Electromagnetic spectrum bands - choose the right model for design and analysis of Circuits, RF (HF, VHF, UHF, microwave), Optics

by Sanjay Mishra

Different analysis and design models must be applied to different bands of the electromagnetic spectrum. The key consideration in deciding which model to apply is the here is the electrical length of the elements of device being made in relation to wavelength of active electromagnetic waves. Electrical length is the ratio of the component length to the wavelength of the signal.

In digital circuits, besides the frequency of operation it is the rise and fall time of the waveforms which is significant. The sharper the edge of the wave (or in other words the shorter the rise and fall time), the more the high frequency harmonics it has. These high frequency harmonics are the most significant cause of electromagnetic radiation noise. This is also the reason that older chips in a design cannot simply be replaced by newer, faster versions of the same chips that have smaller rise and fall times.

The size of the elements is much smaller than the wavelength (<20). The circuit theory model provides a simplification. A circuit is thought of as a flow of electrons through wires just as water flows through pipes. Electric voltage is thought of as being like water pressure, electric current is thought of as being like water flow rate, and electric resistance is compared to frictional resistance to water flow. Kirchoff's current and voltage laws apply. This "lumped circuit" model is extended to Alternating Current by considering the impedance of capacitors and inductors. Connecting wires are considered to be ideal wires with zero resistance and propagation delay. The length and shape of connecting wires is not considered at all.

The size of the circuit elements is very important. When small Surface Mount Devices (SMD) circuit elements are used wave techniques usually need to be used only above 1 GHz or so. When discrete components are used wave techniques need to be used at lower frequencies.

When the size of the elements is comparable to the wavelength the wave guide model applies. The wires of a typical electronic circuit act to guide the the electromagnetic waves. The energy is carried between wires and not inside wires. The movement of electrons serves only to propagate the electromagnetic waves. Maxwell's equations can be directly used and some simulators do use them. Most analysis of devices is done using "scattering" parameters or S parameters. Each device is modeled as a number of ports. Reflection and transmission coefficients for each port and the interactions between ports are calculated. A Vector Network Analyzer can be used to measure these parameters. S parameters can be used to model devices at any position in the electromagnetic spectrum.

When the size of the elements is much larger than the wavelength of the electromagnetic waves the geometrical optics or ray theory model simplification can be used. Electromagnetic waves can be approximated by rays or streams of particles. When studying diffraction or coherent phenomena (like lasers) wave theory must be used though.

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