What turns ratio does a transformer require to match a source impedance of 500 ohms to a load of 10 ohms?

To find the appropriate turns ratio for a transformer that matches a source impedance of 500 ohms to a load of 10 ohms, you need to understand the relationship between the turns ratio and impedance transformation. The formula to calculate the impedance transformation through a transformer is given by:

[ Z_{primary} = Z_{secondary} \times (N_{primary}/N_{secondary})^2 ]

Where:

• ( Z_{primary} ) is the impedance on the primary side (500 ohms),

• ( Z_{secondary} ) is the impedance on the secondary side (10 ohms),

• ( N_{primary}/N_{secondary} ) represents the turns ratio.

Rearranging the formula to find the turns ratio, we can express it as:

[ N_{primary}/N_{secondary} = \sqrt{Z_{primary}/Z_{secondary}} ]

Substituting in the given values:

[ N_{primary}/N_{secondary} = \sqrt{500/10} = \sqrt{50} \approx 7.1 ]

This indicates that the turns ratio required to match a 500-ohm source to a 10-ohm load is approximately 7.1 to 1