Optocoupler Small Signal CTR

[Weston]

For some instructional labs I am going to be having the students take some measurements on optocouplers to better understand transfer functions.

I was running through the exercises myself when I realized the "large signal" current transfer ratio was significantly different from the small signal AC response. Upon thinking about this some more, it makes sense. CTR as measured at DC and specified in the datasheets is total collector current / total diode current, but the small signal gain is the slope of Ic/If. Just for reference, example datasheet plot at the bottom of the post.

What I am a bit confused about is why I can not find discussion of this in app notes. Most of the discussion is on the large signal CTR, which is what the optocouplers are binned on and what the datasheet graphs show as a function of current. This is important to make sure that any circuity using the optocoupler does not saturate / fail to drive the output hard enough. However, when it comes to feedback loop stability the small signal gain is what is important.

While my measurement for the "large signal" CTR is within the datasheet limits, the "small signal" CTR is 2.6dB higher.

Its a bit of a pain to calculate the "small signal" CTR from the datasheet plot, but you can do it. You need to convert to a plot of Ic vs If and then take the slope.

Am I being overly pedantic here? 2.6dB difference is not too high. But this variance is based on the curves of the LED and phototransistor and should be largely independent of the binning. And you can get optocouplers binned tighter than the disparity between the large signal and small signal CRT. I am just a bit confused because a lot of app notes referencing optocouplers for SMPS feedback diligently talk about checking the datasheet for CTR, but not calculating the small signal gain. 

[minifloat]

My guess is, as long as the opto is not driven beyond the monotony region, a linear relationship between diode and phototransistor current can be assumed.

For the characteristics of this region, just two points (Id;Ic) are necessary to define it.

Further simplifying this, the first point is chosen as (0;0) and the second point just before the turnover.

And that's what you've been doing, right?

br, mf

PS. Side thought, beyond the turnover point, the loop gain decreases, which is normally beneficial for stability (OK, I have to admit, noise regulation gets worse).

[Someone]

I am just a bit confused because a lot of app notes referencing optocouplers for SMPS feedback diligently talk about checking the datasheet for CTR, but not calculating the small signal gain.

Problem is CTR varies: by device (binned), with aging, over temperature, and with operating point (that plot). A power supply feedback has to function within all those variations. If you can constrain some of those dimensions then you can use plots such as that to estimate a smaller variation.

[Weston]

Optocouplers are very much not linear, that's why the plot of CTR vs forward current exists.

Whats interesting is that this non-linearity is not often discussed in the context of the variance in addition to all the other factors.

I was curious so I extracted the plot data from the datasheet and used that data to calculate the small signal CTR.

Looking at the data it does not seem like too much variance. I wonder if there is a device physics explanation for the almost constant difference between large signal and small signal CTR before the device starts to saturate. The small signal CTR is ~60% higher, which is not too bad compared to the standard optocoupler binning. However, I do wonder if the additional 60% gain has ever thrown off the stability of a feedback look designed on the upper bound for CTR.

Once the device saturates the small signal CTR really falls off a cliff before the large signal CTR does. I guess the unsurprising takeaway from this is don't operate the optocoupler at a high forward current.

[moffy]

You might be interested in the following article which confirms your concerns: https://www.edn.com/linear-opto-couplers-and-the-loop-gain-booby-trap/
It is a good point that you raise, but generally when designing with optocouplers in a linear feedback situation you have to allow for a wide range in the CTR in your stability considerations, dependent upon the device.
But then you have the HCPL-4562 when run in its linear region is good enough for base band PAL or NTSC, page 10: https://docs.broadcom.com/doc/AV02-1361EN

[Weston]

Cool part! The CTR plots are very flat topped. I am getting interested in the physics of the optocouplers and how the two sides are matched, I should do some more reading.

That article is interesting. Closest thing I have seen so far discussing what I am talking about. The issue in that article is caused by the small signal CTR dropping off before the CTR starts strongly dropping, which my generated plot shows. And it's quite a big disparity.

At lower currents there is also a difference between small signal CTR and the DC CTR. I guess the ~2.6dB difference is small compared to typical opto variation. Just being pedantically annoyed that the CTR plot in the datasheet is mathematically not the value you want to use for small signal analysis!

[moffy]

In electronics it sometimes pays to be a pedant as long as you know when to stop.

[mawyatt]

Optocouplers are very much not linear, that's why the plot of CTR vs forward current exists.

Whats interesting is that this non-linearity is not often discussed in the context of the variance in addition to all the other factors.

I was curious so I extracted the plot data from the datasheet and used that data to calculate the small signal CTR.

Looking at the data it does not seem like too much variance. I wonder if there is a device physics explanation for the almost constant difference between large signal and small signal CTR before the device starts to saturate. The small signal CTR is ~60% higher, which is not too bad compared to the standard optocoupler binning. However, I do wonder if the additional 60% gain has ever thrown off the stability of a feedback look designed on the upper bound for CTR.

Once the device saturates the small signal CTR really falls off a cliff before the large signal CTR does. I guess the unsurprising takeaway from this is don't operate the optocoupler at a high forward current.

(Attachment Link)

This graph doesn't look right wrt to the derivative, which should be going thru zero ~15ma and negative thereafter.

If this represents the small signal transfer function, then the gain is higher at lower currents and positive, decreases in magnitude as current increases and changes polarity to inverting with the magnitude increasing as current continues to increase. 

Best,

[Weston]

This graph doesn't look right wrt to the derivative, which should be going thru zero ~15ma and negative thereafter.

If this represents the small signal transfer function, then the gain is higher at lower currents and positive, decreases in magnitude as current increases and changes polarity to inverting with the magnitude increasing as current continues to increase. 

The CTR plot in the datasheet is Ic/If vs If. The transfer function of the optocoupler is just Ic vs If. The small signal gain is the derivative of Ic vs If.

To compute small signal gain vs If from the datasheet plot you first need to calculate Ic by multiplying CTR by If and then take the derivative of that.

While the slope of CTR does go negative the slope of Ic vs If never does, it just approaches 0 as the device saturates. If optocouplers had phase reversal that would create some some big problems with loop stability.