Why is There a 6 dB Correction on Measured Waveguide to Coax Adapter Return Loss Using a Back to Back Connection?

Many customers will question SAGE Millimeter’s waveguide to coax adapter return loss performance. They will mention that their measured return loss is lower than what is on the provided datasheets or in the specifications provided in their quotes. SAGE Millimeter has noticed that these same customers often test return loss by using the “back to back” connection approach shown in Figure 1. While SAGE is unsure of the reasons for using this method, the guess is that it may be due to the waveguide to coax adapter’s different port configurations, i.e., one end is waveguide and the other is coax while the network analyzer is in either a coaxial or waveguide interface setting.

Fig 1 SAGE Blog Measured Back to Back Return Loss
Figure 1. Back to Back Setting for Network Analyzer Measurement

If the “back to back” approach is used, an approximate 6 dB needs to be added onto the measured return loss value to derive the DUT (Device Under Test), in this case, the waveguide to coax adapter’s, real return loss.

The following process reveals the details behind the 6 dB difference.

As noticed, the waveguide to coax adapter’s return loss is high, usually 18 dB or better, and the insertion loss is low, less than 1.0 dB in general. Based on that, one could assume that the DUT’s input and output return loss are high enough by using the ideal values |S11|, |S22|= 0.0 and insertion loss |S21| = 1.0, respectively.

The relationship of reflection coefficient and [S] parameters of a two port network can be expressed in the Figure 2. Here the Ei is the incident signal level.

Fig 2 SAGE Blog Measured Back to Back Return Loss.PNG
Figure 2. Reflection Coefficient and [S] parameter of a Two Port Network
As we know, the waveguide adapter is a 2-port network. Whose S21 and S11 amplitude values can be calculated from adapter’s insertion loss (IL) and return loss (RL):

|S21│=10-IL/20, │S11│=10-RL/20

The reflected signal is,

Equation 1 SAGE Blog Measured Back to Back Return Loss.PNG

Where ГL is the load reflection coefficient.

The input reflection coefficient of this 2-port network is,

Equation 2 SAGE Blog Measured Back to Back Return Loss.PNG

For a receptacle device, such as waveguide to coax adapter, S12 = S21, S11 = S22, one would have the following relationship if the amplitude is not considered.

Equation 3 SAGE Blog Measured Back to Back Return Loss.PNG

Now the 2-port network setting and its reflection coefficient [S] parameter relationship for back-to-back connected adapters can be represented in Figure 3.

Fig 3 SAGE Blog Measured Back to Back Return Loss.PNG
Figure 3. Reflection Coefficient and [S] Parameter of a Back to Back Adapter Setting
Now we assume that the network is perfectly terminated, and that the loss of the adapters are negligible, i.e., ГL=0.0,|S21|=1.0, then

Equation 4 SAGE Blog Measured Back to Back Return Loss.PNG

With the assumption of good matching and insertion loss, the measured input reflection coefficient can approximately be derived as the following.

Equation 5 SAGE Blog Measured Back to Back Return Loss.PNG

Therefore, the back-to-back return loss can be obtained from the above equation as follows:

Equation 6 SAGE Blog Measured Back to Back Return Loss.PNG

Finally, the actual return loss of the single adapter is obtained.

RL = RL B-to-B +6 dB

That is, when measuring the return loss of a low VSWR DUT by cascading two of them together, in the adapter’s case, back to back, one shall add approximately 6 dB to the measured RL of the cascaded twin DUTs to obtain the RL of the individual DUT. Of course, the assumption is that the DUT has high return loss and low insertion loss. In other words, the maximum absolute largest return loss one could add is 6 dB. In the real world, the actual return loss of the adapter is around 20 dB and the insertion loss is around 0.2 to 1.0 dB. Non-ideal values shall reduce the 6 dB value to 5 dB or 4 dB. Based on that, the conservative added return loss dB for a back to back adapter pair is 5 or 4 dB.

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