## Measure transmission line Zo – nanoVNA – PVC speaker twin – loss model derivation

The article Measure transmission line Zo – nanoVNA – PVC speaker twin demonstrated measurement of transmission line parameters of a sample of line based on measurement of the input impedances of a section of line with both a short circuit and open circuit termination. From Zsc and Zoc we can calculate the Zo, and the complex propagation constant $$\gamma=\alpha + \jmath \beta$$.

## Measurement with nanoVNA

So, let’s measure a sample of 14×0.14, 0.22mm^2, 0.5mm dia PVC insulated small speaker twin.

Above is the nanoVNA setup for measurement. Note that common mode current on the transmission line is likely to impact the measured Zin significantly at some frequencies, the transformer balun (A 1:1 RF transformer for measurements – based on noelec 1:9 balun assembly) is to minimise the risk of that. Nevertheless, it is wise to critically review the measured |s11| for signs of ‘antenna effect’ due to common mode current. Continue reading Measure transmission line Zo – nanoVNA – PVC speaker twin – loss model derivation

## 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.

Above is Oristopo’s graph. Continue reading Return Loss Bridge – some woolly thinking – a Simsmith model of a reflection bridge

## Return Loss Bridge – some woolly thinking

Some discussion on groups.io nanovna-users attempts to explain the behavior of the RF Return Loss Bridge used in some VNAs and other instruments, proof if you will that the instruments are not capable of measuring more than a few hundred ohms.

Above is his diagram. He gives an expression that he states applies when R1=R3=R4=Rm: im = sqrt(Vf*(Rm – R2)/(12*Rm + 4*R2)). Continue reading Return Loss Bridge – some woolly thinking

## A tale of three VNAs

In researching the article Analysis of output matching of a certain 25W 144MHz PA  , I made measurements using a recently ‘upgraded’ nanoVNA-H v3.3 with oneofeleven firmware v1.1.206 nanoVNA-App.exe and default supplied firmware.

Some unexpected ‘bumps’ on the measured response of a short SC transmission line section were concerning, there was no apparent explanation.

The bump around 80MHz had no obvious explanation, and appeared to be an artifact of the measurement fixture, or the instrument. The s11 values from 70-150MHz are suspect. Continue reading A tale of three VNAs

## Analysis of output matching of a certain 25W 144MHz PA

Andrew, ZL2PD, contacted me regarding the matching scheme in a 25W 144MHz amplifier published in (ARRL 1977). The design no doubt appeared in many editions of the handbook. He was resurrecting an old build that just didn’t work as expected, and trying to understand why… which starts with understanding how it works, or should work.

Above is the schematic of the amplifier, analysis here is of the 25W configuration using a 2n5591. Continue reading Analysis of output matching of a certain 25W 144MHz PA

## Measuring OC and SC transmission line sections

Failure estimating transmission line Zo – λ/8 method – nanoVNA discussed the potential for failure using this ‘no-brainer’ method of estimating differential mode characteristic impedance Zo, providing an NEC-4.2 model to demonstrate effects.

This article reports nanoVNA measurement of a two wire line where no common mode countermeasures were taken.

## A little review of behavior of practical transmission lines

Above is a Smith chart of the complex reflection coefficient Γ (s11) looking into a length of nominally 142Ω transmission line of similar type to that in the reference article, the chart is normalised to Zref=142+j0Ω. Note the locus is a spiral, clockwise with increasing frequency, and centred on the chart prime centre Zref. More correctly it is centred on transmission line Zo, and the keen observer might note that the spirals are offset very slightly downwards, actual Zo is not exactly 142Ω, but 142-jXΩ where X is small and frequency dependent, a property of practical lines with loss. Continue reading Measuring OC and SC transmission line sections

## Estimating transmission line Zo – λ/8 method – nanoVNA – success

Failure estimating transmission line Zo – λ/8 method – nanoVNA discussed the potential for failure using this ‘no-brainer’ method of estimating differential mode characteristic impedance Zo.

Well, as the article showed, it is not quite the no-brainer but with care, it can give good results. This article documents such a measurement of a 0.314mm cable.

The nanoVNA was carefully SOLT calibrated from 1 to 201MHz. Care includes that connectors are torqued to specification torque… no room here for hand tight, whether or not with some kind of handwheel adapter or surgical rubber tube etc.

Above is the Smith chart view over the frequency range from a little under λ/8 to a little over λ/8. It is as expected, a quite circular arc with no anomalies. Since the DUT is coax, and the connector is tightened to specification torque, we would expected nothing less. The situation may be different with two wire lines if great care is not taken to minimise common mode excitation. The sotware does not show Marker 2 properly, it should be between ‘c’ and ‘i’ of the word Capacitive. Continue reading Estimating transmission line Zo – λ/8 method – nanoVNA – success

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

Failure estimating transmission line Zo – λ/8 method – nanoVNA discussed traps in using the λ/8 method to estimate Zo… it is not the no-brainer that is often suggested.

This article shows the use of the Smith chart to look for departures from pure transmission line behavior in that test, or any other that depends on measuring purely Zin of a length of line in purely differential mode with short circuit or open circuit termination.

Above is a Smith chart plot of what we should see looking into a line of similar characteristic swept from 1 to 20MHz. There is no magic there, this is basic transmission lines and Smith chart. Continue reading Failure estimating transmission line Zo – λ/8 method – nanoVNA – Smith chart perspective

## 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