The textbook categorization of resistors, based on resistance, tolerance, and power rating, is incomplete. In this article we will demonstrate that real-world resistors have unexpected reactive attributes. This is especially true of wire wound types which exhibit both resistive and a significant inductive reactance at high frequencies.
Figure 1: The Digilent Analog Discovery and impedance analyzer module are used to characterize a large wire wound resistor.
Resistors are manufactured using a wide variety of techniques and material. For a complete description, please see this authoritative page. For our purposes we will focus on the wire wound resistor. Recall that this resistor is literally a length of resistive wire wound on a ceramic core (mandrel), A representative example is the large 50 Ω resistor shown in Figure 1.
The insulating ceramic core serves as a base to hold the wire in a robust compact form. The ideal material can transfer heat away from the wire and can withstand thermal cycling as the bulk resistor heats and cools over its long life. For larger resistors, the ceramic body provides an electrical insulator for chassis mount. The resistor in Figure 1 has tabs that hold the resistor proud of the chassis. Other resistor types may use the chassis or even a large heat sink to dissipate the resistor’s heat.
Tech Tip: To better understand “wire” consider an old-style toaster or a hair dryer. These devices have nichrome-wire heating elements. As an electrical current flows, the wire converts electrical energy into heat. This is seen as the cherry red color. Note that the nichrome wire is used as is relatively immune to oxidation resulting in long life. To see a counter example, consider this article that shows a burning carbon resistor where oxygen consume the red-hot resistor.
An inductor may be constructed by winding a wire onto an insulating mandrel. The closely spaced windings magnetically interact to produce the desired inductive properties.
Perhaps you see the problem. Our description for a wire-wound resistor is the same as our description for an inductor. In the real-world, this is a serious problem if not properly addressed. At low frequencies the inductive reactance is low and can be disregarded. However, as the frequency increases the inductive reactance increases. The reactance may be greater than the resistance. For extreme frequencies, the effects of inter-winding capacitance become apparent. At this point the resistor becomes its own resonant RLC system.
Tech Tip: Wire wound resistors can be designed to mitigate the parasitic inductive. One method is to use bifilar windings. As an analogy, think of an appliance power cord as a resistor. The current in the supply wire is flowing one way while the current in the return wire is flowing the other. With the wires in close proximity, the magnetic fields tend to cancel out. If this structure of insulated wires is now wound on a ceramic mandrel, we have a resistor with minimal inductive properties. Note that this construction adds additional cost as the wires must be insulated. The voltage handling characteristics are also problematic as the two (electrical) connections of the resistor are in close proximity as opposed to the resistor in Figure 1 where the voltage gradient is across the entire 4-inch length. Other techniques are available but beyond the scope of this article.
Figure 2 presents the frequency sweep of the resistor using the Digilent Analog Discover with the impedance analyzer module using the setup shown in Figure 1. The upper graph presents the impedance of the 50 Ω “resistor” with the lower graph presenting the measured phase shift.
For audio frequencies (DC to 20 kHz), this resistor is well behaved. Meaning it presents as a pure resistance. Somewhere around 100 kHz thing start to turn as the inductive reactance has become significant relative to the resistance. By the time it reaches 2 MHz the inductive reactance dominates, and the system has an impedance of 300 Ω.
Figure 3 presents a model that assumes a series connected resistance and inductor. The measured resistance is relatively flat. The measured inductive reactance is generally linearly increasing as expected by the X_L = 2\pi fL relationship. The resistance and inductive reactance are equal at approximately 400 kHz.
Figure 2: Graph of the impedance (upper) and phase shift (lower) for the 50 Ω wire wound resistor. At 2 MHz the impedance has increased to approximately 300 Ω.
Figure 3: Graph showing the equivalent series modeled resistance and inductive reactance.
Tech Tip: Radio transmitters are typically designed to work into a 50 Ω impedance. Transmitters are often bench tested by connecting to a resistive “dummy load.” The resistive element for this non-radiating load must be carefully selected. The 50 Ω resistor showcased in Figure 1 would result in an atrocious impedance mismatch. For example, as 2 MHz this “50 Ω” device has an impedance of approximately 300 Ω. The result is an unacceptable Voltage Standing Wave Ratio (VSWR) that could damage the transmitter’s output stage.
Resistors are not the simple creatures suggested in your textbook. Some types, such as the wire wound device featured in this article, have considerable deviation relative to the stated resistance value. Please keep this in mind as you repair, design, and construct high frequency circuits.
About the Author: Aaron Dahlen, LCDR USCG (Ret.), serves as an application engineer at DigiKey. He has a unique foundation built over a 27-year military career as a technician and engineer which is further enhanced by over a decade of teaching. With an MSEE degree from Minnesota State University, Mankato, Dahlen has taught in an ABET accredited EE program, served as the program coordinator for an EET program, and taught component-level repair to electronics technicians. Dahlen has returned to his Northern Minnesota home and thoroughly enjoys researching and writing articles such as this.