Grebenkember’s original Tandem match

(Grebenkemper 1987) describes a directional coupler that has become very popular, especially in commercial implementation.

screenshot-22_11_16-07_23_25The simplified circuit above from Grebenkemper’s article illustrates the key elements of the directional coupler.

An important detail of the design is that the primary of the right hand transformer appears in shunt with the antenna load, and the magnetising impedance of that transformer core compromises Insertion VSWR. It is important that the magnetising impedance is sufficiently high (or the admittance sufficiently low) to not cause significant Insertion VSWR.
Continue reading Grebenkember’s original Tandem match QRP SWR bridge

The project is to build a test a couple of QRP VSWR detectors by ( rated at 10W.


Above are the completed kits.


Above is the schematic. The bridge uses a type of Sontheimer coupler (Sontheimer 1966) and these are commonly poorly designed. The first question is whether the magnetising impedance of T2 which appears in shunt with the load is sufficiently high to not give rise to poor insertion VSWR. Continue reading QRP SWR bridge

Walter Maxwell’s teachings on system wide conjugate matching

Walt Maxwell (W2DU) made much of conjugate matching in antenna systems, he wrote of his volume in the preface to (Maxwell 2001 24.5):

It explains in great detail how the antenna tuner at the input terminals of the feed line provides a conjugate match at the antenna terminals, and tunes a non-resonant antenna to resonance while also providing an impedance match for the output of the transceiver.

Walt Maxwell made much of conjugate matching, and wrote often of it as though at some optimal adjustment of an ATU there was a system wide state of conjugate match conferred, that at each and every point in an antenna system the impedance looking towards the source was the conjugate of the impedance looking towards the load.

This is popularly held to be some nirvana, a heavenly state where transmitters are “happy” and all is good. Happiness of transmitters is often given in online discussion by hams as the raison d’être for ATUs . Continue reading Walter Maxwell’s teachings on system wide conjugate matching

Zo of two wire line

I saw a recent discussion where the blind were leading the blind on the dimensions of a twisted two wire line for Zo=50Ω for use in a balun.

The poster had used an online calculator which used the well known log function for estimating Zo of an air spaced two wire line… the calculator, like most quotations of the formula do not state clearly that it is only an approximation of limited validity, and the calculator returned results for ridiculous inputs (like negative spacing).


The graph above (Duffy 2008) shows the log approximation, and the underlying acosh based estimate. I say estimate because the acosh function does not account for proximity effect which becomes significant at the very closest spacings, and internal inductance which becomes significant at lower frequencies. Proximity effect depends on more than just the spacing/diameter ratio and so cannot be shown on the above graph.

So how did our poster find dimensions for wires for Zo=50Ω when the log graph above shows that as the wire centre to centre spacing approaches the wire diameter, it the wires approach touching, Zo approaches 83Ω? Continue reading Zo of two wire line

The sign of Return Loss

I was browsing a ham forum recently when I came across a Return Loss plot apparently from a ham grade miniVNA Tiny.

Lets just remind ourselves of the meaning of the term Return Loss. (IEEE 1988) defines Return Loss as:

(1) (data transmission) (A) At a discontinuity in a transmission system the difference between the power incident upon the discontinuity. (B) The ratio in decibels of the power incident upon the discontinuity to the power reflected from the discontinuity. Note: This ratio is also the square of the reciprocal to the magnitude of the reflection coefficient. (C) More broadly, the return loss is a measure of the dissimilarity between two impedances, being equal to the number of decibels that corresponds to the scalar value of the reciprocal of the reflection coefficient, and hence being expressed by the following formula:

20*log10|(Z1+Z2)/(Z1-Z2)| decibel

where Z1 and Z2 = the two impedances.

(2) (or gain) (waveguide). The ratio of incident to reflected power at a reference plane of a network.

Return Loss expressed in dB will ALWAYS be a positive number in passive networks.

Return Loss according to the miniVNA Tiny


Above, the miniVNA Tiny presents Return Loss as a negative value. Continue reading The sign of Return Loss

Effective RF resistance of a braided solenoid – Gilbert’s coil measurements

(Gilbert 1996) gave a set of measurements of impedance of several inductors wound as a single layer close spaced solenoid of RG-213 coaxial cable.

Of particular interest is the measurements of the 6t solenoid as there are several measurements well below the self resonant frequency of the inductor.

Key geometry details used in this analysis are:

  • cable OD 10.287mm;
  • conductor OD 8mm;
  • mean solenoid diameter 117.4mm (ASTM D-2729 pipe + RG-213);
  • cable length 2.213m; and
  • solenoid length 6*10.287mm.

clip-218Above is a plot of Gibert’s measurements from 1 to 5MHz, and curve fits.
Continue reading Effective RF resistance of a braided solenoid – Gilbert’s coil measurements

Exploiting your antenna analyser #25

Find coax cable velocity factor using an antenna analyser without using OSL calibration

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

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

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

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

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


Above is a pic of the test fixture with adapters (in this case on a AA-600). Continue reading Exploiting your antenna analyser #25