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# All About the Characteristic Impedance of Waveguides

### Key Takeaways

• The ratio of voltage (v) to current (i) when the waveguide is in forward propagating mode is called characteristic impedance.

• When the load impedance matches the characteristic impedance, there is no reflected energy in the transmission line, as all the incident energy is absorbed by the load.

• In microstrip lines, the characteristic impedance is a function of thickness, the homogeneous dielectric constant of the dielectric substrate, stripline width, and distance between the line and ground. The characteristic impedance of a waveguide is an important parameter in the design and application of RF systems

Waveguides are used as transmission lines when the signals of interest belong to the high-frequency band. As the wavelength of the signal approaches the cross-sectional dimensions of the waveguide, employing waveguides as transmission lines becomes quite helpful.

The characteristic impedance of a waveguide is an important parameter in the design and application of RF systems. To achieve maximum power transfer, it is necessary for the source and load to match the characteristic impedance of the waveguide. We will take a look at the characteristic impedance of waveguides and transmission lines in this article.

## Characteristic Impedance of Waveguides

The ratio of voltage (v) to current (i) when the waveguide is in forward propagating mode is called the characteristic impedance, which is widely known for relating the voltage across the cross-section of the waveguide to the wall current along the axis and Poynting vector.

The characteristic impedance of a waveguide is not a unique value. The characteristic impedance equation is different for waveguides of different types.

For rectangular waveguides, the characteristic impedance is dependent on the dimensions. In a rectangular waveguide, the characteristic impedance is the product of a coefficient ratio of narrow and broad wall dimensions and the wave impedance.

In circular waveguides, the characteristic impedance is the product of a coefficient and its wave impedance.

In ridge waveguides, the characteristic impedance is calculated as the ratio of the square of gap voltage to the transmitted power in the waveguide at a frequency equal to infinity.

In symmetric ridge waveguides, the gap voltage is mathematically evaluated from the integral of the electric field across the ridge gap along the symmetric plane. The electric field is evaluated across the ridge gap along the line closest to the middle plane to calculate gap voltage in an asymmetric ridge waveguide.

## Characteristic Impedance of Transmission Lines

Transmission lines are special types of waveguides, and the characteristic impedance is a parameter of great importance in TEM two-wire transmission lines. Characteristic impedance is an inherent property of a transmission line, which is independent of the length of the line and the load connected to it.

When the load impedance matches with the characteristic impedance, there is no reflected energy in the transmission line, as all the incident energy is absorbed by the load. The transmission line transfers maximum power when the load impedance matches the characteristic impedance.

In transmission lines, the characteristic impedance can be defined as a function of the series impedance and parallel admittance of the line. For TEM modes of transmission lines, the characteristic impedance can be defined as the ratio of transverse electric field to transverse magnetic field.

Depending on the losses associated with the transmission line, the characteristic impedance varies. For a lossless transmission line, the characteristic impedance is a real number. The characteristic impedance assumes a complex value when the transmission line is lossy. In case the transmission line is not matched to its characteristic impedance, the distribution of power along the line becomes non-uniform due to standing waves and generates heat that is also dissipated non-uniformly.

Let’s look at the characteristic impedance of microstrip transmission lines.

## Characteristic Impedance of Microstrip Transmission Lines

The most commonly used transmission line in microwave and RF systems is the microstrip line due to its excellent layout flexibility and quasi-TEM nature. When designing a microstrip structure, important parameters include the attenuation constant, frequency dispersion, radiation, effective dielectric constant, discontinuity reactances, surface wave excitation, and characteristic impedance.

In microstrip lines, the characteristic impedance is a function of thickness, homogeneous dielectric constant of the dielectric substrate, stripline width, and distance between the line and ground. The characteristic equation of a wide microstrip transmission line can be approximated to: r is the dielectric constant of the medium, h is the height of the center of the microstrip line to the ground, and w is the width of the microstrip line, provided w>>h. While determining the characterisctic impedance of waveguides, the value is found to be within two times the free space impedance of 377 Ω.

The estimation and comparison of characteristic impedance of waveguides or transmission lines is necessary to design microwave and RF systems. The characteristic impedance is an important parameter determining the power handling capacity of a waveguide, both average and peak powers.

Cadence’s suite of PCB design and analysis tools can assist you in designing microwave and RF circuits. The tools from Cadence can help designers create, simulate, and analyze microstrip transmission line-based circuits to ensure excellent performance.

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