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')

]]>

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.

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.

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 a Simsmith simulation of Xin to 1500MHz. This is clearly not a tan curve, it does not turn upwards but turns downwards towards 1500MHz. The shape of the curve is due to all configuration factors, the assumed constraints and l1 and l2.

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 the Agilent E5061A. 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-HPVNA01', 100000000.0-1500000000.0 Hz, 201 pts, z0=[50.+0.j] Model t: t1= 67.9ps, t2=110.6ps σ: σ1= 0.08ps, σ2= 0.09ps Model l: l1= 20.4mm, l2= 33.2mm σ: σ1= 0.02mm, σ2= 0.03mm

Above are the calculated model values, l1=20.3mm with σ=0.025mm, and l2=33.2mm with σ=0.028mm. This is quite a good model.

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

Credit to Bruce (VK4MQ) for making the measurements, pics etc.

]]>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).

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 ReturnLoss (RL) looking into the male port. At the frequency where the right hand branch (l1) is exactly a quarter wavelenth electrically, the SC is transformed to an open circuit (OC) at the internal T junction and so it does not load the circuit at that point. So, the instrument measuring RL at the male connector sees two sections of low loss 50Ω line to the 50Ω load, and RL will be very high.

Above is a simulation in Simsmith. For the line dimensions used here, there it a distinct peak in RL at 2500MHz (and there will be more at odd harmonics).

So, having measured the frequency f where RL peaks, the length l1 is \(\frac {299792458} {4f} m\). Don’t forget to then adjust for the offset of the SC used.

You can then reconnect the parts to find the other two lengths one by one.

So, for typical sizes of N type T adapters, you need an instrument that can measure RL to say 3GHz. A scalar analyser or RL Bridge can do this, it does not have to be a 1 port or 2 port VNA.

There is at least one other solution.

So, put your thinking caps on.

Another solution to follow…

]]>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 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).

Something to keep in mind is that the reference plane for the female connectors is about 9mm inside the T, and you can see the reference plane on the male connector, the nearest end of the shield connection.

With a ruler, the physical length of the left and right female branches looks to be about 13mm, and around 28mm for the male branch… but electrical length will be longer due to an unknown (as yet) deployment of dielectric of unknown type inside the T.

So, put your thinking caps on.

A solution to follow…

]]>From the basic definition \(\mu=B/H\) we can derive the relationship that the flux density in the core with current I flowing through N turns is given by \(B=\frac{\mu_0 \mu_r N I}{2 \pi r}\).

The incremental flux at any incremental radius is proportional to the flux path length \(2 \pi r\), so the total flux due to B(r) is \(\Phi_B=\int_{a}^{b}Bc \, dr=\frac{\mu_0 \mu_r N I}{2 \pi r}c \, dr=\frac{\mu_0 \mu_r N I}{2 \pi} c \, ln \frac b a\).

Note that the core geometry is captured in the term \( c \, ln \frac b a\).

From that we can calculate inductance \(L \equiv \frac{N \Phi_B}I=\frac{\mu_0 \mu_r N^2}{2 \pi} c \, ln \frac b a \) where \(\mu_0=4\pi 10^{-7}\), the permeability of a vacuum.

Ferrite datasheets commonly give \(\mu_r=\mu^{\prime}-j\mu^{\prime\prime}\), a complex value (note it is usually a frequency dependent parameter). The imaginary term represents the core loss.

We can calculate the impedance at frequency f by substituting the values.

\(Z=j 2 \pi f L=j 2 \pi f \frac{\mu_0 (\mu^{\prime}-j\mu^{\prime\prime}) N^2}{2 \pi}c \, ln \frac b a \\\)The model can be improved for frequencies approaching SRF by addition of a small equivalent shunt capacitance \(C_s\).

\(Z=\frac1{\frac1{j 2 \pi f \frac{\mu_0 (\mu^{\prime}-j\mu^{\prime\prime}) N^2}{2 \pi} c \,ln \frac b a}+ j 2 \pi f C_s}\)The calculator Calculate ferrite cored inductor – rectangular cross section does exactly this calculation. Note that a real FT240-43 has chamfered corners, so these calculations based on sharp corners will very slightly overestimate L, but the error is trivial in terms of the tolerance of µr.

µr comes from the datasheet, but you may find Ferrite permeability interpolations convenient.

The value Cs is best obtained by observation of SRF of a particular winding, it is sensitive to winding layout.

The calculated value \(\sum{\frac{A}{l}}=\frac{c \, ln \frac b a}{2 \pi}\) and captures the core geometry in a more general form. It or its inverse often appear in datasheets and can be used to calculate Z (Calculate ferrite cored inductor – ΣA/l or Σl/A).

]]>Two lengths of the same cable were selected to measure with the nanoVNA and calculate using Velocity factor solver. The cables are actually patch cables of nominally 1m and 2.5m length. Importantly they are identical in EVERY respect except the length, same cable off the same roll, same connectors, same temperature etc.

Above is the test setup. The nanoVNA is OSL calibrated at the external side of the SMA saver (the gold coloured thing on the SMA port), then an SMA(M)-N(F) adapter and the test cable. The other end of the test cable is left open (which is fine for N type male connectors).

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 short cable. The short cable measured 1.150m between the insides of the crimp sleeves (which were hard up against the connector body), the long cable measure 2.450m and resonance was at 19.614MHz.

Above is the calculation which tells us that the velocity factor of the coax itself (having deducted the effects of adapters and connectors) is 0.66.

The calculator also reports that it calculated the offset to be 363.9ps, equivalent to 72mm of RG213 length in the adapter and connectors. This reconciles well with physical measurement (allowing that part of the internal path of N connectors is air dielectric, about 13mm in a mated pair so that appears to be 8.6mm equivalent at VF=0.66).

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.

Warning: do not measure cable with a loose UHF series plug at an open end. The loose collar will cause unpredictable / unreliable results, install a UHF(F)-UHF(F) adapter to fix the problem. Likewise for plugs of similar construction (eg SMA).

]]>Online experts offer a range of advice including:

- use the datasheet velocity factor;
- measure velocity factor with your nanoVNA then cut the cable;
- measure the ‘tuned’ length observing input impedance of the section with the nanoVNA; and
- measure the ‘tuned’ length using the nanoVNA TDR facility.

All of these have advantages and pitfalls in some ways, some are better suited to some applications, others may be quite unsuitable.

Let’s make the point that these sections are often not highly critical in length, especially considering that in actual use, the loads are not perfect. One application where they are quite critical is the tuned interconnections in a typical repeater duplexer where the best response depends on quite exact tuning of lengths.

Datasheet velocity factor will be fairly good at VHF for good quality solid PE or PTFE dielectric and sufficiently good for most purposes, but does not take into account connectors.

Foam dielectrics are less well controlled for velocity factor, and warrant measurement of the actual cable to be used.

I make the observation that most attempts to actually measure such cables demonstrate a failure of measurement technique, the datasheet is better than many measurers.

It is difficult to connect nothing but the test cable to the reference plane of the instrument, there is likely to be some transmission line section involved that is not purely test cable, and if the length and Zo are significant then results are degraded. This is more so if there are connectors on one or both ends.

The article Finding velocity factor of coaxial transmission line using the velocity factor solver offers a tool and explains how to use it to overcome some of these problems.

Velocity factor of good cables does not change much above 30MHz, so for VHF/UHF application measure velocity factor at a frequency where measurement is not so sensitive to small errors in length, effects of fringing capacitance etc.

This approach sounds an obvious solution, but by itself it does not properly account for connectors and effects.

This approach also sounds an obviously good solution as you leverage the smarts of the TDR… but it is subject to effects of connectors and the parameters of the TDR sweep. Better resolution and accuracy can usually be obtained by a conventional s11 sweep around section resonance… but connector effects have to be deducted… see 2.

if you come to an accurate figure for velocity factor of cable and measure the resonance of a known length of cable with connectors and terminated in a calibration grade open or short, you can calculate the equivalent electrical length of the connectors.

Sometimes you may wish to find the electrical length to a key circuit node, like the node within a coaxial resonator. Where the node is in a T coax adapter, the distance is not hard to find, but for a resonator with separate input and output connectors, it takes more effort with calibrated cables and terminations to find the point of action of the internal circuits of the resonator. Establishing these reference points is important in finding the physical size of interconnecting cables in a cascade of resonators so that the points at which each resonator section acts are properly spaced electrically for maximum reinforcement of response of the whole duplexer.

- Beware of too much science applied badly.
- If measured velocity factor departs greatly from datasheet values, investigate.

]]>