This calculator will help you determine the cable losses in distributed speaker systems (also known as 100-volt or 70-volt speaker systems). By inputting the cable size and length, and the number and details of the speakers, it will calculate the loss in SPL(dB), Voltage, and Watts. It even calculates the resultant SPL in dB at the target audience. All you have to do is fill in the white cells in the calculator.
First up, select the units of measure: either “Metres & mm²” or “Feet & AWG”. Most countries use metric, meaning the cable lengths are measured in metres, and the cable size is in mm². USA doesn’t use metric, so select “Feet & AWG” – the cable lengths will be in feet, and an extra box appears to enable you to select the cable thickness in AWG.
Then work your way down the top table:
Total number of speaker connected in the cable run.
Tap settings on speakers: Most speakers for distributed speaker systems have some way of selecting different taps, or power, for the speaker. This is normally expressed in watts.
Speaker sensitivity: this is optional, but is used to calculate the SPL level at the target audience. It is normally found in the specifications of the speakers. For example, a ceiling speaker specs might say “Sensitivity: 90dB (1w/1m)”
Distance from speaker to target audience: This is also optional and is used for calculating the SPL loss in the air from the speaker to the target audience. For a ceiling speaker it might be only 1 metre or so from the ceiling to a person standing. For a horn speaker outdoors, it might 10 or 20 metres or more.
Total cable length: is the total length of the cable from the amplifier to the last speaker.
Length of feed cable to first speaker should be self-explanatory. It is the cable length from the amplifier to the first speaker. The calculator then assumes the number of speakers are evenly spread over the remaining length of the cable.
Distributed system maximum voltage is about the amplifier. Its output will be rated at 100 volts, or 70 volts, or perhaps 50 or 25 volts.
Cable c.s.a: This is the important figure as all calculations about the resistance of the cable are based on the cross sectional area (c.s.a.) of the cable. This is convenient for metric users as cables are categorised according to their c.s.a. For other users, who are used to sorting their cables according to their AWG number, the calculator inserts the c.s.a for you (based on the AWG # selected).
Once all those inputs are entered, the results are immediately calculated (actually they are calculated after every entry or change). See the remarks below if you need help in interpreting the results.
What the results mean
The results of this distributed speaker system cable loss calculator basically tell you that if you don’t use too many speakers and they are not drawing much power, then you don’t have to worry too much about the cable size. However, if you have long cable runs, many speakers or high power speakers, you need to pay attention to these results.
The total speaker load tells you the total load on the amplifier. The amplifier needs to cope with this load. Good practice would dictate that you use an amplifier 20%-25% larger than the total load.
The total cable resistance is for information only.
The maximum current in the feed cable is useful to determine if the cable selected is capable of carrying that current.
The SPL difference between the first and last speaker will help determine if you need to use a larger cable or not. Many systems would cope with a difference of up to 6dB (+/-3dB). Any difference larger than 6dB would become noticeable to many users.
The results for various speakers are then tabulated. Speaker #1 is the first speaker. The results are also shown for the last speaker and the middle speaker. Although the middle speaker number can be changed to see the results of any speaker between the first and last speaker.
The Maximum SPL result is determined by the sensitivity of the speaker, the SPL loss in the air between the speaker and the target audience plus the gain of the speaker over of 1 watt.
Finally, a graph showing the calculated distributed speaker system cable losses is shown.
Assumptions of this Distributed Speaker System Cable Loss Calculator
This calculator makes several assumptions:
- The calculator assumes the resistivity of copper cable is 1.724 x 10–8 Ωm. This can change slightly between single or stranded cable. Also not all copper cable is pure copper which change the resistivity slightly. Although in practice, these differences will have little effect on the results.
- The calculator assumes the speakers are spread evenly across the cable length (after the feed cable). If the speakers are not evenly spread, there again will be little difference in the results in most cases.
- The calculation for SPL loss in the air between the speaker and the target audience assumes a non-reflective space (like outdoors). For reflective walled spaces the loss could be as much as 6dB less. However the losses will still be relatively the same across the speakers.
- This distributed speaker system cable loss calculator assumes the speakers are all set at the same tapping (watts) and the same size cable is used throughout the cable run. Changes to these assumptions is beyond the scope of this calculator.
For further information about distributed speaker systems, also known as 100-volt speaker systems, or 70-volts speaker systems, read the article on Understanding Distributed Speaker Systems