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

CNC6040 router project – test cut of a Jiffy box

One of the intended applications of the CNC router is to cut openings in Jiffy boxes for things like LCD displays, tactile button switches, connectors etc.

After a lot of testing, it came time to try it on some target work.

Above is a scrap Jiffy box and the milling job is to cut holes for three pushbuttons (tactile momentary switches on a veroboard base with 10mm caps) and the holes for M3 screws and pillars. Continue reading CNC6040 router project – test cut of a Jiffy box

Last update: 21st October, 2019, 8:54 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

CNC6040 router project – spindle speed linearisation – using new grbl_ESP32 feature

A known issue with the common CNC6040 router and similar devices is very poor calibration / linearity of the spindle motor response to gcode Sx commands.

Above is the system block diagram. The grbl_ESP32 gcode interpeter processes a gcode S (speed) command, converting it to a variable duty cycle PWM waveform on parallel port pin 1. Continue reading CNC6040 router project – spindle speed linearisation – using new grbl_ESP32 feature

Last update: 28th December, 2020, 7:53 AM

CNC6040 router project – spindle speed linearisation

A known issue with the common CNC6040 router and similar devices is very poor calibration / linearity of the spindle motor response to gcode Sx commands.

Above is the system block diagram. The grbl_ESP32 gcode interpeter processes a gcode S (speed) command, converting it to a variable duty cycle PWM waveform on parallel port pin 1. Continue reading CNC6040 router project – spindle speed linearisation

Last update: 12th October, 2019, 5:14 AM

Noise Figure Y factor method calculator updated

Recent updates to Noise Figure Y factor method calculator expose the temperature of each of the attenuators in each scenario and so allow more flexibility in application to real world problems.

The screenshot above demonstrates its use where the DUT and Att12 are cryogenically cooled.

For most applications, the default value of 290K is appropriate, so though the form has a few more fields, there isn’t more data entry for most usage.

The calcs have not changed, just replacement of a global Tatt with T for each instance. The input form and output form have been reformatted to suit.

 

Last update: 6th October, 2019, 9:56 AM

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