Understanding Speaker Cab 16, 8 and 4 Ohm Connections

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I thought I would cover this topic as there are many students – musicians, DJ’s and budding live music sound or stage monitor techs – I see at college who don’t have even a basic electronics or physics education, that may need to understand some of the concepts behind connecting sound systems together, for safety reasons as well as equipment damage prevention.
Last week at DBS I popped a vintage 30W Celestion Greenback out of its magnet housing when doing the higher volume tests there, because I did not check my 60W Carlsbro cab wiring when it arrived.

These speakers were in a sorry state anyway as they had got damp in storage at some point with both being mouldy, and one was blown anyway as it was distorting a little at really low volumes (1) before I turned them up, so it’s always worth fully checking an Ebay/2nd hand buy despite what a seller states (really Steve?), before switching on. I have the moment on video when the sound just failed at volume 6 – so they did well at above half way of the full 60W for 30W speakers. Fortunately it didn’t damage the amp which is all I was worried about.
The 2 x 30W, 16 ohm speakers that were in the cab were wired in parallel and plugged in with the 16 ohm output selector link set. The 8 ohm position is riveted closed even though the schematic has 8 ohm as an option – which is what it should have been set to, so these are the wrong (16 ohm) value speakers for an amp of this power in the first place as will be explained below.


Although I know better – IF I had checked before trying the amp – I can understand why someone else would read 16 ohm on the back of a speaker (and not consider how it was wired with another) and think that was the value the amp output should be set to. What’s worse, is this amp was supposed to have been checked over by an amp tech before sale.
The following explanation of speaker connection options may seem a bit simplistic for many people, but when dealing with valve amps particularly, which can be damaged by not having a speaker load connected when the volume is turned up (nowhere for the energy to dissipate into except back though the system), or modern high wattage stage systems (500W to 30kW festival size rigs) there may be considerable high voltage and current involved in the power stages feeding the speakers that needs to be respected, so it is good to know the consequences of series and parallel connection.
http://en.wikipedia.org/wiki/Sound_reinforcement_system#Power_amplifiers

“The amount of amplifier power used in a performance setting depends on a number of factors, such as the desired Sound Pressure Level of the performers, whether the venue is indoors or outdoors, and the presence of competing background noise. The following list gives a rough “rule of thumb” for the amount of amplifier power used in different settings:

  • “Small Vocal” system – About 500 watts
  • “Large Vocal” system – About 1,000 watts
  • “Small Club” system – About 9,000 watts
  • “Large Club” system – About 18,000 watts
  • “Small Stadium” system – About 28,000 watts”

As I found out a couple of weeks back due to a moment of stupidity – not thinking before acting – when moving the jack lead to another cab, even a 60W valve amp may have sufficient voltage at the output jack to give you a fair shock. This is partly a reason why much modern equipment is now fitted with either multi-pin XLR (Cannon) or the combination type XLR / ¼ inch sockets so that female XLR connectors that shield the power pins are used for higher power systems.
    
The most basic concept needed to be known for speakers in guitar, bass or keys amplifier cabs is probably the first thing to be taught in basic electronics – resistances in series and/or parallel.
For resistance in an AC circuit, the term Impedance is used, but I’m not going into why as it’s unnecessary for this level of understanding.
As most speakers come as 4, 8 or 16 ohm values, (therefore so do most amplifier outputs designed to feed them), then the maths involved is minimal and requires no more thought than being able to double or halve these numbers in your head for any cab wiring combination that houses 4 speakers maximum.
For any two equal impedance speakers, connecting them in series doubles the impedance – it impedes the flow of current by twice as much, and connection in parallel halves the impedance to current, as there is now double the available pathway for the current, so twice as much current can flow.
The 2 equations that describe these connections are:
Series connections: Rtotal = R1 + R2 + R3…
Parallel connections 1/Rtotal = 1/R1 + 1/R2 + 1/R3…

For a simple example of a 2 x 12 cab housing 8 ohm, 50 Watt speakers, there are two wiring options:
In series would give a 100W cab of 8 + 8 = 16 ohm impedance.

In parallel would give a 100W cab of 1/8 + 1/8 = 1/Rtotal = ¼. R = 4 ohms impedance.

In this case is it not possible to have an 8 ohm cab using both speakers, only a 50W, 8 ohm cab using one speaker.
These are the simplest examples, and the same principle applies for other impedance value speakers of course, 2 x 16 ohms in parallel gives 8 ohms, as does 2 x 4 ohms in series.
Things get more complex for a 4 speaker cab now, but it is just combinations of the basic ideas above.
For a 4 x 12 cab of 4 x 8 ohm, 50W speakers, you need to think in pairs. As two in series gives 16 ohm, then you can then join two pairs at 16 ohm in parallel to get 8 ohms overall, but now capable of handling 200W of power.

Note that if you put all 4 in parallel you would get 2 ohms.

If these were 16 ohm speakers in the above diagram, you would two pairs at 2 x 16 ohm in series = 32 ohms, then wired in parallel to give 16 ohms overall. All four in parallel you would get 4 ohms.
Now you can get really carried away with imagining connecting more than one 4 x 12 cab in series or parallel if you have a more powerful amp to drive them – like the Marshall Mode Four 350W amp I tried at DBS two weeks back. You could connect 3 x 100W cabs in series with that thing!
You can now mix and match different impedance and power value speakers in the same cab also – say 2 x 16 ohm, 50W speakers in parallel, to give 100W at 8 ohms, these then connected to 2 x 4 0hm 50W speakers in series as a pair (100W at 8 ohms), which are also then connected in series with the 16 ohm pair, to get a 200W cab of 16 ohm total impedance.

Now do you see that my Carlsbro had the wrong speakers in the cab in the first place, as it only has 16 or 4 ohm output selector options, so the 2 x 30W, 16 ohm speakers wired in parallel (8 ohms) should have been 2 x 8 ohms wired in series to make 16 ohms, or wired in parallel and the 4 ohm selector set.
At best, both 16 ohm speakers could have been wired in series to make 32 ohm capable of handling 60W and at least limit the current that could flow and protect the speakers from full volume as they would share the full 60W, even if this may be a detrimental to the valve and OT stage at worst because the wrong value load impedance is reflected back to the OT primary so loads the valves incorrectly, consequences of which can be:
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So it can be seen that the turns ratio of the transformer determines what impedance will be reflected to the primary by the load impedance of the secondary, and that an improper load on the secondary can have several effects:

  • if the load impedance is too low this will increase the current in the transformer windings. This also reduces the primary impedance that the output tube sees which increases tube current flow.
  • if the load impedance is too high, this reflects a higher than normal impedance in the primary for the output tube.
  • poor sound quality and lack of volume.

Now, armed with the turns ratio, we can calculate the impedance ratio and the impedance that will be reflected to the primary with a given load in the secondary. Remember we said earlier that the impedance ratio is the square of the turns ratio. With our 25:1 turns ratio transformer in figure 2, the impedance ratio is the turns ratio squared or, 25 X 25 = 625:1. So if the transformer is working into an 8 ohm load, the impedance that will be reflected to the primary will be the impedance ratio (625) multiplied by the load impedance (8 ohms), equal 5,000 ohms. If the load in the secondary is changed to a 4 ohm load, the reflected impedance in the primary would be 625 X 4 = 2,500 ohms.

The impedance load seen by the tube and output transformer is not constant. The frequency of the audio signal will vary over a wide range. The inductance in the windings will have a different impedance at different frequencies. At a certain frequency an 8 ohm voice coil may have an impedance of 10 ohms or at low frequencies it my have an impedance of 4 ohms. This varying load impedance is reflected back to the primary, so the tube, and output transformer must work into a varying impedance range.”

This is called the reflected load.

[For a 10:1 turns ratio as in the Laney, a 16 ohm load reflects back 1600 ohms, as per Briggs table (previous Post) and the explanation below]

A 10 ohm load reflects back a 1,000 ohm impedance, while a 5 ohm load reflects back a 500 ohm impedance. The reflected impedance is a function of the turns ratio of the transformer. Notice that the ratio of the primary impedance to the secondary impedance is the square of the turns ratio, or 100:1. In other words, a 10:1 turns ratio will give an impedance ratio of 100:1.”

http://www.radioremembered.org/outimp.htm

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I have now purchased 8ohm, 60W Celestion and 8ohm, 50W Eminence speakers for this cab so I can safely use the 100W Laney with it also. I thought using two different makes would mix up the frequency response a bit to add some individuality to the tone. The 10W difference between the two is only 9% of the 110W total so should be inaudible as a volume difference between them. Each is wired in series now, positive of one connected to the negative of the other so they stay in phase:


I’ll test it at full volume next week at DBS. It sounds absolutely wonderful!
The thing to understand now is regarding the output transformer 4, 8 and 16 ohm windings and their and voltage and current relationships to each other.
The equation for power is:
P = IV
So there is a proportional relationship between voltage and current if power output is the same for each winding which it is in a “perfect” transformer as both primary and secondary sides share power equally. The primary voltage goes across the power valves but a relatively low current flows on this side, as with the Laney example, 1V measured across the cathode resistor of 5 ohms gives about 0.2 amps, though the voltage across them may be above 400V RMS as in the calculation in the previous Post for a 10:1 step down ratio for 16 ohm tap from the Briggs chart below and square of the turns ratio (10 x 10 = 100, x 16 ohms speaker load = 1600 ohms valve load) explained above:


Simply, each output winding has twice the voltage across it as the value below it, BUT the current that will flow in different taps is NOT linearly proportional as the voltage across them is as explained below, and as it is in each side of a transformer.
Ohms Law states V = IR so V/I = R and V/R = I
So, as P = IV, or VxV/R or IxI x R
As the speaker resistance plugged in to a winding is fixed for a given volume level and frequency, and so is the power output, then only the voltage and the current can change for each winding, but in power terms current and voltage are squared values seen above. For example, for a 100W OT at full volume, the 16 ohm tap outputs:
P = V x V / R so
100W x 16 ohms = V x V = 1600, so the voltage is SqRt 1600 = 40V
Or for current:
P = I x I x R so
100W / 16 ohms = I x I = 6.25, so the current is SqRt 6.25 = 2.5A
Substituting to find the 8 and 4 ohm taps:
100W into 8 ohms: 28.2V and 3.5A
100W into 4 ohms: 20V and 5A
So a 4 ohm cab pulls the most current at the lowest voltage of the three taps.
Now imagine the current needed to drive a larger PA system for a festival, like a Funktion1 or similar, though these are modular and the whole system is driven by separate amps and control systems, but the smallest full range (bass, mid and treble) unit Funktion1 do is the res2:
http://www.funktion-one.com/products/resolution-2/

One of the lecturers at DBS owns a full 10k F1 system for his live sound business, and we will be looking at this at a basic level in the Live Sound class. Basically, each range is or can be managed separately by an active management crossover unit so that each can be tweaked for situation, and spreads the power load.
Using the maths above, you can work out the current requirements for its spec. for the bass bin:

Driver 

Operating Band

Sensitivity  

(1W at 1m)

Power  

(rms)*

Nominal

Impedance

15″

28 – 250Hz

102dB

400W

8?

8″

250 – 6k5Hz

106dB

200W

12?

1″

6k5Hz – up

107dB

50W

*AES rated

P = VV/R, IIR
400W/8 ohm = SqRt 50 = 7A
400W x 8 ohm = SqRt 3200 = 56V
If you were connecting this bin with a jack lead from the power amp, you could get a small shock from touching the tip at 56V AC, but if it shorted to metal, 7A could flow which may spark and cause a fire. Also, the tip has to touch the negative of a speaker cab temporarily when plugging in, which is not a problem usually as the cab is not in any completed circuit already, but it is something to be aware of should this jack with a live tip be erroneously plugged in to another live system as it could short the power stage of the amp feeding the cable or cause a problem for the system it is being plugged into and is what causes the surge “pop” sound when plugging in guitar jacks to switched on amps, as a momentary spike is amplified through the system. Turn volumes down before plugging equipment together to avoid this potentially equipment and ear damaging issue, or better still connect all kit BEFORE turning it on.
This is a reason Neutriks Speakon connectors are used in higher power systems so this can’t occur.
http://en.wikipedia.org/wiki/XLR_connector
http://en.wikipedia.org/wiki/Speakon_connector
This is why jack plugs are bad news as the tip is live and exposed if the volume from the amp is turned up at the amp end of the cable and plugged in. XLRs are a safer design. In reality most except bespoke power amps have digital power outputs and have safety circuits built in to shut off the output if shorted.