There are several source of the Al parameter for some common cores, often from resellers rather than manufacturers.

- Fair-rite: 320 (0%)
- Toroids.info: 475 (+48%)
- Amidon: 380 (+19%)

- Fair-rite: 230 (0%)
- Toroids.info: 277 (+20%)
- Amidon: 300 (+30%)

- Fair-rite: 160 (0%)
- Toroids.info: 250 (+56%)
- TheParsPlace: 250 (+56%)

There is large unexplained differences between various source for Al specifications for a core that is quite probably from Fair-rite in all cases.

Be wary of where you source data.

]]>This article documents calculated geometry Σ(A/l) derived for a number of Fair-rite cores from their specified Al (at µi).

This is a relatively low µ core at measurements at 10kHz (as stated in the specifications) will not be affected by self resonance, and so the specified Al should be reliable. Al is a controlled parameter for these #61 products.

Fair-rite part | Al (nH) | Σ(A/l) (m) |
---|---|---|

2861000102 | 300 | 0.001910 |

2861000202 | 320 | 0.002037 |

2861000302 | 230 | 0.001464 |

2861001502 | 145 | 0.000923 |

2861001702 | 440 | 0.002801 |

2861002302 | 60 | 0.000382 |

2861002402 | 160 | 0.001019 |

2861002702 | 80 | 0.000509 |

2861006802 | 600 | 0.003820 |

2861010002 | 800 | 0.005093 |

Many of these parts are dimensionally identical to the BN61-xxxx designations (eg 2861000202 is equivalent to a BN61-202).

The value Σ(A/l) can be plugged into Calculate ferrite cored inductor – ΣA/l or Σl/A to predict the impedance at a given frequency, but note that at higher frequencies approaching SRF selection of an appropriate value of Cs is necessary for good results.

The binocular products are described as having different controlled parameters depending on the mix, so application of the Σ(A/l) implied from the #61 data to the other mixes (using the appropriate µ’,µ” data) that might be tweaked from the nominal material characteristic is prone to some error, even though they are likely to be pressed in the same dies. In any event, backtracking from a controlled Z at 25MHz or more is fraught with problems due to test fixture strays and other things.

Experience with #43 binocular cores is that impedance may be significantly higher than predicted from core Σ(A/l) and µ’,µ” data even are relatively low frequencies.

As always, predictions need to be verified by measurement.

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Distortionless Linesfrom time to time, often in the vein of

they don’t exist, so why discuss them?

The concept derives from the work of Heaviside and others in seeking a solution to distortion in long telegraph lines.

The problem was that digital telegraph pulses were distorted due to different attenuation and propagation time for different components of the square waves.

Heaviside proposed that transmission lines could be modelled as distributed resistance (R), inductance (L), conductance (G) and capacitance (C) elements.

In each incremental length Δx, there is incremental R, L, G and C.

Characteristic impedance Zo and complex propagation coefficient γ can be derived from the model, and it becomes apparent that only under certain conditions is the attenuation and phase velocity independent of frequency.

Heaviside determined that condition was that G/C=R/L, so this is the condition for a Distortionless Line.

That same condition means that Zo is a purely real number, and if Zo is purely real, then the line is Distortionless.

Note that Lossless Line is a special case of Distortionless Line, and necessarily Zo is purely real.

It is true that fabrication of a Distortionless Line is a considerable challenge, though some techniques might deliver an approximately Distortionless Line over a limited frequency range.

Whilst some might dismiss the concept of Distortionless Line as impractical, they probably apply Distortionless Lines freely in their analytical techniques without understanding what they are doing.

Let us look at some common operations.

Waves add, the E and H fields add vectorially, as do their V and I equivalents.

It happens that in the special case of purely real Zo (ie Distortionless Line) that the directional powers add, but they add by virtue of expansion of the expression for adding V and I (which simplify when Zo is real).

Most use of a Smith chart involves normalising plotted values to some real Zref. In so doing, an assumption is made that constant VSWR circles are wrt that Zref, and solutions (eg matching) based on that are conditional on the assumed real (Distortionless) Zref.

The clean separation of real and imaginary Z and Y components and the arcs of constant R, X, B, G on a Smith chart are conditional on real Zo, as is the assumption that all practical values of Z map inside the ρ=1 circle. (The assumption that ρ<=1 depends on real Zo.) The loss of this property quite restricts its usefulness.

None of this is to suggest that a Smith chart with Zref including a significant imaginary part is invalid… just many things we have learned to do with a ‘real’ Smith chart may not be valid (ie within acceptable error limits), and the scales are no longer as simple and useful as the chart devised by Philip Smith.

ρ, Return Loss, and VSWR are derived from the complex reflection coefficient Γ. Calculating Γ wrt some nominal real Zo involves some error, and raises the question of whether application of those to a real scenario (where Zo is different, eg not real) is within acceptable error limits.

S parameter techniques assume additive power, and that may not be appropriate for some problem solutions. The analysis tools effectively coerce a Distortionless Lines treatment.

Practitioners use analytical techniques that depend on an assumption that Zo is real (ie Distortionless Line) widely, and often without acknowledging it or even thinking about the implications.

Virtual Distortionless Lines are everywhere, and worth understanding when Distortionless Line analysis is being applied and whether it is appropriate.

]]>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.

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

Where the magnetising impedance is a shunt component of total Zin=50+j0Ω, Core loss VSWR can be calculated.

Predictions of Insertion VSWR and core loss of the popular BN73-202 transformer with 2t primary for MF and my BN43-202 with 5t primary reveals that the BN43-202+5t is a better transformer for my intended application.

There is no need to follow the traditional design which anecdotally works, but is published without performance predictions or measurements… well that IS traditional.

]]>

This article digs a little further with analyses at both 100kHz and 10MHz.

A plot was given of the components and sum of terms of the expression for power at a point along the line.

Lets look at the power calculated from voltages and currents for the example at 100kHz where Zo=50.71-j8.35Ω and Zload=5+j50Ω.

Above, the four component terms are plotted along with the sum of the terms.

Term1 is often known as Pfwd and -Term4 is often known at Prev, and when Zo is real, Term2=-Term3 and they cancel, and in that circumstance P=Pfwd-Prev.

These are calculated using the actual value of Zo, Zload and propagation constant.

Above is a plot of impedance along the line.

We can use the impedance along the line to calculate the expected result if measurements were made along the line with an instrument calibrated for Zref=50+j0Ω. We will obtain a different values for Γ and ρ as they will not related to the actual line but to the Zref in use.

Above is a plot of actual ρ on the line, and ρ wrt 50+j0Ω (ρ50). You will note that ρ is a smooth exponential curve as determined by the line attenuation, whereas ρ50 varies cyclically and seems inconsistent with expected behavior of a transmission line.

Because ρ50 varies in this way, so will VSWR50 and ReturnLoss50. All of these metrics are of very limited value because Zref is so different to Zo.

We can calculate the expected reading of ‘Directional’ Power (as would be displayed on a directional wattmeter.

Above, the blue line is the actual power along the line and it varies cyclically because for this line, under standing waves more power is lost per unit length in regions of high current that those of high voltage.

An important attribute is that where Zref is real:

- Pfwd and Prev are each meaningful if Zref=Zo; and
- where Zref is not equal to Zo, Pfwd and Prev each are of no stand alone relevance to the actual line, but P does equal Pfwd-Prev.

Let’s plot the components and sum of terms of the expression for power at a point along the line.

Lets look at the power calculated from voltages and currents for the example at 10MHz where Zo=50.01-j0.8025Ω and Zload=5+j50Ω.

Above, the four component terms are plotted along with the sum of the terms.

Term1 is often known as Pfwd and -Term4 is often known at Prev, and when Zo is real, Term2=-Term3 and they cancel, and in that circumstance P=Pfwd-Prev.

These are calculated using the actual value of Zo, Zload and propagation constant.

Above is a plot of impedance along the line.

We can use the impedance along the line to calculate the expected result if measurements were made along the line with an instrument calibrated for Zref=50+j0Ω. We will obtain a different values for Γ and ρ as they will not related to the actual line but to the Zref in use.

Above is a plot of actual ρ on the line, and ρ wrt 50+j0Ω (ρ50). You will note that ρ is a smooth exponential curve as determined by the line attenuation, whereas ρ50 varies cyclically and seems inconsistent with expected behavior of a transmission line.

Because ρ50 varies in this way, so will VSWR50 and ReturnLoss50. All of these metrics are of somewhat limited value because Zref is a little different to Zo.

We can calculate the expected reading of ‘Directional’ Power (as would be displayed on a directional wattmeter.

Above, the blue line is the actual power along the line and it varies cyclically because for this line, under standing waves more power is lost per unit length in regions of high current that those of high voltage.

An important attribute is that where Zref is real:

- Pfwd and Prev are each meaningful if Zref=Zo; and
- where Zref is not equal to Zo, Pfwd and Prev each are of no stand alone relevance to the actual line, but P does equal Pfwd-Prev.

Whilst it is convenient to treat Zo of practical transmission lines as a purely real quantity, it isn’t and the error may be significant.

The departure from ideal Zo is typically worst at lower frequencies, and may be very small, perhaps insignificantly so above 100MHz.

]]>Above is the programmer ($2.50 on eBay) and a small adapter that plugs into the top row of the 2×5 header on the programmer.

DIP-28 are located carefully so that the pins 10-18 are in the socket, the same connections are used for both chip sizes for STC15F104E and STC15F204E.

]]>The thing has a JST 7way XH socket provided for an ISP connection to a target board. It is accessed through a cutout in the acrylic housing, but the cutout is no bigger than the shoulder on an XH plug and one cannot get tools in beside it to pry the plug out without pulling on the wires.

The good thing is that there is an inexpensive “XH plug saver” sold to the RC market, it provides a means of getting a convenient grip on the plug without pulling on the wires.

First step is to mill out the case opening to accommodate the XH plug saver.

Next, add the XH plug saver to the XH plug, and it all works.

Above, the ISP cable with XH plug saver plugged into the U8W through the widened case opening.

The plug saver for a 7way plug is sold to the RC market as a “6S XH plug saver”. They are available on eBay for a few dollars for a pack of 10.

The U8 has an obstructing collar around the connector. Above, the end of the clear housing has been sanded flush to the XH connector so that the cable end with the plug saver mates properly. This also makes it easier to remove ordinary XH plugs as there is room to get a screwdriver in to level the plug out rather than pulling on the wires.

]]>We use reinforced hose that comprises essentially three layers, an inner plastic layer, a braided fibre reinforcing layer and another layer of plastic. Though these layers are bonded in new hose, there is potential for them to separate in service resulting in the reinforcing braid pulling back into the hose length and allowing the hose to expand in diameter at that point (lacking the benefit of the reinforcement). At this point failure of the hose by bursting is inevitable, sooner rather than later.

Some hoses are supplied fitted with factory crimped ferrules, and experience is that they have lasted well except that the fittings are plastic and break if subjected to rough treatment.

User serviceable screw collets fail, either through failure of the collets, or just the outcome of the screw collar loosening and resultant pull-back of the reinforcing braid.

What is needed is a tough and durable coupler with an easily applied ‘permanent’ clamp.

I have conducted a trial of brass fittings modified to remove the screw collar and nylon collet, then used with a stainless steel stepless one ear clamp.

Above at left is the unmodified coupler, and at right the coupler with the collet and screw collar discarded, thread turned off the coupler, and a one ear clamp for installation.

The one ear clamps have a small diameter adjustment range (the inside dimension of the ear divided by π, so different clamps may be need for thicker walled hose and of course 18mm fittings require a larger clamp).

The clamp can be closed with a simple special tool that is much like a pair of end-cutters or carpenter’s pincers, and either of those may substitute effectively (provided the acute edge is very close to the end of the tool).

Above is the coupler installed on a length of hose. The clamp in this case is a nominal 19.8mm clamp to suit the hose wall thickness. The common 17.5mm size (1/2″ PEX) suits thinner wall hose.

A trial through two winters has shown the terminations to be tough and reliable in retaining all layers of the hose clamped securely.

The brass couplers were purchased on eBay, $55 for 12 delivered, and clamps from Aliexpress $7 for 20.

]]>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.

Above is the manufacturers B/H curve for #61 material. Lets take the saturation magnetising force conservatively as 2Oe=2*1000/(4*pi)=159A/m (or At/m for a multi turn coil).

The ID of a FT50 core is 7.15mm, so magnetic path length l=0.00715*pi=0.0225m.

So, we take saturation current as Is=Hs*l/t=159*0.0225/10=0.358A.

Saturation voltage magnitude at 3.5MHz=Is*|Zm|=0.358*144=51.6Vpk. This corresponds to about 25W in a 50Ω system.

Increasing the number of turns decreases Is for a given Hs, and increases Zm which reduces I for a given applied voltage. For example in this example, a 12t primary has |Z|=207, Is=0.298A, Vs=61.7Vpk which corresponds to a 43% 50Ω power increase.

Lets work through an example of a 2643625002 core with 3t primary at 3.6MHz (Small efficient matching transformer for an EFHW).

Magnetic saturation is one limit on power handling capacity of such a transformer. For lossier materials, heat dissipation is likely to be the practical limit in all but low duty cycle applications, but lets calculate the saturation limit.

Let’s calculate the expected magnetising impedance @ 3.6MHz.

Zm=94.1+j197Ω, |Zm|=218Ω.

Above is the manufacturers B/H curve for #43 material. Lets take the saturation magnetising force conservatively as 1Oe=1*1000/(4*pi)=79.6A/m (or At/m for a multi turn coil).

The ID of a 2643625002 core is 7.29mm, so magnetic path length l=0.00729*pi=0.0229m.

So, we take saturation current as Is=Hs*l/t=79.6*0.0229/3=0.607A.

Saturation voltage magnitude at 3.5MHz=Is*|Zm|=0.607*218=132Vpk. This corresponds to about 175W in a 50Ω system. This transformer would not withstand such high power continuously, but pulses or bursts to that level would remain in the substantially linear range of the material characteristic.

- Magnetic saturation is one limit on power handling capacity of ferrite inductors and transformers.
- For very loss cores, magnetic saturation is likely to be the significant limit on power handling.

Read widely, and analyse critically what you read.

]]>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).

For 50/60Hz power transformers, Z1 and Z2 are mainly inductive and small (eg as would account for around 5% voltage sag under full load). Zm varies, it is large and mainly inductive for conservative designs using sufficient and good core material, and less so for designs that drive core magnetic flux into saturation.

For broadband RF transformers, Z1 and Z2 need to be small as they tend to be quite inductive and since inductive reactance is proportional to frequency, they tend to spoil broadband performance.

Zm shunts the input, so it spoils nominal impedance transformation (Zin=Zload/n^2) if it is relatively low. For powdered iron cores Zm is mainly inductive; and for ferrite cores Zm is a combination of inductive reactance and resistance depending on frequency and ferrite type.

Keep in mind that if Zm is sufficiently high, Im is low, and even though Zm may contain a large Rm component, Im^2*Rm may be acceptably low.

There are scores of articles on this website about ferrites, many of which show how to measure or calculate Zm from datasheets.

Proponents of powdered iron will claim that large Im does not create much loss because Rm is small, but large Im destroys broadband nominal impedance transformation (ie Insertion VSWR). Powdered iron tends to be low µ which increases leakage impedance and also destroys broadband nominal impedance transformation.

An online expert on the unsuitability of #43 for HF UNUNs discussed the stuff that masquerades as science in the name of ham radio, and gives one example which questions the exptert’s opinion. Lets work through some examples, calculating and plotting two key metrics that should be considered right up front when designing an efficient broadband RF transformer with close to ideal impedance transformation (ie low InsertionVSWR).

The following analyses are of expected core loss due to the magnetising impedance of the primary winding when the transformer is loaded to present an input impedance of 50+j0Ω. The magnetising impedance can be measured with only that primary winding on the core, the presence of a secondary winding, even if disconnected, may disturb the results.

Note that there is a quite wide tolerance on ferrite materials, and measured results my differ from the predictions based on published datasheets. Designs based on measurements of a single core are exposed to risks of being atypical.

Graph Y axes are not identically scaled.

This configuration is very popular in ham radio. I am not sure who originated the design, PA3HHO’s web article is a commonly cited reference.

Above is the percentage core loss when input impedance of the loaded transformer is 50+j0Ω.

Above is the Insertion VSWR caused by the magnetising impedance in shunt with 50+j0Ω. Note that this is not exactly the same configuration as for the previous chart.

Above is the percentage core loss when input impedance of the loaded transformer is 50+j0Ω.

Above is the Insertion VSWR caused by the magnetising impedance in shunt with 50+j0Ω. Note that this is not exactly the same configuration as for the previous chart.

This is a small #43 core as used in Small efficient matching transformer for an EFHW.

Above is the percentage core loss when input impedance of the loaded transformer is 50+j0Ω.

Above is the Insertion VSWR caused by the magnetising impedance in shunt with 50+j0Ω. Note that this is not exactly the same configuration as for the previous chart.

The Jaycar LO1238 is readily available in Australia, a medium size core of medium to high initial permeability (µi=1500) that seems overlooked by Australian hams in favor of harder to procure products.

Above is the percentage core loss when input impedance of the loaded transformer is 50+j0Ω.

It seems many hams have a “favorite mix”, and many spurn #43, nominating others (#31, #61 often for this application).

All are possibilities that for a given core geometry and mix will require a certain minimum number of turns on the nominal 50Ω primary to meet the designer’s loss and Insertion VSWR criteria. #61 is a lower loss material compared to #43, and it will require more turns to meet Insertion VSWR criteria at low frequencies, the length of the winding may limit the useful upper frequency.

- The context of the article is HF broadband transformers with close to ideal nominal impedance transformation, and does not necessarily apply to other contexts.
- Three of the examples use #43 material, two of those designs have core loss less than 10% at 3.5MHz and lower on higher bands demonstrating that it is possible to design a broadband RF transformer for HF using #43 material.
- The PA3HHO example shows that insufficient turns leads to appalling core loss.
- Traditional wisdom is that higher µ cores will be even worse than #43, but the LO1238 design shows that a low cost core readily available in Australia is a worthy candidate for Australian hams.
- There is more to designing a transformer than presented here, this article describes a first analysis to screen likely candidates and find minimum primary turns for a given core to meet the design loss and InsertionVSWR criteria.
- Successful designs are almost always a compromise to meet sometimes competing / conflicting design criteria.

Read widely, and analyse critically what you read.

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