Above is a modified device with the transformer replaced with a Macom ETC1-1T-2TR 1:1 transformer. The replacement is not exactly the same pads, but it is sufficiently compatible to install easily. The track is cut to disconnect the secondary centre tap, essentially allowing the secondary to float and so have higher common mode impedance than with the centre tap grounded.

The most notable departure from ideal of these small transformers is leakage inductance of 50nH give or take.

The existing compensation capacitor was removed from the original and a sweep done from 1-300MHz.

Above is the sweep presented at R,X (never mind the legend that says RLC)… this is hammy software. Focus on the X (blue) line, it is almost a straight line from 1 to 60MHz, \(X \propto f\), and the slope is about 40nH.

We can make a firts estimate of the compensation capacitance \(C=\frac{L}{Z_0^2}=\frac{42e{-9}}{50^2}=17e{-12}\). We will undercompensate a little so as not to too adversely affect performance above the primary range.

We can partially compensate that with a small shunt input capacitor. To quickly size that, the uncompensated sweep was imported into Simsmith. A shunt capacitor was inserted and its value adjusted for a reasonable response curve to 60MHz+.

Above is a Smith chart presentation of the effect of the 12pF compensation capacitor. The magenta curve is the load characteristic (ie without compensation), and the blue curve is the compensated response.

Above is the VSWR response curve with 12pF configured.

Above, the measured VSWR response of the (12pF) compensated assembly is in line with expectation.

Above, the underside of the terminal block has a 2 pin machined pin socket to allow convenient OSL calibration using the parts shown in

Antenna analyser – what if the device under test does not have a coax plug on it?. The wire terminals are not quite on the reference plane, but the error is small.

So, the result has low InsertionVSWR from 1-60MHz, and can conveniently OSL calibrated using the machine pin strip and small calibration parts.

The common mode impedance of the transformer alone was measured.

Up to 20MHz, the equivalent series impedance is dominated by an equivalent series capacitance of 8pF, and below 20MHz, |Z|>1000Ω

]]>Above, the measurement fixture is simply a short piece of 0.5mm solid copper wire (from data cable) zip tied to the external thread of the SMA jack, and the other end wrapped around the core and just long enough to insert into the inner female pin of the SMA jack.

Based on the datasheet, we can calculate the expected impedance at 1MHz.

So, around 0.5+j6Ω is the expectation.

The two cores I measured are 0.16+j5.34Ω and 0.53+j6.32Ω, not a lot of departure though the first has quite a lot less core loss (the R component).

Above is a wider range prediction based on the published data. At the cross over frequency of 14MHz R=X=24Ω.

Now to the two sample cores that I measured.

Above from the first sample, the R curve is quite similar to expectation, but the X curve is quite different, it does not roll off nearly to the extent predicted above. As a result, the cross over frequency (R=X) is well above the expected 14MHz, around 46MHz in this case.

Above from the second sample, the R curve is quite similar to expectation, but the X curve is quite different, it does not roll off nearly to the extent predicted above. As a result, the cross over frequency (R=X) is well above expectation, greater than 50MHz.

So, in summary, the tested cores exhibited X, and therefore µ’, quite similar to the datasheet at 1MHz, but at higher frequencies X and µ’ were quite higher than expected.

I have tested a lot of #43 material in various shapes and sizes of cores, and this is the first time I have observed this effect. Ferrite products have wide tolerances, and certain characteristics are controlled, I could not say whether these meet the controlled parameters.

Such variation certainly makes identification of core material, designs and prototype measurements more challenging.

I might mention that Fair-rite issued a new table of permeability characteristics for type #43 in Feb 2020. The results measured here for two year old purchases are even further from the ‘new’ #43.

]]>A significant difference in the two wire line is that we want the line to operate in balanced mode during the test, that there is insignificant common mode current. To that end, a balun will be used on the nanoVNA.

Above, the balun is a home made 1:4 balun that was at hand (the ratio is not too important as the fixture is calibrated at the balun secondary terminals). This balun is wound like a voltage balun, but the secondary is isolated from the input in that it does not have a ‘grounded’ centre tap. There is of course some distributed coupling, but the common mode impedance is very high at the frequencies being used for the test.

Above, the underside of the terminal block has a 2 pin machined pin socket to allow convenient OSL calibration using the parts shown in

Antenna analyser – what if the device under test does not have a coax plug on it?. The screw terminals are not quite on the reference plane, but the small error will be adjusted out by the Velocity factor solver.

The fixture was OSL calibrated before measuring the line sections.

Using the method described at Velocity factor solver the quarter wave resonance was measured for each of the test cables with the same adapters.

Above is measurement of the long cable. The long cable measured 8.240m end to end, the short cable measure 4.104m.

Above is the calculation which tells us that the velocity factor of the coax itself is 0.85.

Be aware that velocity factor is frequency dependent, though the error is small for practical low loss cables above 10MHz.

You can now cut the cable based on the measured velocity factor, allowing for the electrical length of connectors and adapters as appropriate.

]]>One expert advised that 100mm wire clip leads would work just fine.

Another expert expanded on that with When lengths approach 1/20 of a wavelength in free space, you should consider and use more rigorous connections.

At Antenna analyser – what if the device under test does not have a coax plug on it? I discussed using clip leads and estimated for those shown that they behaved like a transmission line segment with Zo=200Ω and vf=0.8.

So lets model the scenario of a perfect 50Ω load at 30MHz measured through λ/20 of clip lead with Zo=200Ω and vf=0.8.

The InsertionVSWR of the clip lead fixture is 3.

Note that Zo in this case is quite low because the wires are quite close together, Zo would easily exceed 200Ω with wider spacing and the transformation would be even worse.

Another expert opined as long as the lead is much shorter than about one tenth of a wavelength, it won’t matter much.

(Zo=200, VSWR=6.7)

In fact the InsertionVSWR of a λ/120 section exceeds 1.2 With a λ/120 fixture (80mm @ 30MHz), if the actual VSWR of the DUT was 1.5, you might read anywhere from 1.2 to 1.9 on the nanoVNA.

The outcome is ridiculous, the advice is ridiculous, this is the way we help beginners… or is it principally about inflating the egos of the experts?

At the time of writing this, the advice goes unchallenged… possibly because it is unsociable to call out BS.

A fair question is can accurate VSWR measurements be made of a CB antenna with UHF connector?

The article A check load for antenna analysers with UHF series socket

describes a low cost UHF 50Ω load that will outperform most other types of UHF load. Lets use that and a SMA-UHF(F) adapter to measure insertion loss of the fixture and load adapter.

Above the SMA load with UHF(M) adapter, and a UHF(F) to SMA(M) adapter. UHF connectors do not have a constant through impedance of 50Ω, but how bad are they in this test?

Above, a sweep from 1-200MHz suggests that the adapters are quite suitable for modest accuracy measurements to 200MHz. This is a lot better than improvising with clip leads.

A word of warning, using large connectors and heavy cables might subject the nanoVNA on-board jacks to damaging forces… be careful.

]]>…

This article discusses various measurements and models of Wireman 551 windowed ladder line, including adapting Simsmith’s bimetal line type to bear on the problem.

A starting point for characterising the matched line loss (MLL) of the very popular Wireman 551 (W551) windowed ladder line is the extrapolation of measurements by (Stewart 1999) to 1.8MHz. Since the measurements were made at and above 50MHz where the W551 has copper like performance, this is likely to underestimate actual MLL and such wide extrapolation introduces its own uncertainty. Nevertheless, the datapoint is MLL=0.00227dB/m.

This is a revision of an article written in Feb 2020, capturing revision of Simsmith to v17.2 and revision of my own current distribution model.

…

Dan Maquire recently posted a chart summarising measurements of these lines.

For the purposes of this article, let’s tabulate the MLL at 1.8MHz in dB/m.

- KN5L WM551 MLL=0.148/30.48=0.00486dB/m
- G3TXQ WM551: MLL=0.117/30.48=0.00384dB/m

JSC is an OEM and their 1318 product has the same dimensions as W551, it should be very similar if not the same product.

VK2OMD JSC 1318: MLL=0.0028dB/m

So, there is quite a wide spread from 0.00227 to 0.0049dB/m.

TLDetails gives MLL=0.00824dB/m.

Above is a model in Simsmith using its characterisation of W551, and MLL=0.0083dB/m, nearly twice the highest of the three measurements given earlier. (I used v16.9av, the later version crashes on my machine.)

Simsmith has a new / experimental facility, the bimetal

line model. The model is designed for modelling coax, but lets see if we can use it for this two wire line.

A two wire line can be modelled as a single conductor against the neutral plane. Where the wires are spaced sufficiently that there is insignificant proximity effect (ie that current is uniformly distributed around the conductor), we can curl the neutral plane into a cylinder of diameter to obtain half Zo.

Above is a Simsmith v17.2 model of one wire of half of the W551 type line at 1.8MHz. It is modelled with air dielectric, it has little consequence in this case as the loss is dominated by the copper conductors which are sized as per the W551 specs. The shield is set to zero resistance.

The calculated MLL is 0.00241dB/m.

Above is an revised current distribution plot from (Duffy 2020) for the same dimensions and the calculated MLL is 0.00238dB/m.

Above is a summary in order of ascending MLL.

In the modern ham world where in the absence of much science, popularity is held to determine fact, one might accept the highest two as they are in close agreement… but they use the same model, so their agreement is just a tribute to implementation. In fact they are well above any of the measurements.

Let us consider the N7WS datapoint. This extrapolation is used by most line loss calculators and is likely to be an underestimate clouded with extrapolation uncertainty. An interesting point because of its common use more than anything.

The three measurements fall in the range 0.0028 to 0.0049dB/m, quite a spread but I should note that KN5L’s measurements may have been of JSC 1318 and his writeup of those measurements questions whether the line he had was in fact 30% IACS copper clad. If it was 21% as he writes, it should be discarded from the measurement set here. If that was done, we have two remaining measurements of 0.0028 and 0.0038dB/m.

That leaves two models, Simsmith’s bimetal and revised VK2OMD (Duffy 2017) which use different techniques to model the current distribution within the conductor and arrive at conductor loss.

Above is a chart of the current distribution in the VK2OMD model. Differently to a conductor with well developed skin effect where the phase of the bulk current lags the surface current by 45°, in this case it lags by just 30°.

My own view is that the VK2OMD and Simsmith bimetal models are probably pretty close to correct.

Note that the results here cannot simply be applied to the more popular stranded CCS types of line, they have significantly worse MLL due to the thinner copper that accompanies stranding.

- Duffy, O. Apr 2017. A model of current distribution in copper clad steel conductors at RF.
- Duffy, O. Oct 2020. A model of current distribution in copper clad steel conductors at RF – capturing conductor curvature.
- Harriman, E. May 2019. Modelling coax from first principles. Packaged in Simsmith v16.9av.
- Stewart, W. (N7WS). Mar 1999. Balanced Transmission Lines in Current Amateur Practice.

The single most common factor in their cases is an attempt to use TDR mode of the VNA.

Well, hams do fuss over the accuracy of quarter wave sections used in matching systems when they are not all that critical… but if you are measuring the tuned line lengths that connect the stages of a repeater duplexer, the lengths are quite critical if you want to achieve the best notch depths.

That said, only the naive think that a nanoVNA is suited to the repeater duplexer application where you would typically want to measure notches well over 90dB.

The VNA is not a ‘true’ TDR, but an FDR (Frequency Domain Reflectometer) where a range of frequencies are swept and an equivalent time domain response is constructed using an Inverse Fast Fourier Transform (IFFT).

In the case of a FDR, the maximum cable distance and the resolution are influenced by the frequency range swept and the number of points in the sweep.

\(d_{max}=\frac{c_0 vf (points-1)}{2(F_2-F_1)}\\resolution=\frac{c_0 vf}{2(F_2-F_1)}\\\) where c0 is the speed of light, 299792458m/s.

Let’s consider the hand held nanoVNA which has its best performance below 300MHz and sweeps 101 points. If we sweep from 1 to 299MHz (to avoid the inherent glitch at 300MHz), we have a maximum distance of 33.2m and resolution of 0.332m.

Here is such a sweep of a cable of length around 1.2m.

The marker is close to the apparent peak of the response at about 11.8ns (1.17m), and each step of the marker is 1.3ns (0.129m).

If we sweep to 900MHz, we do get better resolution (albeit for shorter dmax).

The resolution is reduced to 0.435ns (0.043m)

If you want mm resolution for short line sections, you need a VNA that sweeps a much wider frequency range and / or much more sweep points.

Above, nanoVNA-saver results on the same DUT with smoothing of 100 sweeps produces a nice clean looking graph and a calculated distance to fault of 1.222m, mm resolution implied by the number format… but are you mislead?

We can do a s11 sweep of a short circuit or open circuit line section (just as in the FDR / TDR case), but make the sweep quite narrow (ie high resolution) around a quarter wave or half wave resonance.

Above is a very narrow sweep with 1kHz resolution at 40MHz, ie 0.0025% resolution. From the interpolated resonance frequency of 40.4MHz and previously measured vf, we can calculate the physical length to be 1.224m… with resolution of 0.0000306m.

Many analysers and VNAs sport a Distance to Fault mode, and it is commonly a FDR implementation. These can be very effective productivity tools in identifying not just cable opens and shorts, but loose connectors, pinched cable etc.

The foregoing discussion shows that FDR / Distance to Fault may not be adequate for tuning of critical line sections, but it often has sufficient resolution for identifying the locality and severity of a fault.

Things have come a long way in the around 150 years since Oliver Heaviside successfully applied his mind to location of faults in submarine telegraph cables.

Whilst the TDR mode of a VNA looks an appealing way to measure line length, with low end instruments like the nanoVNA it does not have adequate resolution for demanding applications.

]]>A first observation of listening to a SSB telephony signal is an excessive low frequency rumble from the speaker indicative of a baseband response to quite low frequencies, much lower than needed or desirable for SSB telephony.

The most common application of such a filter is reception of A1 Morse code.

Above is a screenshot of the filter settings.

Above is a plot of the response of the filter. It is hardly an idealised rectangular filter response. Though the response might be well suited to Morse code reception, it is an issue when measurements make assumptions about the ENB. The response is not well suited to narrowband data such as RTTY etc.

A summary of the filter response follows.

Locut 0Hz.

sox: bin_width_hz=10.000Hz

Filter -6dB response: 460-770Hz=310Hz.

ENB=224Hz with respect to gain at 610Hz (passband centre frequency).

ENB=222Hz with respect to gain at 590Hz (max gain frequency).

ENB=222Hz with respect to gain at 600Hz.

If we take the gain reference frequency to be 600Hz, there is 3.5dB less noise admitted by this filter than an idealised rectangular filter. Measurements such as the ARRL MDS that might assume 500Hz bandwidth will have 3.5dB error.

A 1000Hz filter might be well suited to narrow band data reception, many of the so-called ham digital modes.

Above is a screenshot of the filter settings.

Above is a plot of the response of the filter. It is fairly close to an idealised rectangular filter response.

There appears to be no means to offset the filter at baseband frequency.

A summary of the filter response follows.

Locut 0Hz.

sox: bin_width_hz=10.000Hz

Filter -6dB response: 110-950Hz=840Hz.

ENB=823Hz with respect to gain at 530Hz (passband centre frequency).

ENB=716Hz with respect to gain at 200Hz (max gain frequency).

ENB=800Hz with respect to gain at 500Hz.

If we take the gain reference frequency to be 500Hz, there is 0.97dB less noise admitted by this filter than an idealised rectangular filter.

Above is a screenshot of the filter settings.

Above is a plot of the response of the filter. It is fairly close to an idealised rectangular filter response.

There appears to be no means to offset the filter at baseband frequency.

A summary of the filter response follows.

Locut 0Hz.

sox: bin_width_hz=10.000Hz

Filter -6dB response: 110-2350Hz=2240Hz.

ENB=2353Hz with respect to gain at 1230Hz (passband centre frequency).

ENB=1829Hz with respect to gain at 210Hz (max gain frequency).

ENB=2255Hz with respect to gain at 1000Hz.

If we take the gain reference frequency to be 1000Hz, there is 0.27dB less noise admitted by this filter than an idealised rectangular filter.

SDR# does not appear to have a convenient facility to shift or offset the baseband response.

Above is the baseband response in 2400Hz USB mode as show in the SDR# window. Note that the response rolls off below 100Hz, whereas good conventional SSB Telephony receivers would have a 6dB response from say 250-2750Hz for a ENB of 2400Hz. The lower -6dB point for this response is 110Hz.

This leads to substantial low frequency component that is not a priority for SSB telephony, and in the case where the transmitter is band limited to 300-2700Hz, the filter admits unnecessary noise and the low end and cuts of a little of the high end. It is a hammy sammy approach where recognised speech characteristics, conventions and compatibility between transmitter and receiver are jettisoned.

The basic 1000Hz USB filter provides a response close to ideal, centred around 530Hz, and its ENB is 800Hz (-0.07dB on 1000Hz).

There appears no facility in SDR# to save a number of filter settings for later recall, so the process of configuring SDR# for measurement is a bit tedious.

My attention has been draw to the facility to drag the upper and lower limits of the IF passband, thanks Martin.

Above is an example where a 500Hz passband is centred on 1500Hz at baseband.

As soon as another mode is selected, the setting is lost and there appears no facility to save a set of settings for later recall. Note the inconsistency between the two displayed bandwidth figures.

Yes, it works but it is not convenient and not practical for save / recall of a standardised set of measurement or reception conditions.

]]>(Ikin 2016) proposes a different method of measuring noise figure NF.

Therefore, the LNA noise figure can be derived by measuring the noise with the LNA input terminated with a resistor equal to its input impedance. Then with the measurement repeated with the resistor removed, so that the LNA input is terminated by its own Dynamic Impedance. The difference in the noise ref. the above measurements will give a figure in dB which is equal to the noise reduction of the LNA verses thermal noise at 290K. Converting the dB difference into an attenuation power ratio then multiplying this by 290K gives the LNA Noise Temperature. Then using the Noise Temperature to dB conversion table yields the LNA Noise Figure. See Table 1.

The explanation is not very clear to me, and there is no mathematical proof of the technique offered… so a bit unsatisfying… but it is oft cited in ham online discussions.

I have taken the liberty to extend Ikin’s Table 1 to include some more values of column 1 for comparison with a more conventional Y factor test of a receiver’s noise figure.

Above is the extended table. The formulas in all cells of a column are the same, the highlighted row is for later reference.

A test setup was arranged to measure the noise output power of an IC-7300 receiver which has a sensitivity specification that hints should have a NF≅5.4dB. The relative noise output power for four conditions was recorded in the table below.

Ikin’s method calls for calculating the third minus second rows, -0.17dB, and looking it up in his table. In my extended table LnaNoiseDifference=-0.17dB corresponds to NF=3.10dB.

We can find the NF using the conventional Y factor method from the values in the third and fourth rows.

The result is NF=5.14dB (quite close to the expected value based on sensistivity specification).

Ikin’s so called dynamic impedance method gave quite a different result in this case, 3.10 vs 5.14dB, quite a large discrepancy.

The chart above shows the relative level of the four measurements. The value of the last two is that they can be used to determine the NF using the well established theory explained at AN 57-1.

The values in the first columns are dependent on the internal implementation of the amplifier, and cannot reliable infer NF.

- Hewlett Packard. Jul 1983. Fundamentals of RF and microwave noise figure measurement. AN 57-1
- Ikin, A. 2016. Measuring noise figure using the dynamic impedance method.

Let’s review of the concepts of noise figure, equivalent noise temperature and measurement.

Firstly let’s consider the nature of noise. The noise we are discussing is dominated by thermal noise, the noise due to random thermal agitation of charge carriers in conductors. Johnson noise (as it is known) has a uniform spectral power density, ie a uniform power/bandwidth. The maximum thermal noise power density available from a resistor at temperature T is given by \(NPD=k_B T\) where Boltzman’s constant k_{B}=1.38064852e-23 (and of course the load must be matched to obtain that maximum noise power density). Temperature is absolute temperature, it is measured in Kelvins and 0°C≅273K.

Noise Figure NF by definition is the reduction in S/N ratio (in dB) across a system component. So, we can write \(NF=10 log \frac{S_{in}}{N_{in}}- 10 log \frac{S_{out}}{N_{out}}\).

One of the many methods of characterising the internal noise contribution of an amplifier is to treat it as noiseless and derive an equivalent temperature of a matched input resistor that delivers equivalent noise, this temperature is known as the equivalent noise temperature Te of the amplifier.

So for example, if we were to place a 50Ω resistor on the input of a nominally 50Ω input amplifier, and raised its temperature from 0K to the point T where the noise output power of the amplifier doubled, would could infer that the internal noise of the amplifier could be represented by an input resistor at temperature T. Fine in concept, but not very practical.

Applying a little maths, we do have a practical measurement method which is known as the Y factor method. It involves measuring the ratio of noise power output (Y) for two different source resistor temperatures, Tc and Th. We can say that \(NF=10 log \frac{(\frac{T_h}{290}-1)-Y(\frac{T_c}{290}-1)}{Y-1}\).

AN 57-1 contains a detailed mathematical explanation / proof of the Y factor method.

We can buy a noise source off the shelf, they come in a range of hot and cold temperatures. For example, one with specified Excess Noise Ratio (a common method of specifying them) has Th=9461K and Tc=290K. If we measured a DUT and observed that Y=3 (4.77dB) we could calculate that NF=12dB.

This method of noise figure measurement is practical and used widely. Note that the DUT always has its nominal terminations applied to the input and output, the system gain is maintained, just the input equivalent noise temperature is varied.

Some amplifiers are not intended to be impedance matched at the input (ie optimised for maximum gain), but are optimised for noise figure by controlling the source impedance seen at the active device. Notwithstanding that the input is not impedance matched, noise figure measurements are made in the same way as for a matched system as they figures are applicable to the application where for example the source might be a nominal 50Ω antenna system.

So, NF is characterised for an amplifier with its intended / nominal source and load impedances.

Nothing about the NF implies the equivalent internal noise with a short circuit SC or open circuit OC input. The behaviour of an amplifier under those conditions is internal implementation dependent (ie variable from one amplifier design to another) and since it is not related to the amplifier’s NF, it is quite wrong to make inferences based on noise measured with SC or OC input.

So this raises the question of NF measurements made with a 50Ω source on an amplifier normally used with a different source impedance, and possibly a frequency dependent source impedance. An example of this might be an active loop amplifier where the source impedance looks more like a simple inductor.

Well clearly the measurement based on a 50Ω source does not apply exactly as amplifier internal noise is often sensitive to the source impedance, but for smallish departures, the error might be smallish.

A better approach might be to measure the amplifier with its intended source impedance. In the case of the example active loop antenna, the amplifier could be connected to a dummy equivalent inductor, all housed in a shielded enclosure and the output noise power measured with a spectrum analyser to give an equivalent noise power density at the output terminals. Knowing the AntennaFactor of the combination, that output power density could be referred to the air interface. This is often done and the active antenna internal noise expressed as an equivalent field strength in 1Hz, eg 0.02µV/m in 1Hz. For example the AAA-1C loop and amplifier specifies Antenna Factor Ka 2 dB meters-1 @ 10 MHz

and MDS @ 10MHz 0.7 uV/m , Noise bandwidth =1KHz and

to mean equivalent internal noise 0.022µV/m in 1Hz @ 10MHz at the air interface. 0.022µV/m in 1Hz infers Te=6.655e6K and NF=43.608dB again, at the air interface. These figures can be used with the ambient noise figure to calculate the S/N degradation (SND).

A spectrum analyser or the like can be used to measure the total noise power density at the output of the loop amplifier with the input connected to a dummy antenna network (all of it shielded) and to calculate the equivalent noise temperature and noise figure at that point. For example, if we measured -116dBm in 1kHz bandwidth, Te=1.793e+5K and NF=27.9dB. Knowledge of the gain from air interface to that reference point is needed to compare ambient noise to the internal noise and to calculate SND, that knowledge might come from published specifications or a mix of measurements and modelling of the loaded antenna.

The mention of a spectrum analyser invites the question about the suitability of an SDR receiver. If the receiver is known to be calibrated, there is no non-linear process like noise cancellation active, and the ENB of the filter is known accurately, it may be a suitable instrument.

In both cases, the instruments are usually calculated for total input power, ie external signal and noise plus internal noise, so to find external noise (ie from the preamp) allowance must be made for the instrument NF (ie it needs to be known if the measured power is anywhere near the instrument noise floor).

Field strength / receive power converter may assist in some of the calculations.

The foregoing discussion assumes a linear receiver, and does not include the effects of intermodulation distortion IMD that can be hugely significant, especially in poor designs.

Part of the problem of IMD is that the effects depend on the individual deployment context, one user may have quite a different experience to another.

There are a huge number of published active loop antenna designs and variant, and a smaller number of commercial products. Most are without useful specifications which is understandable since most of the market are swayed more by anecdotal user experiences and theory based metrics and measurement.

- Hewlett Packard. Jul 1983. Fundamentals of RF and microwave noise figure measurement. AN 57-1

For convenience, here is the problem.

An interesting problem arises in some applications in trying to measure the electrical length of each branch of a N type T piece.

Let’s make some assumptions that the device is of quality, that the connection from each connector to the internal junction is a uniform almost lossless transmission line of Zo=50Ω. Don’t assume that the left and right branches above are of the same length (though they often are) and we should not assume that the nearest branch is of the same length as the others (and they are often not).

Before we start, we will calibrate the VNA entering the offsets appropriate to the OPEN and SHORT cal parts. In the case of my nanoVNA, measurement above 900MHz is very noisy, so the scan will be 100-890MHz (to avoid a glitch at 900MHz due to harmonic mode switching).

So, the problem is all the uncertain things that connect to the internal T junction. Lets connect a calibration quality 50Ω termination to the left hand port. We now know that the path from the male port to the remaining female port comprises lengths l2 and l1 of low loss 50Ω transmission line with a 50Ω resistor shunting at the junction of l1 and l2.

Now lets connect a calibration quality short (SC) to the right hand female port, and measure the X component of the impedance looking into the male port. So, the instrument measuring Z at the male connector sees two sections of low loss 50Ω line to the 50Ω load, and the right hand SC stub shunting at the internal T junction.

Above is a Simsmith simulation of Xin to 900MHz using lengths very close to the DUT. The shape of the curve is due to all configuration factors, the assumed constraints and l1 and l2. We expect Xin vs frequency to be quite similar to above.

Without the 50Ω shunting at the internal T junction, Zin would simply be that of a low loss SC stub, and would be a tan curve turning upwards to a peak at a frequency where l2 is 90°.

Above is the Smith chart of the sweep. From that we can extract the Xin vs frequency dataset for curve fitting. We save this sweep as a .s1p file.

A Python script was written to extract Xin from the .s1p file, and fit a model of the transmission line structure to the measured data, finding l1 and l2.

Above is the measured and modelled curve fit.

1-Port Network: 'T-N-nanoVNA01', 100000000.0-890000000.0 Hz, 101 pts, z0=[50.+0.j] Model t: t1= 87.3ps, t2=100.8ps σ: σ1= 0.41ps, σ2= 0.21ps Model l: l1= 26.2mm, l2= 30.2mm σ: σ1= 0.12mm, σ2= 0.06mm

Above are the calculated model values, l1=26.2mm with σ=0.12mm, and l2=30.2mm with σ=0.063mm. This is quite a good model.

Don’t forget to then adjust for the offset of the SC used.

#!/usr/bin/python3 import os,sys import csv from scipy import stats import getopt import numpy import math import cmath import skrf as rf import matplotlib.pyplot as plt from scipy.optimize import curve_fit def usage(): print("Usage: "+sys.argv[0]+"") sys.exit(1) try: opts, args = getopt.getopt(sys.argv[1:], "ho:vl:u:", ["help", "output="]) except getopt.GetoptError as err: # print help information and exit: print(err) # will print something like "option -a not recognized" usage() # sys.exit(2) output = None verbose = False for o, a in opts: if o == "-v": verbose = True elif o in ("-h", "--help"): usage() sys.exit() else: assert False, "unhandled option" try: pass infile=args[0] except: usage() nw1=rf.Network(infile) print(nw1) print() f=numpy.array(nw1.f) x=numpy.array(nw1.z_im[:,0,0]) c0=299792458 zo=nw1.z0[0][0] def t_xin(freq,t1,t2): p=1/freq*1e12 z=zo*numpy.tan(t1/p*2*math.pi)*1j z=1/(1/z+1/zo) x=(zo*(z+zo*numpy.tan(t2/p*2*math.pi)*1j)/(zo+z*numpy.tan(t2/p*2*math.pi)*1j)).imag return x popt,pcov=curve_fit(t_xin,f,x,bounds=(0, [150,150]),method='trf') perr=numpy.sqrt(numpy.diag(pcov)) print('Model t: t1=%5.1fps, t2=%5.1fps' % tuple(popt)) print(' \u03C3: \u03C31=%5.2fps, \u03C32=%5.2fps' % tuple(perr)) print() print('Model l: l1=%5.1fmm, l2=%5.1fmm' % tuple(popt*1e-9*c0)) print(' \u03C3: \u03C31=%5.2fmm, \u03C32=%5.2fmm' % tuple(perr*1e-9*c0)) plt.figure(figsize=(8, 6), dpi=128) plt.plot(f/1e6,x, 'r-', label='measured') plt.plot(f/1e6,t_xin(f,*popt),'k:',label='fit: t1=%5.2fps, t2=%5.2fps' % tuple(popt)) plt.xlabel('Freq (MHz)') plt.ylabel('X ($\Omega$)') plt.legend() plt.title('T characterisation: '+nw1.name) plt.ylim(bottom=0) plt.xlim(left=0) plt.savefig(nw1.name+'.png')

]]>