A Method to Characterize Resistive Sheets at Microwave Frequencies

Resistive sheets are thin conductive layers which are semi-transparent to microwave radiation. They can be used not only to implement microwave absorbers, but also other applications like electromagnetic shielding are possible. An accurate measurement of the sheet resistance is difficult, especially because the sheet resistance may be dependent on the frequency. The commonly used method is the four-point probe (4PP) measurement which measures the DC resistivity and is highly dependent on a safe and reproducible contact between the sample and the pins of the probe. Here, an accurate and robust method to measure the sheet resistance of samples at microwave frequencies is proposed. It involves measuring the specular reflection coefficient of the sheet for different angles of incidence and both polarizations in a frequency band. By extracting the angle, where the resonance occurs, the sheet resistance can be reliably calculated. The method does not rely on the exact knowledge of the permittivity of the substrate and is particularly accurate when the sheet resistance is in the range of the free space impedance (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$377\,\mathrm {\Omega }$</tex-math> </inline-formula>). As a verification, experimental results are shown for different samples made out of thin carbon nanotube (CNT) layers, whose sheet resistance is below and above the free space impedance, and compared with results from the 4PP measurement. Also, the special case of a sample with a sheet resistance near the free space impedance is shown. In this case, the resonance angle shifts to a very low angle of incidence and emerges for both polarizations.