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Understanding Leakage Current Losses in Transmission Lines

Key Takeaways

  • When transmission lines carry current, there can be leakage current flowing between them through the dielectric substrate. 

  • The loss tangent, also called the dissipation factor, is denoted by tan 𝛿. It gives the rate at which RF energy is carried by the electromagnetic field that travels through the dielectric.

  • A good dielectric substrate possesses a low-loss tangent. The lower the loss tangent value, the lesser the leakage current through the dielectric substrate.

Transmission lines in RF circuits

In RF circuits, conducting paths are formed by microstrip lines, striplines, coplanar waveguides, or coaxial cables

For some time now, researchers that focus on materials have been trying to come up with a perfect dielectric—an insulating material with zero conductivity. If they could, in fact, invent such a material, it would be a major breakthrough in the field of RF communications. 

In RF circuits, communication is realized using transmission lines. These lines are subjected to leakage current between the two lines through dielectric materials. One reason for signal attenuation in RF circuits is leakage current losses in transmission lines.

Leakage Current Losses in Transmission Lines

The parallel resistor symbolizes the conductivity (G) property of the dielectric, which is the reciprocal of resistance

Leakage current losses in transmission lines can be minimized when a nearly perfect dielectric is used. However, the application of silicon has made the share of leakage current losses comparatively higher due to the poor insulating properties of silicon. In an effort to move towards cost-effective circuit design, the engineering community has welcomed the use of CMOS-grade silicon and semi-insulator material GaAs in RF circuits. Both of these materials are used as a foundation or substrate, as they allow for the downsizing of passive elements and make miniaturization of the circuit possible. 

In RF circuits, conducting paths are formed by microstrip lines, striplines, coplanar waveguides, or coaxial cables. When these transmission lines carry current, there is leakage current flowing between them through the dielectric substrate. The dielectric between the transmission lines, in most practical cases, is an imperfect insulator. This non-ideal dielectric acts as a resistor and permits the flow of current. The resistor symbolizes the conductivity (G) property of the dielectric, which is the reciprocal of resistance. The dielectric substrate stray conductivity is modeled as parallel resistors connected between transmission lines, as shown in the figure above. 

The Loss Tangent of Dielectric Substrate

We have seen the stray conductance of a substrate leading to leakage current losses in RF circuits. Apart from the polarization and relaxation phenomenon in a substrate, the loss tangent of a dielectric substrate is responsible for producing the stray conductance. 

At low-frequency applications, the dielectric constant is the property that needs to be considered for the substrate material. As the frequency of operation increases, the loss tangent of the material is a key property. A good dielectric substrate possesses a low-loss tangent. The loss tangent and frequency influences the substrate material, and RF energy is lost due to substrate oscillations or conductance of the material. 

The loss tangent, also called a dissipation factor, is denoted by tan 𝛿. It gives the rate at which the RF energy is carried by the electromagnetic field that travels through the dielectric, where  Ɛi and Ɛr are the imaginary and real parts of the dielectric constant, respectively. The lower the loss tangent value, the lower the stray conductance, which decreases the leakage current through the substrate.

 tan q = Ɛi/Ɛr

When working on high-frequency RF circuits itched on silicon substrate, there can be a considerable amount of leakage current losses in transmission lines. Incorporating the loss tangent values of the dielectric substrate to the S-parameters and impedance parameters is helpful when modeling these transmission lines. Cadence’s software helps model transmission lines with loss tangent data.

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