# The Application of Quarter-Wave Microstrip Lines in RF and Microwave Circuits

### Key Takeaways

• Microstrip lines are commonly used transmission lines in RF and microwave circuits due to their quasi-TEM mode of propagation and flexibility.

• Microstrip lines transfer power from one point to another, divide or combine power signals, and generate phase shifts.

• Half-wave and quarter-wave microstrip lines are used to design lumped elements.

Microstrip lines are a type of transmission line commonly used in RF and microwave circuits due to their quasi-TEM mode of propagation and flexibility. Microstrip lines' primary functions are transferring power from one point to another, dividing or combining power signals, and generating phase shifts. The size of the microstrip section is related to the guide wavelength, and depending on the length, transmission lines are classified into quarter-wave microstrip lines and half-wave microstrip lines. Half-wave and quarter-wave microstrip lines are used to design lumped elements and are a critical part of RF and microwave components such as filters, resonators, and couplers.

Let’s learn more about quarter-wave microstrip lines and some of their applications.

## Quarter-Wave Microstrip Lines

There are several lumped and quasi-lumped element designs based on quarter-wave microstrip lines. Quarter-wave microstrip lines are characterized by parameters such as:

The guided wavelength of a microstrip line can be given by equation 1, where λ0 is the free space wavelength at operation frequency and εre is the effective dielectric constant:

The associated propagation constant (β) and phase velocity (vp) can be given by equations 2 and 3, respectively, where c is the velocity of light in the free space.

The electrical length (θ) for a given physical length l of the microstrip is shown in equation 4:

Microstrip lines are classified into half-wave microstrip lines and quarter-wave microstrip lines based on the electrical length of the transmission line. When the length of the microstrip line is equal to a quarter of the guided wavelength,  l=ƛ/4, θ value is 𝜋/2 , equals a quarter-wave microstrip line.

## Quarter-Wave Microstrip Directional Couplers

RF and microwave circuits use coupled-microstrip directional couplers since they are easily incorporated into microwave integrated circuits (MICs). The difference in odd and even mode wavelengths causes poor directivity in directional couplers. Directivity will improve using a number of different couplers, including:

• Wiggly-line couplers
• Slotting-line couplers
• Anisotropic substrate couplers
• Dielectric overlay couplers
• Couplers with phase-compensation capacitors
• Pseudo-suspended-substrate couplers
• Couplers with phase-compensation matching

Broadband phase-velocity compensation is achieved in wiggling and slotting line couplers by modifying the pattern of the coupled line. The phase velocity compensation approach is introduced into quarter-wave microstrip couplers. This coupler uses a coupled microstrip with periodically floating conductors loading on its inner edges. The coupler structure possesses a planar structure similar to wiggly line couplers. Its coupling is tighter than slotting line couplers and has improved directivity compared to wiggly and slotting type couplers. This quarter-wave microstrip directional coupler provides high directivity over a wide bandwidth operation.

## Quarter-Wave Microstrip Based Stepped Impedance Resonator Filters

Modern wireless communication systems employ high-performance bandpass filters because of their compactness, selectivity, and stopband frequency range. Stepped impedance resonator filters are used due to their reduced filter size and ability to control spurious modes.

In stepped impedance resonator filters, the resonator's length and frequency depend on the impedance ratio. The impedance ratio is dependent on the dimensions of the two sections of the transmission lines in the stepped impedance resonator. For a low impedance ratio, the two sections of low and high impedance transmission lines in the stepped impedance resonator filter need to be thin and wide, respectively, increasing the characteristic impedance difference. This limits the use of ƛ/4 microstrip stepped-impedance resonators in low-frequency filter applications.

## Reducing the Characteristic Impedance of Microstrip Lines

There is a way of reducing the characteristic impedance of microstrip lines so that miniaturized ƛ/4 microstrip line-based stepped impedance resonator filters can be realized.

Inserting signal and ground strips in microstrip lines lowers the characteristic impedance, reducing the impedance ratio of quarter-wave microstrip-based stepped impedance resonator filters significantly. Along with the compact size and wide stopband responses, microstrip lines offer high selectivity due to cross-coupling microstrips.

Lumped elements are realized in RF and microwave circuits using quarter-wave microstrip lines. Modern communication circuits use quarter-wave microstrip lines in couplers, filters, stubs, and impedance matching transformers. Cadence’s software supports the design and analysis of lumped elements based on microstrip transmission lines.

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# About the Author

Solving electromagnetic, electronics, thermal, and electromechanical simulation challenges to ensure your system works under wide-ranging operating conditions