For the simplest case of real input, Rin, to real output impedance Rout, there are two possibilities: Rin > Rout or Rin < Rout. The two L topologies to accomplish this are:Figure 1 - Matching TopologiesFigure 2 - Amplifier ChainIf we assume the Zout is real R2, Zin is real R1, and R2 > R1 (the left-side topology in Figure 2) we can use the Norton transformation to get:For example, to match R1 = 50Ω to R2 =1000Ω at 100 MHz:choosing the positive root to use a shunt capacitor for a lowpass implementation, then:For R2 < R1, simply swap R2 for R1 in the above calculations. The useful bandwidth of the match will depend on the ratio of R2 to R1. Extreme transformations result in very narrow bandwidth results. A broader band match may be implemented using more L-C elements [1] [2].See this and more important radio frequency charts and formulas in this comprehensive application note. [1] G.L. Matthaei, “Tables of Chebyshev impedance–transforming networks of low-pass filter form”, Proceedings of the IEEE, Vol 52, Issue 8[2] R.M. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances”, Journal of the Franklin Institute, Vol 249, Jan 1950, pp 57-83

The inverse of impedance is admittance. Traditionally, impedance is expressed as R+jX, where R is resistance and X is reactance, both in units of ohms. Admittance is the inverse of impedance and is expressed as G+jB, where G is conductance and B is susceptance. Conductance is the inverse of resistance, and B is the inverse of reactance. Both have units of mhos. Capacitive and inductive susceptance are given by:

A coaxial cable is an RF transmission line which consists of a center conductor surrounded by a dielectric medium, a coaxial shield, and often an insulating plastic jacket. Figure 1 - Coaxial Cable The inner conductor of the coaxial cable possesses an intrinsic inductance per unit length L’ just like the wire in free space. By virtue of the coaxial shield and the dielectric material, it also has a capacitance per unit length C’. The inductance and capacitance are distributed along the length of the cable, as shown in Figure 4 below. Figure 2 - Inductance and Capacitance per Unit Length of a Coaxial Cable If the inductance and capacitance per unit length are known, then the characteristic impedance of the cable is given by: Low-loss dielectric materials such as PTFE are common. PTFE has a relative dielectric constant of 2.02 to 2.1, but this is commonly processed to create a PTFE foam with a significant amount of air, resulting in lower loss and a lower dielectric constant. RF travels through the coaxial cable at the guide velocity vg, slower than the speed of light, c: The relative velocity of propagation is expressed as the percentage of c or: This number is approximately 65% for solid PTFE cables, and as high as 90% for low loss foamed PTFE. An air-line coaxial cable with only air as a dielectric would have a relative velocity of 100%. The characteristic impedance of a coaxial transmission line may be calculated from: Where Douter is the diameter of the outer shield to its inner surface, Dcenter is the diameter of the center conductor, and ∈r is the relative dielectric constant of the medium in between the two. See this and more important radio frequency charts and formulas in this comprehensive application note.

Three different methods can be applied to accurately measure passive components with a vector network analyzer. A vector network analyzer (VNA) is a very useful test instrument for characterizing RF circuits and amplifiers. But what about measurements of simple passive components? What’s the best way to characterize a chip capacitor or an inductor—or even a resistor? Senior RF Design Engineer Brian Walker at Copper Mountain Technologies wrote an article for Microwaves & RF discussing how to make accurate impedance measurements using a VNA.