When your monster (or not so monster) power amplifier is switched on, the initial current drawn from the mains is many times that even at full power.
Although the soft start circuit can be added to any sized transformer, the winding resistance of 300VA and smaller transformers is generally sufficient to prevent a massive surge current. Use of a soft start circuit is definitely recommended for 500VA and larger transformers.
As an example, a 500VA transformer is fairly typical of many high power domestic systems. Assuming an ideal load (which the rectifier is not, but that is another story), the current drawn from the mains at full power is …
I = VA / V
Since I live in a 240V supply country I will use this for my calculations, but they are easy for anyone to do. Using equation 1, we will get the following full power current rating from the mains (neglecting the transformer winding resistance) …
At a limit of 200% of full power current, this is 4A AC. The resistance is easily calculated using Ohm’s law …
R = V / I
so from this will get …
Not really a standard value, but 3 x 180 Ohm 5W resistors in parallel will do just fine, giving a combined resistance of exactly 60 Ohms. A single 56 Ohm resistor could be used, but the power rating of over 900W (instantaneous) is a little daunting. We don’t need anything like that for normal use, but be aware that this will be the dissipation under certain fault conditions.
To determine the power rating for the ballast resistor, which is 200% of the transformer power rating at full power …
P = V² / R
For this resistance, this would seem to indicate that a 930W resistor is needed (based on the calculated 60 Ohms), a large and expensive component indeed.
In reality, we need no such thing, since the resistor will be in circuit for a brief period – typically around 100ms, and the amp will (hopefully) not be expected to supply significant output power until stabilised. The only thing we need to be careful about is to ensure that the ballast resistor is capable of handling the inrush current. During testing, I managed to split a ceramic resistor in half because it could not take the current – this effect is sometimes referred to as ‘Chenobyling”, after the nuclear disaster in the USSR some years ago, and is best avoided.
It is common for large professional power amps to use a 50W resistor, usually the chassis mounted aluminium bodied types, but these are expensive and not easy for most constructors to get. For the above example, 3 x 5W ceramic resistors in parallel (each resistor being 180 Ohms) will give us what we want, and is comparatively cheap.
For US (and readers in other 110V countries), the resistance works out to be 12 Ohms, so 3 x 33 Ohm 5W resistors should work fine (this gives 11 Ohms – close enough for this type of circuit).
It has been claimed that the resistance should normally be between 10 and 50 ohms, and that higher values (such as those I suggested above) should not be used. I shall leave this to the reader to decide, since there are (IMO) good arguments for both ideas. As always, this is a compromise situation, and different situations call for different approaches.
A 10 ohm resistor is the absolute minimum I would use, and the resistor needs to be selected with care, as the surge current is likely to demolish lesser resistors, especially with a 240V supply. While it is true that as resistance is reduced, the resistance wire is thicker and more tolerant of overload, worst case instantaneous current with 10 ohms is 24A at 240V. This is an instantaneous dissipation of 5,760W, and it will require an extremely robust resistor to withstand this even for short periods. For 120V operation, the peak current will ‘only’ be 12A, reducing the peak dissipation to 1,440W.
In reality, the worst case peak current will never be reached, since there is the transformer winding resistance and mains impedance to be taken into account. On this basis, a reasonable compromise limiting resistor (and the values that I use) will be in the order of 50 Ohms for 240V (3 x 150 ohm/ 5W), or 11 Ohms (3 x 33 ohm/ 5W) for 120V operation. Resistors are wired in parallel. You may decide to use these values rather than calculate the value from the equations above, and it will be found that this will work very well in nearly all cases, and will still allow the fuse to blow in case of a fault.
This is in contrast to the use of higher values, where the fuse will (in all probability) not blow until the relay closes. Although the time period is short, the resistors will get very hot, very quickly.
Another good reason to use a lower value is that some amplifiers have a turn-on behaviour that may cause a relatively heavy current to be drawn for a brief period. These amplifiers may not reach a stable operating point with a high value resistance in series, and may therefore cause a heavy speaker current to flow until full voltage is applied. This is a potentially disastrous situation, and must be avoided at all costs. If your amplifier exhibits this behaviour, then the lower value limiting resistors must be used.
Due to comments from several readers, I have modified the circuit to allow a much faster relay release time. If flaky mains are a ‘feature’ where you live, then I would suggest that you may need to set up a system where the amplifier is switched off if the mains fails for more than a few cycles at a time. The AC supply to a toroidal transformer only has to ‘go missing’ for a few of cycles to cause a substantial inrush current, so care is needed.