 Good afternoon everyone. Myself, Piyusha Shedgarh. Today in this session we will see the different applications of magic tea. These are the learning outcomes for this session. At the end of this session, students will be able to explain the properties of magic tea junction. They will be able to explain the different applications of magic tea junction. These are the contents. Now, let us define what is microwave tea junction. Microwave tea junction is an interconnection of the three waveguides in the form of English alphabet T. So, there are the several types of the microwave tea junctions. E-plane tea junction, H-plane tea junction and the combination of both that is E-plane tea junction and the H-plane tea junction which is called as a magic tea junction. Now, before going to start the details of the magic tea junction and its application, you can pause video here for a second and recall that what is S matrix? That is scattering matrix. So, generally the scattering matrix is represented by the input network. S parameters are defined for the microwave network. Hence, the instead of voltage and current measurement, the amplitude of the incident and the reflected voltage wave is measured by using the scattering matrix. Now, what is magic tea? So, consider the rectangular waveguide which having already the two ports, one parallel and the other. These two ports are collinear with each other and the another two ports are connected in parallel and the series to these two ports which forms the magic tea junction. This is also called as a hybrid or 3 dB coupler. So, here arms of the rectangular waveguide makes the two ports called collinear ports that is port 1 and port 2 while the port 3 is called as a H-arm or some port or parallel port and port 4 is called as E-arm or difference port or series port. Now, consider this is the figure for the magic tea junction that is this is the rectangular waveguide which having these two ports are collinear with each other. Whereas, these two ports are connected in parallel and the series that is H-arm and the E-arm forms the magic tea plane. So, here in magic tea plane four ports are present that is this is actual how the magic tea looks like. It having the four ports port 1, 2, 3 and 4. Now, let us discuss the characteristics of the magic tea. So, if the same amount of the signal which is in equal phase is sent to the port 1 and port 2 then the output at the port 4 is 0 while the output at port 3 is nothing but the addition of the signal coming from this port 1 and port 2. Therefore, it is called as the additive property of the magic tea junction. Now, suppose the signal is fed to the port 3 then the power is divided between the port 1 and port 2 equally while there is no any output at the port 4. And therefore, the scattering coefficient S43 is equal to 0. So, that is S43 denotes that you are applying the input to third port while you are checking the output at the fourth port. If the signal is fed at one of the collinear ports that is at the port 1 or port 2 then there appears no any output at the other collinear port. Although these two are the collinear ports as the E-arm produces a phase delay and the H-arm produces a phase advanced. So, this is again the how the power is divided in the magic tea junction. So, these are the port 1 and 2 which are collinear with each other and the port 3 is coupled in forward direction towards the port 1 while the port 4 is connected in forward direction. Therefore, whatever is the power at the port 1 is known as the incident power. Power received at the port 2 is known as the received power. Power obtained at the port 4 is the back power and the power at the port 3 is known as the forward power. Therefore, whatever is the signal suppose fed to this input port 3 then it is equally divided into the port 1 and port 2 while the output at this port 4 is equal to 0. Now, by knowing the properties of this magic tea you can define the scattering matrix for the magic tea junction. So, this is nothing but the scattering coefficients defined with this S matrix. So, this is the scattering matrix for the magic tea junction. Now, let us discuss about the different applications of the magic tea. So, the first application measurement of the impedance. Now, magic tea has been used in the form of the bridge for this application. Now, the null detector is connected to the E-arm while the microwave source is connected to the H-arm that is the port 3. The collinear ports together with these two ports make a bridge and impedance measurement is done by using the balancing of this bridge. Now, this is the diagram for this application that is measurement of the unknown impedance value which is connected to the port 2 while the standard variable known impedance is connected to the port 1. Port 4 is connected to the null detector point while the microwave source is connected to the port 3. Suppose the power is fed to the port 3 that is in terms of the input signal A3 then half of the power is goes towards the port 2 and half of the power is goes towards the port 1. At the port 1 and port 2 there is mismatching of the impedance that is the impedance at this port 1 and port 2 are not matches with the characteristics impedance and therefore there will be some reflection of the signal. This reflection of the signal is denoted with the reflection coefficient at the port 1 is rho 1 and at the port 2 is rho 2. So, again from this signal this amount of the power is sent towards the port 4 that is at the null detector and some of the power from this port 2 again sent to this null detector which is added at the port 4. Now, suppose consider that the rho 1 and rho 2 are the reflection coefficients at the port 1 and port 2 respectively. The reflection from the port 1 is given by A3 rho 1 by root 2, A3 times rho 2 by root 2 is the reflection from the port 2. So, resultant wave reaches at the null port that is at the port 4 is given by the addition of these two signals. So, this is the equation at the port 4. Port 4 is connected to the e port therefore you know that the signal R which having the same magnitude, but the phase is 180 degree out of phase. By solving this equation you are getting 1 by 2 A3 times of rho 1 minus rho 2. So, for balancing the bridge this value should be equal to 0. Therefore, it can be equated to 0 thus rho 1 minus rho 2 becomes equal to 0 and by solving this you are getting the equation rho 1 equal to rho 2. That is the reflection coefficient at port 1 is equal to the reflection coefficient at port 2. But you know that the reflection coefficient can be represented in terms of the impedance is z1 minus zed upon z1 plus zz, where z1 is the impedance at the port 1 while the zz is the unknown impedance and rho 2 equal to z2 minus zed upon z2 plus zed. Now, you know that rho 1 is equal to rho 2 therefore equating these two equations in terms of the impedance and by solving this equation you are getting that z1 equal to z2. Thus the unknown impedance can be measured by using the magic T junction as a bridge by adjusting the standard variable impedance till the bridges becomes balanced and both impedances becomes equal. Now, consider another application of the magic T magic T as a duplexer circuit. So, what is duplexer circuit? Duplexer circuit is a circuit which works as a both the transmitter and the receiver thus here the port 1 and port 2 are used as a receiver and the transmitter and antenna is connected one of the E-arm port and the matched load is connected to the H-arm port. So, here it is a duplexer application of the magic T junction one two ports are connected to the receiver and transmitter. So, that there is no any mixing of the signal at the port 1 and port 2 signal. The transmitted signal half of the signal is going towards this antenna and from this antenna the signal is radiated into the free space while the half of the power is goes towards this matched load where the reflection equal to 0 that is the total wave is absorbed at this port 3. Thus here you can see that from antenna the signal is received as well as the transmitting and therefore it is called as a magic T as a duplexer circuit. Now, the next application is the magic T as a mixer circuit. Magic T can also be used as a microwave receiver as a mixer circuit. Here the E-arm and H-arm are connected to the antenna and the local oscillator respectively port 2 has the matched load again matched load is used for the no reflection and port 1 has the mixer circuit where the two signals are mixed with each other to form the third frequency signal that is the intermediate frequency signal. Now, here you can see that the 1 and 2 ports are connected to the mixer and the matched load respectively and the port 3 and port 4 are connected to the local oscillator and the antenna circuit. So, here whatever is the signal received from this antenna half of that signal is going towards this mixer circuit while the half of the local oscillator signal is again going towards this mixer circuit and here these two signals are mixed to get the intermediate frequency. So, half of the local oscillator power and half of the received power from the antenna goes to the mixer to generate the intermediate frequency which is given by input frequency minus local oscillator frequency that is the intermediate frequency can be calculated by f in minus f o where f in is the input frequency while f o is the local oscillator frequency. These are the references for this session. Thank you.