Enter the load impedance and the input impedance into the calculator to determine the characteristic impedance of the quarter wave transformer.

## Quarter Wave Transformer Formula

The following formula is used to calculate the characteristic impedance of a Quarter Wave Transformer.

Z0 = SQRT ( ZL * Zin)

• Where Z0 is the characteristic impedance (ohms)
• ZL is the load impedance (ohms)
• Zin is the input impedance

To calculate the quarter wave transformer impedance, multiply the load impedance by the input impedance, then take the square root of the result.

## What is a Quarter Wave Transformer?

Definition:

A quarter wave transformer is a device designed to match the impedances of two transmission lines with different impedances.

## How to Calculate a Quarter Wave Transformer?

Example Problem:

The following example outlines how to calculate a Quarter Wave Transformer impedance.

First, determine the load impedance. For this example, the load impedance is measured to be 10 ohms.

Next, determine the input impedance. In this case, the input impedance if found to be 20 ohms.

Finally, calculate the characteristic impedance using the formula above:

Z0 = SQRT ( ZL * Zin)

Z0 = SQRT ( 20 * 10)

Z0 = 14.142 ohms