Reactive load
A load that acts like a speaker, built from resistors, inductors and a capacitor. Set the bass peak you want, then see the impedance and phase from 20 Hz to 20 kHz, how hard each part works at your amp’s power, and your own measured cab curves on the same graph.
Swipe sideways for the whole drawing. Tap a part to jump to its value.
A measured curve can be a DATS .zma file, or any text file with one point per line: frequency, ohms, and phase in degrees if you have it. It stays in your browser. Nothing is uploaded. Download an example file.
Driven by an amp
The voltage across this load against a plain resistor of the nominal value, from the same amp. The higher the amp’s output impedance, the more the voltage follows the load, up at the bass peak and in the treble.
How hard each part works
Each part’s worst case with a sine at the amp’s full rated power, 20 Hz to 20 kHz, in rms with the frequency where it happens. Rate the part for the bold figure: watts for a resistor, current for an inductor, voltage for a capacitor (peak is 1.41 times rms). Music runs far lower on average, but a note held on the bass peak gets close. Leave margin for heat and for an amp pushed past its rating. At low damping factors these run high, since they assume the amp’s voltage keeps rising with the load’s impedance, and a real tube amp runs out of plate swing first.
All values
Other parts
How the load acts like a speaker
A speaker’s impedance has three parts. At the bottom is the voice coil’s resistance. In the bass there’s a peak where the cone resonates. Up top, the coil’s inductance takes over and the impedance climbs.
R1 is the coil’s resistance. The tank of R3, L3 and C3 makes the peak: at resonance L3 and C3 cancel, leaving R3, so the peak is about R1 plus R3. Away from resonance one or the other shorts R3 out. L1 makes the treble climb.
A real voice coil’s climb flattens as its iron losses grow. L2 with R2 across it copies that: L2 adds reactance until it reaches R2, then only L1 keeps climbing. A measured speaker also creeps up from a few hundred hertz, and without a second step the fit pushes R1 above the coil’s real resistance. L4 with R4 across it is that second step.
Damping factor
Damping factor is the speaker’s nominal impedance divided by the amp’s output impedance. An amp with 4 Ω of output impedance on an 8 Ω speaker has a damping factor of 2.
The amp’s output impedance and the speaker make a voltage divider. With a low output impedance (a high damping factor), the speaker voltage holds steady and only the current follows the impedance. With a high one, the amp acts more like a current source, and the voltage rises wherever the impedance does, at the bass peak and in the treble. The graph under “Driven by an amp” shows it.
The name comes from the cone. The moving voice coil makes a voltage of its own, most of all at resonance, and a low source impedance lets it push current back through the coil to brake the cone. The coil’s resistance is always in that path, so once the output impedance is well under it, going lower does little. 20 and 200 sound about the same.
Rough ranges: solid-state amps 20 to several hundred at the jack. Tube hi-fi amps with lots of feedback about 5 to 20. Tube guitar amps with the usual speaker feedback, like blackface Fenders and Marshalls, well under 1 (about 0.3 to 0.7 in the power amp tool). Tube guitar amps with no feedback, like a tweed Deluxe or an AC30, under 0.1, since pentodes and beam tubes have a high plate resistance. Feedback from the speaker brings the output impedance down.
The buttons set a damping factor for each kind of amp, from the power amp tool with typical values, not measurements. Real amps vary with the feedback resistor, its tap and the tubes. The slider covers tube amps. Type a bigger number for solid state. For a given power section, see the power amp tool.
Warnings. The summary above the graph turns red if the load can’t be solved.
How this tool works. We solve the load with the circuit bench’s engine at 481 frequencies from 20 Hz to 20 kHz, checked against the textbook formula. The fit sets every part to a measured curve by least squares on the log of the impedance, and on the phase when the file has it (10° counts as 1 dB), using the file’s points from 20 Hz to 20 kHz and starting from values read off the curve. The third inductor stays only if it cuts the error by a fifth or more.
An impedance meter like the DATS uses a small signal. At full power the bass peak usually comes out lower and the coil’s resistance rises as it heats, so a fitted load matches the speaker at low volume.
Real curves show small bumps from a few hundred hertz up, where the cone breaks up. A load like this can’t copy them. The parts here are ideal. A real inductor’s winding resistance adds to R1 (for L1) or lowers the peak’s Q (for L3), and an iron core loses inductance as current rises. Measure what you build. To see what these loads do to an output stage, try them in the power load line tool.
Spot an error, or want a circuit added? Email info@swellamps.com. A schematic or a clear photo of one helps. Anything you send may be used to improve these models and our desktop app.
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