Characteristic impedance of microstrip lines

Original publisher: Hampton, Va. : National Aeronautics and Space Administration, Langley Research Center, [1989] OCLC Number: (OCoLC)25394307 Subject: Impedance (Electricity) Excerpt: ... -Jnok z ' N o [ I 2_ ( 2. ) 2k 2 n = l " • ( kyAy / 2 ) j Q ( k ×, ky ) 6 ( k × + Ke ) m m_ i dk ( 23 ) exp (-jkyyn ) exp ( jk × x + jkyy ) _ dk × Y ) By setting x = 0 in equation 23 and selecting Pm ( y ) as a testing function and multiplying both sides of equation 23 by Pm ( y ) yields-JnokoZ ' N 0 = _ I 2_ ( 2. ) 2k _ n = l n-_in ( kAy / 2 ) ] Q ( k, k ) _ ( k + K )--_--CO dk ( 24 ) Y m y x • P ( y ) exp (-jk y_ ) exp ( jkyy ) } dk Integrating both sides of equation 24 with respect to y and rearranging gives jokNozl { [ siknyyJ21 12_212_k12_f_ n:l "-m-co ( kyAy / 2 ) • Q ( k ×, ky ) 6 ( kx + K ) exp (-jkyy_ ] dk ( 25 ) mf Pm ( y ) exp ( jkyy ) dy dk × y + Ay / 2 ] } Y Ym-Ay / 2 13