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Which transformer turns ratio is required to match a 600-ohm antenna feed point impedance to a 50-ohm coaxial cable?

  1. 2 to 1

  2. 3 to 1

  3. 3.5 to 1

  4. 4 to 1

The correct answer is: 3.5 to 1

To match a 600-ohm antenna feed point impedance to a 50-ohm coaxial cable, you need to use the transformer turns ratio formula, which is derived from the impedance transformation in a transformer. The formula relating the impedance on either side of the transformer to the turns ratio is: Z1/Z2 = (N1/N2)² Here, Z1 is the higher impedance (600 ohms), Z2 is the lower impedance (50 ohms), and N1/N2 is the turns ratio. Rearranging the formula gives: N1/N2 = √(Z1/Z2) Substituting in the values: N1/N2 = √(600/50) = √12 = approximately 3.46. This calculation indicates that to match a 600-ohm impedance to a 50-ohm cable, a transformer with a turns ratio of about 3.5 to 1 is required. This means that for every 3.5 turns of wire on the primary side (the side connected to the antenna), there should be 1 turn on the secondary side (the side connected to the coaxial cable), resulting in an effective impedance transformation that properly matches the two systems. The