Exploiting your antenna analyser #28 gave an example of use of one method to resolve the sign of reactance comparing measurements made with a slightly longer known transmission line.

One way to predict the input impedance to the longer line is using a Smith chart. This article presents a Smith chart prediction of the expected input impedance of a 8′ section of RG8 at 14.17Mhz (vf=0.66, length=0.175λ) for the cases of Zload being 60.3+j26.9Ω and 60.3-j26.9Ω.

The impedance is normalised to 50Ω and plotted on the Smith chart, point 1 above. A radial from the centre through point 1 is drawn to the edge of the chart. Another radial is drawn a distance towards the generator of 0.175λ and using a pair of dividers or ruler, point 2 is plotted on that radial at the same distance from the centre (same VSWR) as point 1.

These points are on a constant VSWR arc but the arc has not been draw because the two arcs would overlap and might be confusing to some readers.

The impedance is normalised to 50Ω and plotted on the Smith chart, point 3 above. A radial from the centre through point 3 is drawn to the edge of the chart. Another radial is drawn a distance towards the generator of 0.175λ and using a pair of dividers or ruler, point 4 is plotted on that radial at the same distance from the centre as point 3.

It is clear that the predicted R value of the points 2 and 4 are very different and will be sufficient to differentiate the +ve and -ve X cases.

Reading of the normalised R value for each and multiplying it, we get R=52Ω for point 2 (the +ve X case) and R=30Ω for point 4 (the +ve X case).

The predicted R values of 52Ω and 30Ω are very slightly different to the more exact values using in the original article a good transmission line calculator because the Smith chart solution above is for a lossless line, and being a graphic solution is it not as precise as the mathematical one.

Nevertheless, the Smith chart solution is quite good enough to differentiate the two possibilities and to show that the sign of X in the original measurement is in fact -ve.

Watch the blog for continuing postings in the series Exploiting your antenna analyser. See also Exploiting your antenna analyser – contents.

]]>Many analysers do not measure the sign of reactance, and display the magnitude of reactance, and likewise for magnitude of phase and magnitude of impedance… though they are often incorrectly and misleadingly labelled otherwise.

The article The sign of reactance explains the problem and dismisses common recipes for resolving the sign of reactance as not general and not reliable.

This article gives an example of one method that may be useful for resolving the sign of reactance.

My correspondent has measured VSWR=1.68 and |Z|=66 and needs to know R and X. From those values we can calculate R=60.3 and |X|=26.9.

The method involves adding a short series section of known line, short enough to provide a measurement difference in R, and that R would be different for the case of =ve and -ve X, all of these measured at the same frequency.

There is a risk when the measurement is of an antenna system that significant common mode current may alter the measurement, so lack of consistency with expectation flags a potential problem that needs to be investigated.

An additional 8′ section of RG-8U was inserted and the impedance looking into that section was measured at 14.17MHz.

Now let us predict the input Z to an 8′ section of RG8 with loads of 60.3+j26.9 and 60.2-j26.9 using a good transmission line calculator.

For the +ve X case, the R component of Zin is predicted to be 57Ω, for the negative case it is predicted to be 32Ω. These are sufficiently different for the test to be conclusive.

In the event, the measured R was close to the 32Ω predicted for the case of X being -ve.

On the basis of Rin being close to prediction for the -ve X case, it can be reliably concluded that at the first point Zin=60.3-j26.9Ω.

The importance of this was that the known value allowed calculation of the feed point impedance of the antenna which was at the end of 6′ of RG8X to be 79.2+j14.6Ω. That informs the design of a matching scheme.

Watch the blog for continuing postings in the series Exploiting your antenna analyser. See also Exploiting your antenna analyser – contents.

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We often learn more from failures than successes, this exercise is one of those opportunities.

An online poster tried to validate his newly purchased MFJ-918 by measuring Insertion VSWR.

That is done preferably by measuring a good termination (dummy load) to validate that it has a very low VSWR, then inserting the Device Under Test (DUT) and measuring the VSWR as a result of insertion of the DUT.

The poster did not mention measurement of the dummy load alone, and it is a type that warrants validation.

Above is the poster’s test setup, his Rigexpert AA-170 is connected to the balun’s input jack using a M-M adapter. The output wires on the balun form a rough circle of about 550mm perimeter by eye.

Above, the Insertion VSWR doesn’t look too good and you might understand him wanting a refund… but is the test valid? One expert opined Sometimes you get what you pay for

.

Above is his measured R,X (ignore the |Z| curve, it is there mainly for hams who don’t understand the nature of Z).

Note that X increases fairly linearly from 1MHz to about 24MHz where it flattens out and turns downwards. The latter is evidence of self resonance, so lets play it simple and focus on the behaviour well before self resonance has an effect. Lets take 15.5MHz where by eye, X looks like 48Ω. If that was caused simply by a series inductance, the inductance L=Xl/(2πf)=48/(2*π*15.5e6)=0.49µH.

Now if we calculate the inductance of a circle of 2mm diameter wire with perimeter of 550mm, we get 0.50µH, which suggests the cause of the R,X response and associated Insertion VSWR. The dimensions used are guessed from the pics.

If the instrument had no error, the reading at 1MHz suggests that the dummy load is a bit below 50Ω at that frequency… but it should be swept before making measurements with it.

There is every appearance that the test is invalidated by long connecting wires to the dummy load, and that the dummy load is of unknown quality.

Things to do to improve the test:

- sweep the dummy load and validate assumptions about its impedance vs frequency; and
- keep test leads and connectors short, prove the fixture by exploring sensitivity to dimensional changes.

Watch the blog for continuing postings in the series Exploiting your antenna analyser. See also Exploiting your antenna analyser – contents.

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A common task is to measure the velocity factor of a sample of coaxial transmission line using an instrument that lacks facility to backout cable sections or measure SOL calibration (as discussed in other articles in this series). The older models and newer budget models often fall into this category.

The manuals for such instruments often explain how to measure coaxial cable velocity factor, and the method assumes there is zero offset at the measurement terminals (whether they be the built-in terminals or some fixture / adapters). In fact even the connectors are a source of error, especially UHF series connectors.

It is the failure to read exactly Z=0+j0Ω with a S/C applied to the measurement terminals that adversely impacts efforts to measure resonant frequency of a test line section.

The method described here approximately nulls out offsets in the instrument, measurement fixture, and even in the connectors used and for that reason may sometimes be of use with more sophisticated analysers.

The method requires measurement of the lowest frequency impedance minimum of two different sections of the SAME cable with the SAME connectors (not just type, EXACTLY the same connectors), and from the measured lengths and frequencies, to calculate the velocity factor.

Note that the method relies upon an assumption that velocity factor is independent of frequency. That assumption may introduce some small error for lossy lines at frequencies below about 10MHz, and is probably not suitable below 1MHz.

I have two lengths of EXACTLY the same cable with EXACTLY the same type of connectors on them. I need to fit an adapter to my analyser to plug the cables onto it, and I have made a female S/C adapter from a panel socket with a strap soldered across the back of it. If we use the same adapters for both measurements, the effects will me nulled out… as will the connector anomalies.

I measure the distance to the mm between the ends of the visible black sheath on both cables, and then measure the lowest frequency impedance minimum of each of them (… write the figures down as you measure them, don’t mix them up).

I then enter them into the calculator Velocity factor solver.

Above is the solution, the velocity factor is calculated to be 66.0%.

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Exploiting your antenna analyser #29 Resolving the sign of reactance – a method – Smith chart detail

Exploiting your antenna analyser #28 Resolving the sign of reactance – a method

Exploiting your antenna analyser #27 An Insertion VSWR test gone wrong

Exploiting your antenna analyser #26 Find coax cable velocity factor using a very basic analyser

Exploiting your antenna analyser #25 Find coax cable velocity factor using an antenna analyser without using SOL calibration

Exploiting your antenna analyser #24 Find coax cable velocity factor using an antenna analyser with SOL calibration

Exploiting your antenna analyser #23 Seeing recent discussion by online experts insisting that power relays are not suitable to RF prompts an interesting and relevant application of a good antenna analyser

Exploiting your antenna analyser #22 Predicting peak voltage at a point from analyser measurements

Exploiting your antenna analyser #21 K0BG’s advice on tuning mobile whips

Exploiting your antenna analyser #20 – Finding resistance and reactance with some low end analysers #2

Exploiting your antenna analyser #19 – Critically review your measurements

Exploiting your antenna analyser #18 – Measure velocity factor of open wire line

Exploiting your antenna analyser #17 – Optimising a G5RV with hybrid feed

Exploiting your antenna analyser #16 – Measure inductor using SOL calibration

Exploiting your antenna analyser #15 – Measure MLL using the half ReturnLoss method – a spot test with a hand held analyser

Exploiting your antenna analyser #14 – Insertion Loss, Mismatch Loss, Transmission Loss

Exploiting your antenna analyser #13 – Insertion Loss, Mismatch Loss, Transmission Loss

Exploiting your antenna analyser #12 – Is there a place for UHF series connectors in critical measurement at UHF?

Exploiting your antenna analyser #11 – Backing out transmission line

Exploiting your antenna analyser #10 – Measuring an RF inductor

Exploiting your antenna analyser #9 – Disturbing the thing you are measuring

Exploiting your antenna analyser #8 – Finding resistance and reactance with some low end analysers

Exploiting your antenna analyser #7 – Application to a loaded mobile HF whip

Exploiting your antenna analyser #6 – Shunt match

Exploiting your antenna analyser #5 – Measure MLL using the Rin where X=0

Exploiting your antenna analyser #4 – Measure MLL using the half ReturnLoss method

Exploiting your antenna analyser #3 – The sign of reactance

Exploiting your antenna analyser #2 – Reconciling the single stub tuner results

Exploiting your antenna analyser #1 – I often see posts in online fora by people struggling to make sense of measurements made with their antenna analyser

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A common task is to measure the velocity factor of a sample of coaxial transmission line using an instrument without using SOL calibration.

Whilst this seems a trivial task with a modern antenna analyser, it seems to challenge many hams.

We will use a little test fixture that I made for measuring small components, and for which I have made test loads for SOL calibration. We will find the frequency where reactance passes through zero at the first parallel resonance of an O/C stub section, this is at a length of approximately λ/2 (a good approximation for low loss coaxial cables above about 10MHz).

We will use a little test fixture that I made for measuring small components, and for which I have made test loads for SOL calibration.

The text fixture used for this demonstration is constructed on a SMA(M) PCB connector using some machined pin connector strip and N(M)-SMA(F) adapters to connect to the instrument.

Above is a pic of the test fixture with adapters (in this case on a AA-600).

Above are the OPEN, SHORT and LOAD components intended for SOL calibration, the left hand one will be used for the cable measurement.

The problem is that these adapters all represent some significant propagation time that needs to be factored out of the measurement. Antscope has a feature to back out a length of transmission line, we will use that. This is not as accurate as SOL calibration, but it is a useful technique when SOL calibration is not available or convenient.

The O test load (the pair of open machined pins is plugged into the adapter, and a scan taken. The scan shows some residual shunt capacitive reactance (viewed in Zpar mode) which is due to the test fixture. We can approximately back that out by using the subtract cable feature, adjusting the length for maximum Zpar.

The cable backout adjusts for the 280ps propagation delay and Zo and resulting impedance transformation from the instruments calibration plane to the fixture’s measurement plane. Measuring balun common mode impedance gives a more detailed procedure for backing out the test fixture.

The prepared cable end is carefully pushed just 1mm onto the pins to connect the inner and outer conductors to inside and an outer pin of the adapter (as shown earlier). The DUT is scanned in search of the consistent sensible first half wave resonance, In this case 184.000MHz.

A half wavelength in free space h0 at that frequency is found by dividing c0 by twice the frequency, so h0=299792458/184000000/2=814.7mm.

Velocity factor is found by dividing the DUT length by h0, vf=661/814.7=0.81.

Now that length can be used in designing tune line lengths such as phasing lines etc. Do not ignore the effect of connectors in such applications.

By all means, design and use your own fixtures but be aware of any change to connection lengths to the DUT that will invalidate the calibration. attempting to measure sample line sections with connectors on them of unknown electrical length, and worse, ones of unknown Zo as well (eg UHF connectors) can introduce significant error.

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A common task is to measure the velocity factor of a sample of coaxial transmission line using an instrument that supports SOL calibration, an AIMuhf in this example.

Whilst this seems a trivial task with a modern antenna analyser, it seems to challenge many hams.

There are a thousand recipes, I am going to demonstrate just one that suits the instrument and application.

We will use a little test fixture that I made for measuring small components, and for which I have made test loads for SOL calibration. We will find the frequency where reactance passes through zero at the first parallel resonance of an O/C stub section, this is at a length of approximately λ/2 (a good approximation for low loss coaxial cables above about 10MHz).

The text fixture used for this demonstration is constructed on a SMA(M) PCB connector using some machined pin connector strip and N(M)-SMA(F) adapters to connect to the instrument.

Above is a pic of the test fixture with adapters (in this case on a AA-600).

Before measurement is made of the inductor, the test fixture must be calibrated with an OPEN, SHORT and LOAD.

Above are the OPEN, SHORT and LOAD components, the load is two 100Ω 1% SMD resistors in parallel. The reference plane is a point about 1mm below the top of the pins. If one was obsessive, 1mm should be trimmed from the OPEN… but the effect will be very hard to measure at these frequencies.

The SOL calibration is performed using the AIMuhf.

A sample of the coaxial line is prepared by cutting both ends clean. The sample was measured at 661mm and will have a half wave resonance somewhere below 200MHz.

The O test load (the pair of open machined pins is plugged into the adapter, and the cable end is carefully pushed just 1mm onto the pins to connect the inner and outer conductors to inside and an outer pin of the adapter (as shown earlier). The DUT is scanned in search of the consistent sensible first half wave resonance which in this case was at 183.6MHz.

A half wavelength in free space H0 at that frequency is found by dividing c0 by twice the frequency, so H0=299792458/183600000/2=816.4mm.

Velocity factor is found by dividing the DUT length by H0, vf=661/816.4=0.81.

Now that length can be used in designing tune line lengths such as phasing lines etc. Do not ignore the effect of connectors in such applications.

Analyser software often has utilities like the one above in Aim910B which I could not get to work and has zero documentation. Give them a miss and just use a hand calculator to perform calculations that you understand.

By all means, design and use your own fixtures but be aware of any change to connection lengths to the DUT that will invalidate the calibration. attempting to measure sample line sections with connectors on them of unknown electrical length, and worse, ones of unknown Zo as well (eg UHF connectors) can introduce significant error.

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Above is a sweep of an A/B changeover relay intended for HF application at up to 100W and lowish VSWR. The sweep is actually from 1 to 61MHz to be confident that there is not poor behaviour just outside of the HF range that might present on another implementation of the same design.

In fact, the InsertionVSWR at 30MHz is just 1.05, better than lots of HF antenna switches, and InsertionVSWR remains quite good to 54 MHz (top of the 6m band)

Now we hear about power relays and inductance, low voltage withstand, yada yada yada… but have these experts made measurements to support their position, have they opened their minds to cost effective solutions?

Above is the changeover relay that was measured. It is an ordinary power relay rated for 5A per contact set at 50Hz (it will be lower at RF) and there are two parallel contact sets, and withstand between contacts of 1400V.

Key to it’s low InsertionVSWR is the compensation provided by the short coax stub connected to the common coax jack as explained at High frequency compensation of T/R relay.

This is where the analyser comes in, finding the optimal length of stub can be done by cutting a stub to longer than needed, and trimming it down whilst sweeping the InsertionVSWR until the response suits the application.

- Duffy, O. May 2012. High frequency compensation of T/R relay. https://owenduffy.net/transmissionline/concept/RelayComp/index.htm.
- Duffy, O. Dec 2012. Another Morse beacon keyer – A/B RF switching. https://owenduffy.net/module/smbk/AB.htm.

This article explains a method to use an analyser to predict the peak voltage level at a point for a given frequency and power based on measurement or estimation of complex Z or Y at that point using a suitable antenna analyser.

Lets say you have some critical voltage breakdown limit and want to use your analyser to find any non-compliance at the proposed power level.

Let us assume that the not-to-exceed voltage at that point is 1000Vpk. Let’s allow a little margin for variation due to factors not fixed, let’s actually use 800Vpk as the limit. We will use the maximum permitted power in Australia, 400W.

At any point on a transmission line, the peak voltage is given by the simple expression Vpk=(2*P/G)^0.5 where P is the real power and G is the conductance component of admittance at that point.

Analysers don’t often directly display admittance (or its conductance component), perhaps a concession to hams who seem to not get their minds around the concept of admittance.

Some analysers do display a parallel equivalent circuit using impedance elements, we can work with the equivalent parallel resistance Rp. In that case, the expression becomes Vpk=(2*P*Rp)^0.5.

More relevant may be the critical value of G or Rp. G=(2*P)/Vpk^2 and R=Vpk^2/(2*P). I will use Rp in the rest of this example as the AA-600 used displays it directly (even if formatted wrongly).

So, for our scenario of 800Vpk maximum at 400W, the critical value Rmax=800^2/(2*400)=800Ω.

Above is a scan viewed in R||+jX format as Antscope calls it. This is using the latest version of Antscope at his time, v4.2.63.

First thing you will note is that the graph scales which are zoomed fully out are scaled to +/-600Ω, pretty useless for analysing this pretty common scenario.

Never mind, if we go back to Antscope v4.2.57 we can display the data more usefully.

Above is a scan viewed in R||+jX format as Antscope calls it in v4.2.57.

Ignore the blue line, it is for hams who think of impedance in scalar terms. Focus on the red curve Rp. The critical value of Rp is 800Ω, so any frequencies within the intended operating bands were Rp>800Ω flag a problem. Note at the cursor, the cursor data shows Zpar=831.2-j111.7. This is a nonsense combination of the parallel components, and is mathematically bogus… but the value 831.2 **is** the equivalent parallel resistance Rp we have been talking about, and at 7.040MHz it exceeds our critical value.

Above is the display from AIM910b of a similar scenario. Note that at the cursor (7.020MHZ), Rp=847Ω which is greater than the critical value calculated.

This method can be used to determine compliance with a maximum voltage that might be imposed by component limits (eg baluns etc) or perhaps surge arrestors if they are employed.

If your instrument does not directly display G or Rp, it can be derived from Z (Rs, Xs), or possibly from some other figures given by some low end analysers (eg VSWR, |Z| and R). The analyser will need to be capable of measuring high impedance with sufficient accuracy, the example given above would not be possible with the ubiquitous MFJ-259B for instance (or the newer MFJ-269C), though they may be useful for lower critical values of Rp.

Duffy, O. Jul 2011. Avoiding flashover in baluns and ATUs. https://owenduffy.net/files/AvoidingFlashoverInBalunsAndAtus.pdf.

]]>For convenience, here is the relevant explanation.

By definition, an antenna’s resonant point will be when the reactive component (j) is equal to zero (X=Ø, or +jØ). At that point in our example shown at left, the R value reads 23 ohms, and the SWR readout will be 2.1:1 (actually 2.17:1). If we raise the analyzer’s frequency slightly, the reactive component will increase (inductively) along with an increase in the resistive component, hence the VSWR will decrease, perhaps to 1.4:1. In this case, the MFJ-259B is connected to an

unmatched, screwdriver antenna mounted on the left quarter panel, and measured through a 12 inch long piece of coax. This fact is shown graphically in the image at right (below).

Note that the graph is unscaled, and that frustrates interpretation. The text is also not very clear, a further frustration. It is easy to draw a graph… but is the graph inspired by a proposition or is it supporting evidence.

The text hints that Z is measured at the antenna input at some frequency where R=23, X=0, and the indicated VSWR is 2.1. Alan correctly notes VSWR(50) for a load of 23+j0Ω is 2.17, so there appears to be some small error in the instrument’s display of one or more of the quantities.

He goes on to state that increasing frequency a little the reactive component will increase (inductively) along with an increase in the resistive component

.

This behaviour is most unlike the feed point impedance of a heavily loaded mobile whip (as indicted by the value of R at resonance). Loaded short monopoles near resonance typically show a value of R (at the feed point) that changes only very slowly as frequency increases and X that changes relatively quickly with frequency from negative below resonance to positive above resonance.

Above is the measured feed point impedance of a MobileOne M40-1 helically loaded 1.5m monopole in the roof of a vehicle. (Forget the blue curve, Rigexpert’s Antscope software does not allow it to be turned off… it is their concession to the ham market that wants to think of impedance as a scalar quantity.)

Concentrate on the red R curve and green X curve:

- R is almost constant, but it does increase by a very small amount (perhaps 1Ω) from left to right;
- X increases from around -40Ω to +40Ω from left to right, a change of perhaps 80 times that of R.

The consequence of the fact that R is changing, albeit VERY slowly about resonance is that resonance (ie X=0) does NOT coincide EXACTLY with minimum VSWR.

Above is the VSWR curve, and VSWR is reported as 2.39 at resonance (X=0), and in fact minimum VSWR occurs 1kHz higher, it is 2.38. This is based on field measurement of a real antenna, and although minimum VSWR does not occur exactly at resonance, it is so close to it with this type of antenna that you are unlikely to notice the difference in the field. (Apologies that the cursor is not visible in the graph above, one of the many defects of Rigexpert’s Antscope is that it does not show the cursor when it coincides with a grid line, 7.065MHz in this case.)

Resonance of the antenna is in this example indicated by X approximately equal to zero, and is at 7.065MHz, not one kHz higher or lower.

Alan’s point about measurement through 12″ (0.3m) of coax is not very clear.

Some simple facts of measuring through 0.3m of RG58A/U coax in the M40-1 example:

- the plot of R and X will be different because the effect of standing waves on the line; and
- the plot of VSWR will be different, but by so little that you are unlikely to notice it in this type of scenario.

Above is the VSWR curve as would be observed looking into 0.3m of RG58A/U coax. If you look really hard, you will see that it is different, and most notably is that Zin at 7.065MHz (the resonant frequency measured earlier of the antenna) is 21.2+j2.9Ω. In fact, X=0 looking into that coax occurs at approximately 7.061MHz.

Alan advises Because of this issue, the SWR readout of any antenna analyzer should be ignored while attempting to match a mobile antenna!

This example with real measurements of a real antenna demonstrates quite the opposite. Looking into the coax, the best indication of resonance of the antenna is minimum VSWR looking into the coax. Indeed it is an error to tune the antenna for X=0 at an arbitrary remote point.

Don’t take my word for it, get your antenna analyser out and conduct a careful experiment. Get familiar with the equipment you use. Make some similar measurements. Be careful that the measurements are valid, particularly that you do not disturb the thing you are measuring… that can give very confusing results (Exploiting your antenna analyser #9).