What is a microwave network • A microwave network is formed when several microwave devices such as • Sources • Attenuators • Resonators • Filters • Amplifiers etc Are coupled together by transmission line or waveguide for the desired transmission of microwave signal Network ports • What is the difference between the port of low frequency network and microwave frequency network ? For low frequency network a port is a pair of terminals where as for a microwave network a port is reference plane transverse to the length of microwave transmission line Network Parameters • Z, h, Y and ABCD parameters are difficult to measure for microwave network because at microwave frequencies the physical length of the component or line is comparable to or much greater than the wavelength. • so the voltage and current are not well defined at a given point for a microwave circuit Why Z, Y,h and ABCD parameters are difficult to measure for MW circuit ? • 1) Non- availability of terminal voltage and current measuring equipment • 2) Short circuit and open circuits are not easily achieved for a wide range of frequencies • 3) Presence of active devices makes the circuit unsuitable for short and open circuit Properties of S - Parameters • a) Zero diagonal elements for perfect matched network For an ideal N-port network with matched termination sii= 0 since there is no reflection from any port so under perfect matched conditions the diagonal elements of [S] are zero Properties …. b) Symmetry of [S] for a reciprocal network A reciprocal device has the same transmission characteristics in either direction of a pair of ports is characerized by a symmetric matrix Sij = Sji ( i not equal to j) Properties • C) Unitary property for a lossless junction For any lossless network the sum of the products of each term of any row or of any column of the S matrix multiplied by its conjugate is unity If all d) Phase shift property Complex S-parameters of a network defined with respect to the positions of the port or reference planes Device S The picture can't be display ed. 1’ 2 1 2’ For unprimed reference planes the S –parameters have definite complex values S11 S S 21 S12 S 22 Phase shift property cont.. If reference planes 1 and 2 are shifted outward to 1’ and 2’ by electrical phase shifts Device S 1’ 2 1 2’ 1 1l1 2 2l 2 The new S matrix is given by j1 e ' S 0 0 S j 2 e S parameters for some microwave components Wave guide sections The S-Matrix for ideal sections are 0 1 S 1 0 S Matrix for 3 – port networks • Wave guide tees are three port components. They are used to connect a branch or sections of the waveguide in series or parallel with the main waveguide transmission line for providing means of splitting and also of combining power in a waveguide system Two basic types of Tees • E-plane T • H-plane T S-parameters of E-plane and Hplane -T E-plane H-plane S11 S S12 S13 S12 S11 S 23 S13 S 23 S33 Because of the symmetry Sij = Sji E-plane T S31 = S13= - S23 = -S32 S12=S21 1/ 2 1/ 2 1 / 2 ai = incident power bi = reflected power I/p power =o/p power 2 (1 S33 ) 2 S13 If S33 =0 , S13 = 1/ 2 2 1/ 2 1/ 2 1/ 2 1/ 2 1/ 2 0 H-plane Tee The picture can't be display ed. In a H-plane tee if two waves are fed into port 1 and port 2 of the collinear arms the output wave at port 3 will be in phase and additive. Reversely an input wave at port 3 will be equally divided into port1 and port 2 in phase. 1/ 2 1/ 2 1/ 2 S 1 / 2 1 / 2 1 / 2 1 / 2 1 / 2 0 S- matrix of a power divider Directional Coupler The coupling factor is defined as: S-parameters of DC • Insertion Loss (IL) = 10*log(P1/P2)=20*log(S21) • Coupling Factor (CF) = 10*log(P1/P4)=20*log(S41) • Isolation (I) = 10*log(P1/P3) = -20*log(S31) • Directivity (D) = 10*log(P4/P3)= - 20*log(S31/S41) Hybrid -T Several Losses in Microwave circuits • The losses in a microwave circuit can be expressed in terms of S-parameters Insertion Loss (dB) Pi = Power fed at Port 1; Pr = Power reflected at the same port Losses … Transmission Loss or Attenuation (dB) Reflection Loss (dB) Losses .. Return Loss (dB)
