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Last page update: 17 January 2017


INTRODUCTION

A FOOL WITH A TOOL IS STILL A FOOL!

WER VIEL MISST, MISST VIEL MIST!
"He who measures a lot, measures a lot of crap"

Ca. 2007, I bought a "miniVNA". It is very small, and (relatively) inexpensive Vector Network Analyzer (ref. 1). I got it primarily for measuring antennas and antenna systems. For obvious reasons, I refer to it as "the little blue box":

Mag Loop

It covers 0.1 to 180 MHz. The miniVNA is controlled by software that runs on a PC. It communicates with the unit via USB (which also powers the unit), and presents the measurement data graphically to the user. VNAs in this price range clearly have significant limitations (ref. 1D). But for most amateur radio purposes, it is quite adequate. This miniVNA is basically "first generation". Subsequent models have expanded range and can be operated via wireless. A top-level block diagram of the miniVNA is shown below.


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Simplified block diagram of the miniVNA



The Device Under Test (DUT) port is the signal generator output port. The gain and phase detectors in the VNA compare the excitation signal from the signal generator against one of two signals:

  • the signal that is reflected by a single-port device (or system) that is attached to the DUT port. This is done via the directional coupler at the DUT port. Not all VNAs on the market have this, and require an external directional coupler for certain types of measurement.
  • the signal at the DET port that output by a two-port device that is excited by the DUT port, or that is captured via coupling to a single-port device.

Measurements that involve only the DUT port, are done in "antenna" mode. Measurements that involve both the DUT port and the DET port are done in "transmission" mode.

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(miniVNA analysis mode selections in the original IW3HEV-IW3IJZ software)


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(miniVNA analysis parameter display selections in the original IW3HEV-IW3IJZ software)


All VNAs must be calibrated to the extent possible, before using them! Check the manual! Also note that relatively (!) inexpensive VNAs such as the miniVNA cannot determine the sign of the reactance part Xs of the measured complex impedance Z = Rs + jXs. I.e., it cannot tell an inductance from a capacitance.

The sections below provide a brief description of some basic measurements that can be done with a VNA such as the miniVNA.

I use the following freeware:

  • On my Windows PCs and laptops: the original software by IW3HEV/IW3IWZ/G3RXQ/IK3ZGB, as well as more recent Java-based vna/J by Dietmar Krause (DL2BSA).
  • On my Android tablet: the nice and flexible Blue VNA application (both via USB & Bluetooth) by Dan Toma (YO3GGX).

There are other applications (e.g., qVNAmax for Linux, and 2012 VB software by PA7N), but I have no experience with them.


DETERMINING UNKNOWN INDUCTANCE

An electromagnetic coil is simply an inductor that is wound so as to have the shape of a coil, helix, or spiral. The current through the coil generates a magnetic field that interacts with the coils itself. For most applications, an ideal coil only has inductive reactance and no losses. A coil is a coil is a coil - it doesn't know (or care) how it is used and for what purpose. Its characteristics and behavior do not depend on the application.

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A coil

And here are some BIG coils.

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One of the antenna tuning coils of the 1 megawatt VLF "Goliath" transmitter (1940s)

(these enormous variometers comprised a fixed coil (3.5 m diameter, 11.5 ft), into which a slightly smaller coil (3.2 m diameter, 10.5 ft) could be inserted hydraulically with a precision of 0.1 mm! The coils were 5 m tall (16 ft) and weighed about 5000 kg (11k lbs)

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Tuning coil of the VLF transmitter at Rugby/UK  (mid-1920s)


In antenna systems, coils - if any - are primarily used in two ways:

  • As part of a "trap". This is a parallel circuit of an inductor coil and a capacitor. At the resonance frequency of this circuit, its impedance becomes quite high. A trap is inserted in the radiating element(s) of an antenna, somewhere between the feedpoint and the tip of that radiator. Around the resonance frequency of the trap, the part of the radiator beyond the trap is basically disconnected. In this case, only the part of the radiator between the feedpoint and the trap is "active". This is used in some multi-band antennas: the full length of the antenna is used on one band, the shortened length is used at a higher band.
  • Note that far enough below the resonant frequency, a trap basically acts like just a loading coil.
  • As a loading coil. This is a coil used by itself. Short antennas have a capacitive reactance at the feedpoint. This can be compensated by introducing inductance somewhere in the radiating element(s). One way to do that is with a "lumped" inductance: an inductor coil. Contrary to popular belief, a loading coil does not add "missing electrical length"!
  • Note that no coil is perfect: there is always loss resistance and stray (parasitic) capacitance. That is, any coil by itself also has a resonance frequency, and the coil will act as a "trap". This is why loading coils should be operated far away enough from that self-resonance frequency.

I am not a expert (real or self-anointed) of coils. So, rather than writing a lot of rubbish here, I refer to the list of references

The impedance of an (ideal) inductor is:

formula

This formula can be re-written as:

formula

where f in MHz and L in μH.  At the frequency where |Z| = 50 ohm, this simplifies to:

formula

Hence, with a simple  |Z| measurement, we can determine an unknown inductance value. Actually, it is "estimate" rather than "determine": VNAs such as the miniVNA are only reasonably accurate around 50 Ω.

Note: in all test set-ups, wiring should be kept as short as practicable.

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Test set-up for impedance-based measurement of Lx

(miniVNA software in "antenna" mode, |Z| parameter displayed)

Outside the range of 20-200 Ω, miniVNA accuracy is very poor. Resonance-based methods are more accurate. The standard formula for the resonance frequency of an (ideal) LC-circuit is:

formula

This equation can be re-arranged as:

formula

which can be re-written as:

formula

where L is in μH, C is in pF, and fres is in MHz. So, if we use a known capacitance C and measure the resonance frequency fres, we can determine the unknown inductance L.

For the special case where C = 253 pF (e.g., 220 pF and 33 pF in parallel), the equation simplifies to:

formula

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Test set-up for parallel-resonance measurement of Lx

(miniVNA software in "antenna" mode, "loss / dB" and "phase" parameters displayed)

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Alternative test set-up for parallel-resonance measurement of Lx

(miniVNA software in "transmission" mode, "loss / dB" and "phase" parameters displayed)


Note that in parallel-resonance configuration, the LC-impedance at the resonance frequency is high. In the series-resonance configuration, it is low.

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Test set-up for series-resonance measurement of Lx

(miniVNA software in "transmission" mode, "loss / dB" and "phase" parameters displayed)

The resonance frequency is easily identified in the loss/phase plot:

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Phase and loss plot for the LC-circuit, miniVNA in "transmission" mode


Note the -30 dB “loss offset” setting on the left hand side of the plot. This was done so as to lower the "loss" curve to where it was fully visible.

Note: accuracy of determination not only depends on the miniVNA accuracy, but also on that of the reference capacitor. Over thirty years of professional engineering experience has taught me that anything within ±20% is within engineering accuracy, hihi! Capacitors typically have poor tolerances with respect to their nominal value. When new, ceramic disk caps typically have +80/-20% tolerance, milar polyester ±5 or ±20%, tantalum ±10 or ±20%, metalized polypropylene typ. ±5, ±10, or ±20%, electrolytic typ. ±20%, silver mica ±0.1 to %±1%. Polystyrene capacitors are available with ±1 and ±2% tolerance. I normally use styroflex capacitors (a special form of styrene). Special capacitors are available down to ±0.01% tolerance.

A full-sweep plot shows some phase "dips" and "reversals" at (much) higher frequencies. They may be related to resonances due to stray capacitance of the coil, wiring of the test setup, etc.:


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Phase plot of parallel LC-circuit

(miniVNA in "antenna" mode, 1-180 MHz sweep)


Obviously, you can use a conventional/classical "dipmeter" to determine the resonance "dip". But the miniVNA can also be configured as a "dipper / sniffer":

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Dipper/Sniffer set-up for parallel-resonance measurement of Lx

(miniVNA software in "transmission" mode, "loss / dB" and "phase" parameters displayed)

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Note that you cannot use "dipper/sniffer" method to determine the Q of the coil: the phase-vs-frequency plot depends on the coupling (i.e., distance, orientation) between the test coil and the “sniffer coil”. As with the classical dipmeter, the resonance frequency also tends to shift with the level of coupling.

I have also used my fancy dipmeter with digital frequency read-out (ref. 3) to determine resonance frequencies. The dipmeter’s excitation coil was coaxially aligned with my test coil. Inserting a fiberglass fishing pole (my dipole is made up of two such poles) into the coil core did not cause the resonance frequency fres to shift. A good thing!


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Test setup with my dipmeter


The "sniffer/dipper" method can also be used to measure coils in-situ:


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The techniques discussed above can be also be used to characterize unknown parallel LC-circuits, such as antenna "trap" filters that are used in many antenna designs.

If Lx and Cx are the unknown parallel elements of the L/C trap, Cp is the additional known parallel capacitor, fres1 is the resonance frequency of the trap without Cp, and fres2 is the resonance frequency of the "trap plus Cp", then:

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After determining fres1 and fres2 with one of the methods discussed above, we can solve for Cx:


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Once Cx is found, the standard resonance formula can be used to determine Lx.

DETERMIINING UNKNOWN CAPACITANCE

Based on duality of inductive and capacitive reactance, basically the same methods described above can also be used to determine an unknown inductance. First the (coarse) impedance method. The impedance of an (ideal) inductor is:

formula

This equation can be re-written as:

formula

where f in MHz and C in pF. At the frequency where |Z| = 50 ohm, this simplifies to:

formula

Hence, with a simple |Z| measurement, we can determine an unknown capacitance value. As stated above for the inductance determination with this method: it is "estimate" rather than "determine", as VNAs such as the miniVNA are only reasonably accurate around 50 Ω (definitely not outside the 20-200 Ω range).


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Test set-up for impedance-based measurement of Cx


Then the resonance-based methods. Again, starting from the LC-resonance equation:

formula

This equation can be re-arranged as:

formula

which can be re-written as:

formula

where L is in μH, C is in pF, and fres is in MHz. So, if we use a known inductance L and measure the resonance frequency fres, we can determine the unknown capacitance C.

For the special case where L = 235 μH (I wish you good luck finding such a coil off-the-shelf, but you can make one...), the equation simplifies to:

formula

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Test set-up for parallel-resonance measurement of Cx

(miniVNA software in "antenna" mode, "loss / dB" and "phase" parameters displayed)

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Alternative test set-up for parallel-resonance measurement of Cx

(miniVNA software in "transmission" mode, "loss / dB" and "phase" parameters displayed)

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Test set-up for series-resonance measurement of Cx

(miniVNA software in "transmission" mode, "loss / dB" and "phase" parameters displayed)

As for the inductance measurement, the resonance frequency is easily identified in the loss/phase plot. Also, the "sniffer/dipper" method or a dipmeter can be used to determine the resonance frequency.


FILTERS

The miniVNA can be used to determine the characteristics of passive filters (LC-circuits and crystal filters). Typical parameters are the corner-frequencies and skirt-steepness of low-pass, high-pass, band-pass, and band-stop filters. Other parameters are insertion loss and ripple. This is very straightforward for filters with a 50 Ω input and output:


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Test set-up for impedance-based measurement of Cx

(miniVNA software in "transmission" mode, "loss / dB" and "phase" parameters displayed)

For filters with I/O port impedance other than 50 Ω, (passive) adapter networks should be used. They can be transformer based (you will need "Un-Un" transformers), or a simple resistor network:


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Test set-up for filter measurements with resistor adapter-networks


With resistor networks, the "loss offset" in the analyzer GUI must be set to 2x the attenuation of resistor network. See examples above. Low-inductance resistors should be used, such as "metal film". For 10:1 adapters, oscilloscope probes may be used (they are 500-to-50).When using transformer adapters, the miniVNA must be calibrated with the input and output adapter connected back-to-back (i.e., without the filter).

For narrow crystal filters, the sampling speed ( = number of samples/sec) of the analyzer sweeps may have to be reduced. Also: some crystal filters require a small capacitor (e.g., 10 or 20 pF) to be installed across the input and across the output. Check the data sheet!

Matching to 50 Ω can be measured with the following set-up:


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Test set-up for impedance-based measurement of Cx

(miniVNA software in "antenna" mode, "loss / dB" and "phase" parameters displayed)


AL OF FERRITE AND IRON-POWDER CORES

The miniVNA can also be used to determine the AL value of an unknown ferrite or iron-powder core. This value expresses how many wire turns have to be wound onto the core, to obtain a certain inductance. So, if we know the number of turns, and measure the resulting inductance, we can determine the AL value. And with the  AL value, we can identify the type of core (if the core manufacturer is known). Here are some AL values for commonly used ferrite and iron-powder cores (note the large tolerances!):

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AL values of some common ferrite and iron-powder toroidal cores (rings)


For whatever reason, the AL is defined differently for ferrite and for iron-powder cores. The difference is a factor of 10. For ferrite cores:

formula

For iron-powder cores:

formula

As stated above, all we need to do is wind a couple of turns on the core, and measure the resulting inductance with one of the methods described above for unknown inductances. Then apply the appropriate AL formula.


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Test set-up for series-resonance measurement of L

(miniVNA software in "transmission" mode, "loss / dB" and "phase" parameters displayed)


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Alternative test set-up for resonance-based measurement of L

(miniVNA software in "transmission" mode, "loss / dB" and phase parameter displayed)


CRYSTALS

A mechanically vibrating quartz crystals can be represented by an equivalent electrical circuit (ref. 4C):

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Hence, measuring the resonance characteristics of a crystal is straightforward:


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Test set-up for the impedance-based measurement of Cx

(miniVNA software in "transmission" mode, "loss / dB" parameter displayed)


The plot below shows the typical resonance curve of a crystal. Note that there are multiple resonances! The lowest resonance frequency is always a series-resonance. It has the lowest damping. The next higher resonance frequency, with higher damping, is a parallel-resonance.

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"Loss / dB" plot of a 10.250 MHz crystal

(miniVNA in "transmission" mode)

The "Q" of the crystal can be determined by zooming in the frequency sweep-range on the lowest frequency, and determining the -3 dB bandwidth. "Q" is the resonance frequency divided by that bandwidth. Typical crystal Q-values range from 104 to 106. This is orders of magnitude higher than typical LC-oscillators.


DIRECTIONAL COUPLERS & POWER-DIVIDERS - INSERTION LOSS & DIRECTIONAL ATTENUATION

A directional coupler is a 3-port or 4-port device. It has an input port, and output port, and one or two coupled ports. Insertion loss between the input and output port is the "through" loss between these ports, plus the "coupling loss" due to the load that is transformed from the coupled port(s) to the through-path between input and output port. The latter amount depends on the coupling ratio: the ratio between the power applied at the input port and the resulting power that appears at the coupled port. All ports must be properly terminated! The miniVNA can be used to measure the coupling (damping / isolation) between any two ports.

Shown below is a simple power divider. The coupled port is transformer-coupled to the 1:1 through-path between the input and output port. My -30 dB divider is described on this page.


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Test set-up for the insertion-loss measurement the 1:1 through-path

(miniVNA software in "transmission" mode, "loss / dB" parameter displayed)

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Test set-up for the coupling ratio between the 1:1 through-path and the coupled port

(miniVNA software in "transmission" mode, "loss / dB" parameter displayed)


COAX SWITCH - INSERTION LOSS & ISOLATION

I wanted to share my antenna between two solid-state transceivers, so I needed a coax switch. One transceiver has an output power of 5 Watt, the other 100 Watt. Clearly, I don't want to blow up the receiver input of the QRP transceiver when the coax-switch connects the antenna to the 100 Watt rig. For the HF-bands, a good coax switch has at least 60-70 dB cross-talk damping (isolation), and less than 0.1 dB insertion-loss.

We can measure this with an antenna/network analyzer, such as the miniVNA that I have. Note that for the insertion-loss measurement, we must account for the loss caused by the connectors between the switch and the miniVNA. Note that coax connectors really depends on production quality ( = price). This is particularly important on VHF and above. N-type connectors typically have negligible insertion loss, whereas cheap "oriental" PL-259/SO-239 connectors may have 0.2 dB insertion loss and frequency-dependent impedance transition.

Coax switch

Cross-talk (isolation) measurement


Coax switch

Insertion-loss measurement measurement


Coax switch

Specification of the above coax switch (Jetstream JTSC-2M)


COMMON-MODE CHOKES

The common-mode attenuation of 1:1 current "chokes" is determined by measuring the loss (damping) on the coax shield (braid), between the two sides of the "choke". On HF, 25-30 dB common-mode damping is "good". The test set-up for some standard common-mode chokes is shown below.

Coax switch

Coax switch

Coax switch

Coax switch

Common-mode attenuation of a W2DU-style choke with 24 beads of #77 ferrite material

(attenuation is about 20-22 dB above 7 MHz)


ANTENNA SYSTEMS

Measurement of antennas (i.e., at the feedpoint) and of antenna systems (antenna + feedline(s) + balun(s) + choke(s) + antenna tuner) is easy. However, quite often, interpreting the data is not! I am not going into detail here, but ref. 4I may provide some practical examples.

Note: antenna resonance-frequencies and SWR-minimum almost never coincide exactly! Per definition, at resonance, the impedance is purely resistive: reactance is zero. The SWR minimum occurs where the impedance is nearest to 50 Ω. Most antennas do not have an impedance of 50 Ω at resonance!

Note: there is no requirement to operate an antenna at a resonance frequency. Doing so only makes matching to a feedline easier.

Note: obviously, you can measure an antenna system by connecting the VNA at the end of the feedline. However, unless the feedline is exactly half a wavelength long (including accounting for the velocity factor) such that it replicates the complex impedance at the opposite end, this does not tell you very much about what the impedance (Rs and Xs) is at the antenna. This also means that an antenna coupler ("tuner") that can match the feedpoint-impedance of the antenna, may not be able to do so at the end of the feedline (and vice versa).

The first plot shows a nice SWR-dip at/near resonance just above 7 MHz. At a slightly lower frequency, around 6.8 MHz, there is a small dip. Where does it come from? In this particular case, the antenna has a radial that is too long with respect to the antenna's resonance frequency. Sometimes such dips occur due to coupling with objects near the antenna.

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SWR dip of an antenna at/near the resonance frequency - secondary dip below it

(source: personal communications with Gerd Koetter (DO1MGK, SK))


The next plot shows the SWR-sweep of a multi-band antenna. Two of the dips (around 8 and 25 MHz) could be deepened by adding radials of the appropriate length.

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REFERENCES

Note: these articles are copyrighted material; all related restrictions regarding access and usage apply.



External links last checked: October 2015


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©1999-2016 F. Dörenberg, unless stated otherwise. All rights reserved worldwide. No part of this publication may be used without permission from the author.