Dummy load 8W using wire-ended resistors

Created: Dec. 2021. Modified: May 2024

Introduction

The obvious way to increase power handling in a dummy load is to connect multiple resistors in parallel (fig. 1). On the flip side, paralleling the resistors has the deleterious effect of summing up the individual resistors's parasitic capacitance.  As a result, the high frequency performances degrades faster than the individual resistors. Hence,  dummy loads constructed by combining axial lead resistors are limited to operation below VHF; i.e. they certainly cannot reach the microwave range! 

Material and method

So, is there a better way to connect multiple resistors? Before we reveal the answer, let's devise a classification system based on "number of resistors in series" x "number of parallel arms". So, "1x4" is shorthand for 4 resistors in parallel (fig. 2). And "2x4" is two resistors in series, 4 parallel arms. In either configuration, the individual resistor value is adjusted to achieve a net 50 ohm.

In the resistor model (inset in fig. 2), the parameters Ls (10.3 nH) and Cp (0.79 pF) represent the resistor's parasitic inductance and  parasitic capacitance, respectively. Ls2 (1 nH) represents the parasitic inductance of the resistor's leads. These parasitic values are representative of a 1W axial resistor. 

Simulating both "1x4" and "2x4" configurations reveals that the latter can achieve a higher maximum frequency (fig. 3).  At the 10 dB Return Loss line (SWR ~2), the "2x4" (red trace) is 1.4 GHz, whereas the "1x4" (blue trace) is 1.0 GHz; i.e. a 40% improvement. The "2x2" (green) has the worst matching and so, will not be discussed further. 

The reason for the 2x4 superior bandwidth is its parasitic capacitance is partially cancelled by the parasitic inductance. At low frequencies, it is predominantly inductive; i.e. in the upper half of the Smith chart (fig. 4). As the frequency increases, the "2x4" becomes capacitive and the impedance trace moves downwards. In contrast, the all-parallel "1x4" is purely capacitive over frequency. 

Simulation shows that further improvement in matched bandwidth can be achieved by connecting a small inductance in series with the resistor network (fig 5). A 4 nH inductance value (blue trace) can increase the matched bandwidth by ~64% over the zero inductance condition (red trace); i.e. from 1.4 GHz to 2.3 GHz. The 4 nH inductance is physically implemented using the BNC's centre pin which protrudes outside the shielded section.

To validate the hypothesis, a prototype dummy load was build using 8 pieces of 100 ohm resistors (fig. 6). These are garden variety axial lead resistors. The resistors are combined in the aforementioned "2x4" configuration. As each resistor is rated 1W, the total maximum dissipation is 8W. The combined resistors are connected to a BNC female panel connector. The BNC's centre conductor which protrudes outside the shield is modeled as a 3.9 nH inductance. This inductance is the "strike-through" (bypassed) component in the fig. 2 simulation circuit. The inductance is activated for modeling the experimental dummy load. 

The experimental dummy load (solid black) achieves a 2.6 GHz bandwidth at the -10 dB RL point (SWR =2) (fig. 7). This maximum frequency is previously unattainable using axial lead resistors. Simulated (red dash) & measured return loss / SWR show an almost perfect agreement over DC~2.1 GHz. The model's main weakness is the failure to account for the other resonance at 2.45 GHz. 

Discussion

When I built an 8W dummy load in 1993, I wasn't aware of the better configuration -  I just stumbled into it by accident. Furthermore, I was baffled by a strange behaviour - why did the match suddenly improves at 1950 MHz (fig. 6)? Today, armed with a circuit simulator and basic component modeling knowledge, I can understand better. The unintended resonance at 1950 MHz has the effect of extending the usable bandwidth, up to 2600 MHz at the -10 RL point. Beginner's luck! 

The model's main weakness is the failure to account for the other resonance at 2.45 GHz. Any suggestion on how to rectify this weakness?

Conclusion

A novel method of combining axial lead resistors can extend the dummy load's maximum frequency into the microwave range. The prototype built to validate the design has achieved an unprecedented maximum frequency of 2600 MHz. To our knowledge, this is the highest maximum frequency reported for a dummy load constructed using wire-ended resistors.    

Another possible application for the proposed scheme to compensate for chip resistors' parasitics. Chip resistors like the EIA 1206 have much smaller parasitic cap of ~0.5 pF, but they can still limit the maximum frequency, especially when they are combined in parallel. 

References

[1] Tuck Choy, Facebook group, Building  transistor radio, 11 Dec 2021. www.facebook.com/groups/678676552256627/posts/3228778327246424/

[2] "50-ohm dummy load", www.reaksi.org.my/homebrew/aksesori-radio