The physical dimensions table is important since we must know how big the toroid is to allow sufficient space in our project. The cross sectional area and mean length (magnetic path) are included so that flux density and magnetising force calculations can be made. Iron powder toroids use a type number which begins with "T" followed by a figure which denotes the outside diameter in hundredths of an inch and a second figure denoting the type of material.
Another table lists the AL values for all core sizes and material types, and these values remain substantially constant for each iron powder material up to VHF frequencies. The different materials have different values of permeability (µ), which also determines the useful range of frequencies for each type of material. In addition, iron powder cores are colour coded for easy recognition. In general, the smaller cores are used at the high end of the specified useful frequency range and the larger ones at the low end, so that a better Q factor is obtained. Typical unloaded Q factors of 100 - 200 are achieved.
A table lists the maximum turns vs wiregauge for each core size using single layer windings. This saves a lot of cut and try so that we can make a good first approximation for our winding.
Suppose we wish to wind a toroid coil for use in a receiver front-end tuned to 7.0MHz. Since there is no rf power involved we do not have to worry about saturation of the core and can choose almost any size core. Without going overboard, it is best to choose on the larger side so that we can achieve a better Q. If we want to tune this coil with a 100pF capacitor we will require an inductance of approximately 5uH. With a frequency of 7MHz we have a choice of 2 or 6 material, but let us decide on a T-50-2 as our core. The AL value of this core is given as 4.9 and so we can calculate the required turns to produce 5uH by using the formula listed earlier. This works out to 31.9 which we will round up to 32 since we cannot have fractional turns on a toroid. (A wire passing straight through the core is defined as 1 turn). Next we look at the table showing turns vs core size for different wire gauges and see that we can fit 39 turns of 24g enamelled wire on a T-50-2 core. For any toroid winding it is not good practice to fill the circumference with the winding since the distributed winding capacitance causes a "self resonance" in the winding which lowers the effective Q. A correctly designed winding should cover about 300 degrees of circumference but not more then 330. Slight adjustment to the inductance can then be made by compressing or spreading the turns to either increase or decrease the winding inductance. Our toroidal inductor should have an unloaded Q of about 200, which is quite a respectable figure for this application. The finished winding can be secured with some polystyrene cement (Q-dope). If a coupling link is required on the toroid, it should be put on at the cold (earthy) end of the winding, and in this case, could consist of 2 or 3 turns. It is important to know how to measure the resonance of a tuned circuit containing a toroidal inductor with a "dipper". With the lack of an appreciable external field we are unable to inductively couple the dipper coil to the toroidal coil directly, so we must use a link to couple between the toroid and dipper coil. Use the minimum number of link turns (at the cold end) which gives a noticeable dip.
Three data tables list the dimensions, AL values and wire table for ferrite toroids as for iron powder toroids.
Unlike iron powder material, the permeability of ferites changes with frequency and therefore the listed AL values for ferrite cannot be used directly for calculating inductance. Excel programs incorporating all the necessary parameters are provided for calculations.
One important table lists the ferrite material type and shows the useful range of frequencies for resonant circuits (narrow band) and wideband circuits. This table indicates the low loss frequency limits for each type of ferrite, and you can see that for some frequencies there is more than one type available. Notice that the lower permeability materials operate with low loss at the higher frequencies. This initial permeability (µi) is the permeability measured at about 10kHz.
Suppose that we want to design a wideband transformer for use between 3.5MHz and 30MHz and it has to match a 200 ohm source to a 50 ohm load. Since this is an RF application we must use the program FT_calc_1.xls, located under Program on the homepage. A common Rule of Thumb states that the winding should have an inductive reactance of not less than (4 x load) i.e.800 ohms at 3.5MHz. Calculating the required inductance to get 800 ohms at 3.5MHz gives a result of 37uH. Similarly the secondary winding would need an inductive reactance of 200 ohms which works out to be 9.2uH. Now let's work out the turns required for a ferrite core of suitable material for the frequency range. Assuming this a low power application (e.g. receiver or very low power interstage transformer in a transmitter) we will use an FT-50-43, which is listed as suitable for 1 - 50MHz.
Opening program FT_calc_1.xls we first have to place the physical data for the FT-50-43 under the Manufacturers Data in the Program sheet. This data is listed in the MyData or Data worksheet and can be copied into the Program sheet. The #43 ferrite data is located in the Data sheet and can be copied and pasted if necessary into the Program sheet. We now have all the manufacturers data inserted into the Program sheet, and need to insert our particular User Data. This application is for a low level transformer so we will enter 1 for Power, 200 for Load impedance and 1 for Stack. The result shows Winding voltage = 14.1. For a temperature rise of 30C we see Pmax is 0.7W.
We now come to Winding Calculations which will provide a lot of data. In Table 3.1 we can enter values for Pcore and Turns for each listed frequency. On the line for 4MHz we will enter 0.7 under Pcore and intially 10 under Turns. This produces an XL value of 621, which is less than our required 800 ohms. By increasing Turns to 12 the XL value increases to 895. The value at 3.5MHz will still be near enough to 800 ohms. It is interesting to see that at 30MHz XL is 1342 -- well above 800 ohms, and the values for L are close to our initial calulations. Since this transformer has a 2:1 turns ratio the windings are made up of 12 turns and 6 turns and would best be made as a trifilar winding of 3 x 6 turns.
If we were designing a current (Guanella) balun for use with a coax feeder, the design should also be checked with program Balun_cmr_1.xls located under Program on the homepage.07/01/11