Impedance

Conductor impedance

Any conductor can be represented by a combination of R, L, C, G parameters. In most conductors, L and C are the most important. The characteristic impedance Z₀ is in first approximation the square root of L/C. We say that the conductor is adapted with its load if |Z₀|= R. In that case, although existing physically and electrically, the conductor is almost transparent to the signal from the generator to the load.

Impedance adaptation

If |Z₀| is equal to R, the aspect of the signal (close to R at the far end of conductor) is very similar to the near end of the conductor (close to Volt generator). Now, if |Z₀| is different from R, ringing may be observed meaning that the signal is disturbed significantly.

This effect is significant above 10 MHz in cables, 100 MHz in packaging and 1 GHz inside ICs.

Exercise: Optimum impedance

Why do we often talk about 50 ohm adaptation? Why not 1Ω or 1 k Ω?. The answer may be found in cable design. A small radius a for the signal conductor would mean an easy bending, light cable, with low loss. But the high L/C ratio means a high impedance, and the small radius high dielectric loss due to a thick conductor. A conductor with large radius would be heavy, low impedance, uneasy to bend, but with high dielectric loss due to this oxide. The minimization of dielectric loss leads to Z0=77 Ω, the minimization of power loss leads to Z0=32 Ω. The compromise Z0=50 Ω is a worldwide accepted standard.

Power handling
Bending
Light
Low loss
Low Impedance
Small capacitance
Small inductance

Maximum power: Z0=32Ω
Minimum loss: Z0=77Ω
Compromise: Z0=50Ω

50 ohm adapted systems

All these systems have something to do with 50 ohm adaptation. The spectrum analyser has a 50 ohm input impedance. It corresponds in this case to a physical resistance connected between the input signal and the ground. The waveform generator is 50 ohm adapted, meaning that its output resistance is 50 ohm. The amplifier input and output also feature a 50 ohm resistance. The TEM cell and GTEM cell used in EMC characterization are also 50 ohm adapted, meaning that the internal conductor is sized and placed in such a way the square root of the L/C ratio is 50ohm.