Ferrites in HF-applications
inductors and transformers
(published in Electron #11, 2001)
This chapter is the third in a series of articles on ferrite materials in HF-applications. The first article is an introduction to this field with an overview of some widely applied materials and most important properties. The second article is on materials back-ground and most important HF-application formulas. It is advisable to read the articles in the above order especially since each next chapter is building on information and formula's already explained earlier and referencing to this.
In a first approximation inductors in electronic circuits are considered as purely inductive components. Next it appears these inductors are far from ideal and losses have to be taken into account, in general to be expressed as a ratio of reactance to (copper) loss in the quality factor: Q, as in formula 15.
Q = XL / rs = w.L / rs.
When applying (ferrite) core materials, most losses stem from the core material, especially when applied at HF frequencies. In formula 16 we showed the inductor quality could be expressed as a ratio of the inductance factor, m and core-loss factor, m of ferrite materials as specified by the manufacturer.
Q = m / m.
with materials data as in table 2.
Core properties will influence the type of application. HF- amateur and author, Moxon writes in his book: "HF antenna's for all locations", `...we should be careful at applying core materials in antenna trap inductors as these should exhibit a quality factor of over 200, which makes ferrites in general unfit for these applications...`.
With the 'tools' from chapter 2, we may examine Moxon's remarks. As an example we will investigate a few properties of the antenna trap inductor of 5,4 mH as being applied in Multiband trap antenna. In this design an inductor without core materials has been applied, for reasons that will become obvious later on.
We may consider to design a very compact trap
by applying a small 23/14/7 toroide of 4C65 material exhibiting a core factor
L = n2 . AL (nH). out of which: n = 7,87 , we take n = 8 (only integer values).
When calculating the antenna with EZNEC, we find largest voltage across the trap to appear around 7 MHz, at an antenna input power of 100 Watt to rise to 450 volt.
As we may find in table 2 and formula 16, 4C65 material is exhibiting a high quality factor of 125 at 7 MHz. To avoid non-linear behavior, voltage across an inductor on ferrite material should be limited. Using formula 5 we calculate maximum voltage across this inductor.
UL (induction) = 0,89 . Bsat . f . n . A
With Bsat = 380 mT for 4C65, n = 8 turns, f = 7 MHz. and the area for this core size A = 31 mm2, we find a maximum voltage: UL (induction) = 590 volt. Since maximum voltage for 100 Watt is 450 volt, no non-linear behavior will occur up to this input power.
A different problem however is popping up. At
7 MHz. inductor reactance is XL =
wL = 248 W. With 450 volt across, effective
H = n . I / l
With l =
Manufacturers specification (data
books) is showing that permeability m is diminishing form
125 to 70 under this magnetic field strength. Since we started our
calculations from m = 125 (
Because permeability is down to 70 with loss unchanged, quality factor for this material has changed as well:
Q = m / m = 70/1 = 70.
Parallel loss resistance may be calculated from:
RFp = Q . XL = 70 . 248 = 17360 W.
Since we found 450 volt across the inductor, this amounts to 4502 / 17360 = 11,7 watt per trap, so 23,4 Watt in total. Not only will this amount of power be lost to our transmission, but it will probably also destroy the toroide since maximum internal dissipation for this core volume is 4 Watt for a maximum temperature rise of 30 K.
The origin of the Moxon remark as above is now complete clear.
In general ferrite materials are not recommended for very precise HF tuning inductors in general (permeability vs temperature characteristic) and in power tuning applications in particular (internal loss).
The impedance between inductor terminals is the most important parameter in choke application, much more so than the precise phase relation between current and voltage; as long as this is impedance is high (usually at low DC resistance), the application will function well.
As an example we perform some calculations
around the 10 mH inductor we designed on a 3E25 ferrite toroide in the first
chapter. In this design we started from table 1, where we found winding
AZ(4 MHz) = AL . mC(4 MHz) / mi
Table 2 is presenting permeability (μ') and loss factor (μ") for a number of well known ferrite materials, including the complex assembly (μc ). Recalculating the winding factor for our choke at an operating frequency of 4 MHz., we start from the complex permeability factor, μc , as in table 2 (μc = 601), so
AZ(4 MHz) = AL(DC) . 601 / 6000 = 0,1 . AL (DC) (nH)
Impedance at our operating frequency of 4 MHz. will follow from:
|Zt| = w . n² . (0,1 . AL (DC))
At still higher frequencies, the complex
permeability, μc will be still lower, at 30 MHz. only 90. So
between 4 and 30 MHz. (factor of
This is clearly demonstrating the importance of (even relatively low frequency) ferrite materials in wide band applications.
What ferrites for HF chokes?
A HF choke will perform well up to the moment of (parallel) resonance of the inductance with its parasitic parallel capacity. Past this resonance frequency, this parasitic capacitance is becoming the dominating impedance and this will fall with frequency up to the moment total impedance is too low for the designed choking action. It follows, that for wide band use, this parasitic capacitance should be as low as possible, which usually translates into designing a choke with as low a number of turns as possible. This in turn translates into selecting a ferrite material with as high a (complex) permeability (mC) as possible over the operational frequency range.
In table 2 one may find various materials exhibiting such high permeability over the HF range of frequencies, e.g. 3S4, 3F4, 4A11, 33, 43 4B1. The widely applied 4C65 (61) type is not in this list since it is much easier to reach high impedance with less turns over this frequency range with the lower frequency materials. In high(er) power systems though, one has to compare maximal band-width performance (high m, less turns, low parasitics) to maximum core load (high Q, lower internal core dissipation, lower temperature rise). We will come back to this in the next chapter.
For HF choke applications, ferrite type 4A11 (43) in general is the material of choice. Therefore one may also find this material applied in the transformer in the Multiband trap antenna.
From table 2 it may also be appreciated the higher frequency materials 4C65, 61, and 68 to be more suitable for choke applications above 30 MHz. because only here the complex permeability tends to rise above the other materials. At these frequencies however maximum load is also diminishing since materials loss factor is becoming dominant above the ferrimagnetic resonance frequency.
How ferrites in HF chokes?
We already noticed for high permeability materials, every time a wire passes through the center hole in the toroide coil former will account for a complete turn. Therefore, it is possible to stack ferrites of different (ferrite) materials to design ultra wide bandwidth chokes. The low frequency, high permeability material is dominant at lower frequencies while the high frequency, lower permeability type takes over at the high frequency side. This can have chokes perform at high and constant impedance over very wide band width; this idea is taken somewhat further in Ferrites in EMC applications.
Sometimes one may come across a stack of an orange core (3E25) and a purple core (4C65) for the purpose of achieving wide band-width. In table 2 we find at 4 MHz., 4A11 (43) type of ferrite to already exhibit a higher (complex) permeability than 3E25 type while this first material is also superior to 4C65 (61) at 30 MHz. It follows that a single 4A11 toroide choke with the same number of turns is superior to the stack of the other two materials for all of the HF amateur frequency bands.
Stacking therefore usually only makes sense for very wide bandwidth, including LF, MF and HF frequencies.
It should be noted that stacking ferrite toroides is superior to constructing two chokes, each with the same number of turns but on separate toroides. At low frequencies no difference will be measured, but a high(er) frequencies one may be in for a surprise. Inductance of one choke may resonate with the parasitic capacitance of the other, creating a low impedance path across this combination instead of the high impedance this system was designed for in the first place!
Ferrites may be successfully employed in various types of transformers, usually at higher that mains frequency. Ferrite cores may also be found in pulse transformers (1- 100 kHz.), switch mode power supplies (20 - 1000 kHz.) and HF voltage or impedance transformers in small- or wide-band applications (1 - 50 MHz.)
In this chapter we will only discuss linear wide band HF-transformers for small and medium size power applications. By wide band we mean at least a few octaves in frequency and medium power up to around 2 kW. More power is quite possible, but this will be outside this story. For this chapter we will distinguish two main categories, based on different principles:
· Induction type of transformers based on magnetic field coupling for energy transport. Core material is employed to concentrate the electromagnetic field. This is the conventional type of transformer
· Transmission-line transformers with energy transported by transmission lines. Core material is employed for better input to output separation.
Latter type will be discussed in two separate chapters: Transmission-line transformers, introduction and Transmission-line transformers, examples and analysis.
Basic induction type of transformer consists of a primary and a secondary winding, usually around a magnetic core. This core will concentrate magnetic field-lines to ensure both windings sharing the same flux and so optimize transformer coupling. In this chapter transformers will be constructed on ferrite type core material that mainly determines transformer properties and application area.
Next to inter-winding coupling, core material will also enhance transformer inductance. Induction transformers are mainly applied in parallel to the signal path and since the inductor current is out of phase to the (resistive) load current, a phase shift will be introduced in the signal path. We prefer this disturbance to be as small as possible so the transformer inductance should be high compared to the system impedance.
To create a high impedance, we need a number of turns around some ferrite material. This will inevitably create a parasitic parallel capacitance across this transformer, that will further increase with each next turn. Again, this capacitance will be parallel to the transformer and so parallel to the signal path. To keep this influence small, the number of turns should be kept small.
To balance these contradicting effects we like to apply high permeability material to keep inductance high while at the same time keeping the number of turns low; this is where ferrite core materials come in.
In figure 5 one will find the general lay-out of a basic transformer, with turns ratio t = n2 / n1, which is also the ratio of the voltages, or the reverse ratio of the currents. The impedance ratio follows from t2.
An example of such voltage transformer for wide-band HF frequencies is known as the 'Magnetic Longwire Balun', MLB, that according to the commercials is recommended to match the receiver to any long-wire antenna.
This MLB actually is a 3 : 1 voltage transformer, usually constructed as an autotransformer for LW, MW and SW frequencies.
Looking into a few examples I
found most transformers to consist of a ferrite toroide 14 x 9 x
The MLB is not constructed as a
balun (balance to unbalance transformer) but as an unun, and not very
'friendly' to real long-wire impedances. This may not be a problem since a
long-wire antenna is at least one wavelength long with means at least
Stories may be told about all fantastic performance claims around this component and also about precisely the opposite. Whether friend or foe, all agree that this is a receiving-only component, which makes us curious as to the performance in a transmitter environment.
As an example we will look at the performance of the transformer in a 50 to 450 Ohm system as may be found at a Windom-type of antenna at various HF bands. From the core dimensions we calculate core volume (0,63 cm3) and from this maximum internal dissipation at 1 Watt (see Materials and properties, Maximum core temperatures).
In table 7 we calculated primary impedance (Zp @ 10 turns) at various HF frequencies, maximum allowable voltage for 1 Watt loss in the core (Udiss., formula 19) and maximum voltage for linear performance (Uinduction, formula 5).
Table 7. MLB, maximum voltages at 50 Ohm side
We find the transformer already to exhibit high impedance at the lowest HF frequency. In chapter 2 we found this parallel impedance should be at least four times system impedance (200 Ohm in a 50 Ohm environment) which will make this component's lower cut-off frequency (200 / 1036) x 1,5 MHz.) = 290 kHz, which is somewhere in the LW broadcast band.
Third columns is showing that the transformer may be applied at up to 44 volt across, which allows this component to be applied at up to 38 Watt system power in a 50 Ohm system, or even at over 100 Watt PEP when only SSB type of modulation is employed. This ensures the MLB may be safely employed at a small transmitter to well over QRP levels, especially since maximum voltage for non-linear behavior is much higher at minimum 70 volt (last column). We should keep in mind though that the maximum voltage for internal dissipation is based on a component that is free to radiate. Some of the MLB's however have been encapsulated in (isolating) compound, lowering the internal dissipation.
Please note since the MLB is no balun we will have to add a good balun when applying this transformer at a Windom antenna as in our example.
The high impedance as in column two has been obtained by the high permeability type of ferrite together with the high number of turns (30 turns at the secondary side). At this small core, so many turn will be very close together and even overlap, making parasitic parallel capacity relatively high. Transformer behavior will therefore drop-off quickly at higher HF frequencies. Since this HF behavior is very much depending on the exact way these 30 turns are being applied, each device has to be assessed separately.
When designing wide-band transformers it often is more convenient to operate with parallel circuits. Therefore we may recalculate series values we were discussing up to now into parallel values:
μp'= μs' (1 + 1/Q2) en μp'' = μs'' (1 + Q2) (27)
From these formula's we may quickly appreciate that for Q > 3, parallel induction (μp') is roughly equal to series induction, while the parallel loss (resistor, μp'') quickly rises to high values. As an example we will calculate a simplified model of a 1 : 1 transformer and its effects on circuit parameters. The model may be found in figure 6, after applying formula 27 to the series values.
The transformer on the right hand side is considered to be 'perfect' in this model. Transformer inductance Lp and loss RFp are in parallel to the input with the load resistor Rb at the secondary side, to be re-calculated to the input side (with the perfect 1 : 1 transformer, Rb = R'b). This simplified model is allowed at lower HF frequencies, with high-permeability (ferrite) core material and not too many turns ( low parasitic capacitance).
Let's calculate this transformer when
constructed with two times 6 turns on a
Behavior at 1,5 MHz
In table 2 we will find for this material
that µ = 0, meaning no loss. Since 4C65 is a high frequency material, we may
use the factory value of
XLp = XL = j
w L = j w n ²
This reactance is in parallel tot the load resistance Rb (50 Ohm), when transformed to the left-hand side (same value, 1 : 1 transformer). Total input impedance:
ZT = j.XL . Rb / (j.XL + Rb) = 28,6 + j.24,7 (note: complex multiplication / division!)
This is different from system impedance without the transformer, when the 50 Ohm load was ensuring characteristic termination and so SWR = 1. We have to re-calculate SWR with the new termination value of ZT while being aware this to be a complex calculation instead of the simple and better known formula SWR = Z0 / R (or reverse).
SWR = ( |Z0 + ZT| + |Z0 - ZT| ) / ( |Z0+ ZT| - |Z0 - ZT|) = 2,32 (vertical bars express absolute values)
If this is not acceptable, we have to enhance the number of turns while keeping in mind that more turns also mean higher parasitic capacitance so earlier fall-off at the high frequency side. With the transformer as is (6 turns), SWR will be 1,5 at 3,5 MHz., which usually will be considered as the lower application limit.
Behavior at 30 MHz.
In table 2 we will find µ = 150 and µ = 45, which means Q = 3,33 (low) and we will have to re-calculate basic values. First we calculate the shape factor F using formula 8:
F = m0 . A / l = AL / mi ,
after which reactance and loss may be calculated according to formula 11 and 12:
XLs = j w L = j.w.n².m .F = j.2.p.30.106. 6².150.1,36.10-9 = j.1020 W
RFs = w.n².m .F = 2.p.30.106. 6². 45.1,36.10-9 = 305 W
Since these are series values, we recalculate to parallel with formula 27:
XLp = XLs (1 + 1/Q²) = j. 1380 (1 + 1/3,33²) = j.1110 W
RFp = RFs (1 + Q²) = 415 (1 + 3,33²) = 3700 W
With Rb = 50 Ohm in parallel, total input impedance is 49,3 Ohm with negligible inductance in parallel. This will make SWR = 1,05 which represents an almost ideal situation if not for the parasitic parallel capacitance, we will leave out for now.
We might have considered constructing this transformer on the same toroide size, but different ferrite material e.g. 4A11. At a frequency of 1,5 MHz. we would have found parallel values XLp = j. 425 W and RFp = 2250 W., (calculation as above, try for yourself). This will yield SWR=1,13, meaning this transformer is already much better at 1,5 MHz. than our earlier design on 4C65 material at 4 MHz.
At a frequency of 30 MHz. we find parallel values for 4A11 material XLp = j. 9350 W and RFp = 2430 W., making SWR = 1,02, which makes this transformer as good as the 4C65 design.
This example is showing that different ferrite materials will really make a difference when designing transformers. Depending on the particular application, other system parameters have to be taken into account as well. These basic calculation have been showing how to start the design and how to apply table 2.
Model of an induction transformer
In figure 6 we saw a first order model that may be applied with satisfactory results at low(er) frequencies. For a better model, also copper loss should be incorporated as a series resistance with the transformer. Since HF transformers usually employ a limited number of turns, this copper loss may usually be left out of the model. Next non-ideal factor is the loss of magnetic coupling. At higher frequencies and especially past the ferrimagnetic resonance frequency, permeability is going down allowing flux-lines to escape from the core center. This coupling loss may be measured at the desired frequency by determining input inductance while shortening the output. Coupling loss may be incorporated in the model as a series inductance, known as leakage inductance. The effect of this series inductance may be measures as a high-frequency roll-off.
Various schemes are going around to reduce HF leakage: tight winding and / or twisting secondary and primary windings before winding the transformer. All of these methods will indeed enhance inter-winding coupling but will also enhance parasitic capacitance across the windings which has the same high-frequency roll-off effect.
A better way is to spread the primary winding across the entire circumference of the toroide and placing the secondary winding in between the primary turns, like a screw within a screw. Best to start with the winding with the lowest number of turns. When the transformer is ready, windings are spread-out evenly at the inside of the toroide tot minimize parasitic capacitance. The effects of this winding technique will be already noticeable at 15 MHz. and more so at higher frequencies.
The better model should also contain a capacitance across both inductances. The effect of this parasitic capacitor is almost negligible at lower frequencies (< 10 MHz, at Z < 100 W), but has to be taken into account at higher frequencies as this usually is one of the important parameters for high-frequency roll-off. Capacitor values may be determined from parallel resonance of primary and secondary winding.
In figure 7, non-ideal effects as discussed have been incorporated in the transformer model.
Rb: Load impedance, transform to primary by division by n2
Cs: Transformed secondary winding parasitic capacity
Lp: Parallel inductance (from unloaded transformer measurement)
RFP: Total core loss
Ls: Leakage inductance
Rs: Generator output impedance
From this model it is obvious that a spread-sheet program should be applied when calculating transformer behavior over frequency. Please keep in mind this model is no different from LF transformer models as applied to microphone transformers, LF tube / transistor input- and output-transformers, modulation transformers etc.
A special type of transformer arises when primary turns and currents are equal to secondary turns and currents. Principle is modeled in figure 8.
In this induction transformer, currents i1 and i2 are equal and in opposite phase. With also the number of turns to be equal, the magnetic fields in the transformer core will cancel. This effect will be found at bifilarly wound transformers and also at transformers constructed around transmission-lines, either balanced or coaxial.
The current balancing effect is fully comparable to what is happening inside a transmission-line. This current transformer therefore is also known as a transmission-line transformer. Basic principles are the currents to be equal and in opposite phase and so the voltage of the generator at the input will also be found at the output of the transformer and across the load.
Voltage induction-transformer in general are lagging behind to current transformers as far as power transfer is concerned. Since a voltage transformer is always in parallel to the signal path, a (small) portion of power is dissipated inside the transformer. Furthermore, at un-equal turns ratio's, internal transformer fields do not cancel any more making this type of transformer prone to non-linear effects at high voltage and power load.
In current transformers, parasitic core currents may only originate from un-balancing effects, which we try to make as small as possible by design and / or by minimizing outside return currents by means of high common-mode impedance.
A more elaborate description will be found in the next chapter on Transmission-line transformers, introduction.
Bob J. van Donselaar,