Transformer Design - Impedance Matching

The Turns Ratio of a Transformer calculator computes a transformer turns ratio using the source and load resistances.

INSTRUCTIONS: Choose units and enter the following:

• (SR) This is the source resistance
• (LR) This is the load resistance

Turns Ratio (TR):  The calculator returns the turns ratio as a real number.  However this can be automatically converted to percentage or dB via the pull-down menu.

Related Calculators

• Ohms Law Calculator
• Power (P) = I • V
• Power (P) = R • I²
• Power (P) = V² / R
• Volts (V) = I • R 
• Volts (V) = P / I
• Volts(V) = √(P • R)  
• Resistance (R) = V²/P
• Resistance (R) = P / I² 
• Resistance (R) =  V / I 
• Current (I) = V / R
• Current (I) = P / V 
• Current (I) = √(P/R)

The Math / Science

The formula for the transformer turns ratio is:

    `TR = sqrt( (SR)/(LR) )`

where:

• TR is the turns ratio of a transformer
• SR is the source resistance
• LR is the load resistance

Transformers are sometimes used to match the impedances of circuits. A transformer converts alternating current at one voltage to the same waveform at another voltage. The power input to the transformer and output from the transformer is the same (except for conversion losses). The side with the lower voltage is at low impedance (because this has the lower number of turns), and the side with the higher voltage is at a higher impedance (as it has more turns in its coil).

One example of this method involves a television balun transformer. This transformer converts a balanced signal from the antenna (via 300-ohm twin-lead) into an unbalanced signal (75-ohm coaxial cable such as RG-6). To match the impedances of both devices, both cables must be connected to a matching transformer with a turns ratio of 2 (such as a 2:1 transformer). In this example, the 75-ohm cable is connected to the transformer side with fewer turns; the 300-ohm line is connected to the transformer side with more turns. 

References

This description was obtained from wikipedia.