A Zobel for the IDS-25
by Roger Russell

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Power factor

I was always interested in AC power transmission and some of the problems that are encountered by a power company. To efficiently deliver useful power to customers requires an understanding of the kind of load the equipment places on the power connection. Here are a few basics in alternating current. The effectiveness of power transmission is determined by the relationship of the voltage and current delivered to the load. It reminds me of the basic course in electronics at school. I remember the words ELI the ICE man. This means that for an inductor L, the voltage E leads the current I. For a capacitor C, the current I leads the voltage E.

Typical loads found in power transmission

Resistive

Incandescent lamps, heating elements in stoves or furnaces

Inductive

Motors and relay coils

Capacitive

Start and run capacitors or power factor correction capacitors.

Inductive	Capacitive	Resistive

For a power company, AC power is used most efficiently when the current is aligned with the voltage and is shown in the resistive picture. However, most equipment is inductive and tends to draw current with a delay, misaligning it with the voltage as shown in the inductive picture above. Because of the inductive reactance that is introduced, the apparent power is then higher than the useful or true power supplied to the load.

The relationship can be seen for motors and capacitors when illustrated in a polar diagram.

Power factor is a way of measuring how efficiently electrical power is being used within a customer's electrical system. These components are referred to as True Power (watts), Apparent Power (VA) and Reactive Power (VAR).

The cosine of the angle between the apparent power and true power is a measure of the power factor. True power is volts times amps times the power factor. When the current and voltage occur at the same time, the power factor is unity and is an optimum load. The greater the reactive power, the lower the power factor.

To realign the current and voltage for an inductive load, a bank of appropriate capacitors are inserted at the load. The higher apparent power delivered by the power company is then reduced to the true power. The cancellation of inductive reactance reduces excessive current and cost to the power company. This can also be thought of as a zobel used to compensate for an inductive element. A zobel is also known as a Boucherot cell. Most power systems operate at 50Hz or 60 Hz but amplifiers and speakers operate through the whole audio spectrum and even beyond. In a similar way, loudspeaker systems are loads for the power amplifier. Zobels can also be used to cancel the reactive part of a loudspeaker load as seen by the amplifier.

IDS-25 loudspeaker and Zobels

The green curve of impedance versus frequency shows a typical IDS-25 system impedance. It is unique because it has no crossovers and is very close to that of a single driver in a test box. This is because the series-parallel connection of the 25 identical drivers comes out to the same impedance as a single driver. Impedance is 6.3 ohms at 20Hz and rises to a 13 ohm resonant peak at 180Hz If we were to look at the phase relationship between voltage and current, we would see the voltage leading the current before the impedance peak. Beyond the impedance peak, reactance is capacitive and the current leads the voltage. Rising impedance at the higher frequencies is caused by the inductance of the voice coil winding. The impedance is 7.1 ohms in the area of 500Hz and rises to 9.5 ohms at 20kHz. Unlike some wide-range drivers, the impedance at the higher frequencies would be greater if it were not for the copper shorting ring used in the voice coil gap.

Adding the Zobels

The red curve is the result of neutralizing the reactive components in the system. A series RLC circuit (zobel) having the opposite impedance characteristic is placed across the input terminals of the system. This cancels out the impedance peak. A series RC (zobel) is also placed across the system terminals to cancel out the rising impedance at higher frequencies. The overall system impedance is now essentially reduced to a resistive value ranging from 5.6 to 7.1 ohms while the driver DC resistance remains at 6.3 ohms. The system effectively presents a true power load to the amplifier.

Here are the components I used to create the entire IDS zobel. All of the components are 5% tolerance)

The capacitors are low loss polycarbonate. Electrolytic capacitors are not used because they have high ESR (effective series resistance) and make the series resonant circuit too broad. For the first circuit, I used three 25mfd capacitors in parallel to make a total of 75mfd. The coil is made with many turns of #19 magnet wire supplemented with a low distortion iron core to provide a total of 11 mH inductance. There were no 14-ohm resistors in the parts box so I used 12 ohms plus 2 ohms in series. The second circuit compensates for the rising high frequency impedance. I use a 12mfd capacitor in series with an 8-ohm 15-watt resistor.

To make a comparison, I use my remote relay switching boxes (master and slave) The zobel boards are placed at either end of the couch and can be switched in or out at the system input terminals. A remote button is used to control the relay switching. I use a McIntosh MC252 power amplifier to drive the prototype systems.

One of the first questions is what happens to the response of the system after this adjustment? Little change, if any, should be expected by eliminating the reactive parts with the zobels. Measurements show that the acoustic output of the system decreases overall by less than 0.5dB through the whole frequency range. This means that if the system was driven by 1 watt before the change, then 1.06 watts is needed for the same listening level and can be considered negligible.

Can all of this be heard? The relay box provides an instant A-B comparison. After playing a wide variety of music, no listening difference can be heard. Then I resort to using random phase pink noise and only then can I hear a very slight difference in the overall level. To compensate for the difference when the zobels are not connected, I reduce the level slightly. Then there is no listening difference even with random noise. In fact, for full-range drivers like this, zobels are not needed at all. In this case, zobels may be a benefit for some users who might like to know the zobels are connected and doing the right thing for their power amplifier. This said, however, for special amplifiers that tend toward current source behavior, a zobel like this one can preserve the original IDS-25 performance. A resistive load can be a benefit for them. High capacitance speaker wire can even create load problems for some of these amplifiers.

For some amplifiers that have several output impedance taps from an output transformer or autoformer, a 6-ohm impedance with the zobels is right in the middle between 4 and 8 ohms. 6- ohm taps are normally not provided. The standard “safe” answer would be to connect to the 4 ohm tap. The reason is that the lower impedance on an 8 ohm tap could otherwise cause extra heating of the amplifier by drawing extra current. However, the 6 ohms presented with the zobels draws only true power and none of the reactive power that would draw extra current from the amplifier. The 8-ohm tap is still safe in that respect.

Multi-way Systems

The above impedance curve is for a small 2-way speaker system that is rated at 4 ohms. In this system there are several reactive elements that hide the true resistance of the system. The lowest impedance is 4.7 ohms in the area of 20Hz, 4.0 ohms at 300Hz and 5.9 ohms at 11kHz. The maximum impedance is 20 ohms at 125Hz and 28 ohms at 2500Hz. An ideal load for an amplifier would be a constant resistance of 4 ohms versus frequency. Although zobels can be placed at the input terminals of the IDS-25 system, a multi-way system such as this 2-way system is more complicated. Zobels must be connected directly across each driver. This will reduce each driver to essentially a true resistive load. However, the crossover components might need adjustment if previous calculations were using a different driver impedance. Consequently, this adjustment could make an audible difference.

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