# High and low Z responses of a resonant / antiresonant shorted / open transmission line section

At KB1CKT measurement of a roll of RG6/U I stated:

The technique he followed was to make a series of measurements of Rin at low Z resonances of the length of line with open circuit at the far end, and to calculate the MLL using Calculate transmission line Matched Line Loss from Rin of o/c or s/c resonant section.

Though the calculator can use high Z resonances, the high Z resonances are very narrow and it is very difficult to measure Rin at the true resonant frequency. So, only his reported low Z measurements will be used.

This article illustrates the response expected from a 13.7m length of Belden 8262 (RG58C/U). Above, the response at the first low Z resonance with open end. The rate of change of X with frequency is 2.2Ω/kHz, quite modest and given the low slope of the Rin line, frequency need only be set to within 1kHz for reasonably good accuracy of the Rin value obtained. (Slope will be steeper on a lower loss line section.) Above, the response at the first high Z resonance (antiresonance) with shorted end. The rate of change of X with frequency is -12.7Ω/kHz, quite rapid and smaller frequency steps (~0.1kHz) are needed to resolve an accurate value for Rin. (Slope will be steeper on a lower loss line section.)

The response depends on the line type, length and frequency.

## Testing the calculator

Let's test the calculator on both the above cases. The exact length is used in the calcs, it is a nominal 90° of Belden 8262 at 3.6MHz. The two calcs reconcile, keeping in mind that the calculation is an approximation… but a good approximation if the measurements of Rin and length are accurate, and Ro is known to good accuracy.

## Conclusions

• It takes more care to make good measurements at a high Z resonance (antiresonance).