Using Lumped Element Modeling with Equivalent Circuits to Reduce Simulation Time

Key Takeaways

• The lumped element models of RF and microwave components, such as monolithic chips, substrate-integrated components, or RF MEMS, are useful in simulating their electrical characteristics. 

• Lumped element models consume less simulation time and provide accurate results regarding electrical and thermal performance and loss. Lumped element model-based simulation is faster than full-wave electromagnetic simulation. 

• The values of an equivalent circuit element can be extracted from S-parameter data by using genetic algorithms or artificial neural networks. 

Lumped element modeling with equivalent circuits is useful for circuit design and simulation

In RF and microwave engineering, an extensive range of monolithic, substrate-integrated devices or MEMS are utilized. It is important for circuit design and simulation to extract lumped element modeling with equivalent circuits for these miniaturized RF components. The electric performance, thermal behavior, stresses, and losses in micro RF devices can be accurately analyzed with lumped element equivalent circuit models.

Lumped Element Modeling With Equivalent Circuits

As part of miniaturization in RF and microwave circuits, monolithic or substrate-integrated devices or microelectromechanical structures are used. These devices fit in a tiny footprint area and help make the circuit compact. They are lightweight, consume minimal energy, are low cost, and easily integrate with other circuit elements. 

Simulating Electrical Characteristics

Usually, to accurately determine the electrical characteristics of these devices, full-wave electromagnetic simulation is used. When the simulation model becomes complex, full-wave simulation takes longer to provide results. The complexity of RF circuits can also arise out of memory problems. 

The lumped element models of RF and microwave components—such as monolithic chips, substrate-integrated components, or RF MEMS—are helpful in simulating their electrical characteristics. The lumped element modeling of miniaturized RF and microwave components provides an equivalent circuit consisting of lumped elements—mainly resistance, inductance, capacitance, impedance, and admittance. Lumped element models consume less simulation time and give accurate results about electrical and thermal performances and losses. Lumped element model-based simulation is faster than full-wave electromagnetic simulation. 

The Merits Of Lumped Element Equivalent Circuit Models

A lumped element model converts the RF MEMS switch or substrate-integrated cavity resonator into two-port or multiport networks composed of resistors, inductors, and capacitors. The frequency dependence on the operation of the RF device can be studied from the lumped element equivalent circuit. The interconnects in the circuit can be modeled using lumped element equivalent circuits, which take into consideration the skin effect and proximity effect. The dielectric substrate losses, conductor losses, radiation losses, and substrate eddy currents should be taken into account in lumped element equivalent circuit models. 

The lumped element model of an RF circuit can incorporate the presence of saturating magnetic materials and parasitic effects in the equivalent circuit. The ferromagnetic resonance effects, coupling between the transmission lines and PCB laminates, or silicon substrate should be considered in lumped element modeling. In substrate integrated inductors and capacitors, the lumped lament equivalent circuit model can describe the effect of the quality factor. In tunable devices such as resonators and filters, the magnetic and electric tunability and substrate characteristics can be easily predicted. Lumped element modeling with equivalent circuits is advantageous in predicting band characteristics of RF devices, especially the center frequency and the frequency bandwidth.

Lumped Element Circuit Values

The geometrical dimensions of RF devices are less than the wavelength of the signal passing through them. Such miniaturized RF devices are modeled as lumped lament equivalent circuits. The values of lumped elements are dependent on the dimensions of the RF device. Some of the lumped elements in the equivalent circuit are exclusively for including effects such as coupling effects, fringing effects, or parasitic effects. 

An Example Using the Lumped Element Model of Silicon Substrate Inductors

For example, in the lumped element model of silicon substrate inductor, resistances are included to represent the finite conductivity of the metals and losses associated with the electrical coupling with the silicon substrate. The geometry of the inductor influences the resistance, symbolizing the finite conductivity of the metal. Several capacitances in a lumped element equivalent circuit represent fringing field capacitances, capacitance due to the oxide layers in the device, or capacitive coupling with the silicon substrate. 

Lumped element values are mostly kept positive, which ensures the passivity of the model. The values of an equivalent circuit element can be extracted from S-parameter data or by using genetic algorithms or artificial neural networks. The arrangements of the lumped circuit elements form different types of equivalent circuit models—such as the ladder model, pi-model, or T-model. 

Reduce Computational Time of RF Device Simulations With Lumped Element Modeling

Lumped element modeling using equivalent circuits is beneficial in reducing the computational time of RF device simulations. Cadence’s software offers simulation tools for analyzing the characteristics, performance, and efficiency of RF and microwave components.  

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