This is how I might chart a compression ratio of 20:1, 2:1 and upward expansion at .5:1. I included upward expansion because compressors reduce gain above threshold, not raise gain. A 20:1 ratio reduces gain by -19dB for every +20dB that passes the threshold point. You can look at it going backwards from rotation point to threshold, but the signal is still reduced in gain, not raised in gain, "because the signal is always to the right side of 45 degrees". Even Morgan when he offsets the two ratios on his graph and puts input gain above equity, is showing that at threshold, the signal is reduced in gain. An easy way to show what a compressor does, IMHO and one that is mirrored by every compressor designer on the many compressors and limiters that I own is below.
1. All 3 signals enter the compressor at unity gain (45 degree diagonal line). The red line is there also, it's just covered up by the blue line. This does not signify make up gain, just the signal as it goes through the compressor and just before the make up gain structure, which is not on this chart.
2. The 20:1 line shows that for every +20dB that passes threshold, only 1dB is output "from the compression stage". This is a "gain reduction" of -19dB, not a gain increase of +19dB. When signal rises above threshold, compression is applied, "gain is reduced" NOT raised.
3. The 2:1 line show that for every +20dB that passes threshold, that +10dB leaves the compressor. This is before make up gain. These two lines fall to the "right" of the 45 degree diagonal "unity gain" line, signifing that "signal is reduced in gain from where compression is applied at the threshold". For these 3 examples I've chosen a hard knee as to make it less complicated to understand. Hard knees are not exclusive to "just limiters".
4. The red line signifies that for every half a dB that passes threshold the signal is expanded upwards by 1dB. The line shows gain "because it's on the left side of the 45 degree unity gain line". Signal does not start at the top and go down on my chart, it starts at the bottom left and goes up at unity gain 45 degree diagonal until the threshold is met, where the 20:1 and 2:1 ratios reduce signal and where the upward expansion threshold is met, the signal is raised in gain by 2 to 1, a half dB = 1dB rise in gain. If you follow the lines, they follow the input and output decibal marks on the X-Y graph, showing that the red line is actually showing that when signal is +10dB above threshold, gain is raised to +20dB a .5:1 ratio form input to output "of the compression stage". My compressors typically only output +12dB to +18dB, I couldn't raise gain "after the compression stage", by +19, even if I wanted to.
The upward expansion ratio you can call theoretical if you like and is just there to show where the line has to go to the left of unity gain to show an increase as on the right side of the unity gain line it's signifying reduction. Gain drops on the right side of unity gain on an X-Y graph and rises on the left side of unity gain. I don't really want to side track into expansion as it's mostly used downward, for example a downward expander that lowers gain below threshold and is the reverse of compression.
This is the way that I was taught when I first started working with compressors and limiters some 35 years or so ago. I haven't changed my view or way of thinking since than and I've never had any problem getting compressors and limiters to do exactly what I want. I threw this together rather quick, if anyone finds a flaw in what I'm relating, I'd be happy to hear it explained in a calmly manner in their own words.
If anyone understands it in a similiar manner as I've just explained, I'd like to hear from you too.
Thanks,