The Nonideal Resistor

There are three common types of resistors: carbon resistors, wire-wound resistors, and metal film resistors. Carbon resistors are inexpensive

Figure 7.1 The hidden schematic of a real-world resistor includes lead inductance (Llead) and parasitic capacitance (Cp). Most often (except in the case of very low resistance values) it is the parasitic capacitance that limits the high-frequency performance.

Figure 7.1 The hidden schematic of a real-world resistor includes lead inductance (Llead) and parasitic capacitance (Cp). Most often (except in the case of very low resistance values) it is the parasitic capacitance that limits the high-frequency performance.

components that can use the low conductivity of carbon to create resistance. Wire-wound resistors are simply a very long wire, wound into a tight form. Metal film resistors are thin films that create resistance due to their small cross-sectional area. Wire-wound and metal film resistors are available in tighter tolerances and lower temperature coefficients than are carbon resistors. Low price is typically the only benefit of carbon resistors. Another consideration for resistors is their power-handling capability. If too much current is forced through a resistor, it will become too hot and will burn up or experience other permanent damage. Resistors are therefore given power ratings.

Real resistors also have frequency limitations. An equivalent circuit is shown in Figure 7.1. The leads of a resistor create a capacitance that is in parallel to the resistance. The leads of the resistor, and the resistive material itself create a series inductance. Both parasitic effects limit the frequency range of the resistor. For large resistances, the capacitance dominates the high-frequency response, shunting out the resistance and reducing the effective impedance of the resistor. Figure 7.2 shows the frequency response of two resistors.

The resistance remains constant until a corner frequency, defined by f = 1/(RC). The frequency performance of a resistor, therefore, is worse for large resistances and for large parasitic capacitances. For this reason, high-resistance resistors are not used at high frequencies. To improve performance, the leads of a resistor can be shortened, reducing the parasitic capacitance. Surface-mount chip resistors, which are rectangular

Figure 7.2 Simulated frequency-dependent behavior of typical axial (through-hole mount) resistors: A) R = 50kohm, Llead = 8nH, Cp = 0.3 pF; B) R = 5ohm, Lead = 8nH, Cp = 0.3 pF.

Frequency [Hz]

Frequency [Hz]

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blocks of resistive material with metal ends, reduce capacitance greatly because they do not have extended leads.

For small-valued resistors, the parasitic inductance dominates the high-frequency response, increasing the effective impedance. Wire-wound resistors have notoriously high inductance, and cannot be used at high frequencies. Therefore, at high frequencies the very high- and very low-valued resistors will change the most. It turns out that 50ohms, the most common characteristic impedance for use at high frequencies, serves as a good gauge for determining whether or not a resistor is very high or very low. A general, but somewhat arbitrary, guideline to use for selecting chip resistors is where f is the frequency of operation in Hz and R is resistance in ohms. Of course this is a rule of thumb and is not a substitute for measurements or simulation.

An ideal capacitor has a reactive impedance of Zc = -j/(2nfC). All real capacitors have several parasitic elements, as shown in Figure 7.3.

The leads of the capacitor have inductance and resistance. In addition, the dielectric material between the plates does not have infinite

Figure 7.3 The hidden schematic of a real-world capacitor includes lead inductance (Llead), lead resistance (R/eod), dielectric leakage (RDC), and dielectric "frictional" loss (RAC). The resistances are often combined and called Equivalent Series Resistance (ESR). Dielectric losses (and hence ESR) are typically frequency dependent.

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Solar Panel Basics

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