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Discontinuities, TEM Models, and Impedance Matching

Where discontinuities occur, energy is stored and some losses occur.

 

As far as energy flow is concern, energy flow is typically thought as being contained in wires and dissipated in resistive elements. Energy flow is in the electric and magnetic fields guided by the conductors and is converted to heat when the fields are incident on lossy dielectrics or conductors. In other words the energy flows in the gaps around the conductors and NOT in the conductors. The result, of all of this, is that at high frequencies the spaces between the conductors are as important to signal conduction as the conductors themselves are.

 

TEM modes.

 

Transverse Electric Magnetic modes describe waves that are propagated down a waveguide or cavity. At high frequencies TEM waves travel down dielectric materials to let us consider PCB material an open-boundary waveguide. This condition will support modes of propagation Called surface waves. Field strength of these waves falls off exponentially outside the dielectric. Many types of launches have very high susceptibility to launching surface wave modes. TEM10 are allowed in the dielectric and TEM01 is also possible if the electric field can penetrate deep enough into the dielectric to couple into these modes. Surface wave modes have historically been shown to have noticeable effect on structures with frequencies as low as 100 MHz.

 

Impedance Matching.

 

L networks: Used to match Impedance at one frequency (or very narrow

 

band; most of the L networks will work 300 kHz to 1.5 GHz without too

 

much care to transmission line effects.)

 

Filling out the User Defined table, the physical lengths can be used to calculate the electrical lengths. This information should be entered into the Network analyzer with Standard class assignments and Label Class assignments to establish a proper calibration kit. (There are a few work nstructions describing the use of these kits.)

 

After the kit is constructed and verified, the L network on each Network Analyzer port will allow testing at the Impedance of Z2 only! Load resistor and Short standards will also need to be constructed for each port.

 

Device Z  =  50  ohms

 

Test cable = 150 ohms

 

R1 = Z1 [ Z2 / (Z2-Z1)^0.5 ]

 

R1 = 61.237

 

R2 = [Z2 * (Z2-Z1)]^0.5

 

R2 = 122.474