# Quarter-Wave Impedance Transformer in Impedance Matching Applications

### Key Takeaways

• In a quarter-wave impedance transformer, a quarter wavelength transmission line is used to change the impedance of the load to another value so that impedance is matched.

• Quarter-wave impedance transformers are designed for a particular frequency and the length of the transformer is equal to λ0/4 only at this designed frequency.

• The disadvantage of a quarter-wave impedance transformer is that impedance matching is only possible if the load impedance is real. Impedance matching techniques can be used in transmission lines for maximum power transfer and zero reflections

In RF and microwave circuits, the expectation is that transmission lines transfer maximum power to the load. To ensure maximum power transfer and zero reflections, impedance matching techniques can be used in transmission lines.

Impedance matching can be accomplished with matching circuits, including:

• Single stubs

• Double stubs

• Quarter-wave impedance transformers

In stub matching, short-circuit transmission lines of tunable lengths are used for impedance matching. In a quarter-wave impedance transformer, a quarter wavelength transmission line is used to change the impedance of the load to another value so that impedance is matched.

Let’s explore quarter-wave impedance transformers a little further.

## The Quarter-Wave Impedance Transformer

A quarter-wave impedance transformer is an impedance transformer that is useful in matching the real load impedance to the transmission lines. A quarter-wave impedance transformer is generally the transmission line of length equal to one-quarter of the guided wavelength (to match the impedance). The characteristic impedance associated with quarter-wave impedance transformers differs and it minimizes the energy reflections in the transmission lines connected to the load.

### A Single-Section Quarter-Wave Impedance Transformer The equation above gives us a single-section quarter-wave impedance transformer’s characteristic impedance of the matching section. This transformer is designed for a particular frequency and the length of the transformer is equal to λ0/4 only at this designed frequency. At other frequencies, the length is different and impedance matching is impossible.

The input impedance of the combination of quarter-wave impedance transformer and load can be given by the following equation: The reflection coefficient can be obtained in the equation below: The magnitude of the reflection coefficient is given by the equation below. The reflection coefficient is zero only at the desired frequency, where θ=𝜋/2. For narrow-band impedance matching, a single-section quarter-wave impedance transformer can be used. The quarter-wave impedance transformer can be employed in multisection designs to provide broader bandwidth. Optimum matching characteristics are achieved in the desired frequency band using multi-section quarter-wave transformers.

## How to Use a Quarter-Wave Impedance Transformer for Impedance Matching

A quarter-wave impedance transformer is used for impedance matching in circuits where the load impedance is real. It is particularly suitable for impedance matching in the following cases:

1. Impedance matching between a resistive load and transmission lines.

2. Impedance matching between two resistive loads.

3. Impedance matching between two transmission lines of unequal characteristic impedances.

## The Disadvantages of Impedance Matching With a Quarter-Wave Impedance Transformer

One disadvantage of the quarter-wave impedance transformer is that impedance matching is only possible if the load impedance is real. For impedance matching using a quarter-wave impedance transformer, the complex load impedance needs to be converted to real load impedance using shunt reactive elements or an appropriate length of transmission line between load and quarter-wave impedance. However, this approach affects the frequency dependence of the load and reduces the bandwidth of the match.

Overall, using quarter-wave impedance transformers offers more advantages than disadvantages. Engineers can benefit from understanding these transformers and how best to apply them in their designs. If you need support in the design process, Cadence’s software can help with impedance matching techniques using quarter-wave impedance transformers.