Speaker Impedance (Z)

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A speaker voice coil is specified in Impedance, because its Resistance changes with frequency.
Impedance (Z) is Resistance that changes in reference to frequency (simple description).
Resistance (R) may also be symbolised as (Ohm) or the Geek letter omega (Ω)
8 Ω is the standard Z Impedance for speakers, measured at 400Hz.
4 Ω is the standard Z Impedance for car speakers (because of the low supply 12V battery, explained in amplifiers).

Speaker impedance Z

Back E.M.F. At fundamental resonance (Fs) a reactive effect called Back EMF, causes the speaker (Z) Impedance to rise many times. E.M.F. Electro Motive Force is a term that applies to electric motors and generators. Externally moving the cone causes the voice coil to generate electricity. A speaker can work well as a microphone especially for bass drums.

Fs is fundamental resonance. Fs is the natural resonance the cone will vibrate at when externally taped by a finger. Similar to tapping a drum skin. The natural Fs of a speaker cone is measured in free air outside of the box. Hold the speaker in your hands (not connected to the amplifier) and tap the cone. It will sound like a drum skin. The system Fs is measured with the speaker inside of the box. A smaller box will cause the Fs to raise to a higher frequency. This is dependent on the box being sealed. Fs becomes more complicated with a ported box.

At Fs the cone vibrates naturally, almost of its own accord and because the voice coil is in a magnetic field it will partially generate electricity. It appears from the outside, that the voice coil Impedance Z has risen. At ‘Fs’ the speaker is also at maximum efficiency, requiring only the smallest amount of input signal for the cone to vibrate.

Natural Damping. If you put a screwdriver or a piece of wire across the speaker terminals (as a short circuit) (without the amplifier connected to the speaker) and tap the speaker cone it will sound dead. Also while keeping the short circuit across the speaker terminals, gently but firmly grip the cone between your fingers and try to move the cone back and forth, it will noticeably resist moving.

Electric motors. With many large industrial machines, when the electric motor is turned off, a short circuit may be placed across the terminals. With the power off a spinning electric motor becomes a generator and shorting the input terminals will cause the motor to brake (Damped) and stop almost instantly.

Amplifier Damping. With the speaker connected to the amplifier (solid state not valve) that is not turned on, tap the cone with a finger, notice its resonant frequency. When the amplifier is turned on (quiesent without music), notice the difference. The speaker will now behave the same as when a short circuit was placed across the speaker terminals.

Negative feedback. All solid state amplifiers are designed with negative feedback. The output of the amplifier is fed back to a second input (inverting input). Any signal that appears at the amplifier output that was not from the amplifier, is fed back to this second inverting input and amplified in the reverse polarity, hereby shorting out any electricity generated by the Fs resonance of the speaker.

Valve amplifiers do not have a second inverting input connected to the output of the amplifier, therefore only have a limited ability to provide damping. The speaker will sound more resonant and produce a greater amount of bass with less energy from the valve amplifier.

 

Efficiency

 

We can now review speaker efficiency by including radiation resistance, frequency, wave-length and fundamental resonance. Efficiency of a speaker is frequency dependent as shown in the below pic. Efficiency specifications of speakers are very misleading but this is not meant to be intentional. This also reflects the reason that musical instruments are not specified with efficiency. Simply too complicated.

Speaker efficiency

The efficiency specification of a speaker is typically referenced at 1 Watt at 1k Hz measured at one point at a distance of 1 meter 3ft. (dB/mW) This measurement shows the efficiency of the on-axis directivity of the speaker only. This measurement does not give the actual efficiency of conversion of electrical energy to sound energy, across the frequency spectrum.

In reality speakers are not measured at 1 Watt, but with a fixed voltage of (2.83 V) that would give 1 Watt if the speaker was exactly 8Ω Ohm. At Fs fundamental resonance the speaker Z impedance could be 32Ω Ohm, and with 2.83 Volt this would be 1/4 of a Watt. If this measurement is done with a typical solid state amp with negative feedback then the natural Fs resonance of the speaker will be damped showing a large reduction of efficiency at Fs. Correctly designed test equipment will have a switch to disconnect the negative feedback enabling the increased efficiency at Fs to be shown.

At the higher frequencies the speaker impedance also rises, and can give a misleading efficiency reading. At higher frequencies depending on the cone diameter the directivity of the speaker increases to a beam, making it appear that the speaker is increasing in efficiency.

The efficiency specification of a speaker is relative to the application of listening at one point on-axis only and not to the overall sound energy it produces at all frequencies. However if a speaker is fed with a constant power of 1 Watt (allowing the voltage to vary as the impedance changes) the efficiency measurement would look similar to the impedance graph.

 

Tonal Quality

 

Speaker tonal colour

The tonal quality a speaker has when it is physically tapped by a finger is also the tonal quality it reflects in the music. There is no such thing as a speaker without its own tonal colour. Musical instruments and speakers share similar characteristics of the physics that governs tonal quality and sound colour. This physics has not yet been specified. Research was conducted in the 1980s by Dr Simon Marty in the department of electrical engineering Sydney University using holographic technology studying classical guitars. Recently he received a grant to continue this research into loudspeaker tonal colour. Hopefully this will enable faithful reproduction of electrified classical instruments and we eagerly await the outcome.

 

Resonance Q

 

The springiness of the suspension and mass of the cone, cause it to have a natural fundamental resonance like a drum skin. Q is a number specifying Quality of resonance (duration of sustain time). This resonance is often tuned to the lowest bass notes, to help improve their efficiency.

Speaker Q

Some manufacturers deliberately make the cone very heavy, shifting the fundamental resonance well below the musical range eg. 20Hz. Doping compound (tacky tar like substance) can be painted around the surround, damping the cone movement, reducing its Q at resonance. If this is overdone it can reduce speaker efficiency so it becomes virtually useless. There is a compromise between over damping the cone to flatten its response causing it to be inefficient and sound dead, or under-damping, allowing the cone to resonate (sounding alive) but will exaggerate the resonant note. This choice is personal. A Q of 1.4 tends to be the optimum for musical enjoyment.

 

Valve Amplifiers and Speaker Q

 

Speaker damping

Complications regarding back EMF and fundamental cone resonance are often not fully understood by amplifier and speaker manufacturers. When technology changed from valve to solid-state it was noticed that solid-state amplifiers lacked warmth and bass performance and had to be twice as powerful as valve amplifiers to sound as loud.

Solid-state amplifiers function in voltage drive (zero output impedance) (100% damping factor) and act as a short circuit across speakers’ effectively damping their performance. The larger the magnet and voice coil (BL) the greater the effect of damping. This becomes self-defeating for reproducing the lowest bass notes, and the primary reason for boxes to be ported to reproduce bass. However, there are other factors involved and this explanation needs to be expanded.

Speakers were originally made as efficient as possible. Early valve amplifier for domestic use were only a few Watts. The easiest way to make a bass speaker system efficient is to have a (lite) low mass cone, soft surround, with the speaker in a large box. The speaker would naturally be very resonant at the deepest bass notes. When solid state amplifiers arrived, the resonance of the speaker was damped by the zero output Impedance of the solid-state amplifier which reduced the bass energy of the speaker well below the higher frequencies. The simple solution was to increase the mass of cone. This made the speaker less efficient. The efficiency of many speakers were reduced by approx 10dB. The zero output Impedance of a solid-state amplifier has less effect on further reducing the energy of the bass notes of a heavy cone speaker in comparison the higher frequencies. Also at the time solid-state amplifiers were introduced social aesthetic changes in society preferred smaller speaker boxes as TV and Video became the dominant form of entertainment. Bass speakers with (heavy) high mass cones can work well in smaller boxes. Solid-state amplifiers are capable of much greater power at lower cost therefore, speaker efficiency or the lack of, is no longer a problem.

Valve amplifiers naturally function in current drive (high output impedance) (less than 50% damping factor). This allowed speakers to function at maximum efficiency allowing the bass notes to be highly resonant. Valve amps are sensitive to speaker impedance variations. Some speakers had copper caped pole pieces, which helped damp impedance variations. Had the effect of output Impedance differences between valve and solid-state amplifiers been fully understood at that time, solid-state amplifiers would have had a control to vary between voltage and current drive to change their output Impedance to control the resonance of bass speakers, as a standard function.

A detailed explanation of amplifier output Impedance in reference to Voltage-drive Current-drive as the reason for why valve and solid-state amps sound different is described in the amplifiers chapter.

 

Load Impedance

 

Review. R or Ω or Ohm, are the 3 symbols for Resistance.
This text uses R for Resistance. Other text may use Ω or Ohm for Resistance.
Z Impedance is, Resistance Ω that varies with frequency.

Zero 0R is a short circuit. Infinite ∞ R is an open circuit.

Load Impedance is the load speakers represent to the Amplifier. The maximum power rating of an amplifier is in reference to the load impedance. (Eg: a 100 Watt amplifier rated into 4Ω.) Only with a load of 4Ω is this amplifier capable of 100 Watts.

With a speaker load of 8Ω this amplifier will only be capable of 50 Watt. With a speaker load of 16Ω this amplifier will only be capable of 25 Watt and so on. The higher the load impedance, the cooler and more reliable the amplifier will be, and the lower the internal distortion but less power.

This 100 Watt amplifier must not have a speaker load that goes below 4Ω impedance. With a load of 2Ω this amplifier will attempt 200 Watt. The amplifier output transistors will get excessively hot and may/will fail. Heat is the enemy of amplifiers. The more speakers that are connected to the amplifier the lower the load impedance, and hotter the amplifier will get. Accidentally shorting the amplifier speaker terminals, represents a load of 0Ω and may instantly destroy the amplifier.

One 8Ω speaker the amplifier will only give 50 Watt run cool and reliable.
Two 8Ω speakers in parallel is 4Ω 50 Watt into each 8Ω speaker (100 Watt).
Four 8Ω speakers in parallel is 2Ω 50 Watt into each 8Ω speaker (200 Watt).

The speakers must not represent a load lower than amp Z rating.
The speakers can represent a load higher than amp Z rating.

Repeat-

An amp must not have a load, lower than the impedance the amp is rated for.
An amp can have a load higher than the impedance the amp is rated for.

Speaker calculation

Calculations

Speakers in parallel, divide speaker Ω by the number of speakers.
2 8Ω speakers in parallel is 8Ω/2 = 4R.
4 8Ω speakers in parallel is 8Ω/4 = 2R.

Speakers in series, x speaker Ω by the number of speakers.
2 8Ω speakers in series is 8Ω x 2 = 16R.

Speakers in series-parallel with even numbers of speakers only.
put each pair of speakers in series put each series pair in parallel with other series pair.
2 8Ω speakers in series is 8Ω x 2 = 16R.
2 8Ω speakers in series is 8Ω x 2 = 16R.
2 16Ω pairs in parallel is 16Ω/2 = 8R.

4 8Ω speakers in series-parallel = 8R.

The points

  • Speaker Z load must not go below amp Z rating.
  • Speakers in parallel or series must be identical.
  • Speakers in series multiply speaker distortion but do not effect reliability.
  • Speakers in parallel do not multiply speaker distortion.

Connecting speakers in series and series parallel may be essential in certain applications where many speakers are required to be connected to one amplifier. However connecting speakers in series causes the distortion of each speaker to be reflected into the others. But connecting speakers in series does not effect the reliability of the speakers or amplifier.

Speaker test

Speaker polarity Test The standard test for a speaker is to put a battery across the speaker terminals. When the + of a battery is put on to the + marked terminal of the speaker the cone should move out. This is also the correct test for checking the polarity of speakers in stereo systems. 1.5 Volt battery is safe to use.
Warning never use this test on a compression driver.

 

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© 2013 Lenard Audio Institute
High Engineering