Lumped Components at Radio Frequency

Lumped (physical) resistors, capacitors, and inductors are not the “pure” components they are assumed to be at lower frequencies. Their true nature at higher frequencies has undesirable resistances, capacitances, and inductances, which must be taken into account during design, simulation, and layout of any wireless circuit.
At microwave frequencies the lengths of all component leads must be minimized in order to decrease losses due to lead inductance. Surface-mount devices (SMDs) are perfect for decreasing this lead length, and thus the series inductance, of any component. Even the board traces that connect the passive components, if the trace is longer than approximately 1/20th of a wavelength, must be converted to transmission line structures.
On printed circuit boards (PCBs), microstrip is ideal for this, since it maintains a constant 50-Ω impedance throughout its entire length without adding any undesired inductance or capacitance.
As the frequency of operation of any wireless circuit begins to increase, so does the requirement that the actual physical structure of all of the lumped components themselves be as small as possible, since the part’s effective frequency of operation increases as it shrinks in size. The smaller package decreases the typically detrimental distributed reactances, and raises the frequency of the series and parallel resonances.
Maintaining a high unloaded quality factor (Q) in each individual component is vital to minimize circuit losses. And  the unloaded Q of a capacitor decreases with frequency, while the unloaded Q of an inductor will actually increase with frequency, after which the Q will drop rapidly.

Resistors

A resistor with a value of over a few hundred ohms will begin to decrease in resistance as the frequency of operation is increased. This is caused by the distributed capacitance that is always effectively in parallel with the resistor, shunting the radio frequency (RF) signal around the component, and thus lowering its effective value of resistance. The distributed capacitance is especially problematic not only as the frequency increases, but also as the resistance value increases. Indeed, if the resistor is not of the high-frequency, thin-film type, a high-value resistor may lose much of its marked resistance to this capacitive effect at relatively low microwave frequencies. Nonetheless, even thin-film resistors will begin to deviate from their rated resistance values when operated above a few hundred megahertz.

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To reduce unwanted lead inductance and capacitance, a smaller package size with shorter leads is preferred.  This result in the birth of surface-mounted technologies (SMT).  SMT also enable miniaturization of the physical circuits.

Resistors

Capacitors

As shown in the figure below, a capacitor will have an undesired lead inductance that begins to adversely change the capacitor’s characteristics as the frequency is increased.

1Inductors

4Approximate model for a practical inductor:

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Surface-Mounted Package

Surface-mount technology (SMT) was developed in the 1960s and became widely used in the late 1980s. Much of the pioneering work in this technology was done at IBM.
Instead of leads, components were mechanically redesigned to have small metal tabs or end caps to be directly soldered to the surface of the PCB.
Components became much smaller.  Elimination of leads also reduces parasitic inductance and capacitance within the component, allowing operation at higher frequency.

6Who Determines the Package Dimension?

A package dimension and style is usually determined by the needs of the electronic industry. Usually a dominant component manufacturing company will introducea new package type based on current needs. If sufficient players adopt the package, it will become an accepted standard and a formal document is drafted to describe its characteristics. At present in North America the standards for SMT and other components is drafted by the JEDEC Solid State Technology Association  (JEDEC – Joint Electron Device Engineering Council ). JEDEC also works closely with Electronic Industries Association of Japan (EIAJ) to focus on similar package outlines from each organization into one world-wide standard package outline.

Passive Lumped Components for UHF Frequencies  (>300MHz) Application

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8Passive Lumped Components for Incorporation into PCB and other Substrate

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