Types of SSRs

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A relay is a device controls one electrical circuit when a control is sent to it from another electrical circuit. In this way, a low-voltage signal can be used to control power for a much larger circuit. Many relays are mechanical devices and work by making two metal contacts touch one another, usually by the use of an electromagnet: when the electromagnet is energized, it pulls on a metal lever causing contacts to touch and electricity to flow; when power is cut from the electromagnet, a spring separates the contacts and the electricity stops flowing.
An 'SSR' is a solid-state version of the mechanical switch but essentially does the same thing using electronics instead of magnetism, metal levers and springs. As such, an SSR, or 'solid state relay' is much quieter and can operate much more quickly than a mechanical device.
An SSR can control either AC or DC electricity, but the control signal itself that turns it on or off is almost always low-voltage DC. This allows small computer chips to be able to do the task, such as the PIC16F688 or other chip. Typically, these chips utilize 5vdc signaling, which is usually enough to trigger an SSR to turn on or off when the signal current stops.

SSR Design

Most SSRs are designed similar to the diagram below:

Anatomy of ssr.png

The low power, low voltage control signal emanates from the computer and turns on an LED inside the optocoupler. The optocoupler provides a measure of electrical safety to the computer by physically isolating the low power side of the circuit from the high power side. The optocoupler's internal LED shines on a light-sensitive plate inside the optocoupler which then allows a small bit of electricty to flow through the that side of the optocoupler to the "gate" of the TRIAC (or other high power control device). The TRIAC's gate then "opens" and allows power to flow through the TRIAC to the lights and the lights turn on. This is the basic design of an SSR for AC current.
DC SSRs work in much the same way although instead of a TRIAC to control the powerful DC current, they usually use a MOSFET, which is a special type of transistor. Low power DC SSRs sometimes substitute a power transistor in place of the MOSFET, but the concept is essentially the same as above: a low voltage signal activates an optocoupler which lets higher voltage/current flow through a power control device which then turns on the lights.
To limit the electrical current coming from the computer into the optocoupler to within the optocoupler's tolerance, a resistor is often used. In like fashion, a resistor is often used to limit the current that flows to the TRIAC's gate from the optocoupler. The values of these two resistors are often 680 and 180 ohms respectively, but these values aren't universal -- the values depend on the components selected and the current present in the circuit.
Popular optocouplers are the MOC3023 or MOC3023M for AC SSRs or the K847PH and PC817 for DC SSRs. Popular TRIACS are BTA06 or BTA08 types. BTA implies that the metal tab on the back side of the TRIAC is isolated and not electrically connected, which is ideal for putting a heat sink across multiple TRIACS to help keep them cool. BTB TRIACS can also work, but the BTB type has a "hot" metal tab that carries electrical current and cannot be safely used with a common heat sink across all TRIACS. Therefore, the BTA type is much preferred. Popular power transistors for DC SSRs are the 2N2222A, PN2222ABU and KSC2328AYBU. A popular MOSFET is the FQPF13N06L.
The popular DirkCheapSSR uses the VO2223A chip, a phototriac-type optocoupler that is quite similar to the MOC3023 chip except with the capability to handle greater current loads. Therefore the VO2223A provides for both the low power and high power sides of the circuit on one chip. Very handy indeed, but the chip's limit is about 1 amp of current. But 1 amp is quite adequate for a half-dozen LED strings or single strings of incandescent mini lights, and because it uses fewer components, it is much smaller and less expensive than most every other SSR on the planet.

Considerations for Use

"How many lights can I put on a channel?" is a common question asked by newbies. Since each TRIAC is its own channel, this is really a simple mathematics problem, really. If you follow the guideline that you shouldn't put more current draw on a TRIAC than more than half its rated maximum, a BTA06 TRIAC should be pretty safe if you never drew more than 3 amps on it. If a single light string draws .39A for example, 3 amps divided by .39 amps per string = 7.69 strings, so rounding down, you could put 7 strings on that channel's TRIAC. Why is the guideline only half of the rating? Because sudden on-rush current usually is greater than a steady current so for a moment, sudden on-rush current could conceivably be between 5-6 amps. A secondary reason is that the more current you put through an electrical component, the hotter it will get. Even at 3 amps, you're likely to need a heat sink on the TRIAC to help keep it from being destroyed by heat, and you certainly don't want to create a fire -- the ultimate result from too much heat!
Another consideration is the total capacity of the SSR itself. If you put 3amps on each channel of a 4-channel SSR, the total draw of that one SSR will be 12 amps -- and that's the maximum recommended draw on an home's entire 15A circuit! You'd also have to verify that the circuitry on the SSR's circuitboard can support that much electricity, since many SSRs have fuses that limit the SSR's total to 5, 7 or 10 amps.
Light string manufacturers usually specify that you should not connect more than 3 (or 5, 8, 12, etc.) strings together end-to-end. There's a reason for this. The strings themselves are designed with a relatively small gauge wire and when you plug too many together, the total draw on the wire is too great, which can heat up the wire, melt the insulation and result in a fire. Be sure to consult the tags that are normally attached to the strings to determine what the safety limit is and don't go past it. "One more string won't hurt" is not the right attitude to take; it could be exactly one more string that causes a fire.
Other considerations are the gauges of wire that you use to supply power to the SSR as well as the wire that goes to the lights from the SSR. SPT-1 wire is very popular for wiring DIY displays but SPT-1 is limited to a maximum draw of 7amps.
The point of all the above is that the TRIAC in the SSR is just one part of the whole pie -- you always need to take the total into consideration when it comes to deciding how many lights you can put where. There's a lot more to this than simply plugging in another string of lights wherever you want.

Making Your Own

There aren't many parts required to construct a basic SSR. The four important parts are the optocoupler, a TRIAC and two resistors. The other parts you might add for convenience are various connectors for taking the control signal from the computer and perhaps other plug connectors for mains power and connecting the output to the lights. So really, there's not much to it and that's good, because there's not much that can go wrong when there are so few parts! Common problems associated with "my SSR stopped working" are poor soldering, poor physical connections for the control signal from the computer or the connections to power and the lights. Electrical-wise, usual problems are short circuits in the power output wire/connectors to lights or too much current draw, either one of which will overheat and burn out the TRIAC very quickly -- almost instantly, in fact.
But because there are so few parts in an SSR, one can even use simple perfboard to mount the components and use direct, point-to-point wiring on the bottom side. The only tricky part is the resistor calculation to properly limit current and that's dependent on the parts used. The MOC3023 optocoupler has a fairly wide tolerance on the control input side and a 1/8 or 1/4 watt resistor between 120-750 ohms will likely work fine for a 5vdc trigger signal from the computer, but 680 ohms is the optimum value. If the trigger signal is greater than that, such as 12v, you may have to go up to a 1K - 1.5K resistor instead. For most TRIACS that you'll use, a gate resistor value between 120-200 ohms will generally work okay but 180 ohms at 1/4 watt will likely be the most utilitarian. Heat sinks (if you determine that you need them) can be easily fashioned from a short piece of thin, 1/16" or 1/8" flat or angled aluminum. A heat sink isn't necessary or beneficial if the current draw never exceeds 1 amp on a TRIAC.
There are many, many SSR circuits on the Internet using many different component parts. Many use various MOCxxxx chips as the optocoupler component and different resistor values. Take some time to study them!