Speaker With Conjugate Network
I previously wrote a piece about the Peak Current Requirement of Speakers. This was based on reports in recent audio design books, which refered to a paper, Peak Current Requirement of Commercial Loudspeaker Systems. which shows that certain rectangular pulses applied to speakers can require unexpected high current peaks. This applies to any rectangular pulse, simply because the reactive components of the speaker impedance cause a frequency dependent phase shift of the current, which changes its shape and increases its peak level. This can be prevented by adding a 'conjugate network' in parallel with the speaker so that some of that peak current is provided via the network, and less is required from the amplifier.
Here is a simple equivalent circuit of a single speaker with a not very accurate conjugate network connected in parallel to flatten the impedance plot. I just used an estimated network and made a few adjustments in the Spice simulation to get close enough to a flat impedance. The 0.01 resistors are used to measure the currents in the various paths by plotting the voltages across these resistors.
The first plot is the speaker impedance without the network connected, as expected there is a peak at the bass resonance frequency and a rising impedance at high frequencies because of the inductance of the voice coil.
Next is the impedance plot with the conjugate network connected. The result is not perfect, but good enough for the present demonstration.
If we connect an amplifier and apply a voltage pulse the currents are as shown next. After the end of the pulse the speaker current (green) has a negative peak over 3A, but the conjugate network current (red) at the same instant is a positive peak about +1.3A. The total current taken from the amplifier (blue) is therefore the sum of the speaker and network currents and is only -1.7A. The shape of the current is about the same as the voltage pulse, so the speaker plus network is almost exactly resistive.
It is quite common to just add a simple RC Zobel across the speaker to prevent just the high frequency impedance rise, and this is far more convenient if we look at the component values needed for the full conjugate network; there is a high value capacitor which needs to be non-polar. If however we leave out the series LCR part and just use the RC Zobel we find the current through the RC is in the same direction as the speaker current after the pulse, and the peak current taken from the amplifier is even higher than the speaker alone, as shown next:
Fortunately it appears that full level rectangular pulses are not a common feature of music signals, and tests published in Stereophile and also my own tests failed to find any large unexpected current peaks, so adding conjugate networks or leaving out RC Zobels generally appear to be unnecessary.
1. Designing Audio Power Amplifiers, by Bob Cordell, (McGraw-Hill 2011) p373-375. The diagrams on page 374 include the voltage and current waveforms, with high current peaks.
2. Self On Audio, 2nd Edition, by Douglas Self includes a similar treatment on page 402. The idea appears to have orriginated with a paper by Otala and Huttunen. They mention peak currents up to 6.6 times those expected for a 8 ohm resistor for a commercially available speaker, using a complex signal cleverly contrived to maximise the effect.
3. How Speakers Torture Amplifiers. This piece from Stereophile, 2007, mentions two examples of experimental checks which failed to find any unexpectedly high current demands.