## Phase of s11 and Z

Antenna system resonance and the nanoVNA contained the following:

## Relationship between angle of reflection coefficient and angle of impedance

It was stated above that the angle (or phase) of s11 or Γ is not the same as the angle (or phase) of Z.

Given Zo and Γ, we can find θ, the angle of Z.

$$Z=Z_0\frac{1+\Gamma}{1-\Gamma}$$

Zo and Γ are complex values, so we will separate them into the modulus and angle.

$$\left | Z \right | \angle \theta =\left | Z_0 \right | \angle \psi \frac{1+\left| \Gamma \right | \angle \phi}{1-\left| \Gamma \right | \angle \phi} \\ \theta =arg \left ( \left | Z_0 \right | \angle \psi \frac{1+\left| \Gamma \right | \angle \phi}{1-\left| \Gamma \right | \angle \phi} \right )$$

We can see that the θ, the angle of Z, is not simply equal to φ, the angle of Γ, but is a function of four variables: $$\left | Z_0 \right |, \psi , \left| \Gamma \right |, \& \: \phi$$ .

It is true that if ψ=0 and φ=0 that θ=0, but that does not imply a wider simple equality. This particular combination is sometimes convenient, particularly when ψ=0 as if often the case with a VNA.

This article offers a simulation of a load similar to a 7MHz half wave dipole.

The load comprises L, L1, and C1 and the phase of s11 (or Γ) and phase of Z (seen at the source G) are plotted, along with VSWR. Continue reading Phase of s11 and Z

## The quarter sized G5RV with hybrid feed

(Varney 1958) described his G5RV antenna in two forms, one with tuned feeders and the more popular form with hybrid feed consisting of a matching section of open wire line and then an arbitrary length of lower Zo coax or twin to the transmitter.

(Duffy 2005) showed that the hybrid feed is susceptible to high losses in the low Zo line as it is often longish, is relatively high loss line and operates with standing waves.

Lets look at measurement of a real antenna, broadly typical of the G5RV. The antenna measured is a G5RV rigged in Inverted V form, 11m height at the apex and around 8m at the ends. The feed line is 2mm diameter copper spaced 50mm with occasional plastic insulators.

To some extent, the measurements are dependent on the environment, and whilst there will be variation from one implementation to another, the measurements provide a basis for exposing the configuration challenge.

Above is a plot of VSWR(50) essentially at the lower end of the matching section and low Zo line. The measurement is made looking into 0.5m of RG142 and a Guanella current balun that uses about 1m of 110Ω pair, it is essentially the load end VSWR of a hybrid feed were it used. Continue reading The quarter sized G5RV with hybrid feed

## Antenna system resonance and the nanoVNA

With the popularity of the nanoVNA, the matter of optimisation of antenna systems comes up and the hoary chestnuts of ham radio are trotted out yet again.

Having skimmed a presentation published on the net, an interesting example is presented of an 80m half wave centre dipole with feed line and various plots from the nanoVNA used to illustrate the author’s take on things.

The author is obsessed with resonance and obsessed with phase, guiding the audience to phase as ‘the’ optimisation target. Phase of what you might ask… all the plots the author used to illustrate his point are phase of s11.

## A model for discussion

I have constructed an NEC-4.2 model of a somewhat similar antenna to illustrate sound concepts. Since NEC-4.2 does not model lossy transmission lines (TL elements), we will import the feed point data into Simsmith to include transmission line loss in the model.

Above is the Simsmith model. Continue reading Antenna system resonance and the nanoVNA

## Jaycar LO1238 ferrite core

Over many years, the Jaycar LO1238 has appeared in some of my projects. I recommended them for a range of applications, particularly applications optimised for low HF.

Above, the core is 35x21x13mm, a mid sized core, two used in my redesign of a commercial balun and implemented by VK4MQ . The mid size limits dissipation, but compactness can be an advantage. The cores sell for less than $4.00 per core and are readily available in Australia. Continue reading Jaycar LO1238 ferrite core ## Disturbing the thing being measured – coax line An issue that often arises in online discussions inability to reconcile the VSWR indicated by a transceiver (or possibly an inline VSWR meter) and an antenna analyser. Is this Segal’s law at play? There are several common contributors including: • faulty, dirty, or not properly mated connectors and cables; • VSWR meters that are not accurate at low power levels; and • influence of the common mode current path on VSWR. ## Quantifying performance of a simple broadcast receive system on MF I see online discussions struggling to try to work out if a receiving system is sufficiently good for a certain application. Let’s work an example using Simsmith to do some of the calculations. Scenario: • 20m ground mounted vertical base fed against a 2.4m driven earth electrode @ 0.5MHz; • 10m RG58A/U coax; and • Receiver with 500+j0Ω ohms input impedance and Noise Figure 20dB. An NEC-4.2 model of the antenna gives a feed point impedance of 146-j4714Ω and radiation efficiency of 0.043%, so radiation resistance $$Rr=146 \cdot 0.00043=0.0063$$. Above, the NEC antenna model summary. Continue reading Quantifying performance of a simple broadcast receive system on MF ## KL7AJ on the Conjugate Match Theorem – analytical solution – Simsmith KL7AJ on the Conjugate Match Theorem asked the question Should we have expected this outcome? Let us solve a very similar problem analytically where measurement errors do not contribute to the outcome. Taking the load impedance to be the same 10.1+j0.2Ω, and calculating for a T match similar to the MFJ-949E (assuming L=26µH, QL=200, and ideal capacitors) with Simsmith we can find a near perfect match. The capacitors are 177.2 and 92.9pF for the match. Continue reading KL7AJ on the Conjugate Match Theorem – analytical solution – Simsmith ## Applying the RG6/U to a 40m Inverted V Dipole antenna This article describes an antenna system for 40m based on: • an inverted V dipole; • Guanella 1:1 balun; and • a ‘tuned’ length of RG6/U CCS coax. The antenna system will be centred on 7.080MHz to suit my own operating preferences. The coax is that featured at nanoVNA – RG6/U with CCS centre conductor MLL measurement and the matched line loss is taken from measurement as 4.1dB/100m @ 7.1MHz (all conductor loss). The feed line cost$50 for 100m incl delivery, so this project uses $12 worth of cable. The broad concept is that the dipole is tuned a little shorter than a half wavelength to excite a standing wave on the coax. The VSWR desired is a little over 1.5, and the length of the coax is tuned so that the impedance looking into the coax is close to 50+j0Ω. “A little over” is so that the VSWR at the source end is very close to 1.5. Above, the topology of the Inverted V Dipole with modelled current distribution in green. The apex of the dipole is at 11m and it is over ‘average ground’ (σ=0.005 εr=13). Continue reading Applying the RG6/U to a 40m Inverted V Dipole antenna ## Applying the RG11A/U to a 40m Inverted V Dipole antenna This article describes an antenna system for 40m based on: • an inverted V dipole; • Guanella 1:1 balun; and • a ‘tuned’ length of RG11A/U CCS coax. The antenna system will be centred on 7.080MHz to suit my own operating preferences. The coax is that featured at Checkout of a roll of Commscope 4510404 CCS RG11A/U – Zoc, Zsc based MLL calculation and the matched line loss is taken from measurement as 1.2dB/100m @ 7MHz (all conductor loss). The feed line cost$99 for 305m incl delivery, so this project uses \$6.50 worth of cable. The feed line is not good because it is cheap, it is good because it suits the application very well, and as a bonus, it is inexpensive.

The broad concept is that the dipole is tuned a little shorter than a half wavelength to excite a standing wave on the coax. The VSWR desired is a little over 1.5, and the length of the coax is tuned so that the impedance looking into the coax is close to 50+j0Ω. “A little over” is so that the VSWR at the source end is very close to 1.5.

Above, the topology of the Inverted V Dipole with modelled current distribution in green. The apex of the dipole is at 11m and it is over ‘average ground’ (σ=0.005 εr=13). Continue reading Applying the RG11A/U to a 40m Inverted V Dipole antenna

## 144MHz beacon observation from Wellington NSW – 3 aircraft reflections

VK2TP at Wellington has been making observations of aircraft enhancement of the path between my 144MHz beacon and Wellington, an obstructed direct path of 259km. The beacon modulation pattern includes a long steady carrier which permits better observation of the nature of these aircraft enhanced paths. Continue reading 144MHz beacon observation from Wellington NSW – 3 aircraft reflections