It is an interesting application, and contrary to the initial responses on social media, there is a simple solution.

Let’s take a half wave dipole and lengthen it a little so the feed point admittance becomes 1/200-jB (or 200 || jX). We will build an NEC model of the thing in free space.

Above is a sweep of the dipole which is 3.14m long (we will talk about how we came to that length later), and the Smith chart prime centre is 200+j0… the target impedance.

Note here that at 45.4MHz, the feed point impedance is 72Ω.

Above, spinning up to 50.2MHz, feed point impedance expressed as a parallel equivalent is 201||j203. So, if we shunt the feed point with 203Ω of capacitive reactance (15.6pF) we have impedance close to 200+j0.

So, the length was adjusted so that Rp=200Ω with some Xp>0 at the desired frequency.

Now in case you think that Smith charts MUST have a prime centre of 50Ω…

… there is the solution wrt 50Ω.

Now it is probably more convenient to make the dipole short and use a shunt inductive reactance… so let’s work that through.

This time on a 50Ω chart, the necessary shunt element is an inductive reactance of 119Ω which will yield a feed point impedance of about 200Ω. That could be provided by a small solenoid inductor, or a shorted transmission line stub (aka a hairpin or beta match).

Above is a Simsmith model based on the NEC model imported into element L, and a shunt inductance created by a hairpin of 3mm wire spaced 100mm (Zo=500Ω) and length 222mm.

Contrary to some expert opinions, there is a simple practical solution to the stated problem.

There are many ways, but a simple one if you have an analyser that can be OSL calibrated, or a VNA (eg NanoVNA) is to calibrate it to measure the impedance or admittance at the dipole centre.

Now sweep the frequency range of interest, and adjust the dipole length until the conductance at the desired frequency is 1/200S of parallel resistance component of impedance is 200Ω. Then connect the shunt matching element and adjust it so that susceptance is zero, or the parallel reactance component of impedance is extremely high.

Connect the feed line up in the normal working configuration with the 1:4 coax half wave balun, and the impedance looking into the coax should now be close to 50+jΩ at the desired frequency.

This can provide a simple solution for a rotatable dipole with good match to 50Ω line.

]]>Before looking at the specifics of the Hirose U.FL connector, clean connectors work better and last longer. That should not be a revelation.

A can of IPA cleaner and a good air puffer are invaluable for cleaning connectors. The air puffer show has a valve in the right hand end, it doesn’t suck the dirt and solvent out of the connector and blow it back like most cheap Chinese puffers, this one was harder to find and expensive ($10!).

A clean tooth brush and / or small paint brush may prove useful. I would not put cotton buds, Q-tips or anything with free lint into the connector unless you are sure you can remove any lint (like with a strong jet of clean oil free compressed air).

The Hirose U.FL connector is widely used on miniature equipment for connecting RF coax cables.

I use them in lots of projects, mainly 2.4GHz WiFi and 915MHz LoRa. Above is an example where a 2.4GHz WiFi antenna is attached to an ESP8266 module in a project providing telemetry of dam level sensed with a 4-20mA pressure transducer.

The connector above has been on and off a development board more than 30 times, it is still in good working order. Visually, it cannot be faulted. The connector is on a Molex 105262 915MHz antenna which cost about $6 a few years ago, it is inexpensive hardware, but good quality.

If you take care of quality connectors they last more than 30 cycles, but if you do not, they might not last 10 cycles.

Above is a close up of the U.FL connector, it has two ears for lifting it off the male part without cocking it sideways (which will damage the connector).

Above, a DIY tool hooked under the ears. It snuggly fits so it cannot disengage, and it does not prevent expansion of the spring rim which must expand to disengage the male part. Note that it does not apply force to the cable or its crimp.

Above, the other end of my DIY tool is ground flat and square to the shaft, and allows pressure to be applied to the connector whilst without allowing it to cock sideways (which will damage the connector). Note that it does not apply force to the cable or its crimp.

This tool can reach down into confined spaces, so there is almost never an excuse to not use it.

With all that, IMHO opinion the use of U.FL connectors on boards like that above does not make a lot of sense for several reasons, but if you have one, and take care with the connectors as discussed above, you should get good value from the thing.

]]>I can advise that exactly the same change works in 4NEC2 v5.9.3

It appears that 4NEC2 enforces a requirement that Zo>=0.1, so having discovered that by trial and error, one wondered if it was possible to change that threshold by hacking the exe file.

The IEEE754 Double representation of 0.1 is 0x3FB999999999999A, and of course it would be stored backwords in the exe file. Searching for 0x9A9999999999B93F found only one occurrence, offset 0x1490. That was changed to 0xfca0f1d24d62503f (the backwords representation of 0.001) and the exe tested. (It might be tempting to set it so zero, but that would permit entering zero which may cause run time errors).

To my delight, it now permits directly changing Zo down to 0.001Ω.

There is a side effect of this change, it appears that the literal constant is used by (at least) one other function, and current graphs on the geometry window need to be scaled up with the page up key to be useful.

You do not need to use xdelta3, but if you do, download 4NEC2-5.9.3-ZoPatch.zip .

]]>To some extent, the project was inspired by KK5JY’s Loop on Ground (LoG).

This article presents measurements and the three terminal equivalent impedance model.

Above is the three terminal equivalent impedance model. Elements Z1, Z2 and Z3 are derived from measurements Za, Zb, and ZC as discussed at Find three terminal equivalent circuit for an antenna system.

A NanoVNA was calibrated for a fixture designed for such measurements, and a scan from 1-30MHz for each of Za, Zb, and ZC was captured and saved to the SD card.

Above is the measurement of ZC, the common mode impedance Zcm which is of interest as it informs strategies for minimising injection of common mode feed line current into the coax interior.

Whilst a small loop in air tends to have a very high common mode impedance, the LiG is quite the opposite.

Above is a plot of the Za and Zb measurements. Though the wire geometry is quite symmetric, the electrical symmetry is not perfect, probably due to less than uniform soil characteristic over the antenna site.

Above is a calculation of the various elements at 3.61MHz.

A work in progress…

]]>For those who may have used or want to use my G/T spreadsheet tool I have released an improved version 1.12. This is not a bug fix.

An updated version of the spreadsheet GT.xlsm is at https://github.com/owenduffy/xl.

If Microsoft has frightened you off using spreadsheets with macros, you could use this with macros disabled, it just stops the green sort button working, all the cells still calculate properly.

]]>Harald Friis gave us the familiar transmission equation: \(\frac{P_r}{P_t}=\frac{A_r A_t}{r^2 \lambda^2}\\\).

More common usage is to use Gain instead of aperture: \(\frac{P_r}{P_t}=G_r G_t (\frac{\lambda}{4 \pi r})^2\\\).

Let’s convert to dB and use frequency instead of wavelength: \(PdB_r-PdB_t=GdB_r + GdB_t +20 log \frac{c_0}{4 \pi f r}\\\).

We can express path gain as \(G_p=GdB_r + GdB_t +G_{fs}\), Gfs is the free space component of the path, \(G_{fs}=20 log \frac{c_0}{4 \pi f r}\\\).

Rearranging, \(GdB_r + GdB_t =G_{p}-G_{fs}\) and making \(GdB_r + GdB_t =G_{rt}\) we can write \(G_{rt} =G_{p}-G_{fs}\).

This leads to three simultaneous equations in three unknowns.

\(1G_1+1G_2+0G_3=G_{p_{12}}-G_{fs}\\0G_1+1G_2+1G_3=G_{p_{23}}-G_{fs}\\

1G_1+0G_2+1G_3=G_{p_{31}}-G_{fs}\\\)

We can write the three simultaneous equations out in matrix form and calculate the solution.

\(\begin{vmatrix}G_1\\G_2\\G_3 \end{vmatrix}=\begin{vmatrix}1 & 1 & 0\\0 & 1 & 1 \\ 1 & 0 & 1\end{vmatrix}^{-1} \times\begin{vmatrix}G_{p_{12}}-G_{fs}\\G_{p_{23}}-G_{fs}\\G_{p_{31}}-G_{fs}\end{vmatrix}\\

\)

So, we have calculated the three gain figures, G1, G2, and G3.

The online calculator Antenna gain calculator – three antenna method is a convenient way to document the measurements and calculate the gain of each antenna.

This case is pretty trivial to solve by elimination.

\(1G_1+1G_2+0G_3=G_{p_{12}}-G_{fs} \tag 1 \label{eq:eq1}\)

\(0G_1+1G_2+1G_3=G_{p_{23}}-G_{fs} \tag 2 \label{eq:eq2}\)

\(1G_1+0G_2+1G_3=G_{p_{31}}-G_{fs} \tag 3 \label{eq:eq3}\)

Taking \(\eqref{eq:eq1}-\eqref{eq:eq2}+\eqref{eq:eq3}\) we get \(G_1=\frac{G_{p_{12}}+G_{p_{31}}-G_{p_{23}}-G_{fs}}{2}\) and so on.

Note that if you load the calculator with frequency, distance and set \(s21dB_{12}=s21dB_{23}=s21dB_{31}=0\) then \(G_{fs}=-2G_1\), a quick way to evaluate G_{fs} to check feasibility of the proposed test range and instruments.

- Since the method depends on the Friis transmission equation, all the conditions for its validity must apply.
- An antenna test range is not a trivial exercise, read widely before you rush into measurements that might be disturbed by multi-path / ground reflection etc.
- This article does not address measurement uncertainty, but it is very important to the outcome.

The tapped coil could also be considered an autotransformer.

Above is a screenshot of the Simsmith model. The elements D1 and Coil will be explained.

The above figure shows two coupled coils with inductances L1 and L2, and mutual inductance M, and the equivalent T circuit.

Let’s remind ourselves of the meaning of the term autotransformer:

An autotransformer has only one winding with connections to three different points on the winding making two active portions. One portion is shared by both primary and secondary circuits, and the other portion of the winding is exclusive to the primary or secondary circuit (depending on whether it is a step-down or step-up transformer).

The first figure uses an autotransformer.

The above is not an autotransformer configuration as none of the winding portions are shared by both primary and secondary circuits.

Recognise that an autotransformer can be viewed as two partial winds magnetically coupled and sharing one terminal.

Now to apply the T equivalent circuit to the matching autotransformer, we must ‘rotate’ and flip the schematic so that the common terminal connects to the coax centre conductor, and L1 is from that point to ground, L2 is from the coax centre conductor to the top of the matching autotransformer.

The Simsmith model calculates the equivalent circuit values in the D1 element, it uses Wheeler’s Continuous Formula to calculate the inductance Lt of the whole winding, and L1 and L2 of the partial windings using the specified total turns n, pitch n and tapping %. From that, mutual inductance is calculated. The resistance of the whole winding is calculated (using Q etc) and the resistance is apportioned to the partial winds.

The equivalent circuit is implemented / evaluated in the Coil element.

Above is the Coil element schematic.

Note that because Simsmith does things backwards, the right hand side of the schematic (P2) is the source, the coax in the first figure.

It contains some redundancy in pursuit of clarity. The values L1_, L2_ and M_ are supplied from element D1.

]]>For this discussion, I will use the amplifier developed at A high performance active antenna for the high frequency band, but applied to the antenna described at Ambient noise measurement using whip on vehicle – #1 – estimate Antenna Factor.

Let’s assume that the antenna + amplifier will be used with a HF receiver with Noise Figure 6dB, Teq=864.5K.

From (Martinsen 2018) Fig 3.8, the amplifier internal noise at the output terminals is -118dBm in 100kHz @ 3.5MHz. That implies that the amplifier Noise Temperature is 857.93K. The amplifier has 6.4dB voltage gain which needs to be subtracted from the AF calculated for unity gain (at the amplifier input terminals).

Amplifier characteristics:

- Voltage gain 6.4dB;
- AF=6.05-6.4=-0.35dB/m;
- input Z=1MΩ||15pF;

From (Martinsen 2018) Fig 3.8, the amplifier internal noise at the output terminals is -118dBm in 100kHz @ 3.5MHz. The equivalent noise temperature is 857.9K.

The amplifier output terminals will be used as the reference plane for the following calculations.

Total internal noise (amplifier and receiver) \(T’=857.9+864.5=1722 \text{ K}\).

Using Field strength / receive power converter for measurements made in a 1kHz wide ENB,

we obtain:

The Ambient Noise Figure Fa is 57.5dB, similar to that predicted for a Residential precinct in ITU P.372-14.

It may be tempting to assume a simple linear relationship between the measure power and ambient noise figure.

In most cases, the measured power includes internal noise of the receive system (both active antenna and the receiver), and when external noise dominates, the relationship is close to linear.

Above is a plot of Fa vs measured (total) power for this (exact) scenario. In this case, Fa=Pt+174 is a good estimator for Pt>-145dBm or Fa>29dB. You would not expect to measure such low Fa in this scenario (frequency and equipment), but that may not be true of other scenarios… you need to check.

Field strength / receive power converter properly accounts for internal noise.

- Martinsen, W. Aug 2018. A high performance active antenna for the high frequency band. Cyber and Electronic Warfare Division

Defence Science and Technology Group DST-Group-TR-3522.

Ambient noise is commonly dominated by man made noise, and it often arrives equally from all directions. For measurement of such noise, the captured power depends on average antenna gain, and so the calculations below focus on gain averaged over the hemisphere.

Antenna Factor is often very convenient for field strength measurement as it relates the external E field strength to the receiver terminal voltage given a certain antenna (system). In fact, given a short vertical terminated by a high impedance amplifier, Antenna Factor is often fairly independent of frequency over several octaves of frequency.

Whilst it is easy to come up with Rules of Thumb or simple approximations for a short monopole over perfect earth conductor (PEC) either matched for maximum power transfer, or essentially unloaded, the case of a short vertical on the roof of a motor vehicle suspended above natural ground is not so easy.

Some underlying assumptions:

- a vertically polarised antenna will be most sensitive to ground wave noise on the lower HF bands (as horizontally polarised ground waves are more quickly attenuated with distance);
- the system uses an active antenna, the amplifier having a high input impedance and unity voltage gain; and
- reciprocity can be used to infer certain receive performance from transmit performance.

So, the approach is to:

- calculate the power captured by a lossless isotropic antenna, and the Thevenin source voltage for a given E field (1V/m);
- use an NEC model to find the (matched) average gain of the antenna system (so accounting for ground losses etc), source impedance, and radiation resistance (which is used as the Thevenin source impedance); and
- calculate the loaded voltage at the amplifier input terminals, and Antenna Factor at the amplifier input terminals.

An NEC-5.0 model was created for a 1.215m (4′) vertical mounted on the roof of a motor vehicle at 3.5MHz. The model was derived from a sample model supplied with NEC-5, the vertical was lengthened and moved to mid roof, and the unused antennas deleted. The model was changed to introduced real ground (σ=0.005, εr=13).

Above is a 3D pattern plot, the pattern is an almost omnidirectional donut.

Above is an elevation profile.

Above is the azmuth plot at θ=-70° (elevation 30°).

Some key values are extracted from the NEC output report.

The calculated equivalent series source capacitance Cs is given for interest sake, it is not used directly here, but is often estimated for so-called E-field probe antennas.

Thevenin source voltage of a lossless isotropic antenna is found by calculating the available power to be captured by a matched antenna given the excitation scenario (E=1V/m). The available power is given by the product of the effective aperture Ae and the power flux density S (for E=1V/m). Ae is calculated from average gain (unity for a lossless isotropic antenna) and frequency.

Having calculated available power, we can calculate the voltage in a matched load, and the Thevenin source voltage Vth is twice that.

The Thevenin source impedance is radiation resistance Rr calculated earlier from the NEC output.

We are interested in the Antenna Factor when the antenna is loaded by the high impedance amplifier. The amplifier is approximated as some resistance Rp in shunt with some capacitance Cp.

Antenna Factor is given by \(AF=20 log \frac{E}{V_{in}} \text{ dB}\) where E is the electric field strength and Vin is the amplifier input terminal voltage.

AF is quite sensitive to Cp, efforts need to be made in circuit configuration, device selection, and circuit layout to minimise Cp and achieve optimal AF.

The above discussion is based on a unity gain amplifier, if otherwise, the gain in dB should be subtracted from the calculated AF to get AF wrt the amplifier output terminals (ie, the input terminals to the following receiver).

]]>To some extent, the project was inspired by KK5JY’s Loop on Ground (LoG).

This article presents a comparison of Signal to Noise Degradation metric (see Signal to noise degradation (SND) concept) for both antennas, the common elements being:

- based on NEC-5.0 models (as detailed in earlier LiG articles);
- soil parameters used are σ=0.01, εr=20 (calibrated to measurements at the LiG test site);

The LoG models are for 4.6m sides, 2mm wire at 10mm height above ground, and an approximately optimal 450Ω:50Ω transformer.

The LiG models are for 3.0m sides, 2mm wire at 20mm below ground, and an approximately optimal 200Ω:50Ω transformer.

Above is a plot of SND for both antennas over the range 0.5-15MHz.

They are quite different responses.

It can be seen that from about 3-11MHz there is not a lot of difference between the antennas, but the LiG degrades slowly above 11MHz whereas the LoG degrades quickly below 3MHz.

A work in progress…

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