When the size of the component in the MIC is comparable to the wavelength of the microwave, the elements are called lumped elements.
The equivalent circuits of lumped elements are called lumped element models, and they are used in circuit analysis of MIC.
The microstrip transmission lines encounter discontinuities in width and length for the construction of microwave filters and the lumped element model of each of these discontinuities is different.
Wireless communication equips our lives with various convenient solutions for a wide range of human activities, including talking on the phone, sending an email—even exploring space. Radio Frequency (RF) and microwave circuits serve as amplifiers, mixers, filters, oscillators, and antennas in wireless communication systems. These circuits are crucial in facilitating wireless services.
With innovations in Microwave Integrated Circuits ❲MIC❳, passive elements such as resistors ❲R❳, capacitors ❲C❳, and inductors ❲L❳ and active elements in microwave circuits are fabricated as monolithic elements, or lumped elements. The size of the lumped elements are comparable to the wavelength of microwave incident on them. The lumped elements are constructed on the same substrate of the IC through the photolithography process. The lumped elements in the microwave circuit overcome the drawbacks of the distributed elements in terms of cost and geometric dimensions.
To study the electrical behavior of lumped elements, an accurate equivalent circuit that completely characterizes the components in the microwave circuit is required. The lumped element model—or lumped element equivalent circuit—accurately characterizes the losses, parasitic effects, and fringing fields associated with lumped elements fabricated on the wafer of the IC. The lumped element model fills the gap between the electromagnetic field analysis and classical circuit theory in microwave engineering.
Lumped Elements in MIC
In microwave circuits, when the size of the components are much smaller than the wavelength, such elements are defined as lumped elements. Due to the small dimension, the signals propagate without any delay in microwave circuits made of lumped elements. The incorporation of lumped elements is one of the cost-reduction techniques employed in S-band (2.0-4.0 GHz) microwave circuits. It is possible to fabricate a large number of lumped elements in a single substrate or wafer, and this leads to cost-effective MICs.
Merits of Lumped Elements
Apart from cost-effective fabrication, other merits of lumped elements include:
Size reduction- The size of lumped elements in the L (1.0-2.0 GHz) and S-band MIC is within length is the wavelength of the microwave.
Relatively high Q-factor- The Q-factor of the lower S-band microwave circuits are comparable with the distributed elements, and the values have gone beyond 50.
Dimensional dependency of losses- Improvements in component design and structure can result in the reduction of losses in lumped elements.
Physical support- Lumped elements can be constructed by changing the dimension of microstrip, or by depositing layers of dielectric or semiconductors on a substrate. This type of constructional structure in MIC offers incredible physical support and isolation between various lumped elements.
Lumped Element Model and Parameters
In addition to the general construction and advantages of lumped elements, let’s take a look into the constructional details of several lumped elements and begin with the most well behaved lumped element -- resistors:
Resistors- In MIC, lumped resistors are fabricated either by implanting semiconductor on the substrate surface, or by depositing a thin film of resistive materials such as NiCrTa or Cr on the wafer.
Diode- Beam lead technology in semiconductor device fabrication is used for constructing lumped element diodes. These diodes find immense application in Hybrid MICs ❲HMIC❳ and Monolithic MICs ❲MMIC❳ in the frequency bands such as S, X (8.0-12.0 GHz), Ku (20.0-40.0 GHz), and Ka (26.5-40.0 GHz). The parameters present in the lumped element model of the beam diode are R and C, and the values are dependent on the applied voltage across it. You can get the electrical specifications, mounting details, and outline drawings of beam lead diode from its datasheet.
Connectors- In MIC, connectors are the embodiment of electrically conductive paths between two microstrips, which play a significant role in ensuring signal integrity in circuits. Dielectric bridges, via holes (ground through contact) and air bridges or vias, are the types of connectors that are commonly in use. Airbridge connectors are the derived application of beam lead technology.
Capacitors-The Metal-Insulator-Metal ❲MIM❳ is the commonly used lumped element capacitor constructed by depositing an insulator layer between two metal plates. The capacitance value is dependent on the thickness of the insulator, length, and overlap of the metal plates.
Figure.1 (a) Implanted semiconductor resistance; (b)Beam-lead diode; (c)Air bridge via; (d) MIM capacitor
Figure. 1 illustrates all the lumped elements we have mentioned here. Now let's examine the lumped element model of the MIM capacitor:
Figure.2 Lumped element model of the MIM capacitor
Figure.2 presents the lumped equivalent circuit of the MIM capacitor. The lumped element model of the capacitor addresses the losses and parasitics in the capacitor as resistance R and series inductance L respectively. The capacitance due to the fringing electric field between the plates and ground is represented by capacitance C1and C2respectively. The MIM capacitance value C is much greater than C1and C2.
Effect of Microstrip Transmission Line Discontinuities on Lumped Element Models
Microstrips are the transmission lines in the microwave circuits, which are usually fabricated by etching gold (microstrip is shown in Figure.1a) or copper metal strips on non-conducting substrates. In MICs, gallium arsenide is used for fabricating microstrips. The lumped model of a unit length of microstrip is composed of four parameters: R, L, G, and C (as shown in Figure.3). The parameters R, L, G, and C give the per unit length combined series resistance, inductance, shunt conductance, and capacitance respectively.
Figure.3 Lumped element model of unit length of the microstrip
As the microstrip width is comparable to the wavelength of the microwave, any dimensional change in the strip causes variations in the electric and magnetic field associated with it. The changes in the width of the microstrip transmission line are generally termed as discontinuities.
The discontinuities such as steps, gaps, bends, open-ends, and junctions are deliberately incorporated in the microstrip to construct passive element based filters for use in MIC. By adjusting the length, width, and gap between the microstrips, the lumped element microwave filters can be tuned to any required frequency. Figure.4 shows the various microstrip discontinuities and the corresponding lumped element models. The capacitor and inductor values in the lumped element model are dependent on the physical dimensions of the microstrip.
Figure.4 Microstrip discontinuities (a) step ; (b) gap ; (c)bend ; (d) open ends
A powerful circuit analysis requires a consistent lumped element model representing the passive and active elements present in the MIC. This model should address the properties, as well as the imperfections, associated with the microwave circuit. RF simulation allows microwave design engineers to come up with improved circuit productivity and performance.