Significance of inductance in transformers
Jason Hsu
SWR/wattmeter I have been working on this semester for an independent
study project in my graduate work. I put my device together, and it
works. Though it doesn't quite have the performance I hoped for, it
still runs rings around the MFJ cross-needle meters (high SWR and QRP
capability as well as 100W capability). In case you are wondering, I
am using FT82-43 toroids for the transformers with #30 wire for the
primary (high voltage, low current) windings. I really pushed the
limits on many things, such as the capability of LM324s, the
capability of LM3914s, the current capacity of wire (>1A and #30 wire
on an FT50-43 core do not mix), the space needed for the wires
connecting 20-40 LEDs, and what happens when you accidentally connect
a capacitor the wrong way (leaking fluid, noise, mess on the
breadboard).
I am working on my report, and one thing that still puzzles me is the
significance of the inductive reactance in transformers. The design I
am using is based on the one at
http://engphys.mcmaster.ca/~elmer101/rfpower/swrtheory.html
I have heard that the inductive reactance across a transformer winding
should be at least 4 times the resistance that is connected across it.
There is 100 ohms of resistance across the voltage transformer, so
that should mean j400 ohms of resistance are required in the winding.
According to the software programs of Reg Edwards (and the ARRL
formulas), the secondary winding (the 1-turn side) of the voltage
transformer would have only .45uH with one of the FT82-43 cores I am
using. Most other SWR meter designs actually use SMALLER cores (FT50,
even FT37), which have even less inductance per turn. The .45uH is
only j5 ohms on 160m and j84 ohms on 10m, a far cry from j400 ohms.
Could someone please shed some light on what is going on? How much
inductive reactance is REALLY needed, and what would have happened if
I did not have enough? Why can't RF transformers use plastic or air
cores? (They would be much cheaper.)
Jason Hsu, AG4DG
usenet@@@jasonhsu.com
Bob
with solid cores. It's just that they are larger.
Inductance is necessary because the primary current includes both reactive
(due to inductance and reflected reactance) and resistive (load real power)
components. If inductance is too low, the primary current will rise to a
point where it might cause a problem with the source.
With solid cores, there needs to be some primary current that can be used to
magnetize the core. This current has no external function but must be
provided by the source.
Transformer theory is not trivial, and can't be given in a few words.
73, Bob K6DDX
Avery Fineman
jaso...@my-deja.com (Jason Hsu) writes:
>Could someone please shed some light on what is going on? How much
>inductive reactance is REALLY needed, and what would have happened if
>I did not have enough? Why can't RF transformers use plastic or air
>cores? (They would be much cheaper.)
"What is going on" should be outlined in detail in electronics
texts at your university. That's the best place to realize what
really happens in a "transformer," including its inductance,
interaction between windings, power transfer and loss with
loads of various impedances. Winding resistance, per se, is
associated with power loss within the transformer.
"Reactance" is the equivalent inductive or capacitive component
at ONE frequency. You need to respecify your question as "how
much inductance you need," not reactance without giving any
frequency value. That inductance will be dictated by the desired
operating frequency range...but it is modifiable by many other
things.
What you "really need" in terms of inductance of any winding in
a transformer is related to everything I stated in the first para-
graph above. Using an equivalent model of a transformer is a
good start to better see the relationship of a transformer to its
driving circuit and to its load. Almost any textbook has those.
If you have insufficient inductance for your circuit, you will
probably have some power loss at lower frequencies if untuned
(not resonated at a desired frequency). Many, if not most,
broadband RF transformers have extremely little inductance if
measured open-circuit (without any other connections to driving
circuit or load). An example of low-inductance broadband
transformers with little inductance is the 4:1 impedance matching
transformer for TV adapting a 75 Ohm to 300 Ohm characteristic
characteristic and working over the entire VHF and UHF portion
of the EM spectrum.
There are many, many examples of "air core transformers" in
older amateur radio texts. These are almost exclusively a high
impedance source (power amplifier, 2K to 10K in source
impedance) to a low impedance load (50 to 600 Ohms resistive).
They are also almost all resonated at the primary or high
impedance winding at a single frequency by a capacitor.
Another example is the older 455 KHz Intermediate Amplifier
transformer ("IF can") with both primary and secondary windings
resonated at 455 KHz with trimmer capacitors mounted in the
shield can. Cheaper AM BC radios used air cores. Slightly
more expensive AM BC radios had powdered-iron cores to
improve the coefficient of coupling to do two things: The
structure could be slightly smaller (less inductance required in
windings due to increased inductance effect of the iron core);
the relatively narrow passband could be shaped to a more even
amplitude response through control of the coefficient of coupling.
Air core transformers have losses primarily from the loss of the
resonating capacitance and the resistance of the winding
relative to winding inductance at one frequency. There can be
some additional losses due to coupling to the shielding
structure (conductive, all around the transformer) and the
reduction of inductance from shield proximity.
A powdered-iron core in any inductor (and transformer) will
contain the magnetic field closer to the winding itself. In a
toroidal inductor (or transformer) the topology/geometry of the
torus does the greatest magnetic field containment. Toroids
can be very close (relatively speaking to other shapes) to
other conductive elements without appreciably changing the
open or away-from any other conductive element inductance.
"Blank" toroidal cores are a standard catalog item such as in
the Micrometals product list. That "core" is solid plastic and
will have little effect relative to a completely air core toroid. It
is very hard to make a self-supporting, completely air-core
toroid but it can be done. The magnetic field is less contained
than with a powdered-iron core material but that field is still
contained more than with a solenoidal core structure.
At lower frequencies, such as AF, various solid iron forms will
work just fine as laminations (example: E-I plates) or wound
tape (as in toroids). The AF range is several decades of
frequency in bandwidth. Very broadband AF transformers, as
in old "Hi-Fi" or music systems, can have relatively flat power
transfer from 30 to 15,000 Hz, almost 3 decades. Their high
frequency response is dictated more by circuit and distributed
capacity across the primary windings. The low frequency
response is dictated by the permeability of the iron core.
Core material will always affect the inductance value and the
coupling of multiple windings on the same core as with
transformers. Core material and its form (sheet, tape, or
powder) will be broadly frequency sensitive. Certain materials
work best at certain octave to decade wide bands for best
power transfer in transformers and for least loss component in
single inductors.
A good example of very low winding inductance transformers
over a decade bandwidth is the "binocular" shape low-impedance
matching transformer in most modern-day transistor power
amplifiers. The primary winding inductance is on the order of
a microhenry for a source impedance of 100 to 500 Ohms and a
secondary load impedance of about 50 Ohms. But, the low-
frequency end of their operating range is around 3 MHz while
the upper frequency end is 30 MHz or more and power transfer
is relatively flat over the decade bandwidth. How?
The "how" is more complex than realized. Going back to basics,
a secondary winding reflects the secondary load impedance to
the primary's driving circuit...but that load impedance is changed
in magnitude by several factors, primarily the turns ratio of the
two windings; secondarily by the magnetic field coupling between
the two windings (or others if multi-winding). A part of the latter is
frequency sensitivity to core material other than air. "Looking at"
the primary when the secondary is loaded with a pure resistance
will show a combination of the primary winding inductance plus
the transformed secondary winding inductance as the reactive
part at one frequency AND the transformed load resistance plus
any loss component of both windings. The impedance presented
to the driving circuit is largely resistive. Reactive components of
that impedance only begin to manifest themselves (usually) at
the higher frequency end. Low frequency end is affected (like the
AF transformer example) by the permeability and resultant
coupling of the core material, several powdered-iron toroids in
two stacks of several toroids each.
With tuned air-core transformers it is almost the same within the
resonance range. Resistance components of an impedance
predominate, the "transformation" governed by relative turns
ratios and amount of magnetic field coupling. Away from
resonance the reactive components predominate and the
other-winding impedance reflection is much reduced...power
transfer from one winding to another is also greatly reduced.
There is some slight parallel to L-C filter structures when
compared to an equivalent circuit of a transformer (see various
texts). L-C filter structures can also affect a "transformation"
of load to source impedance (and vice-versa) but that requires
a much deeper examination of the complex voltages and
currents circulating in the branches of a filter, in-band as well
as out-of-band. In a filter's bandpass, the impedance trans-
formation is still a complex matter but a resistive load will
show up transformed at the source end (and vice-versa).
A much easier route for homebrewers is to examine how others
do their transforming over a specified frequency range and then
just copy that. Not a crime or ethical badness. Saves a heap
of time which few of us have to spare. If you want "answers"
for an academic report you will have to hit the books and figure
it out for yourself. The material IS out there in the libraries.
Len Anderson
retired (from regular hours) electronic engineer person
Roger Leone
cores? (They would be much cheaper.)
Jason:
I seem to recall that the 0 (zero) mix toroids from Amidon have the same
permeability as air and contain no ferrite or powdered iron. They are
useful in the VHF region and otherwise have the same benefits as other
toroids.
Roger K6XQ
Michael Black
not the core material. I didn't catch this until Doug DeMaw wrote
about it in the mid-seventies.
The core material is needed because the needed inductance is often large
enough that the core helps, or because one is building a broad-band device
and the permability of a ferrite core works in that favor.
By the time you get to inductances low enough that some sort of core
is unnecessary, you're usually talking of a few turns of wire, and why
waste money on a fancy core at that point, when you can just air wind it?
You're probably going to need shielding anyway at those higher frequencies,
so the self-shielding of the donut-shape may be far less important than
at lower frequencies.
I had not noticed that you could buy neutral toroid cores. Doug DeMaw
showed a few that he had made in that article, I think it was a "Hints &
Kinks", but I've not really stumbled on anything that looked suitable
to make into such cores.
Michael VE2BVW
Roy Lewallen
appears in parallel across the transformer winding. So to keep from
disturbing the circuit the transformer is connected to, this impedance
should be considerably higher than the impedance of the circuit. Making
it more than 5 or 10 times greater than the circuit impedance doesn't
cause any problems, but it's often hard to do and a waste of effort.
Many of the ferrites used for broadband transformers exhibit primarily
resistive winding impedance at the frequency of use. This is often an
advantage over inductive impedance, since it stays relatively constant
over a wide frequency range and doesn't introduce undesirable resonance
effects. A purely or almost purely inductive impedance is only necessary
when enough power is involved to make transformer dissipation a problem.
Roy Lewallen, W7EL
W5DXP
> Winding impedance, whether inductive, resistive, or a combination,
> appears in parallel across the transformer winding. So to keep from
> disturbing the circuit the transformer is connected to, this impedance
> should be considerably higher than the impedance of the circuit. Making
> it more than 5 or 10 times greater than the circuit impedance doesn't
> cause any problems, but it's often hard to do and a waste of effort.
While learning transformer design at Texas A&M, we used a rule-of-thumb
of 10x. I notice that 5x seems to be acceptable for a balun.
--
73, Cecil http://www.qsl.net/w5dxp
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