INDRAPRASTHA INSTITUTE OF INFORMATION TECHNOLOGY DELHI ECE321521 LECTURE – 7

Công Nghệ Thông Tin, it, phầm mềm, website, web, mobile app, trí tuệ nhân tạo, blockchain, AI, machine learning - Kỹ thuật - Công nghệ thông tin Indraprastha Institute of Information Technology Delhi ECE321521 Lecture – 7 Date: 28.01.2017 Admittance Smith Chart High Frequency Network Analysis (intro) Impedance, Admittance and Scattering Matrix Matched, Lossless, and Reciprocal Networks Indraprastha Institute of Information Technology Delhi ECE321521 Admittance Transformation RFMicrowave network, similar to any electrical network, has impedance elements in series and parallel Impedance Smith chart is well suited while working with series configurations while admittance Smith chart is more useful for parallel configurations The impedance Smith chart can easily be used as an admittance calculator    1 ( ) 1 in z z z z           1 1 in z y z z      Hence,          0 0 0 1 1 1 1 in in in in in Y z Z z y z Y Z Z z Z z z          1 1 j in j e z y z e z          It means, to obtain normalized admittance → take the normalized impedance and multiply associated reflection coefficient by -1 = e-jπ → it is equivalent to a 180⁰ rotation of the reflection coefficient in complex Γ-plane Indraprastha Institute of Information Technology Delhi ECE321521 Example – 1 Convert the following normalized input impedance

Indraprastha Institute of ECE321/521 Information Technology Delhi Lecture – Date: 28.01.2017 • Admittance Smith Chart • High Frequency Network Analysis (intro) • Impedance, Admittance and Scattering Matrix • Matched, Lossless, and Reciprocal Networks Indraprastha Institute of ECE321/521 Information Technology Delhi Admittance Transformation • RF/Microwave network, similar to any electrical network, has impedance elements in series and parallel • Impedance Smith chart is well suited while working with series configurations while admittance Smith chart is more useful for parallel configurations • The impedance Smith chart can easily be used as an admittance calculator zin (z)  1   z  yin  z   Yin  z   1/ Zin  z    1z Y0 / Z0 Zin  z  / Z0 zin  z  • Hence, yin  z  1   z 1 e j   z  1  z yin  z    j 1e z It means, to obtain normalized admittance → take the normalized impedance and multiply associated reflection coefficient by -1 = e-jπ → it is equivalent to a 180⁰ rotation of the reflection coefficient in complex Γ-plane Indraprastha Institute of ECE321/521 Information Technology Delhi Example – • Convert the following normalized input impedance 𝑧𝑖𝑛′ into normalized input admittance 𝑦𝑖𝑛′ using the Smith chart: zin'  1 j1  2e j( /4) First approach: The normalized admittance can be found by direct inversion as: yin'  '1   e j( /4)   j zin 1 j1 22 Alternative approach: • Mark the normalized impedance on Smith chart • Identify phase angle and magnitude of the associated reflection coefficient • Rotate the reflection coefficient by 180⁰ • Identify the x-circle and r-circle intersection of the rotated reflection coefficient Indraprastha Institute of ECE321/521 Information Technology Delhi Normalized Example – (contd.) impedance (zin’) is the intersection of r-circle Quick investigation of and x-circle of shows that the normalized Rotate this by 180⁰ to obtain normalized impedance (yin’ ) is the intersection of admittance r-circle of 1/2 and x-circle of -1/2 To denormalize, multiply with the inverse of Z0 Yin  yin'  Y0 yin' Z0 Indraprastha Institute of ECE321/521 Information Technology Delhi Example – Given: zin'  1 j2 • Find the normalized admittance l/8 away from the load Steps: Mark the normalized impedance on Smith Chart Clockwise rotate it by 180⁰ Identify the normalized admittance and the phase angle of the associated reflection coefficient Clockwise rotate the reflection coefficient (associated with the normalized admittance) by 2βl (here l = λ/8) The new location gives the required normalized admittance Indraprastha Institute of ECE321/521 Information Technology Delhi zin'  1 j2 Example – (contd.) 180⁰ clockwise yin'  0.20  j0.40 rotation Clockwise rotation by l 2l  4   l yin'  0.2  j0.4 l  l /  2l  90o Indraprastha Institute of ECE321/521 Information Technology Delhi Admittance Smith chart • Alternative approach to solve parallel network elements is through 180⁰ rotated Smith chart • This rotated Smith chart is called admittance Smith chart or Y-Smith chart • The corresponding normalized resistances become normalized conductances & normalized reactances become normalized suceptances r  R  g  G  Z0G Z0 Y0 x  X  b  b  Z0B Z0 Y0 • The Y-Smith chart preserves: • The direction in which the angle of the reflection coefficient is measured • The direction of rotation (either toward or away from the generator) Indraprastha Institute of ECE321/521 Information Technology Delhi Angle of reflection Admittance Smith chart (contd.) coefficient Negative Values of Suceptances →Inductive Behavior Open Circuit Positive Values of Suceptances →Capacitive Behavior Short Circuit In this chart, admittance is represented in exactly the Real Component of Admittances same manner as the impedance in the Z-smith Chart Decrease from Left to Right → without 180⁰ rotation Indraprastha Institute of ECE321/521 Information Technology Delhi Red: Z – Smith Chart Combined Z- and Y- Smith Charts Blue: Y – Smith Chart Indraprastha Institute of ECE321/521 Information Technology Delhi Example – • Identify (a) the normalized impedance z’ = 0.5 + j0.5, and (b) the normalized admittance value y’ = + j2 in the combined ZY-Smith Chart and find the corresponding values of normalized admittance and impedance y'  1 j1 z'  0.5  j0.5 z'  0.2  j0.4 y' 1 j2