## 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?

## Surely there cannot be more forward power than the transmitter makes?

Let’s explore a simple numerical example of a practical line operating in Transverse Electro Magnetic (TEM) mode (the usual thing for practical coax lines at HF).

## Let’s review the meaning of 50Ω line.

It means that the line geometry imposes a natural constraint on a wave travelling in the line that V/I=50… but remember that TEM waves are free to travel in (only) two directions. This natural ratio of V/I is called the characteristic impedance Zo. Continue reading Surely there cannot be more forward power than the transmitter makes?

## 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

## A DIY thermostat based on the MS1230A controller

This article documents the build of a DIY thermostat based on an inexpensive (\$12) Chinese temperature controller.

## Controller module

The controller used is a 220VAC MH1230A. Above is an internal view of the controller. Importantly it has a relay rated at 240V 30A, and 15A at PF=0.4. The datasheet rates the relay for a 2HP (1.5kW) motor. It uses a ‘conventional’ power supply, the brown component is the power transformer. Most similar products use inadequate relays and have low grade switched mode power supplies that create RF noise. Continue reading A DIY thermostat based on the MS1230A controller

## 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 quarter sized G5RV with hybrid feed

(Varney 1958) described his G5RV antenna in two forms, one with tuned feeders and the more popular form with hybrid feed consisting of a matching section of open wire line and then an arbitrary length of lower Zo coax or twin to the transmitter.

(Duffy 2005) showed that the hybrid feed is susceptible to high losses in the low Zo line as it is often longish, is relatively high loss line and operates with standing waves.

Lets look at measurement of a real antenna, broadly typical of the G5RV. The antenna measured is a G5RV rigged in Inverted V form, 11m height at the apex and around 8m at the ends. The feed line is 2mm diameter copper spaced 50mm with occasional plastic insulators.

To some extent, the measurements are dependent on the environment, and whilst there will be variation from one implementation to another, the measurements provide a basis for exposing the configuration challenge. Above is a plot of VSWR(50) essentially at the lower end of the matching section and low Zo line. The measurement is made looking into 0.5m of RG142 and a Guanella current balun that uses about 1m of 110Ω pair, it is essentially the load end VSWR of a hybrid feed were it used. Continue reading The quarter sized G5RV with hybrid feed