# Toroid RF Transformer Calculation

Toroid RF transformer is often used for impedance matching in RF circuits. That is match the source and load impedance. In this tutorial we explain the process of making RF transformer for impedance matching with detailed calculation for constructing toroid RF transformer. This involves calculating the primary and secondary number of windings, calculating inductances at the primary or secondary, and choosing toroid core size.

To build the toroid RF transformer we need the number of turns for the primary and secondary and select a toroid core. For calculating the number of turns we need to know the source and load impedances and frequency range over which the circuit is operated.

The process of making RF transformer using toroid core is explained briefly. First we calculate the turn ratio using the knowledge of source and load impedance to be matched. Then we estimate the inductive reactance at the primary side(or secondary side) for given frequency and calculate the inductance for the primary winding. Once we know the primary winding inductance we next select toroid core based on frequency of operation and suitable size for winding the core. By selecting the toroid core we will know the inductance factor AL and together with the primary inductance knowledge we will know the number of turns for the primary winding. Then using the primary number of turns and the turn ratio we calculate the number of the secondary winding. Then the turns are wound on the toroid core to build the RF transformer

Consider the following circuit. In this the toroid transformer is connected with its primary winding on the signal source side and the secondary winding connected to the base of an RF amplifier transistor.

The number of turns of primary winding and the secondary winding are Np and Ns respectively. The impedance at the primary and secondary are Zp and Zs. The number of windings and the impedance is related by the following equation.

$\frac{N_p}{N_s} = \sqrt{\frac{Z_p}{Z_s}}$

This relationship is used for matching source and load impedance in RF circuits.

Let suppose that the source impedance is Zp= 50Ohm. Also suppose the impedance at the transistor base is 4Ohm. This impedance is then the secondary impedance Zs(Zs=4Ohm). Then using the above equation we have,

$$\frac{N_p}{N_s} = \sqrt{\frac{50Ohm}{4Ohm}}$$

or,  $$\frac{N_p}{N_s} = \sqrt{\frac{50Ohm}{4Ohm}}$$

or, $$\frac{N_p}{N_s} = 3.53$$

or, $$N = 3.53$$

where N is called turn ratio

The inductive reactance of an inductor is,

$$X_L = 2 \pi f L$$

When designing RF transformer a general rule is that the inductive reactance should be 4 times the impedance connected to that inductor. Here consider the primary winding coil. The primary winding coil is connected to 50Ohm source impedance. Hence its inductive reactance should be 4 times 50Ohms which is 200Ohm. Hence the inductive reactance of primary coil winding should be 200Ohm.

So, $$X_L = 200Ohm$$

or, $$2 \pi f L_p =200Ohm$$

that is, or, $$L_p = \frac{200Ohm}{2 \pi f }$$

The frequency f is lowest frequency of operation. If the frequency of operation of the circuit is 3MHz to 30MHz then f is 3MHz. This gives,

$$L_p = \frac{200Ohm}{2 \pi 30MHz }$$

that is $$L_p = 10.6\mu H$$

After we know the inductance needed for primary we can choose toroidal core matching our signal requirement. Once we have selected the toroidal core we will know the $$A_L$$ value and with this knowledge we can calculate the number of turns for the primary winding.

The following shows the iron powered core material mixture numbers and their properties.

For our frequency range of 3MHz to 30MHz, the material type 2 can be selected. Next we select the size of the powered iron toroid core based on the material mixture type 2.

The size 50(0.5" diameter) with material mixture type 2 is selected. Thus the toroid transformer will be of T-50-2 core. From the table above the $$A_L$$ value for this core is 49.

Next we calculate the number of turns for primary Np for the selected powered iron toroid core using the following formula.

$N_p = 100 \sqrt{\frac{L_{\mu H}}{A_L}}$

Substituting the values,

$N_p = 100 \sqrt{\frac{10.6 \mu H}{49}}$

we get, $$N_p=46.5 \approx 47$$

Then we can calculate the number of turns for the secondary winding using the turn ratio formula:

$$N=\frac{N_p}{N_s}$$

Here N=3.53 and Np=47, so  $$N_s=\frac{N_p}{N} = \frac{47}{3.53}=13.3 \approx 13$$

So we need 47 turns for primary winding and 13 turns for secondary winding on T-50-2 toroid core to make the RF transformation for impedance matching. This RF transformer then matches the 50Ohm source impedance with 4Ohm load impedance which is the base impedance.

So in this way you can make your own RF transformer using toroid for impedance matching. See also the toroid inductor online calculator which is helpful to build your own toroid inductor.