The ideal resistor exhibits a linear V — I relationship defined by Ohm’s Law (V = IR). This holds true from DC all the way to Radio Frequencies (RF).
However, this relationship fails for wire-wound resistors. Instead of a pure resistance, we see an resistance plus inductance. The reason is obvious when we consider the construction (Figure 1). We can see the individual wire strands wound on a ceramic mandrel. This is the same construction used to construct inductors.
This engineering brief shows the departure for a real resistor using a frequency sweep it also provides guidelines.
Figure 1: Lab setup for frequency sweep of a wire-wound resistor.
Frequency Domain Analysis of a Resistor
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 shows the measured phase shift.
For audio frequencies (DC to 20 kHz), this resistor is well behaved. Meaning it presents as a pure resistance. Around 100 kHz thing start to turn as the inductive reactance has become significant relative to the resistance. By 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.
Resistor Similarities to Inductors
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.
Inductance Mitigation in Wire-Wound Resistors
Wire wound resistor inductance can be mitigated using bifilar windings. Mechanically, this resembles winding a power cord on a mandrel. 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. However:
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The construction method adds additional cost as the wires must be insulated.
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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.
Potential Misuse of a Wire-Wound Resistor
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.
Parting Thoughts
Resistors are not as simple as the textbook definitions. 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.
Best Wishes,
APDahlen
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.