## Designing a Gamma Match – Simsmith design tool and confirmation of as-built antenna – comparison with Healey

A correspondent reading Designing a Gamma Match – Simsmith design tool and confirmation of as-built antenna referred me to (Healey 1969) and questioned my method.

I have tried several times to reconcile built and tuned antennas and NEC models with Healey and failed, leading me to think of the problem and devise a good approximation that did reconcile (for me).

This article attempts to reconcile the example given at Designing a Gamma Match – Simsmith design tool and confirmation of as-built antenna, an example where the two built antennas reconcile well with the ARRL published design article and NEC model.

## Example for reconciliation

The example antennas are 4 element 144MHz Yagis built around 1970. They were originally designed with a 50Ω split dipole feed, or the option of a folded dipole with 4:1 half wave coax balun. Continue reading Designing a Gamma Match – Simsmith design tool and confirmation of as-built antenna – comparison with Healey

## Transmission lines – forward and reflected phasors and the reflection coefficient

Let’s consider the following transmission line scenario:

• Lossless;
• Characteristic Impedance Z0=1+j0Ω; and
• load impedance other than 1+j0Ω, and such that Vf=1∠0 and Vr=0.447∠-63.4° at this point.

The ratio Vr/Vf is known as the reflection coefficient, Γ. (It is also synonymous with S parameters S11, S22… Snn at the respective network ports.)

Above is a  phasor diagram of the forward and reflected voltages at the load. Continue reading Transmission lines – forward and reflected phasors and the reflection coefficient

## Design / build project: Guanella 1:1 ‘tuner balun for HF’ – #7

Seventh part in the series documenting the design and build of a Guanella 1:1 (current) balun for use on HF with wire antennas and an ATU.

• This article describes a measurment of common mode impedance Zcm of the packaged balun.

## Packaging

The prototype fits in a range of standard electrical boxes. The one featured here has a gasket seal (a PTFE membrane vent was added later).

Above, the exterior of the package with M4 brass screw terminals each side for the open wire feed line, and an N(F) connector for the coax connection. N type is chosen as it is waterproof when mated. Continue reading Design / build project: Guanella 1:1 ‘tuner balun for HF’ – #7

## Designing a Gamma Match – Simsmith design tool – how to

Designing a Gamma Match – Simsmith design tool and confirmation of as-built antenna posted a Simsmith design tool to assist in designing a Gamma Match.

Let’s walk through an example.

Above is an example for discussing the Gamma Match. In this case, the assumed feed point impedance of a simple split dipole feed is 17+j2Ω, and the challenge is to design a practical Gamma Match to match it to 50+j0Ω.

The design tool assumes that the connections to the open circuit stub are at the feed point, ie that the gap in the gamma arm outer is at the inboard end. There are other ways to build a gamma match and the model may not suit them without tweaking. Continue reading Designing a Gamma Match – Simsmith design tool – how to

## Designing a Gamma Match – Simsmith design tool and confirmation of as-built antenna

Designing a Gamma Match – confirmation of as-built antennas was based on some online calculators to provide key values to a Simsmith model of a Gamma Match.

This article provides an updated Simsmith model that incorporates the necessary calculations (ie without depending on external calculators).

Much is written about the virtue of the Gamma Match, and near as much about how they work, and the difficulty in design and implementation.

Designing a Gamma match using a Smith chart showed a design method for a simple Gamma Match using a Smith chart as the design tool.

This article visits the implementation on a pair of antennas that I built 50 years ago, and are still in use today (albeit with some small preventative maintenance once during that interval). The basic antenna is a four element Yagi for 144MHz copied from an ARRL handbook of the time, probably based on NBS 688. It was designed to deliver a split dipole feed point impedance of 50+j0Ω.

I built them using a Gamma Match, partly to get some familiarity, but mostly to implement a Gamma Match that was reliable, weatherproof and lasting… features that are alien to most implementations I had seen at that point.

Both antennas were constructed and the Gamma Match adjusted for VSWR<1.1 using a Bird 43 directional wattmeter. The dimensions of each (including the key gamma dimensions) are the same, not surprising, but a confirmation of repeatability. See Novel Gamma Match Construction for more discussion.

Above is a dimensioned drawing of the construction. Continue reading Designing a Gamma Match – Simsmith design tool and confirmation of as-built antenna

## PVC speaker twin – loss model applied

One of the many gems of ham lore that I was fed as a beginner almost sixty years ago was that 23/0.076 (0.67mm^2) PVC insulated twin flex was suitable as an RF transmission line at HF, and that it had a Characteristic Impedance Z0 close to 75Ω.

It seems that these claims have been extended to apply to lighter gauge cables often called speaker cable or bell wire.

This article explores two cases of the application of a light grade of speaker twin to a G5RV antenna. The scenarios is a G5RV Inverted V with 7m of speaker twin from dipole to the coax section, and loss is calculated for the speaker twin section at 14.1 and 3.6MHz.

## PVC speaker twin copper / PVC 0.2mm^2 characteristics

The following articles report measurement of a sample of speaker twin, and derivation of a simple loss model:

From those articles, the loss model is copied for reader convenience.

Above is a plot of the calculated MLL (red dots) based on the s11 measurements, and a curve fit to the model $$MLL = k_1\sqrt f+k_2f \text{ dB/m}$$. Continue reading PVC speaker twin – loss model applied

## Where is the best place to measure feed point VSWR – error in Z0

At Where is the best place to measure feed point VSWR I discussed location of the VSWR meter and projection of its reading to another point on a known transmission line.

One of the conclusions drawn in that article is:

Feed point VSWR can be estimated from measurements made at another place if the transmission line parameters are known. It, like all measurements, is subject to error but it may be a manageable error and indeed possibly better overall than direct measurement.

This article discusses some issues that may arise in referring measurements from one place to another (eg near transmitter to antenna feed point).

## Characteristics of transmission line categories

Let’s consider two categories of transmission lines in terms of characteristic impedance Z0 and propagation constant γ:

• Lossless line; and
• practical line.

A lot of theoretical analysis uses lossless line for simple explanations, and whilst for a lot of purposes, approximation of practical line as lossless line serves well, at other times the error may be significant.

### Lossless Line

A Lossless Line has imaginary part of Z0 equal to zero and the real part of γ equal to zero.

### Practical line

A practical line has non-zero imaginary part of Z0 and non-zero real part of γ, and these are frequency dependent.

Under standing waves, attenuation along a practical line is not uniform, in most practical applications conductor loss/m is higher than dielectric loss so loss is higher near current maxima than near current minima.

For the purpose of this article, it is the frequency dependence of Z0, particularly the non-zero imaginary part that is significant.

## A model

A model of a load similar to a 7MHz half wave dipole fed with 10m of RG58A/U was created in Simsmith to provide a basis for discussion. Whilst the model is subject to some errors computation, it is much less than comparing two field measurements at both ends of a transmission line.

## VSWR at each end of the transmission line

Let’s look at the ACTUAL VSWR. Actual means that if you were to observe the standing waves on the line (eg with a voltage probe), this is the VSWR you would expect to observe.

Firstly, observe that the source end VSWR (orange) is a little lower than the load end VSWR. This is by virtue of the attenuation on the line. The difference between the two can be calculated, but it is moderately complicated. Continue reading Where is the best place to measure feed point VSWR – error in Z0

## Determination of transmission line characteristic impedance from impedance measurements – eighth wave method

For a lossless line, the reactance looking into short section and open circuit terminated line sections is $$X_{sc}=Z_0 \tan \beta l$$ and $$X_{oc}=Z_0 \frac1{\tan \beta l}$$.

Noting that when $$\beta l= \frac{\pi}{4}, \tan \beta l=1$$ so when the line section is π/4ᶜ or 45° or λ/8, then $$|X_{sc}|=|X_{oc}|=Z_0$$.

We can use this property to estimate Z0 of an unknown practical low loss transmission line by finding the frequency where $$|X_{sc}|=|X_{oc}|$$ and inferring that $$Z_0 \approx |X|$$.

Above is a chart created using Simsmith’s transmission line modelling of the reactance looking into short section and open circuit terminated 10m sections of RF174. The blue and magenta lines intersect at X=51.16Ω whereas red R0=51.85Ω, about -1.3% error. The error depends on line loss, line length, frequency and the characteristics of the terminations. Continue reading Determination of transmission line characteristic impedance from impedance measurements – eighth wave method

## Determination of transmission line characteristic impedance from impedance measurements #2

Determination of transmission line characteristic impedance from impedance measurements discussed issues with the short circuit and open circuit terminations used with measurement of Zoc and Zsc for calculation of characteristic impedance of a line section.

Included was a model of the effect of small delay offset in one of the termination parts on an example scenario.

This article gives a Simsmith model that readers might find interesting to explore the effects of line length, offset, line characteristics, and frequency.

I have issues with Simsmith modelling of transmission lines, but nevertheless the model is informing.

The above example is 6m of RG58A/U with 5mm offset in the short circuit termination. Continue reading Determination of transmission line characteristic impedance from impedance measurements #2