :Analysis and Design by Balanis