开云体育

Subject: single 31 material 2.4" OD core
12 bifilar turns of insulated AWG #12 stranded
wire

1.90 MHz 3.0 kΩ
3.75 MHz 4.3 k
7.15 MHz 4.5 k
10.125 MHz 4.4 k
14.20 MHz 4.1 k
18.1 MHz 3.8 k
21.30 MHz 3.5 k
28.40 MHz 3.0 k

Except for 160, there is general agreement with a bit less Z than K9YC with
my single 2.4" 31 material core. You can compare the numbers as they're
not too far apart. I don't know how he got more than 12 bifilar turns on
the 2.4" OD core! I squeezed and could not get more than 12 bifilar
turns. I might get a tight 13th if input and output were immediately next
to eachother. He must be overlapping turns to get upwards of 18 bifilar
turns on the single 2.4" core.

What I do observe over my multi-core CMCs is that the linear magnitude is
far more constant over the HF frequencies with the single core and no
suggestion of resonances, just a nice smooth curve. Of course, Z-Mag takes
a nose dive below 1 MHz.

Dave - W ?LEV

Based on the cookbook plus have two single #31 cores in series with 15T and 11T using salvaged 12 AWG wire.

So using all the good data here from the fabulous Dave W0LEV, and K9YC, will I have >5K resistance from 160 to 10?

My goal was to use my nano and answer that question myself, but my lack of actual technical qualifications, and limited understanding of RF-related math, has made that near impossible. So I thought I would ask.

Hi Dave,

Looking at your data, I see that it differs from my plot of 12 turns of #14 twisted pair on the same type of core (see attached plot). I would like to detemine why, so a couple of questions...

1. Does your data represent |Z|, or is it the resistance of the CMC impedance? (Note that I'm plotting the resistance, because, to me, this is the more important parameter of a CMC).

2. How did you wind your CMC? (I used what I call a "crossover" technique that was described in Ham Radio Magazine: "Simple and Efficient Broadband Balun", by Joe Reisert, W1JR, in the September, 1978 issue). See the attached drawing...

Thanks!

- Jeff, k6jca

1. Does your data represent |Z|, or is it the resistance of the CMC
impedance? (Note that I'm plotting the resistance, because, to me, this is
the more important parameter of a CMC).
I am plotting CM resistance. As you wrote, this is what the choke is
placed in the transmission line to accomplish. The initial job of any CMC,
current choke, or single layer air wound solenoid is to prevent CM current
from flowing on the feedline (outer surface of the braid with coax). A
true CMC choke also through the interaction of currents in the two
conductors and the induced magnetic currents in the core assure equal
amplitude with opposite phase on the output of the choke. The current
choke or single layer air wound solenoid can not accomplish this second
operation. This is especially important for those who use open wire,
parallel conductor, and/or window line as feeders, which I do.


2. How did you wind your CMC? (I used wha
t I call a "crossover" technique that was described in Ham Radio Magazine:
"Simple and Efficient Broadband Balun", by Joe Reisert, W1JR, in the
September, 1978 issue). See the attached drawing...
I do not cross or twist my windings. They are flat bifilar windings of the
noted conductors. I'll attach a picture of the last choke I would
yesterday and documented last evening to this group.

Dave - W?LEV

--
*Dave - W?LEV*
*Just Let Darwin Work*

BTW, the general shape of your real part of Z looks extremely similar to my
overall curve. You obtained about 2k more CM resistance, but the shapes
are nearly identical.

Dave - W?LEV

On Sun, Jan 17, 2021 at 5:35 PM David Eckhardt <davearea51a@...>
wrote:

1. Does your data represent |Z|, or is it the resistance of the CMC
impedance? (Note that I'm plotting the resistance, because, to me, this is
the more important parameter of a CMC).
I am plotting CM resistance. As you wrote, this is what the choke is
placed in the transmission line to accomplish. The initial job of any CMC,
current choke, or single layer air wound solenoid is to prevent CM current
from flowing on the feedline (outer surface of the braid with coax). A
true CMC choke also through the interaction of currents in the two
conductors and the induced magnetic currents in the core assure equal
amplitude with opposite phase on the output of the choke. The current
choke or single layer air wound solenoid can not accomplish this second
operation. This is especially important for those who use open wire,
parallel conductor, and/or window line as feeders, which I do.


2. How did you wind your CMC? (I used wha
t I call a "crossover" technique that was described in Ham Radio Magazine:
"Simple and Efficient Broadband Balun", by Joe Reisert, W1JR, in the
September, 1978 issue). See the attached drawing...
I do not cross or twist my windings. They are flat bifilar windings of
the noted conductors. I'll attach a picture of the last choke I would
yesterday and documented last evening to this group.

Dave - W?LEV

On Sun, Jan 17, 2021 at 2:56 PM Jeff Anderson <jca1955@...>
wrote:

Hi Dave,

Looking at your data, I see that it differs from my plot of 12 turns of
#14 twisted pair on the same type of core (see attached plot). I would
like to detemine why, so a couple of questions...

1. Does your data represent |Z|, or is it the resistance of the CMC
impedance? (Note that I'm plotting the resistance, because, to me, this is
the more important parameter of a CMC).

2. How did you wind your CMC? (I used what I call a "crossover"
technique that was described in Ham Radio Magazine: "Simple and Efficient
Broadband Balun", by Joe Reisert, W1JR, in the September, 1978 issue). See
the attached drawing...

Thanks!

- Jeff, k6jca

--
*Dave - W?LEV*
*Just Let Darwin Work*

--
*Dave - W?LEV*
*Just Let Darwin Work*

See the pictures of T240-31 core and coax.

I use these? from 3.5 Mhz to 10 MHz as CMC

73,

Arie PA3A

So far, so good, regarding impedance. The other point one needs to look at is power handling, or rather, core losses per applied voltage.

With that core, and 12 turns, approximately 170V RMS, end-to end over the 12 turns, will cause a core loss of roughly 300mW per cubic cm, which given the core's size makes about 8W total core loss. Under continuous carrier conditions this would probably overheat the core, unless there is some forced convection, but under ICAS conditions it should be fine. Slightly lower voltage would be fine under continuous carrier conditions.

If that common mode choke is used in a 50? antenna system operating under textbook conditions, 170V end-to-end means 340V between conductors, and that would be about 2.3kW into a 50? load. So this CMC could actually be used at legal limit power. But if the conditions are not textbook-like or specially if the system impedance is higher, your mileage may vary.

These values are for 1.8MHz. On higher bands the core loss goes down.

Stacking two cores allows using 7 turns to get about the same total core loss. The inductance will be slightly more than half, so the impedance at the low spectrum end will be lower, but the stray capacitance will also be lower if the turns are kept optimally spaced, improving the performance on the high bands. At least so says the theory...

On Sun, Jan 17, 2021 at 12:05 PM, Manfred Mornhinweg wrote:

With that core, and 12 turns, approximately 170V RMS, end-to end over the 12
turns, will cause a core loss of roughly 300mW per cubic cm, which given the
core's size makes about 8W total core loss. Under continuous carrier
conditions this would probably overheat the core, unless there is some forced
convection, but under ICAS conditions it should be fine. Slightly lower
voltage would be fine under continuous carrier conditions.

Hi Manfred,

Could you please explain what you mean by "end-to-end"? There are four "ends" in the CMC and I'm trying to understand which ends you are referencing -- input-pair to output-pair, or between in and out of one wire, or...?

Also, why 170V RMS?

Thanks,

- Jeff, k6jca

On Sun, Jan 17, 2021 at 09:36 AM, David Eckhardt wrote:

BTW, the general shape of your real part of Z looks extremely similar to my
overall curve. You obtained about 2k more CM resistance, but the shapes
are nearly identical.

Thanks very much, Dave.

In addition to my CMC having about 2K more CM resistance, it peaks at about 21 MHz, whereas yours seems to peak somewhere in the range of 7 MHz (very roughly).

I'll have to wind a bifilar style CMC (to mimic yours) when I return home later this next week. I'm curious if your bifilar-winding (rather than twisted-pair winding) or the winding style (your continuous winding versus my flip of the windings halfway through) is enough to explain this difference.

Of course, other possibilities are variations between cores as well as differences in VNA fixtures and calibration.

I'm including a couple of photos showing my fixture, which is similar to the fixture G3TXQ described for his S21 technique (if my memory serves). The second photo shows better how the toroid clips to the fixture (using alligator clips) -- by the way, that's the 14-turn CMC. The other image is of the 10-turn CMC.

The fixture uses female BNC connectors, and it installs into male BNC connectors on the VNA side. Two-port Reflection-calibration (open, short, load) is done at the ends of these two male BNC connectors with the fixture removed (using female-BNC SOL standards). For through calibration, the fixture is installed onto the VNA's male BNC connectors and a wire is connected between the two alligator clips. This is the only part of the cal procedure that I am unsure of -- ideally, for through calibration the through should be characterized (and these characteristics stored as in the VNA's calibration tables) with respect to its Delay, Zo, etc. But I believe the VNA defaults to assuming that the through length is 0, which it is not.

Anyway -- I'm curious how you handle fixturing and calibration.

Thanks,

- Jeff, k6jca

...and attached please find the promised photos:

- Jeff, k6jca

Jeff, your fixture is virtually identical to what I built. My BNCs are a
bit closer to each other, but just about the same. I also use the same
fixture to characterize ferrite Z to match to the published curves. Thank
you.

Dave - W?LEV

--
*Dave - W?LEV*
*Just Let Darwin Work*

This works well with coaxial feeds, but using open wire feeders, I also
take the luxury of forcing a balance between the two conductors of the open
wire feeders. I used to use such a choke wound with RG-142, high power
silver coated teflon 50-ohm coax. When I finally got it through my head
that it had no way of balancing the DM output, I went to the bifilar wound
CMCs.

Dave - W?LEV

--
*Dave - W?LEV*
*Just Let Darwin Work*

OK guys and gals, attached is my final contribution (try me.....) to the
CMC choke evaluation. The bottom line I believe is that there is no single
choke that addresses everything. Coax is much easier as the CM currents on
the outside of the shield have no effect on the internal fields (assuming
good integrity of the shield material). All one needs to accomplish is to
choke off and/or dissipate them before they have a chance to enter the
antenna and introduce local noise sources to the receiver. My open wire
feeders are a bit different. I certainly also require getting rid of the
CM currents on the open wire feeders, but I also strive to assure balance
of the DM CMC output port (equal amplitudes with opposite phases of the
current and voltage).

QUESTION on MY PART: Do my measured loss numbers made in a 50 ± j0 ohm
system impedance (as best I could) correlate with core or conductor heating
at power in my antenna system impedance? TBD (when the bands are dead).


Please see the attachment. Of all I wound and tested, my choice would be
the single 31 material core (most right in the table), but I doubt it will
handle the legal limit power. Also, likely, all these could be made to
perform better at the upper HF frequencies by winding fewer turns on the
cores. As I mentioned earlier, my main interest falls from 160 through
(maybe) 30-meters. So I attempt to cram as many bifilar turns on my CMCs
as I can without overlapping windings.

Yet another consideration is the system impedance in which the CMCs are
installed. Therefore, I made a measurement of my 450-foot long doublet
with the open wire feeders in the shack where I connect the CMCs. I used a
small instrument not connected to anything other than the open wire feeders
in the shack to make the measurements - the RF Vector Impedance Analyzer,
Model N2061SA. I could have used one of the NANOs, but the frequency
change operations on that particular instrument were far easier than
setting and calibrating each individual sweep using the NANOs. Forgive me,
please........ I'll also attach that set of measurements just to scope
what I'm dealing with (40-meters is scary). You guys and gals who use
resonant systems and coaxial feeders have it easy? But, since I have the
instruments to make the measurements, I prefer the more difficult path to a
'will oiled' antenna system. Besides, I don't want to support a feedline
and set of wires for each band even though I have the real estate
(40-acres, but typical of the Front Range of the Rockies, not much is
flat).

Dave - W?LEV

--
*Dave - W?LEV*
*Just Let Darwin Work*

Jeff,

Could you please explain what you mean by "end-to-end"? There are four "ends"
in the CMC and I'm trying to understand which ends you are referencing --
input-pair to output-pair, or between in and out of one wire, or...?

I mean, voltage applied to those 12 turns. Short the input pair to make one connection, short the output pair to make the other connection, apply the voltage between those two points.

In a "textbook" antenna installation, such as a perfectly symmetrical horizontal dipole, symmetrically over ground, with the feedline coming down straight and vertical, no other objects nearby, and fed from an unbalanced, perfectly grounded transmitter, with the dipole impedance and cable impedance being identical and the CMC's impedance being infinite, the voltage appearing end-to-end on a CMC used as balun is one half of the transmitter's output voltage. In a typical practical installation it's usually lower, but with some bad luck it could also be higher.

Also, why 170V RMS?

Because the applied voltage defines the flux density in the core, along with frequency, number of turns, and core dimensions. And for the core size (FT-240) and turns number (12) considered here, 170V at 1.8MHz results in a flux density of about 11mT, which for this particular core material (31) results in a volumetric loss of roughly 300mW per cm?, which I somewhat arbitrarily defined as a reasonable value for intermittent service.

And I made the calculations at 1.8MHz because it's the worst case. On higher frequencies the loss gets lower.

Manfred

On Sun, Jan 17, 2021 at 04:41 PM, David Eckhardt wrote:

OK guys and gals, attached is my final contribution (try me.....) to the
CMC choke evaluation.

First, thanks for kicking off a terrific discussion, I've learned a lot! Then, a couple of questions… can say more about your actual antenna-feeder-CMC configuration? Have you tried placing a CMC at the feedpoint of your doublet? Or tried using CMCs at both ends of the feedline? If so, what difference did it make? Last question, does the insulation material of the wire used for the CMC make a difference?

Thanks!
Bill K7WXW

1) The operation of any CMC, current balun, true balun, or..... does not
depend on voltage. It's all about current. Voltage alone does not, I
repeat, not induce magnetic current in the ferrite toroids! Only current,
flowing current (that's a double whatever), produces magnetic currents in
the toroids. Capacitance is all about voltage and voltage is responsible
for aligning the polarization vector in dielectrics. Current alone can not
accomplish that. Inductance (magnetic currents in the ferrite material) is
all about current and flowing charges are responsible for producing the
magnetic currents in the toroids. Voltage alone can not accomplish that.
Visit Lenz's Law for a clearer explanation:
's_law

2) A bifilar wound toroidal CMC is a bilateral device. From a circuit
aspect, both ends are identical. In place between the output of the
matching network and the open wire feeders, it converts CM to DM. This is
the function and only function of a true balun - NOT a transformer. One
could turn the CMC completely around - swap port for port - and the result
would be identical.

Dave - W?LEV

On Mon, Jan 18, 2021 at 3:22 PM Manfred Mornhinweg <manfred@...>
wrote:

Jeff,

Could you please explain what you mean by "end-to-end"? There are four

"ends"

in the CMC and I'm trying to understand which ends you are referencing --
input-pair to output-pair, or between in and out of one wire, or...?

I mean, voltage applied to those 12 turns. Short the input pair to make
one connection, short the output pair to make the other connection, apply
the voltage between those two points.

In a "textbook" antenna installation, such as a perfectly symmetrical
horizontal dipole, symmetrically over ground, with the feedline coming down
straight and vertical, no other objects nearby, and fed from an unbalanced,
perfectly grounded transmitter, with the dipole impedance and cable
impedance being identical and the CMC's impedance being infinite, the
voltage appearing end-to-end on a CMC used as balun is one half of the
transmitter's output voltage. In a typical practical installation it's
usually lower, but with some bad luck it could also be higher.

Also, why 170V RMS?

Because the applied voltage defines the flux density in the core, along
with frequency, number of turns, and core dimensions. And for the core size
(FT-240) and turns number (12) considered here, 170V at 1.8MHz results in a
flux density of about 11mT, which for this particular core material (31)
results in a volumetric loss of roughly 300mW per cm?, which I somewhat
arbitrarily defined as a reasonable value for intermittent service.

And I made the calculations at 1.8MHz because it's the worst case. On
higher frequencies the loss gets lower.

Manfred

--
*Dave - W?LEV*
*Just Let Darwin Work*

Dave,

1) The operation of any CMC, current balun, true balun, or..... does not
depend on voltage. It's all about current. Voltage alone does not, I
repeat, not induce magnetic current in the ferrite toroids! Only current,
flowing current (that's a double whatever), produces magnetic currents in
the toroids.

Whether you like it or not, both current and voltage are facts of life, and are present and involved in these phenomena.

Current is electrical, not magnetic. When you write "magnetic current", what do you mean? Magnetic flux, or the magnetizing current flowing in a transformer primary? I assume you mean magnetic flux. It would be good to use the standarized, usual terminology.

Sure, for a given inductor, and as long as its core operates linearly, the magnetic flux depends directly on the current flowing in the winding. For a transformer, that's the equivalent net current in all windings, properly considering the number of turns of each winding and the direction of each current. For the CMC in question, thus, it's the common-mode current.

Since the inductor or CMC has a certain finite impedance, several kiloohm in this case, the RF current that causes magnetic flux requires a RF voltage applied to the windings. If there is no end-to-end voltage, such as in a CMC that has the same conductor grounded at both ends, or which has one end connected to a floating load without any coupling anywhere else, then there is no flux in the core, regardless of how much differential-mode current is flowing.

When a CMC is connected in an antenna system, typically there is a significant end-to-end voltage (significant relative to the signal levels present). If there was none, there would be no need to use a CMC! This end-to-end voltage, divided by the CMC's impedance, defines the value of the common-mode current, which in turn defines the flux in the core.

Instead of calculating the flux from the current, it's often more practical to calculate it directly from the applied voltage, because doing so is independent from inductance. When calculating flux from current, we need to know the actual core permeability, which varies with frequency and with drive level. When calculating flux from voltage, the effect of permeability cancels out, allowing us to calculate the flux without knowing the actual permeability at the specific frequency and drive level.

The physical relationships are so easy that the change of flux is given directly by the voltage, multiplied by time it acts, and divided by turns number. No constants are needed. One volt applied for one second to a coil of one turn produces a flux of one weber, no matter what the size of the coil is, whether or not it contains any magnetic core, and what permeability it has! The only caution about this is that "voltage" means that part of the voltage that actually is applied to the inductance of that coil. In situations where the inductance is low, and the voltage or the time are large, the resulting current might become so high that the wire resistance will drop most or all of the voltage. The voltage dropped on wire resistance doesn't count in this formula.

In a properly used CMC we are far from that, though, so the equation is totally usable. By factoring in the ratio between time and frequency, and a factor to convert between RMS and average, we can use frequency and RMS voltage of an AC signal instead of the voltage×time product. Those who like calculus can also integrate the instantaneous voltage over the time span in question, to calculate flux change over any arbitrary period while a complex waveform signal is applied. But that's not my cup of tea...

Once we have the flux, we can calculate the flux density in the core, simply by dividing the flux by the core's cross sectional area. And we don't even need to know the current! This calculation is reasonably accurate only as long as the core captures most of the flux, which is the case when using closed-loop cores of high permeability.

Calculating flux density from voltage instead of current is also better in cases where the impedance is extremely high. The function of a CMC is reducing the common-mode current as much as possible. Assuming a theoretical case of a CMC having infinite impedance, because it's wound on a core having infinite permeability, we cannot calculate its flux density from current! Because the current would be zero, and with the permeability being infinite, the equation for flux density would include a multiplication of zero by infinite, which is undefined. Instead by using the applied voltage we can calculate the flux density even for this case. Not that there would be practical applications, but it's good matter for mental exercise!

Capacitance is all about voltage and voltage is responsible
for aligning the polarization vector in dielectrics. Current alone can not
accomplish that.

But to charge a capacitor you need a current... You see, current and voltage are facts of life. In practical electronics and radio they always come together.

Inductance (magnetic currents in the ferrite material) is
all about current and flowing charges are responsible for producing the
magnetic currents in the toroids. Voltage alone can not accomplish that.

Your use of this term "magnetic current" bothers me. The correct term is "magnetic flux", and it's not the same as inductance.

Sure, voltage alone doesn't cause magnetic flux. But voltage is involved whenever current flows in a circuit having nonzero impedance.

Visit Lenz's Law for a clearer explanation:
's_law

Lenz defines just the polarities and directions.

2) A bifilar wound toroidal CMC is a bilateral device. From a circuit
aspect, both ends are identical.

Yes, of course.

In place between the output of the
matching network and the open wire feeders, it converts CM to DM.

I object to that. What a CMC does is opposing CM current to a high degree, while allowing DM current to flow unhindered. Whether or not that action results in any additional DM current depends on the rest of the circuit.

One
could turn the CMC completely around - swap port for port - and the result
would be identical.

Yes, of course. But I don't see why you mention this in the context of how to calculate flux, and how (or if) voltage is involved. I fear that you might have misunderstood something I wrote. At least I can't remember having written anything about a CMC having unidirectional behavior. I did use the terms "input" and "output", because Jeff used them in his question, but I didn't mean nor imply that they can't be reversed.

Electromagnetics, like so many things, is simple after you understand it, but not before! :-)

Manfred

A practical example that some may find interesting:

Yes, Mr. Ohm said it all: both voltage and current are required.

A cloud can accumulate a voltage but nothing happens until the breakdown
potential is reached. Then and only then does current flow as evidenced as
a lightning discharge. Current can't happen without voltage AND a path for
discharge. Both voltage and current are required to make things
'happen'.

Dave - W?LEV

On Mon, Jan 18, 2021 at 6:49 PM Manfred Mornhinweg <manfred@...>
wrote:

Dave,

1) The operation of any CMC, current balun, true balun, or..... does

not

depend on voltage. It's all about current. Voltage alone does not, I
repeat, not induce magnetic current in the ferrite toroids! Only

current,

flowing current (that's a double whatever), produces magnetic currents in
the toroids.

Whether you like it or not, both current and voltage are facts of life,
and are present and involved in these phenomena.

Current is electrical, not magnetic. When you write "magnetic current",
what do you mean? Magnetic flux, or the magnetizing current flowing in a
transformer primary? I assume you mean magnetic flux. It would be good to
use the standarized, usual terminology.

Sure, for a given inductor, and as long as its core operates linearly, the
magnetic flux depends directly on the current flowing in the winding. For a
transformer, that's the equivalent net current in all windings, properly
considering the number of turns of each winding and the direction of each
current. For the CMC in question, thus, it's the common-mode current.

Since the inductor or CMC has a certain finite impedance, several kiloohm
in this case, the RF current that causes magnetic flux requires a RF
voltage applied to the windings. If there is no end-to-end voltage, such as
in a CMC that has the same conductor grounded at both ends, or which has
one end connected to a floating load without any coupling anywhere else,
then there is no flux in the core, regardless of how much differential-mode
current is flowing.

When a CMC is connected in an antenna system, typically there is a
significant end-to-end voltage (significant relative to the signal levels
present). If there was none, there would be no need to use a CMC! This
end-to-end voltage, divided by the CMC's impedance, defines the value of
the common-mode current, which in turn defines the flux in the core.

Instead of calculating the flux from the current, it's often more
practical to calculate it directly from the applied voltage, because doing
so is independent from inductance. When calculating flux from current, we
need to know the actual core permeability, which varies with frequency and
with drive level. When calculating flux from voltage, the effect of
permeability cancels out, allowing us to calculate the flux without knowing
the actual permeability at the specific frequency and drive level.

The physical relationships are so easy that the change of flux is given
directly by the voltage, multiplied by time it acts, and divided by turns
number. No constants are needed. One volt applied for one second to a coil
of one turn produces a flux of one weber, no matter what the size of the
coil is, whether or not it contains any magnetic core, and what
permeability it has! The only caution about this is that "voltage" means
that part of the voltage that actually is applied to the inductance of that
coil. In situations where the inductance is low, and the voltage or the
time are large, the resulting current might become so high that the wire
resistance will drop most or all of the voltage. The voltage dropped on
wire resistance doesn't count in this formula.

In a properly used CMC we are far from that, though, so the equation is
totally usable. By factoring in the ratio between time and frequency, and a
factor to convert between RMS and average, we can use frequency and RMS
voltage of an AC signal instead of the voltage×time product. Those who like
calculus can also integrate the instantaneous voltage over the time span in
question, to calculate flux change over any arbitrary period while a
complex waveform signal is applied. But that's not my cup of tea...

Once we have the flux, we can calculate the flux density in the core,
simply by dividing the flux by the core's cross sectional area. And we
don't even need to know the current! This calculation is reasonably
accurate only as long as the core captures most of the flux, which is the
case when using closed-loop cores of high permeability.

Calculating flux density from voltage instead of current is also better in
cases where the impedance is extremely high. The function of a CMC is
reducing the common-mode current as much as possible. Assuming a
theoretical case of a CMC having infinite impedance, because it's wound on
a core having infinite permeability, we cannot calculate its flux density
from current! Because the current would be zero, and with the permeability
being infinite, the equation for flux density would include a
multiplication of zero by infinite, which is undefined. Instead by using
the applied voltage we can calculate the flux density even for this case.
Not that there would be practical applications, but it's good matter for
mental exercise!

Capacitance is all about voltage and voltage is responsible
for aligning the polarization vector in dielectrics. Current alone can

not

accomplish that.

But to charge a capacitor you need a current... You see, current and
voltage are facts of life. In practical electronics and radio they always
come together.

Inductance (magnetic currents in the ferrite material) is
all about current and flowing charges are responsible for producing the
magnetic currents in the toroids. Voltage alone can not accomplish that.

Your use of this term "magnetic current" bothers me. The correct term is
"magnetic flux", and it's not the same as inductance.

Sure, voltage alone doesn't cause magnetic flux. But voltage is involved
whenever current flows in a circuit having nonzero impedance.

Visit Lenz's Law for a clearer explanation:
's_law

Lenz defines just the polarities and directions.

2) A bifilar wound toroidal CMC is a bilateral device. From a circuit
aspect, both ends are identical.

Yes, of course.

In place between the output of the
matching network and the open wire feeders, it converts CM to DM.

I object to that. What a CMC does is opposing CM current to a high degree,
while allowing DM current to flow unhindered. Whether or not that action
results in any additional DM current depends on the rest of the circuit.

One
could turn the CMC completely around - swap port for port - and the

result

would be identical.

Yes, of course. But I don't see why you mention this in the context of how
to calculate flux, and how (or if) voltage is involved. I fear that you
might have misunderstood something I wrote. At least I can't remember
having written anything about a CMC having unidirectional behavior. I did
use the terms "input" and "output", because Jeff used them in his question,
but I didn't mean nor imply that they can't be reversed.

Electromagnetics, like so many things, is simple after you understand it,
but not before! :-)

Manfred

--
*Dave - W?LEV*
*Just Let Darwin Work*

Manfred, thanks very much for your reply defining "end-to-end" and the reasoning for 170VRMS.

After I'd read it I still didn't understand why the voltage across the CMC end-to-end was half the transmitter voltage, and a simple example that I'd come up with (in which I reduced the feedline length to 0 and replaced 1) the antenna with a floating load resistor and 2) the CMC with a perfect transformer) resulted in the CMC end-to-end voltage being unknown. In other words, the loop equation for the this very simple circuit reduced to Vload = Vsource with Vcmc cancelled out.

Clearly I was missing something, and the answer was in your reply to Dave in which you said that there would be no end-to-end voltage across the CMC if the CMC "has one end connected to a floating load without any coupling anywhere else".

Ah ha! That was my error -- my load was floating. If I instead split the load into two series-connected resistors (each with half the value of the original load, i.e. a center-tapped load) and added a resistance from the load's "center-tap" to ground (i.e. a common-mode path), then the load's center-tapped is forced to be 0 volts.

(The CMC, in this case, being an ideal transformer, forces the currents to be equal and thus no current "bleeds off" through the common-mode resistor. And with no current through this Common-mode resistor there is no voltage drop across it, and thus, because one end of this path is grounded (0 volts), the other end at the load's center-tap must therefore also be 0 volts. And the voltage across each of the CMC's windings will then be equal to half the load voltage by virtue of the load's center-tap being 0 volts and the fact that Vsource = Vload.

Interestingly, it seems that if the common-mode path is unbalanced with respect to the load (i.e. the load is not tapped at its center, but off-center), the voltage across the CMC will be less than half the source voltage -- so a "balanced" load would seem to present the worst-case voltage across the CMC.

Anyway, lots of assumptions in my "ideal" model (e.g. CMC = ideal transformer), so there could easily be a flaw in my reasoning. Please let me know if I've missed something.

Thanks,

- Jeff, k6jca