Transcript Lumped Elements

LUMPED ELEMENTS
ECB 3211 – RF & Microwave Engineering
Module - I
SOURCE: RF & Microwave Handbook, CRC Press
1
Lumped Components
• Lumped
components
provide
impedance
matching, attenuation,
filtering, DC bypassing,
and DC blocking
• Surface
mount
techniques and evershrinking package sizes
now allow solderable
lumped
components
useful to 10 GHz.1
SOURCE: RF & Microwave Handbook, CRC
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2
RESISTORS
SOURCE: RF & Microwave Handbook, CRC
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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
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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
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Resistance
• The resistive material is deposited in a uniform
thickness, tR, and has a finite conductivity, σR.
• 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
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Surface Mount Resistor
SOURCE: RF & Microwave Handbook, CRC
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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
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8
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
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Intrinsic Capacitive Parasitics
• There are two types of capacitive parasitics.
– There is the shunt distributed capacitance to the
ground plane, CP.
• 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, CS. This capacitance can be dominated
by mounting parasitics such as microstrip gap
capacitances.
SOURCE: RF & Microwave Handbook, CRC
Press
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CAPACITORS
SOURCE: RF & Microwave Handbook, CRC
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11
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
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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
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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
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Capacitors & Equivalent circuit
SOURCE: RF & Microwave Handbook, CRC
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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
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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
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Equivalent circuit
• The series resistance of the capacitor, Rs, is determined
by the parallel combination of all the plate resistance.
• The conductive loss, Gp, 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 halfwavelength resonances due to the parallel coupled line
structure.
SOURCE: RF & Microwave Handbook, CRC
Press
18
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
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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
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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
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INDUCTORS
SOURCE: RF & Microwave Handbook, CRC
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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
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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.
SOURCE: RF & Microwave Handbook, CRC
Press
Wound chip inductor
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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
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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
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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
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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.
• ρR is the perimeter of the wire and δ is the skin depth,
SOURCE: RF & Microwave Handbook, CRC
Press
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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
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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
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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
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