Microwave Network Analysis PDF

# Week X N-Port Network ## **Microwave Network Analysis** - We are interested in transfer function of a microwave system, device, component. - We prefer circuit analysis instead of EM - We are interested in V, I, their ratio "Z" - @ terminal port of micro wave device (DUD) can many ports depending...

# Week X N-Port Network ## **Microwave Network Analysis** - We are interested in transfer function of a microwave system, device, component. - We prefer circuit analysis instead of EM - We are interested in V, I, their ratio "Z" - @ terminal port of micro wave device (DUD) can many ports depending on it's app. ## **[Z] and [Y] Matrices** - [Z] -> [V] = [Z] [I] - Zij = Vi / Ii, i = 0 for ks (other part opened) - i = 1, 2 for i = 1, 2, 3, 14; i = 0 for ks - [Y] -> [I] = [Y] [V] Yis: Di / Vi, i = 0 for k = s (other part shorted) - [V] = [Z] [I] = [Z] [Y] [V] - [U]= Identity Matrix ## **[S] Matrix** - Why s parameters? - [S] relates to v and I at ports. Because of that hard to measure them in opened port and high fregs. - Then [S] provides solution where only represent ratios of Voutput and Vinput at porns that is relative value and easy to measure. - **S-Parameter** - Incident Wave (i) - Reflected Wave (i) - Reflection Coeff : Γ = Γi/Γi - Transmitted Wave (B) - Transmitted Wave (B) - Transmission Coeff: T: Γb/Γi ## **Reciprocal And Lossless Network** - Reciprocal network means not containing any active device, non reciprocal material nor anistotropic material (ferrite, bsymmetric) [Z] = [Z]t plus Zij = Zji - Lossless network: means non containing any lossy material or lossy component (imaginary only) - [V-] + [V+] = [Z] (I-) _ [I+] - [V-] + [V+] = [Z] [I+] _ [Z] [I-] - (U) (Identity matrix) [V-] ([U] + [Z]) [I+] (U) - [Y] ## **S Matrix Example** - Matched network Smin = 0 for all n - [S] = - 0 1 0 0 - 0 1 0 0 - 0 0 3 0 - 0 0 0 1 - Reciprocal network Smin = Sum, [S] = [S]t - Lossless network [S]t [S]* = [U ] or [S] = (csgt) [U]: - ∑ Ski Ski = 1 and ∑ Ski Sks = 0 - k=1 - F=1 if s ## **ABCD Matrix** - For example: 2x2 matrix - [V] = [Z] [I] - [I] = [S] (-^) - [V] = [A] [Z] [I] - ABCD Parameters - - 1 2 0 1 - 0 2 0 1 - 1 0 1 0 - 0 1 0 1 - CHART ## **Lossless Network** - For lossless network Pin = Pout (ex: 3 port) - Pin = 1/2 [Vt]t [Vt]* + 1/2 [V+]t [V+] * - Pout = 1/2 [Vt]t [Vt]* + 1/2 [V+] t [V+] * - 2Pin = [Vt]t [Vt]* + [V+]t [V+] * - 2Pout = - [Vt]t [Vt]* + [V+]t [V+] * = - Pin = Pout - [Vt]t [Vt]* = [V-]t [J-J* = ([S] [Vt]) ([S] [V+]*) - [Vt]t [Vt]* = [V-]t [J-J* = ([S] [Vt]) ([S] [V+]*) - IF [S]= unitary or [S] = (csgt) [U]: - IF [S] unitary or [S] = (csgt) [U]: - [S]t [S]: [U] - ∑ Ski Ski = 1 - Then 51 su* + 5215 24 + 531 531* = 1 - ∑ Ski Sks = 0 - 512 5 + 522 521*+ 532 531* = 0 - Conclusion: - Dot product of any column of [S] w/ conjugate w/ the same column = 1 - Dot product of a column of [S) w/ compuyate n/ another column is 0 ## **Also, All of this we can check in the table** - Also, [ABCD],[S],[Z],[Y] convert each other, we can see in the table.