## A thinking exercise on Jacobi Maximum Power Transfer #3

At A thinking exercise on Jacobi Maximum Power Transfer #2 I posed the question of a metric for the mismatch at the L2L1 junction in the following network where the calculated values L2L1_lZ is the load impedance at the L2L1 junction (looking left as Simsmith is unconventional), and L2L1_sZ is the source impedance at the L2L1 junction (looking right). The left three components are the fixed antenna representation. Common practice is to speak of a “source VSWR” to mean the VSWR calculated or measured looking towards the source, and very commonly this is taken wrt 50+j0Ω which may be neither the source or load impedance but an arbitrary reference. Continue reading A thinking exercise on Jacobi Maximum Power Transfer #3

## A thinking exercise on Jacobi Maximum Power Transfer #2

At A thinking exercise on Jacobi Maximum Power Transfer I posed an unanswered Q2:

Keeping in mind that C2 and L2 are an adjustable matching network, usually adjusted for minimum VSWR as seen at the source G. So, the questions are:

1. Does the system take maximum available power from the source G when the load impedance seen by source G is equal to the conjugate of its Thevenin equivalent source impedance (ie C2.Z=G.Zo in Simsmith speak)?

2. Does that ‘matched’ condition result in maximum power in the load L? Above for reader’s convenience is the model conjugate matched at the GC2 interface. The calculated Po figure (lower right) is the power in the load L to high resolution. Continue reading A thinking exercise on Jacobi Maximum Power Transfer #2

## A thinking exercise on Jacobi Maximum Power Transfer

At The system wide conjugate match stuff crashes out again I discussed the failure of Walt Maxwell’s teachings on system wide simultaneous conjugate match using an example drawn from an online expert’s posting.

The replicated scenario with matching with an L network where the inductor has a Q of 100, no other loss elements is shown below. (Quality real capacitor losses are very small, and the behavior will not change much, the inductor loss dominates.) Above is a model in Simsmith where I have adjusted the lossy L network for a near perfect match. I have used a facility in Simsmith to calculate the impedance looking back from L1, often known as the source impedance at a node but in Simsmith speak the calculated L1_revZ on the form, (ie back into the L network)  from the equivalent load. Continue reading A thinking exercise on Jacobi Maximum Power Transfer

## The system wide conjugate match stuff crashes out again

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 was recently cited in a discussion about techniques to measure high impedances with a VNA:

WHEN the L and C’s of the tuner are set to produce a high performance return loss as measured by the vna, then in essence, if the tuner were terminated (where the vna was positioned) with 50 ohms and we were to look into the TUNER where the antenna was connected, we would see the ANTENNA Z CONJUGATE. Wow, that’s a mouth full. The best was to see this is to do an example problem and a simulator like LT Spice is a nice tool to learn. Or there are other SMITH GRAPHIC programs that are quite helpful to assist in this process. Standby and I will see what I can assemble.

The example subsequently described set about demonstrating the effect. The example characterised a certain antenna as having an equivalent circuit of 500Ω resistance in series with 4.19µH of inductance and 120pF of capacitance (@ 7.1MHz, Z=500-j0.119, not quite resonant, but very close). A lossless L network (where do you get them?) was then found that gave a near perfect match to 50+j0Ω. The proposition is that if you now look into the L network from the load end, that you see the complex conjugate of the antenna, Z=500+j0.119.

I asked where do you get a lossless L network? Only in the imagination, they are not a thing of the real world. Continue reading The system wide conjugate match stuff crashes out again

## 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).

## Online calculator of ferrite material permeability interpolations – more detail

The Ferrite permeability interpolations calculator performs interpolations of tables of complex permeability data.

## From manufacturer’s curves Some of the data is derived from manufacturer’s published complex permeability curves. The plot above shows the Ferroxcube’s published curve for 3C81 material, and points at which it was digitised to extract a table of µ’ and µ”. Continue reading Online calculator of ferrite material permeability interpolations – more detail

## Comparison of BN43-202 / 5t with BN73-202 / 2t for rx only on low HF – small broadband RF transformer – 50:200Ω

Several correspondents refer to my article Feasibility study – loop in ground for rx only on low HF – small broadband RF transformer using medium µ ferrite core for receiving use – 50:200Ω and suggest “I got it wrong, #73 is the proven material choice for such a thing, and a 2t primary is optimal”.

In fact, I did explore #73 as an option, this article presents some key comparisons. The two key statistics shown in this article provided the basis for selecting the design.

Note that the scales are different from plot to plot.

## Insertion VSWR

Where the magnetising impedance appears in shunt with an ideal transformer with Zin=50+j0Ω, Insertion VSWR can be calculated.

### 2t on BN73-202 ## RF transformer design with ferrite cores – saturation calcs

Ferrite cored inductors and transformers saturate at relatively low magnetising force.

## #61 material example

Lets work through an example of a FT50-61 core with 10t primary at 3.5MHz.

Magnetic saturation is one limit on power handling capacity of such a transformer, and likely the most significant one for very low loss cores (#61 material losses are very low at 3.5MHz).

Let’s calculate the expected magnetising impedance @ 3.5MHz.

## A review of transformer design

In a process of designing a transformer, we often start with an approximate low frequency equivalent circuit. “Low frequency” is a relative term, it means at frequencies where each winding current phase is uniform, and the effects of distributed capacitance are insignificant. Above is a commonly used low frequency equivalent of a transformer. Z1 and Z2 represent leakage impedances (ie the effect of magnetic flux leakage) and winding conductor loss. Zm is the magnetising impedance and represents the self inductance of the primary winding and core losses (hysteresis and eddy current losses). Continue reading RF transformer design with ferrite cores – initial steps