A Zobel for the IDS-25
by Roger Russell

 

This page is copyrighted
No portion of this site may be reproduced in whole or in part
without written permission of the author.

 

Power factor

 

 

I was always interested in AC power transmission and some of the solutions for problems that are encountered. In a way they are similar to the behavior in loudspeakers and amplifiers. One of the problems for a power company is efficiency and control to deliver useful power to the customers. Here are a few basics in alternating current theory. The effectiveness of power transmission is determined by the relationship of the voltage and current delivered to the load.

 

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 X amps X power factor. When the current and voltage occur at the same time, the power factor is one 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. Zobels can also be used to cancel the reactive part of a loudspeaker load as seen by the amplifier.

Speaker Impedance and Frequency

 

 

 

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 off 4 ohms versus frequency.

IDS-25 loudspeaker and Zobels

In comparison, the IDS system has no crossovers and is far better than those systems having many reactive elements that can cause much greater variations in impedance throughout the audio spectrum

 

 

For comparison, the green curve above is the impedance curve of an IDS-25 system. It is very close to that of a single driver in the test box. This is because the series-parallel connection of the 25 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. Resonance is between the effective moving mass of the cone/voice coil assembly and stiffness of the cone/voice coil suspension combined with the air spring of the enclosure. Resonance is where the speaker acts as a generator. It creates a back emf that causes current to flow back to the power amplifier and is due to the voice coil moving in the magnetic field of the gap.

 

This interaction between the speaker and the amplifier can be easily demonstrated by connecting a voltmeter to the terminals of a driver in free air. By pushing or pulling the cone, a positive or negative voltage can be generated. If a short circuit is placed across the terminals, the cone will resist motion and is an indication of how much control the internal impedance of an amplifier might have on damping this cone motion.

 

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 in the voice coil gap.

 

Adding the Zobels

 

Unlike many other speaker systems, The IDS impedance curve is relatively simple to make adjustments. The red curve is the result of neutralizing the reactive components in the system. A shunt RLC circuit (zobel) having the opposite impedance characteristic is placed at the input to the system. This cancels out the impedance peak. A shunt 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. The driver DC resistance is 6.3 ohms. The zobel effectively eliminates the reactive power components and presents a resistive load to the amplifier. Power delivered to the system is then only true power.

 

One of the first questions is what happens to the response of the system and what about the lower overall impedance and consequent change in power requirements? Most of the frequency range is affected except below 50Hz. Remember that the impedance above 6.3 ohms represents reactive power and that 6.3 ohms represents the true or real power delivered to the system. 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 by less than 1/2dB. This means that if the system is driven by 1 watt before the change, then 1.06 watts is needed for the same listening level and can be considered negligible.

 

If the acoustic output is just about the same, it is necessary to use a zobel for the IDS system? Most companies consider this to be a waste of money, particularly for the woofer resonant frequency. The cost for parts to make the IDS zobels can be up to $200 for a stereo pair and they must be high quality parts to be effective. They can be connected right at the system input terminals.

 

Can all of this be heard? In an instant A-B comparison, a very small difference can be heard using random phase pink noise but it takes careful listening. The small difference of 0.5dB that is measured over such a wide frequency range can explain why it is heard. By increasing the listening level after switching in the zobels I am able to make the sound the same to my ears. Then, there is no audible difference except for level and is in agreement with the measurements. This does point out that a close level match for A-B testing is supercritical. Switching the zobels in or out with music becomes too close to have any confidence that there is any difference at all. As far as transients or other listening qualities, no change is noticed to date.

 

The IDS-25 is rated at an 8 ohm impedance and can be described as an easy drive for a power amplifier even without the zobel. With it, this is also an easy drive and may not be needed at all except for some listeners who know it is there doing the right thing for their power amplifier. Another point to consider is that some amplifiers are very sensitive to load impedance variations for both capacitive and inductive reactance found in speaker systems. A resistive load can be a benefit for them. High capacitance speaker wire can also create load problems for some 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. The same true power is being delivered to the load with or without the zobels. The 8 ohm tap is still safe in that respect.

 

Direct coupled amplifiers just deliver more power to lower impedances and have no matching transformers. Of course, they must have internal current limiting to protect the output stages.

 

Even the Magnepan that is said to present a resistive load has an impedance glitch right in the mid-range where it is not wanted. 

 

 

 From Stereophile magazine.
The dotted curve shows the associated phase variations.
The right side has the phase values.

The B&W 804 Diamond impedance is reported by Stereophile magazine September 2013 page 68, shows wide impedance variations.
This is a 3-way vented speaker system.