QuarterWave Impedance Transformer in Impedance Matching Applications
Key Takeaways

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

Quarterwave 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 quarterwave 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

Quarterwave impedance transformers
In stub matching, shortcircuit transmission lines of tunable lengths are used for impedance matching. In a quarterwave 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 quarterwave impedance transformers a little further.
The QuarterWave Impedance Transformer
A quarterwave impedance transformer is an impedance transformer that is useful in matching the real load impedance to the transmission lines. A quarterwave impedance transformer is generally the transmission line of length equal to onequarter of the guided wavelength (to match the impedance). The characteristic impedance associated with quarterwave impedance transformers differs and it minimizes the energy reflections in the transmission lines connected to the load.
A SingleSection QuarterWave Impedance Transformer
The equation above gives us a singlesection quarterwave 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 quarterwave 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 narrowband impedance matching, a singlesection quarterwave impedance transformer can be used. The quarterwave impedance transformer can be employed in multisection designs to provide broader bandwidth. Optimum matching characteristics are achieved in the desired frequency band using multisection quarterwave transformers.
How to Use a QuarterWave Impedance Transformer for Impedance Matching
A quarterwave 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:

Impedance matching between a resistive load and transmission lines.

Impedance matching between two resistive loads.

Impedance matching between two transmission lines of unequal characteristic impedances.
The Disadvantages of Impedance Matching With a QuarterWave Impedance Transformer
One disadvantage of the quarterwave impedance transformer is that impedance matching is only possible if the load impedance is real. For impedance matching using a quarterwave 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 quarterwave impedance. However, this approach affects the frequency dependence of the load and reduces the bandwidth of the match.
Overall, using quarterwave 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 quarterwave impedance transformers.
Subscribe to our newsletter for the latest updates. If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.