An impedance matching network having a first port and a second port, the impedance matching network comprising: a substrate; and a slow wave, wrapped, tapered-transformer transmission line disposed on said substrate and having first and second ends with the first end of the transmission line corresponding to the first port of the impedance matching network and the second end of the transmission line corresponding to the second port of the impedance matching network wherein said slow wave, wrapped, tapered-transformer transmission line is provided to match a first impedance characteristic at the first port of the impedance matching network to a second different impedance characteristic at the second port of the impedance matching network wherein: the first and second ports of the impedance matching network are each provided having complex impedance values with the complex impedance value of the first port being lower than the complex impedance value of the second port; said slow-wave, wrapped, tapered-transformer transmission line is provided having a length which is less than the length of a tapered-transformer transmission line having the first impedance characteristic at a first port thereof and the second, different impedance characteristic at a second port thereof and having a Klopfenstein impedance taper between the first and second ports; said slow wave, wrapped, tapered-transformer transmission line has an insertion loss characteristic that is substantially the same as an insertion loss characteristic of a tapered-transformer transmission line having a Klopfenstein impedance taper along a length thereof between the first and second ports; and the dielectric parameters of at least portions of said substrate are varied along the length of the slow wave portions of said transmission line to add additional shunt capacitance such that the width of the transmission line does not increase in a direction moving from the first port to the second port of the transmission line. a substrate; and a slow wave, wrapped, tapered-transformer transmission line disposed on said substrate and having first and second ends with the first end of the transmission line corresponding to the first port of the impedance matching network and the second end of the transmission line corresponding to the second port of the impedance matching network wherein said slow wave, wrapped, tapered-transformer transmission line is provided to match a first impedance characteristic at the first port of the impedance matching network to a second different impedance characteristic at the second port of the impedance matching network wherein: the first and second ports of the impedance matching network are each provided having complex impedance values with the complex impedance value of the first port being lower than the complex impedance value of the second port; said slow-wave, wrapped, tapered-transformer transmission line is provided having a length which is less than the length of a tapered-transformer transmission line having the first impedance characteristic at a first port thereof and the second, different impedance characteristic at a second port thereof and having a Klopfenstein impedance taper between the first and second ports; said slow wave, wrapped, tapered-transformer transmission line has an insertion loss characteristic that is substantially the same as an insertion loss characteristic of a tapered-transformer transmission line having a Klopfenstein impedance taper along a length thereof between the first and second ports; and the dielectric parameters of at least portions of said substrate are varied along the length of the slow wave portions of said transmission line to add additional shunt capacitance such that the width of the transmission line does not increase in a direction moving from the first port to the second port of the transmission line. the first and second ports of the impedance matching network are each provided having complex impedance values with the complex impedance value of the first port being lower than the complex impedance value of the second port; said slow-wave, wrapped, tapered-transformer transmission line is provided having a length which is less than the length of a tapered-transformer transmission line having the first impedance characteristic at a first port thereof and the second, different impedance characteristic at a second port thereof and having a Klopfenstein impedance taper between the first and second ports; said slow wave, wrapped, tapered-transformer transmission line has an insertion loss characteristic that is substantially the same as an insertion loss characteristic of a tapered-transformer transmission line having a Klopfenstein impedance taper along a length thereof between the first and second ports; and the dielectric parameters of at least portions of said substrate are varied along the length of the slow wave portions of said transmission line to add additional shunt capacitance such that the width of the transmission line does not increase in a direction moving from the first port to the second port of the transmission line.