I had wound some wire on an FT-114-77 ferrite core and was looking at it's impedance. There was a resistive component and a capacitive component that looked so strange to me that I began to wonder if my measurements were correct. The purpose of this paper is to share with you some additional understanding of ferrites that I acquired from these measurements. I hope to show that:

The impedance of a wire passing through or wound around
a ferrite core can be ** inductive** which is associated with

The ** maximum attenuation** of a ferrite core
is not where the inductance is maximum, but instead is where the

The frequencies that you are trying to attenuate determine
the core that you should use.

In order to make sense of these measurements, an understanding of complex impedance is necessary. Those of you who are conversant in the complex number representation of impedance should skip the next section unless you want to read it and keep me honest so that I don't mislead some one :)

Let me explain the basics of complex impedance a little
so the following graphs will make sense to those of you who might be new
to the field. Impedance is generally made up of two components, resistance
and reactance. These two components are vector components i.e. they
have a ** magnitude** and a

Since the resistance and reactance vectors form a 90 degree
right angle, the magnitude of the sum of the two, R+JX which we will call
Zmag , can be found by taking the square root of the sum of the squares
i.e. ** Zmag = SQRT(R^2 + X^2)**. Since Z is a vector and
Zmag is its magnitude, we need some way to specify which way it is pointing.
The convention for this is to measure the angle from the X-axis or in this
case the R-axis. If you remember any trigonometry at all, recall
that the

The following graphs were made using the AIM 4170 mentioned above. I first connected a 12 inch wire to the fixture forming a loop from the center pin of the connector to the common, and ran a scan from 0.1 MHz to 30 Mhz. I set the cursor at about 30 MHz, so the values listed to the right of the curve represent the values at this frequency. This is a busy curve, so bear with me as I point out some of the features. The color code on the curves is:

Black: Reactance

Tan: Resistance

Green: Zmagnitude

Purple: Phase angle (theta)

The horizontal axis is frequency and it runs from 0.1
MHz to about 30 MHz. ** Figure 2** is the plot from the
12 inch wire in the fixture.

Figure 2: Single 12 Inch Wire. (click herefor a higher resolution graph)

Observe from the curves and the listings on the right
of ** Figure 2** that

Figure 3: Single Turn of a 12 Inch Wire with a Snap-On
Ferrite of Unknown Material. (click here
for a higher resolution graph)

Now you can see that there is a resistive and an inductive reactance component to the impedance. If you look at the values on the right for a frequency of 29.736 MHz, you will see that the resistance, Rs (the s stands for series resistance), equals 147 ohms and the reactance, Xs (the s stands for series reactance), equals 162 ohms. Solving for Zmag which is equal to the square root of the sum of the squares of the resistance and reactance, we get the value 218. Since the reactance is just slightly larger than the resistance, we would expect theta to be slightly larger than 45 degrees. And indeed it is, Theta = 48 degrees.

Now what does all this mean? Well, first of all,
** the
impedance now has a resistive component**, which must come from the
core since there was

The next plot,

Figure 4: Two Turns of a 12 Inch Wire with a Snap-On Ferrite of Unknown Material. (click here for a higher resolution graph)

One would expect the inductance and hence the inductive
reactance to increase by a factor of four since the turns were doubled
and the increase is a function of turns increase squared. That is
not what happened. The ** inductive reactance is starting to fold
over** as can be seen by the black curve. However, the resistance
increase was close to a factor of four. The important thing is that

One interesting feature in ** Figure 4** is

Figure 5: Extended Frequency Scan Two Turns of a 12 Inch Wire With a Snap-On Ferrite of Unknown Material. (click here for a higher resolution graph)

As one can see from ** Figure 5**, theta goes
through zero and becomes negative at 53.506 MHz.

So what does all this mean. Traditionally one thinks
of a core material as a concentrator of magnetic field lines. In
other words, the core brings the field lines closer together which raises
the inductance. The amount that this is done is reflected in the
permeability of the core. Air has a permeability of one. A
type 43 material ferrite has an initial permeability of 850. The
interesting thing about ferrite **permeability** is that it is not a
constant, but instead ** a complex quantity consisting of resistance
and reactance**. I am certainly no expert on magnetics, so
for a good discussion on this subject, click
HERE.

In contrast, to the ferrite core plots above, I scanned a T-80-2, powdered iron core, with 19 turns. That scan is shown below in

Figure 6: Nineteen Turns on a T-80-2 Powdered Iron Core. (click here for a higher resolution graph)

As you can see from ** Figure 6**, the

Figure 7: Test Jig for Measuring Attenuation of Cores

In order to determine the actual attenuating capability
of a ferrite core, I wound several FT-114-43 and FT-114-77 cores and placed
them in the jig shown in ** Figure 7**. In order to
determine a reference level, I substituted a short for Z unknown and recorded
the reading. When Z unknown is of some value that causes an attenuation
of > 20 db, then the output of the 10 db pad is essentially open so the
output rises by 6 db. To compensate for this, 6 db of attenuation
should be added to every reading. When one does this, one can calculate
the expected attenuation by using the measured Zmag from the AIM
4170. The expected attenuation factor in db is given by :

Figure 8: 30 Turns on an FT-114-77 Core. (click
here
for a higher resolution graph)

Figure 9: 30 Turns on an FT-114-77 Core Expanded View for 40 Meters. (click here for a higher resolution graph)

When you first look at ** Figure 8**, it looks
terrible. But let's take a closer look. First of all, the reactive
part of the impedance is

The curves shown in ** Figure 10** are the results
of attenuation measurements of both FT-114-43 and FT-114-77 cores on all
the HF ham bands.

Figure 10: Attenuation of FT-114-77 and FT-114-43 Cores vs Frequency. (click here for a higher resolution graph)

As you can see from ** Figure 10**, more turns
do not always mean more attenuation as seen in the blue and tan curves.
The literature has always recommended a type 77 material ferrite for the
lower HF bands and a type 43 ferrite for the upper HF bands, and the red
and black curves confirm that. And, not surprisingly, a 43 core in
series with a 77 core yields good attenuation across the whole HF band
as seen by the green curve.

One of the most common uses of ferrites in the ham community consists of a series of ferrite beads slipped over the coaxial feed line of an antenna in the form of a choke balun. These ferrite beads attenuate the RF current that may be flowing on the outside of the coax due to an unbalanced feed line feeding a balanced antenna or radiation of the antenna onto the feed line.

Figure 11: Attenuation of Seven SB-1020-43 Ferrite Beads. (click here for a higher resolution graph)

As you can see from the plot in ** Figure 11**,
the attenuation on 160 meters is mainly due to the inductive reactance
part of the impedance, whereas the attenuation at 10 meters is mainly due
to the resistive part of the impedance. If we assume the minimum
impedance is 4 X 50 = 200 ohms, seven beads is just adequate for the 160
meter band. From our experience from previous measurements, if we
slipped a few more beads on the coax, we would see that the reactive part
of the impedance would be capacitive at the 10 meters frequency, but Zmag
would still be large and give plenty of attenuation.

I hope that this analysis has been interesting and has explained some of the strange results you may have gotten when using ferrites in the past. Ferrites are wonderful materials that I feel we as hams will be using more and more. With antennas being forced down lower, the chances of interference to less and less robust consumer electronics are increasing. A common mode choke using either ferrite snap-ons or ferrite cores can eliminate a lot of this interference. Also, many new lighting plans include halogen lights with switching power supplies that generate interference at high frequencies. Common mode chokes may be useful in these situations, also. Many consumer devices such as plasma TVs will radiate into our HF bands. Common mode chokes on leads emanating from these devices may very well cure the problem.Conclusions

I learned from these measurements that the ** ferrite
material** itself can be responsible for an inductor having a

The ** maximum attenuation** of a wire passing
through or wound on a ferrite core does not necessarily occur at the frequency
where the inductive reactance is maximum, but instead where the

The type of material one uses for a common mode choke whether it be 33, 43, 61, or 77 material is a function of the band of frequencies that need to be attenuated. A core material should be chosen such that the frequencies to be attenuated are near the frequency where theta crosses zero. However, good attenuation may be had at frequencies removed from this resonant point because of the low Q of the coil.

One must consider ** resistivity and permeability**
when slipping ferrite beads over a conductor to gain some common mode attenuation,
because the

Also, a good understanding of the loss factor of a ferrite might save you from a very hot core.

Remember that there is *big*** difference**
between a

If nothing else this strange phenomenon of a coil of wire
looking resistive and even capacitive has been interesting to me.
I hope you have found it interesting, too!