## Failure estimating transmission line Zo – λ/8 method – nanoVNA

Countless online discussions have online experts describing their various preferred methods for estimating the characteristic impedance of a transmission line… often without really testing whether their simple results are realistic, ie believable. Of course, being social media, it would be unsocial for another participant to question the results, so the unchallenged becomes part of ham lore.

Apparent gross failures are often wrongly attributed to factors like manufacturing tolerances, polluted line surface, other esoteric factors etc that might imply a knowledgeable author… but that is social media, an unreliable source of information.

Let’s explore an estimate using measurements with a nanoVNA using the popular eighth wavelength (λ/8) method.

## λ/8 method

The λ/8 method relies upon the property of a lossless line terminated in an open circuit that differential impedance $$Z_d=\jmath X=- \jmath \left| Z_0 \right| cot \left(\pi/4\right)=- \jmath\left| Z_0 \right|$$. So, if you measure the reactance looking into the λ/8 ($$\frac{\piᶜ}{4} \:or\: 45°$$), you can estimate Zo as equal to the magnitude of the reactance.

A similar expression can be written for the case of a short circuit termination and it leads to the same result that you can estimate Zo as equal to the magnitude of the reactance (an exercise for the reader).

The fact that the two cases lead to the same result can be used to verify that the line length is in fact λ/8 (they will not be equal if the length is a little different to λ/8)… though writeups rarely mention this, or perform the test.

So, the method depends critically on:

• whether the line length is λ/8;
• whether it is sufficiently low loss; and
• whether the differential impedance measurement is valid.

Most online articles do not include details of the measurement setup, perhaps thinking that it not all that relevant. Of course, one of the greatest failings in experiments is to ignore some factor that is in fact relevant. Continue reading Failure estimating transmission line Zo – λ/8 method – nanoVNA

## Select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer – comparison of measured and predicted

Select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer – nanoVNA described a method of using a nanoVNA to select by trial possible core and turns combinations for a transformer.

This article compares the results for the FT240-43 example at 3.5MHz with calculation using tools on this web site.

## Simple low frequency equivalent circuit

Above is a very simple approximation of an ideal 1:1 transformer where the effects of flux leakage and conductor loss are ignored. A 1:n transformer can be modelled the same way, as if flux leakage and conductor loss are ignored, the now ideally transformed secondary load becomes 50Ω. Continue reading Select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer – comparison of measured and predicted

## Fair-rite’s ‘new’ #43 permeability data (2020)

Fair-rite publishes spreadsheets of the complex permeability characteristic of many of the ferrite mixes. This note is about #43 mix and clarification I sought from Fair-rite.

### Question

I note that recently, the published table of #43 permeability changed subtly but significantly. Does this table apply to historical product, or does it only apply to new product, ie was there an actual change in the mix, or what it the result of better measurement of characteristics?

## Select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer – nanoVNA – loss components graph

Select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer – nanoVNA gave an explanation of how to use a nanoVNA or the like to select a suitable core and sufficient turns for a low InsertionVSWR broad band 50Ω transformer. Continue reading Select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer – nanoVNA – loss components graph

## Select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer – nanoVNA

This article demonstrates the use of a nanoVNA to select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer.

## Simple low frequency equivalent circuit

Above is a very simple approximation of an ideal 1:1 transformer where the effects of flux leakage and conductor loss are ignored. A 1:n transformer can be modelled the same way, as if flux leakage and conductor loss are ignored, the now ideally transformed secondary load becomes 50Ω. Continue reading Select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer – nanoVNA

## Phase of s11 and Z

Antenna system resonance and the nanoVNA contained the following:

## Relationship between angle of reflection coefficient and angle of impedance

It was stated above that the angle (or phase) of s11 or Γ is not the same as the angle (or phase) of Z.

Given Zo and Γ, we can find θ, the angle of Z.

$$Z=Z_0\frac{1+\Gamma}{1-\Gamma}$$

Zo and Γ are complex values, so we will separate them into the modulus and angle.

$$\left | Z \right | \angle \theta =\left | Z_0 \right | \angle \psi \frac{1+\left| \Gamma \right | \angle \phi}{1-\left| \Gamma \right | \angle \phi} \\ \theta =arg \left ( \left | Z_0 \right | \angle \psi \frac{1+\left| \Gamma \right | \angle \phi}{1-\left| \Gamma \right | \angle \phi} \right )$$

We can see that the θ, the angle of Z, is not simply equal to φ, the angle of Γ, but is a function of four variables: $$\left | Z_0 \right |, \psi , \left| \Gamma \right |, \& \: \phi$$ .

It is true that if ψ=0 and φ=0 that θ=0, but that does not imply a wider simple equality. This particular combination is sometimes convenient, particularly when ψ=0 as if often the case with a VNA.

This article offers a simulation of a load similar to a 7MHz half wave dipole.

The load comprises L, L1, and C1 and the phase of s11 (or Γ) and phase of Z (seen at the source G) are plotted, along with VSWR. Continue reading Phase of s11 and Z

## The devil is in the detail…

An image from one of my articles has been posted online in some discussions, with attribution of the underlying image, but it includes some changes / annotations.

I think that this is a better image.

The difference is in the two pin assembly at lower centre, an addition to my original image. My recommendation is that the DUT is attached to the same side of the pin strip as was used for the calibration parts, as shown. Though I did not intend that this jig be used much above 100MHz, small details like this might improve its accuracy. Continue reading The devil is in the detail…

## Improving ‘s21 shunt-through’ measurement of low impedances – more detail

Improving ‘s21 shunt-through’ measurement of low impedances canvassed a possible improvement of the s21 series-through measurement of impedance to compensate for errors in VNA port impedances that are not corrected in simpler calibration / correction schemes.

This article provides more detail on the practical test case.

A small test inductor was measured with a ‘bare’ nanoVNA SOLT calibrated, firstly using s11 reflection.

Above is the R,X,|Z| plot from the s11 reflection measurement of the unknown Zu. It shows small negative resistance, a frustration with these low end VNAs that suffer thermal drift after just a few measurements. It is less than 3min since SOLT calibration. Continue reading Improving ‘s21 shunt-through’ measurement of low impedances – more detail

## Improving ‘s21 shunt-through’ measurement of low impedances

This article canvasses a possible improvement of the s21 shunt-through measurement of impedance to compensate for errors in VNA port impedances that are not corrected in simpler calibration / correction schemes.

The diagram above is from (Agilent 2009) and illustrates the configuration of a shunt-through impedance measurement. Continue reading Improving ‘s21 shunt-through’ measurement of low impedances