1. LUMPED ELEMENTS ECB 3211 – RF & Microwave Engineering Module - I SOURCE: RF & Microwave Handbook, CRC Press 1

2. Lumped Components Lumped components provide impedance matching, attenuation, filtering, DC bypassing, and DC blocking Surface mount techniques and ever- shrinking package sizes now allow solderable lumped components useful to 10 GHz.1 SOURCE: RF & Microwave Handbook, CRC Press 2

3. RESISTORS SOURCE: RF & Microwave Handbook, CRC Press 3

4. Resistors A film of resistive material deposited on a ceramic substrate with solderable terminations on the ends of the component Individual surface mount resistors are available in industry standard sizes from over 2512 to as small as 0201. The package size determines the intrinsic component parasitic to the first order, and in the case of resistors determines the allowable dissipation. For resistors the most important specifications are power dissipation and tolerance of value. SOURCE: RF & Microwave Handbook, CRC Press 4

5. Resistors Chip resistors have plated, wrap-around end contacts that overlap the resistive material deposited on the top surface of the ceramic carrier. Circuits built from film on alumina can have multiple thin or thick film resistors on one substrate. The same principles for determining resistance, heat dissipation limits, parasitic inductance, and parasitic capacitance apply to both chips and thin film circuits. Standard chip resistors come in 10% and 1% tolerances, with tighter tolerances available. SOURCE: RF & Microwave Handbook, CRC Press 5

6. Resistance The resistive material is deposited in a uniform thickness, t R, and has a finite conductivity, σ R. The material is almost always in a rectangle that allows the resistance to be calculated by the following equation. Resistor physical size determines the heat dissipation, parasitic inductance and capacitance, cost, packing density, and mounting difficulty. SOURCE: RF & Microwave Handbook, CRC Press 6

7. Surface Mount Resistor SOURCE: RF & Microwave Handbook, CRC Press 7

8. Heat Dissipation Heat dissipation is determined mostly by resistor area, although a large amount of heat can be conducted through the resistor terminations. SOURCE: RF & Microwave Handbook, CRC Press 8

9. Intrinsic Inductive Parasitics The resistor length and width determine its effective series inductance. This inductance can be computed from a transmission line model or as a ribbon inductor if the resistor is far enough above the ground plane. If the resistor width equals the transmission line width, then no parasitic inductance will be seen because the resistor appears to be part of the transmission line. The ribbon inductor equation is SOURCE: RF & Microwave Handbook, CRC Press 9

10. Intrinsic Capacitive Parasitics There are two types of capacitive parasitics. – There is the shunt distributed capacitance to the ground plane, C P. The film resistor essentially forms an RC transmission line and is often modeled as such. In this case, a first order approximation can be based on the parallel plate capacitance plus fringing of the resistor area above the ground plane. – An additional capacitance is the contact-to-contact capacitance, C S. This capacitance can be dominated by mounting parasitics such as microstrip gap capacitances. SOURCE: RF & Microwave Handbook, CRC Press 10

11. CAPACITORS SOURCE: RF & Microwave Handbook, CRC Press 11

12. Capacitors Multilayer chip capacitors are available in the same package styles as chip resistors. Parallel plate capacitors are available with typically lower maximum capacitance for a given size. The critical specification for these capacitors is the voltage rating. Secondary specifications include temperature stability, Q, tolerance, and equivalent series resistance (ESR). SOURCE: RF & Microwave Handbook, CRC Press 12

13. Capacitors Many different types of dielectric materials are available, such as NPO, X7R, and Z5U. Low dielectric constant materials, such as NPO, usually have low loss and either very small temperature sensitivity, or well-defined temperature variation for compensation. Higher dielectric constant materials, such as X7R and Z5U, vary more with temperature than NPO. Z5U will lose almost half its capacitance at very low and very high temperatures. Higher dielectric constant materials, such as X7R and Z5U, also have a reduction in capacitance as voltage is applied. SOURCE: RF & Microwave Handbook, CRC Press 13

14. Parallel Plate Capacitors Parallel plate capacitors, can use a thin dielectric layer mounted on a low resistance substrate such as silicon, or they can be a thick ceramic with plated terminations on top and bottom. These capacitors can be attached by soldering or bonding with gold wire. Some capacitors come with several pads, each pad typically twice the area of the next smaller, which allows tuning. These capacitors obey the parallel plate capacitance equation. SOURCE: RF & Microwave Handbook, CRC Press 14

15. Capacitors & Equivalent circuit SOURCE: RF & Microwave Handbook, CRC Press 15

16. Parallel Plate Capacitors Parasitic resistances, RS, for these capacitors are typically small and well controlled by the contact resistance and the substrate resistance. Parasitic conductances, GP, are due to dielectric loss. These capacitors have limited maximum values because of using a single plate pair. The voltage ratings are determined by the dielectric thickness, td, and the material type. Once the voltage rating and material are chosen, the capacitor area determines the maximum capacitance. The parasitic inductance of these capacitors, which determines their self-resonance frequency, is dominated by the wire connection to the top plate. In some cases these capacitors are mounted with tabs from the top and bottom plate. When this occurs, the parasitic inductance will be the length of the tab from the top plate to the transmission line, as well as the length of the capacitor acting as a coupled transmission line due to the end launch from the tab. SOURCE: RF & Microwave Handbook, CRC Press 16

17. Multilayer Capacitors Multilayer chip capacitors are a sandwich of many thin electrodes between dielectric layers. The end terminations connect to alternating electrodes. Multilayer capacitors have a more complicated structure than parallel plate capacitors. SOURCE: RF & Microwave Handbook, CRC Press 17

18. Equivalent circuit The series resistance of the capacitor, Rs, is determined by the parallel combination of all the plate resistance. The conductive loss, G p, is due to the dielectric loss. Often the series resistance of these capacitors dominates the loss due to the very thin plate electrodes. By using the package length inductance, the first series resonance of a capacitor can be estimated. In reality many resonances will be observed as the multilayer transmission line cycles through quarter- and half- wavelength resonances due to the parallel coupled line structure. SOURCE: RF & Microwave Handbook, CRC Press 18

19. Printed Capacitors Printed capacitors form very convenient and inexpensive small capacitance values because they are printed directly on the printed circuit board. (a)Gap Capacitors (b)Interdigital Capacitors SOURCE: RF & Microwave Handbook, CRC Press 19

20. Gap capacitors The capacitance values for a gap capacitor are very low, typically much less than 1 pF. Gap capacitors are best used for very weak coupling and signal sampling because they are not particularly high Q. Equation can also be used to estimate coupling between two circuit points to make sure a minimum of coupling is obtained. SOURCE: RF & Microwave Handbook, CRC Press 20

21. Interdigital capacitors Interdigital capacitors are a planar version of the multilayer capacitor. Medium Q ; Accurate; Typically less than 1 pF. These capacitors can also be tuned by cutting off fingers. Because interdigital capacitors have a distributed transmission line structure, they will show multiple resonances as frequency increases. The first resonance occurs when the structure is a quarter wavelength. The Q of this structure is limited by the current crowding at the thin edges of the fingers. SOURCE: RF & Microwave Handbook, CRC Press 21

22. INDUCTORS SOURCE: RF & Microwave Handbook, CRC Press 22

23. Inductors Inductors are typically printed on the PCB or surface mount chips. Important specifications for inductors are their Q, self-resonance frequency, and maximum current. Wire inductors have their maximum current determined by the ampacity of the wire or trace. Inductors made on ferrite or iron cores will saturate the core if too much current is applied. Just as with capacitors, using the largest inductance in a small area means dealing with the parasitics of a nonlinear core material. SOURCE: RF & Microwave Handbook, CRC Press 23

24. Surface Mount & Wound Chip Inductors Surface mount inductors come in the same sizes as chip resistors and capacitors, as well as in air-core “springs.” “Spring” inductors have the highest Q because they are wound from relatively heavy gauge wire, and they have the highest self-resonance because of their air core. Wound chip inductors, use a fine gauge wire wrapped on a ceramic or ferrite core. These inductors have a mediocre Q of 10 to 100 and a lowered self-resonance frequency because of the dielectric loading of the ceramic or ferrite core. These inductors are available from 1 nH to 1 mH in packages from 402 to 1812. Wound chip inductor SOURCE: RF & Microwave Handbook, CRC Press 24

25. Chip Inductors The chip inductors use a multilayer ceramic technology, although some planar spiral inductors are found in chip packages. These inductors typically have lower Q than wound inductors, but Qs can still reach 100. Multilayer chip inductors use 805 and smaller packages with a maximum inductance of 470 nH. The self-resonance frequency of these inductors is high because of the few turns involved, the dielectric loading of the sandwich makes the resonance lower than that of an equivalent “spring” or even a wound inductor. Multilayer chip inductors SOURCE: RF & Microwave Handbook, CRC Press 25

26. Inductors The inductance of the wound and “spring” inductors can be defined as, where, n is the number of turns, d is the coil diameter, and l is the coil length. The equivalent circuit is, SOURCE: RF & Microwave Handbook, CRC Press 26

27. Current Capability Chip inductors have limited current-carrying capability. The internal conductor size limits the allowable current. When the inductor core contains ferrite or iron, magnetic core saturation will limit the useful current capability of the inductor, causing the inductance to decrease well before conductor fusing takes place. SOURCE: RF & Microwave Handbook, CRC Press 27

28. Parasitic Resistance The inductor Q is determined by the frequency, inductance, and effective series resistance. The effective series resistance, Rs, comes from the conductor resistance and the core loss when a magnetic core is used. The conductor resistance is due to both DC and skin effect resistance as given by the following Equations. ρ R is the perimeter of the wire and δ is the skin depth, SOURCE: RF & Microwave Handbook, CRC Press 28

29. Parasitic Capacitance Wound inductors can be modeled as a helical transmission line. The inductance per unit length is the total solenoid inductance divided by the length of the inductor. The capacitance to ground can be modeled as a cylinder of diameter equal to the coil diameter. The first quarter wave resonance of this helical transmission line is the parallel resonance of the inductor, while the higher resonances follow from transmission line theory. When the inductor is tightly wound, or put on a high dielectric core, the interwinding capacitance increases and lowers the fundamental resonance frequency. SOURCE: RF & Microwave Handbook, CRC Press 29

30. Bond Wires and Vias The inductance of a length of wire is given by Equation This equation is a useful first order approximation, but rarely accurate because wires usually have other conductors nearby. Parallel conductors such as ground planes or other wires reduce the net inductance because of mutual inductance canceling some of the flux. Perpendicular conductors, such as a ground plane terminating a wire varies the inductance up to a factor of 2 as shown by the Biot-Savart law. SOURCE: RF & Microwave Handbook, CRC Press 30

31. Spiral Inductors Planar spiral inductors are even implemented in some low-value chip inductors. Low Q because the spiral blocks the magnetic flux; ground planes, which reduce the inductance tend to be close by; and the current crowds to the wire edges, which increases the resistance. With considerable effort Qs of 20 can be approached in planar spiral inductors. In some cases, simple formulas can produce reasonable approximations. SOURCE: RF & Microwave Handbook, CRC Press 31