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RF Electronics Chapter 3: Transformers and Hybrids Page 53 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. The inductance and impedance is proportional to the square of the number of turns. Thus, for the required 50 transformer impedance, we need 11 x (50/12.65) = 21.8 turns. The number if turns needs to be an integer. The 22 turn winding one will thus have a leakage inductance of 256 nH and a magnetising inductance of 256 H. The number of turns for 1 Ω, N1 =11 x (1/12.65) = 3.093 is a useful parameter that can be used for calculating the number of turns required for different impedances. For an impedance Z, the number of turns required is Nz = N1 Z. The ratio of the open circuit to the short circuit impedance is 1000:1. The ratio of the upper and lower cut off frequency is thus also 1000:1, with the centre frequency being at the geometric mean of the upper and lower cut off frequencies. The upper cut off frequency is thus 1MHz*(1000) = 32 MHz. The lower cut off is 1MHz/(1000) = 32 KHz. The measured performance normally agrees closely with the calculated one. The actual upper corner frequency is often a little lower than the calculated one, since the losses in the ferrite increase non-linearly with frequency and are thus proportionally higher at the centre frequency, where the measurements of the leakage and magnetising inductance are made. RF transformers using bifilar and trifilar windings operate well at frequencies up to several GHz. Bifilar and Trifilar Windings For a bifilar winding, two wires are twisted together to form a primary and secondary winding of a transformer, with close capacitive coupling between the windings, which result in a wide frequency response. Bifilar windings are used for inverting transformers. Trifilar windings use three wires twisted together as shown in figures 3.4 and 3.5. Trifilar windings are used for Baluns (Balanced-Unbalanced transformers) [3] and for transformers with a 4:1 impedance transformation ratio, as shown in figure 3.4. For most TV antennae, the output from the antenna is a balanced signal, on two active wires carrying signals of opposite polarity. For low loss transmission without interference, a coaxial cable is normally used to transmit this signal between the antenna and the TV set. A Balun is used to convert the balanced signals from the antenna to the match the unbalanced signal for the coaxial cable. Figure 3.4. Trifilar winding diagram. If port 2F-3S is earthed in figure 3.4, then the transformer is a balanced to unbalanced transformer, called Balun. For a 75 input impedance, a 300 output-impedance is obtained. Such a Balun is often used in TV antenna systems. RF Electronics: Design and Simulation 53 www.cadence.com/go/awr

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