RF Electronic Devices and Systems

Impedance in microwave network analysis

Impedance in microwave network analysis

This post tells about impedance in microwave network analysis. 

Impedance was first used to describe the relationship VIin AC circuits. Later the concept of impedance was extended as the link between field theory and transmission line theory.

So far we know three types of impedance:

  • intrinsic impedance η=με;
  • wave impedance Zw=1Yw;
  • characteristic impedance Z0=1Y0.

Let’s consider random one-port network (depicted below).

Impedance in microwave network analysis

To consider calculate the impedance in the microwave network analysis let’s consider the term of power. The complex power for this network is described with the following expression: P=12SE×H*dSE and H fields through the network are defined the following way:  E(x,y,z)=V(z)e(x,y)ejβz and H(x, y, z)=I(z)h(x,y)ejβz.

So we get P=12VI*.

On the other hand, we know for complex power of the network: P=Pl+2jω(WmWe). Then 12VI*=Pl+2jω(WmWe). As soon as Zin=VI=VI*I2, then Zin=2(Pl+2jω(WmWe))I2.

Real part of the impedance is related to the dissipated power 2PlI2, and imaginary part is related to the energy stored in the network 4ω(WmWe)I2.

Educational content can also be reached via Reddit community r/ElectronicsEasy.