Category: Amateur Radio

Transmitter / antenna systems and the maximum power transfer theorem

Jacobi’s Maximum Power Transfer Theorem

Jacobi’s law (also known as Jacobi’s Maximum Power Transfer Theorem) of nearly 200 years ago stated

Maximum power is transferred when the internal resistance of the source equals the resistance of the load.

Implied is that the internal resistance of the source is held constant, it does not work otherwise. The source must be one that can validly be represented by a Thevenin equivalent circuit. This was in the very early days of harnessing electric current, direct current initially.

Later adaptation dealt with alternating current and it became

Maximum power is transferred when the load impedance is equal to the complex conjugate of the internal impedance of the source.

Again a necessary condition is that the source must be one that can validly be represented by a Thevenin equivalent circuit. Continue reading Transmitter / antenna systems and the maximum power transfer theorem

Last update: 21st October, 2019, 4:34 AM

Walter Maxwell’s teachings on system wide conjugate matching – a SimSmith example

I have written on Walt Maxell’s proposition about simultaneous system wide conjugate matching in antenna systems. I will repeat a little to set the context…

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, anthropomorphism over science. Continue reading Walter Maxwell’s teachings on system wide conjugate matching – a SimSmith example

Last update: 29th November, 2023, 7:31 AM

Cooking the books on VSWR – Bird43 indication

A reader of Cooking the books on VSWR asked

…so you are telling me that I could measure this Prev>Pfwd with a directional wattmeter like my Bird43… I have never seen it and I don’t believe it.

For clarification, I did not discuss Prev or Pfwd in respect of the three scenarios (other than to say Pref cannot exceed Pfwd).

I did discuss line voltage measurements you can make with a simple RF volt meter which was in the article’s reference quote. But, let’s discuss what you might measure by inserting a 50Ω Bird43 directional wattmeter in the Load case 2 scenario.

Above is a calculated plot of the expected Pfwd and -Prev readings, Prev is shown negated so you can add it by eye with Pfwd to obtain the net power Power (blue line). Continue reading Cooking the books on VSWR – Bird43 indication

Last update: 17th October, 2019, 8:40 PM

Cooking the books on VSWR

Having recently seen the suggestion that …

Most tools and most derivations of SWR will produce negative SWR reports because they are more interested in mathematics than in measurements you can make with a simple RF volt meter.

…, this article explores the expected voltage on a practical transmission line under two mismatch scenarios, voltage that ought be measurable with a simple RF voltmeter.

VSWR concepts… by the book

Textbooks on transmission lines often introduce the concept of standing waves by presenting a plot of voltage along a mismatched lossless transmission line.

Above is a plot of calculated line voltage vs displacement from the load, -ve is towards the source. Continue reading Cooking the books on VSWR

Last update: 17th October, 2019, 4:57 PM

Noise Figure – Equivalent Noise Bandwidth

Harald Friis (Friis 1944) gave guidance on measuring the noise figure of receivers, and explains the concept of Effective Bandwidth.

Effective Bandwidth

The contribution to the available output noise by the Johnson-noise sources in the signal generator is readily calculated for and ideal or square-top band-pass characteristic and it is GKTB where B is the bandwidth in cycles per second. In practice, however, the band is not flat; ie, the gain over the band is not constant but varies with frequency. In this case the total contribution is ∫GfKTdf where Gf is the gain at frequency f. The effective bandwidth B of the network is defined as the bandwidth of an ideal band-pass network with gain G that gives this contribution to the noise output.

Continue reading Noise Figure – Equivalent Noise Bandwidth

Last update: 4th October, 2019, 7:49 AM

nanovna-saver – a first look

The NanoVNA is a new low cost community developed VNA with assembled units coming out of China for <$50.

I have long held the view that these things are most useful when accompanied by a capable PC client that performs flexible text book presentations of data.

Considering buying one, my first step was to perform a desk evaluation of a popular PC client, which seems to be nanovna-saver.

Before downloading it, I examined the first screenshot on the github page.

It gives evidence that the author does not follow industry standard convention for transmission line terms and theory.

In the results shown above (s11) impedance is 39.105+j39.292Ω and some transformations of that value. Continue reading nanovna-saver – a first look

Last update: 2nd February, 2020, 7:11 AM

Update for NFM software (v1.19.0)

NFM has been updated to v1.19.0.

The update corrects an error in conversion between ENR and temperature where Tcold<>290K.

References

  • Duffy, O. 2007. Noise Figure Meter software (NFM). https://owenduffy.net/software/nfm/index.htm (accessed 01/04/2014).
Last update: 28th September, 2019, 7:19 PM

Antenna analyser – what if the device under test does not have a coax plug on it?

I have written a few articles on fixtures for adapting the device under test (DUT) to an antenna analyser’s coax jack.

Antenna analysers come with a range of connectors, the UHF connector is very popular, perhaps less so are N-type, SMA and BNC.

I use a range of fixtures made to suit specific applications, but the most flexible are the two shown in the following pic.

Above are two adapters: Continue reading Antenna analyser – what if the device under test does not have a coax plug on it?

Last update: 27th September, 2019, 3:57 AM

Noise Figure measurement of a converter / transverter

I recently came across an article Signal level measurement with PowerSDR and external transverters in which Carol (KP4MD) details a set of measurements of a Flex 1500 transceiver and Electraft XV144 transverter.

Carol gives the following table of measurements and calculated results.

Table 1.  Transverter Measurements
Freq
MHz		 Noise
Source
ENR (dB)		 Noise/10
kHz		 Conversion
Gain (dB)		 Noise
Figure
(db)
50 Ω expected Noise On Noise Off On-Off (Y)
144 15.2 -134 dBm -118.8 dBm -132.1 dBm 13.3 dB 26.5 2.1
432 15.3 -134 dBm -118.7 dBm -131.7 dBm 13 dB 24.1 2.5

Lets focus on the 144MHz measurements. Continue reading Noise Figure measurement of a converter / transverter

Last update: 28th September, 2019, 7:02 AM

Franklin antenna – how does it work?

(Franklin 1924) described a technique to cophase sections of a long antenna by “concentrating alternating half wave length portions of the wire within a small space, by winding such portions as inductance coils or by doubling such portions back on themselves so that there is practically no radiation from these portions”.

Let’s explore his second option, as unlike the first, it does work reliably.

Above is an NEC-4.2 model with current shown (magnitude and phase). The stubs conductors are all defined from top to bottom. Continue reading Franklin antenna – how does it work?

Last update: 20th September, 2019, 5:40 AM