Design of an Interdigitated Capacitor using Altair Feko
Lumped element planar capacitors play a major role in RF system design, especially at high frequencies as they offer miniaturization in comparison to microstrip based circuits. An interdigitated (interdigital) capacitor is a type of planar capacitor with a multi-finger periodic element printed or fabricated on a dielectric substrate and is commonly used as a passive lumped component. Interdigital capacitors are used for evaluating the near zone electrical properties such as permittivity, permeability and conductivity of materials. The effective capacitance of the interdigital capacitor depends on the physical dimensions of the fingers and the electrical properties of the substrate on which it is fabricated. An interesting application of the interdigital capacitor is that it can be used as a transducer for sensing by tracking the change in impedance due to target loading in the near zone of the capacitor. Typically, the area of the capacitor should be smaller in comparison with the wavelength of operation to be treated as a lumped element. Fig 1. Shows the schematic of an interdigitated capacitor.
Fig 1. Schematic of an example interdigitated capacitor.
An approximate expression for computing the interdigitated capacitor fabricated on a dielectric substrate is given by (1)
where,
For a finite substrate, the exterior and interior capacitances are computed using (2) & (3) and substituted in (1) to obtain the total effective capacitance.
where,
h – Height of the dielectric substrate.
For example, let us consider h = 0.25 mm, L = 10 mm, w = 0.25, and N = 21, the effective capacitance is calculated using (1), (2) & (3) is 9.09 pF.
You can simulate the interdigitated structure in Feko using the method of moments solver and applying edge port in between the fingers on a substrate with dielectric constant of 3 and loss tangent of 0 as shown in Fig 2.
Fig 2. Interdigitated capacitor design fed using an edge port.
The impedance of the port is plotted with respect to frequency as shown in Fig 3.
Fig 3. Reactance versus frequency plot for the interdigitated capacitor.
To validate the analytical expression used to choose the design variables, the reverse problem is solved by computing the capacitance from the imaginary part of impedance plotted in Fig 3 by using a simple expression as shown in (4).
From (4), the simulated capacitance is ~ 7.34 pF. The analytical value and the simulated value agrees very well establishing the validity of eq (1). Once the effective capacitance is validated, an appropriate inductor can be parallelly coupled to form an inductor-capacitor (LC) resonant tank and can be used as a transducer for sensing.