The Effect of Impedance Mismatch of Coaxial Connectors on System Performance

This program calculates the degradation in system performance caused by insertion of a length of transmission line of different impedance to system Zo. It is applicable to either balanced or coaxial transmission lines.

It is capable therefore of predicting the effects of using coaxial connectors of different or incorrect Zo in the middle of, or at the end of a transmission line. The program is worded in these terms.

Assumption: Line and connector Zo impedances are purely resistive. This may cause small calculating uncertainties, but is of little consequence. Greater uncertainty is caused by the manufacturing variation from nominal Zo of a line or connector amounting to several percent. The program can demonstrate this.

There are two loss components: transmission loss in the connector when incorrectly terminated, and mismatch or reflection loss in the system on the side of the system nearest to the generator. The high SWR which occurs at the higher frequencies is also on the transmission line between connector and generator.

When the system and connector both have same Zo then reflection loss is zero regardless of frequency and length of connector. The only loss is the attenuation through the connector which may be extremely small at low frequencies.

At low frequencies the input impedance of the connector converges on system Zo for a considerable difference between their Zo's. There is little loss. When connector input impedance converges on system Zo the line from the generator is correctly terminated and so no reflection occurs.

When the length of the connector is an odd number of 1/4-wavelengths, SWR and reflection loss are at a maximum. Vary frequency to fine-change length. Observe how a 1/4-wave connector transforms system impedance to Zin.

When the length of the connector is a whole number of 1/2-wavelengths, SWR and reflection loss are at a minimum. Vary frequency to fine-change length.

Normally, a mismatched connector would not be used at frequencies where length of the connector approaches 1/4-wavelength at its own velocity factor.

Enter the length of male and female connectors AFTER being mated together. It is usual to specify system performance by stating that SWR shall not exceed a given value at a given UHF. Example: SWR max = 1.1 at 1 GHz.

More Notes

• The connector's source and load impedances are both equal to the system Zo.
• Input impedance, Zin, is that of the connector when loaded with system Zo.
  • Zin = Rin + jXin
  • The reflection coefficient Gamma = (Zin - Zo)/(Zin + Zo)
  • Reflection Loss = -10*Log(1-Square(Gamma)) dB
  • Return Loss = -10*Log(Square(Gamma)) dB
  • SWR = (1 + Gamma)/(1 - Gamma)
    • where Gamma is now the magnitude of the reflection coefficient.
• SWR is on the line between generator and connector.
• Transmission loss is that through the connector when it is loaded with system Zo. It is not the attenuation when it is terminated with its own Zo.

Run this Program from the Web or Download and Run it from Your Computer
This program is self-contained and ready to use. It does not require installation. Click this link connect then click Open to run from the web or Save to save the program to your hard drive. If you save it to your hard drive, double-click the file name from Windows Explorer (Right-click Start then left-click Explore to start Windows Explorer) and it will run.