Passive Components, Part 3: Capacitors

Undoubtedly, rx the basic building block of any circuit is the lowly resistor. The apparent simplicity of this device often allows designers to overlook some non-ideal properties that cause to performance degradation in high-performance circuits. Here, approved
I will try to go over some of these properties of resistors so as to help others avoid common pit-falls.

The popular designs of through-hole resistors falls into several categories: wire wound, for sale carbon composite, carbon film and metal film. The wire wound resistors, as the name implies, get their precise characteristics from lengths of wire wrapped around a core in either an inductive or non-inductive manner. The carbon composite resistor is a cylinder composed of a mixture of black carbon and an insulator to give the required characteristics. The film resistors fall into two categories, those whose film composition is varied to give appropriate resistance or those where the film is uniform and the path from one terminal to the other is laser trimmed for a fixed resistance. SMT resistors can also be obtained in the previous designs, however, film resistors are by far the most popular. One can see from the start that the inherent series inductance of various resistor designs can contribute a significant impedance at high frequencies. Furthermore, there can be non-negligible capacitance between “traces” on film resistors and the wire loops on wire wound resistors. Now the simple resistor model becomes a ideal resistance in parallel with a capacitance and in series with an inductance, so, if care is not taken, one can design a resistor bridge that can cause ringing at circuit operating frequencies. Inductive wire wound resistors suffer the poorest frequency response with possible inductances on the order of 10uH and shunt capacitance of 5pF for a resistance of about 10kOhm.

Another important characteristic of a resistor is its temperature coefficient (TC). This is the value (usually in ppm/C) which describes the change in resistance per degree celsius. So the resistor specifies a nominal resistance value, say 10kOhm, with a tolerance of 1%, so it is actually 10kOhm +/- 100Ohm. Assuming that this is a precision resistor, it can have a respectable TC of 10ppm/C, so if your circuit is exposed to 100C temperature ranges, then that gives you 1000ppm variation, or 1/1000 of the 10kOhm. This may not seem significant, but if the resistor involved is used to somehow interface a ADC, the best resolution over the temperature range is 10bit (1/1024 of full swing) due to the resistor TC alone. Having noted that, 10ppm/C is very, very good. The TC for copper PCB traces is often on the order of 3000-4000ppm/C, so if the resistor is very small, the copper TC will have a significant contribution to errors. Further problems arise when there are networks of resistors that dissipate power. Resistors have a specified thermal dissipation coefficients so the temperature change of a resistor due to power dissipation can be calculated. If a pair of resistors are nominally matched, once they dissipate different power, they can become unmatched due to different temperatures. Furthermore, the values of resistors can change with applied voltage on the order of 1-200ppm/V (for high MOhm resistors) and with age, on the order of 10-100ppm/year.

Finally, there are thermocouple effects. Whenever dis-similar materials are joined that are at different temperatures, they develop a voltage drop across the interface. Schematically, most resistors have at least two of these: one from metal terminal to resistor material and one from resistor material to the other terminal. If the whole resistor is at a uniform temperature then these two cancel each other out, otherwise, the resistor can develop an additional voltage drop that is not really there. For this reason, it is suggested that resistors are mounted so that their terminal-terminal axis is perpendicular to the thermal gradient (meaning, the whole resistor is at a constant temperature).
There are also some interesting noise properties of resistors, but I will write about that later.

Inductors can be separated into two categories: those specifically chosen to be inductors and stray inductances in PCBs and components. For inductors, visit this site
parasitic characteristics arise from the ohmic losses in the conductor, viagra 60mg
from capacitance between coils from the core and from mutual inductances with other magnetic components.

The ohmic losses are straightforward as it is understood that there is a resistance associated with the length of conductor used to make the inductor. The capacitance effects are similar to those of the resistors, ask so those are also fairly clear. As for the inductor cores, the effects are a bit interesting. The ferro-magnetic cores of some inductors can “saturate” with strong fields, and thereby modulate the inductance as a function of applied field. As far as magnetic coupling, this all depends on the amount of magnetic flux that enters the coils of the inductor. Unlike electric fields, which can be shielded by Faraday cages, magnetic fields must be shielded with solid metal enclosures, where the skin-penetration depth of magnetic radiation is much smaller than the metal thickness. For this reason, it is much easier to pick up magnetic noise than electric noise in a shielded circuit. As far as tolerances go, it is hard to manufacture precision inductors, so they have a lower inherent quality (Q) factor are not often used for precise applications beyond power regulation.

Sometimes the inductors do act as precise resonators, but not in the way they were intended. When a series inductor is connected to a parallel capacitance, the pair can act as a tuned-LC circuit and ring at certain frequencies. This can happen intentionally, as in a power system, or unintentionally, where the capacitor is a by-pass capacitor by an IC and the inductor is the trace inductance (~10nH per cm for 10 mil trace), so unwanted ringing can be introduced into the circuit. The amount of ringing depends on how well tuned the circuit is, and thereby how high the Q factors for the various components are. For this reason, a small resistance is sometimes put in series with the inductance to specifically degrade the Q factor of the inductor and thus reduce the ringing.
Capacitors are the most interesting electrically in the same way that the sickest person in an emergency room is the most interesting medically. They have more fine details than the resistors and inductors, cheap
so I will try to attack the problem in four sections: device parasitics, dielectric absorption, dissipation and temperature effects.

As for parasitics, we first take an ideal capacitor (C) and put a resistor in series, this will be the leakage resistance (RL), then we add a series RC circuit (DA), which will be due to dielectric properties, then we put in a series resistance (ESR) and inductance (ESL), which will be due to the packaging. Starting from the simplest part first, the capacitor is a real device and the conductors have real resistances, so the sum of all of these ohmic losses can be described as the ESR. Next, we have the ESL. This is a physical property of a real device and is heavily dependant on capacitor construction. Capacitors that are radially wrapped, like some electrolytics, have the highest ESL while parallel plate chip capacitors have the lowest. For this reason some datasheets recommend two bypass capacitors of different sizes for fast ICs. That is, due to the series LC, each capacitor has a frequency at which they have the lowest impedance, so the bypass capacitors are tuned in such a way that they have lowest impedances at frequencies at which other components operate. This way one IC can decouple from other ICs running at different frequencies etc. The leakage resistance is due to the finite resistance of the dielectric material as well as the finite resistance of the packaging material.

Dielectric absorption deserves a long essay, but will get a mere paragraph. The best description of the phenomenon is an analog memory in a capacitor. That is, if a capacitor is charged to a voltage V1, then disconnected from the voltage and the leads are shorted for a brief period of time, and then opened again, the capacitor will show a slight voltage across the terminals when the device should be discharged and the voltage should be zero. This voltage depends non-linearly on the input voltage and can create errors in sample-and-hold circuits and integrators. Not all capacitors exhibit DA on the same scale: electrolytic are the worse while polystyrene and polypropylene are the best.

The dissipation factor describes the various finite resistances in the non-ideal capacitor model. It is effectively a measure of how long a capacitor can hold its charge after the charging voltage is disconnected. The leakage parameter is often specified as a megaohm-microfarad product which describes self-discharge time in seconds. This can be anywhere from 1 second in electrolytic capacitors to 1,000,000 seconds in Teflon and film devices. The leakage, ESL and ESR are lumped together to define the dissipation factor (DF), where DF is inversely proportional to the Q factor.

As far as temperature effects go, capacitors suffer from all of the problems that inductors and resistors suffer from along with non-linear changes in dielectric properties due to change in temperature. These are often specified in ppm around a certain temperature where they are linear-like. It is also important to note that the capacitors maximum working temperature is heavily dependant on the manufacturing technology. Polystyrene capacitors have a upper working limit of about 80C while Teflon capacitors can be used all the way up to 200C.

This is by no means a comprehensive overview of non-ideal capacitor properties, merely an introduction.

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