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A Solid State Relay is so different than an ordinary electromechanical relay that you can not use a simple ohmmeter to get much useful information.
There are a number of different types of SSRs and their characteristics are different. First, you need to know what is inside the SSR to determine how to test it. Second, you need to know what is the objective of the test or tests.
In its very simplest form an SSR would be a bi-polar transistor, FET, SCR, Triac, or other similar device. These basic elements have no isolation between input and output. To test these basic elements you get their datasheet and from this decide how to perform the desired test.
Now lets move on to what you may consider an SSR. You need some general idea of what is inside the black box. A datasheet for the device may provide all the information you need and it may not. Get the datasheet and study the specifications.
As an example I will pick on an Opto-22 OAC5. However, in my experiment I will use a unit made by Potter & Brumfield from about 25 years ago.
The main Opto-22 site is
http://www.opto22.com/
http://www.opto22.com/site/solidstaterelays.aspx
http://www.opto22.com/site/pr_details.aspx?cid=4&item=OAC5
http://www.opto22.com/site/pr_details.aspx?cid=4&item=OAC5 click on SPECIFICATIONS for details
No circuit diagram of the internal circuit is provided. However, I believe the basic internal components are Triac, snubber (capacitor and resistor), optical coupler, and drive circuitry. Older OAC5s I do not believe had zero voltage turn-on.
The primary leakage current of this device is from the snubber and this will be frequency dependent because of the capacitor.
Note: the open circuit voltage of a Simpson 260 is less than 6 or 9 V in the high resistance ranges and 1.5 V on low resistance. A Fluke is about 0.75 V with a 10 megohm load in resistance mode, and 2.5 V in diode mode.
Across the P&B OAC5 output terminals Fluke 27 in resistance reads 27 to 20 megohms, and OL in diode mode. This is for both polarities. Simpson on Rx10,000 shows maximum resistance, no current flow. Steady-state leakage current using a 1 K load resistor (1.4 V) is 1.4 MA @ 125 VAC 60 Hz. Do not test with a milliampere meter. Can be large initial inrush current with zero capacitor charge and connection at peak voltage.
SCRs and Triacs have a minimum holding current specification that must be exceeded to maintain current conduction following triggering. For the OAC5 it is listed as 20 MA. This means that the ON state of the SSR must be tested with some minimum load to insure exceeding this requirement. Also note the high voltage drop in the ON state.
On the input side some minimum current must be supplied to trigger the output element. There will also be some maximum allowed input current. Opto lists this as 2.5 to 8 V input. Internally there is a resistor that provides current limiting to the opto isolator.
Once turned on an SCR or Triac with a load current exceeding its holding current will remain on until the current drops below its holding current. Thus, the basic SCR or Triac SSR turns on as soon as the input trigger occurs and turns off at the first current zero crossing. If the input excitation is maintained, then the device turns on again at the beginning of the next half cycle. When input excitation is removed and current is above the holding current level, then current continues to flow unit the next current zero crossing.
In the present Opto-22 OAC5 turn-on of the output Triac after the leading edge of the input signal does not occur until the first voltage zero crossing following the leading edge.
As mentioned by Larry and iwire in previous posts a 100 W light bulb would be a good test load for an OAC5 at 120 V 60 Hz. Other types of SSRs, such as an ODC5, require a different type of testing.
Using a sample of one of my P&B OAC5s, 50 W bulb, 125 V @ 60 Hz the results were:
Half cycled at 3.82 V and 5.4 MA input. Voltage across OAC5 68.7 V AC on Fluke 27.
Full cycle 3.87 V and 5.6 MA input. Voltage across OAC5 0.947 V AC.
A standard input I used to interface from 120 V machine signals to our equipment, starting in 1971, was a 5 K input resistor to a bridge rectifier to the input of a 4N35. In older PLC systems it was necessary to shunt the input with a 1 K to 2 K resistor to prevent the output leakage current from the PLC triggering my input when the PLC was supposed to be in the zero state. Later I switched to 24 VDC as our input because everything was PLC and there was no need for 120 V interfacing.
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