Return Loss Bridge – some woolly thinking – a Simsmith model of a reflection bridge

Return Loss Bridge – some woolly thinking discussed some online opinions on the practical measurement range of nanoVNA, and underlying reasons… but both were flawed.

Reflection Bridge and Return Loss Bridge are somewhat synonymous, in practice to measure Return Loss one is interested in the magnitude of the response, and to measure the complex reflection coefficient or s11, both magnitude and phase are of interest.

He derives a flawed expression for bridge response, then plots a dodged up version to demonstrate the asymmetry of the response.

Above is Oristopo’s graph.

So, how does it work?

We can create a model of a Return Loss Bridge or Reflection Bridge in Simsmith and plot its response for swept Zu.

Above is the Simsmith model with plot for R swept from 1-2500Ω and X=0Ω (for simplicity). When plotted on a log frequency scale, the |s11| response is symmetric, and the markers at 50/10 and 50*10 both produce |s11|=-1.73dB.

Note that this simulated bridge complies with ALL the requirements for correct response:

  • source impedance is 50+j0Ω by virtue of the G element definition;
  • the three known elements of the bridge are specified as 50(+j0)Ω;
  • the bridge detector load impedance is 50+j0Ω by virtue of the definition of element L.

For convenience, the source power is defined as 16W so that it produces 1W or 0dBW at the detector when Zu=0 (or ∞).

The calculated |s11| (or -ReturnLoss) can be calculated easily to verify these two cases using a calculator, or good online calculator. For example using Calculate VSWR and Return Loss from Zload (or Yload or S11) and Zo.

From a point of digitising the s11 response, the challenge is as great for 5Ω as it is for 500Ω. Very low and very high impedances are sensitive to different aspects of the fixture, so it is easy to make a fixture that compromises high or low impedances.

When |s11| becomes relatively large (ie approaching 1, or 0dB) as it does for measurement of very high and very low impedances, the ADC resolution becomes an issue, internal noise of the instrument becomes significant, and accurate phase measurement is more difficult, and as a result, measurement accuracy is compromised.

Several recent articles have used measurements of transmission line sections with SC and OC terminations.

Above is an example where at HF, |s11| >-0.05dB, which is the magnitude of |s11| with a load of 17370+j0Ω, or 0.1439Ω. Sure, there is some noise, but the measurements are usable for the purpose at hand.

One wonders if some online experts have condemned high impedance measurements as grossly inaccurate based on their own experience, perhaps with flawed fixtures, maybe they are just quoting another online expert they have read.

Generalised assertions by online experts that VNAs cannot accurately measure impedance above a few hundred ohms are not borne out by careful measurement experience of known DUTs in appropriate fixtures… or they have unreal expectations about the accuracy required for common analyses.