Page 291 - Analog and Digital Filter Design

288 Analog and Digital Filter Design

running parallel with one. If, however, the capacitor is axial leaded and mounted
horizontally on the circuit board, a different inductance equation is necessary.
This equation takes into account both the vertical and horizontal sections of
the lead.

L = 0.00046056 { log,, [2h( - b+e)]}
a b + w
- -+0.25b
+0.0002(~ -%+a),
where L is the inductance in pH, “a” is the lead radius, “6” is the wire length
that runs parallel with the ground plane and “h” is the wire height above the
earth plane. All dimensions are in millimeters. This equation is far more com-
plicated than the previous one, but fortunately it is not often needed.

Surface mount capacitors are often used for high-frequency circuits because
there is no lead inductance to worry about. The most popular type of surface
mount capacitor is the multilayer ceramic; its conducting plates are planar,
interleaved, and have very little inductance. Some conventional leaded ceramic
capacitors use surface-mount devices with wire leads attached. They are usually
dipped in epoxy resin or similar coating material before having their value
marked on the outside.
Ceramic capacitors generally have a temperature coefficient that is zero or
negative. The terms NPO (Negative Positive Zero) or COG are used to describe
ceramic capacitors with a zero temperature coefficient. Other ceramic dielectrics
are described by the temperature coefficient; N750 describes a dielectric that has
a negative temperature coefficient of -750 PPM/”C.

Polystyrene and polypropylene capacitors are often used where the filter design
is sensitive to component value changes. These types of capacitor have a nega-
tive temperature coefficient that closely matches the positive temperature
coefficient of a ferrite-cored inductor. Unfortunately, with these dielectrics,
capacitors tend to be physically large for a given capacitance value.

Polyester and polycarbonate capacitors are very common. Polyester capacitors
are the worst in that they have a poor power factor (high ESR) and a poor (and
positive) temperature coefficient. Polyester capacitors are popular because they
have a high-capacitance density (high-capacitance-value devices are small). Poly-
carbonate capacitors have a better power factor and a slightly positive tempera-
ture coefficient. Another useful feature of polycarbonate capacitors is that they
are “self-healing”; in the event of an insulation breakdown due to over-voltage
stress, the device will return to its nonconducting state, rather than short circuit.

Temperature effects are very important. Consider what would happen if a nar-
rowband bandstop filter was built without considering the temperature effects.