Compression Ratio Calculation

[changes]

Is there an easy way to calculate the compression ratio of an optical compressor like the Demeter Compulator???

[samhay]

In this case, the ratio is 10k divided by the resistance of the vactrol's LDR.
The datasheet says the on resistance of the vactrol is 400R with 2 mA through the LED, which the circuit can probably just about deliver.
So, max ratio = 10/0.400 = 25. 
The circuit won't be compressing this hard very often. The make up gain can be set from 2-22 with the trimmer, suggesting that in the real world, the max ratio is probably somewhere between 2-22.

[Transmogrifox]

I'll give a little more detail into samhay's answer as a feedback compressor is a bit tricky and it can't be meaningfully described by the traditional definition of "ratio" for a dynamic range compressor.

A compression ratio is X dB increase in input above threshold to get a 1 dB increase on the output, assuming the slope is log-linear above the threshold.

For a feedback compressor, the compression ratio is continually increasing with increasing input level to the point that 1 of 3 things happen:
1)  Ideal feedback compressor will approach ratio of infinity:1 for large signals.
2)  Most practical compressors will reach their gain reduction limit (such as above) and will have a ratio of 1:1 for signal levels higher than their maximum control range.  The compression ratio before loss of control will be pretty high.  This can be approximated according to samhay's calculation which represents the maximum available gain reduction.  This is an approximation because it assumes the slope has remained log-linear since the onset of compression. To be more exact the ratio is technically a rate of change (slope) so you would need to know the rate of change of the resistance in response to a very small change of signal level.  In the end it will probably be more than 20:1.  Beyond 20:1 is practically a limiter (infinity:1).
3)  Because of gain reduction limits or headroom limitations the circuit starts clipping and is no longer acting like a dynamic range compressor.  For example in the circuit above if you fed it a signal much greater than 4Vpp into this circuit it the gain reduction would be maxed out and the input buffer would be clipping. 

Between 1Vpp and 4Vpp it's not acting like a compressor -- just an attenuator.  Below 1Vpp it's a gradually increasing compression ratio toward something north of 20:1 as signal level increases.

The "compress" knob is a combination of threshold control and in a loose sense ratio as it causes a slower rate of gain change with output signal level change, but here you're still left with the solution of approximating ratio as an average, or a linearized approximation.

The short answer is you really can't come up with a single number for compression ratio that is meaningful in context of the traditional measure "ratio".  You need a compressor that behaves like a traditional compressor where the slope is log-linear after the knee in order for "ratio" to be meaningful.

However, this circuit has more than enough gain reduction to be able to get to amount of compression equal to a limiter, so for all practical purposes you have compression ranging from barely detectable on up to as much squish as you would expect a guitar player to need.

[changes]

Thank you samhay and Transmogrifox for the in depth reply
So if i get it right one way to maximize ratio and make sure that it works as a limiter would be to increase the 10k resistor before the photoresistor?

[samhay]

Maybe.
That will increase the maximum possible compression ratio, but as Transmogrifox mentioned (nice post BTW), it's more complicated that that and it is not my first recommendation.
The biggest issue with your plan is that this will feed less signal into the sidechain (which does some rectification and drives the LED), so you will potentially get a higher minimum resistance out of the LDR, and thus less compression - remember it's the ratio that matters.

Are you using a VTL5C10 vactrol? If not, and you have rolled-your-own, it's quite likely that the minimum resistance is much higher than 600R. I would start here.

You could try to drive the LED harder by decreasing the value of the 619R resistor, but if you go too low, you will burn out the LED. A better option might be to try increasing the value of the 10k resistor in the negative feedback loop of the sidechain op-amp (connected between output and negative input). This will increase the gain of the rectifier, but will still limit the maximum current to the LED as the signal can't exceed the power rail.

[Transmogrifox]

Increasing 10k feeding the photoresistor will extend your dynamic range of input levels.

As samhay mentioned increasing the value of the 10k resistor in the feedback loop will make it approach a high compression ratio with much lower input signal levels.  He didn't mention the trimpot but this will have the same effect as messing with the 10k feedback resistor.  Start by dialing the trimpot to its minimum setting and only change the 10k if this doesn't give you as much compression as you want.

I think the final answer will be "all of the above"
Increase 10k going to photoresistor
Decrease trimpot or replace with short.
Increase 10k in feedback.

Increasing the control loop gain pushes it to limiting much faster while adjusting divider resistor against photo resistor gives it a wider range of control.

If you make this stuff too extreme then it will sound terrible, so do this in moderately-sized steps so you can experience the change with each parameter.

[changes]

Thank you once again guys!!!
I'll try messing with the trim and 10k resistors