# Q. How is constant loudness maintained when balancing the Mid and Sides channels?

Grace Design m201 mic preamp.Photo: Mike Cameron

I have a question regarding the Grace Design m201 mic preamp, and specifically its Mid-Sides matrix rotary switch, which adjusts the balance of the Mid and Sides signals to control the stereo width.

When I set up a mixer to decode M-S to left-right, I understand the process of summing the Mid signal and the linked Sides and inverted-Sides signals to achieve different stereo widths — and there’s no maths involved when you adjust the three faders. However, I am puzzled by how the Grace matrix step switch can process and deliver the different percentages of Mid and Sides because on the mixer I would have a hard time to set my faders to get 70 percent Mid and 30 percent Sides, or other percentage ratios, by ear — and this must be further complicated if I have to take into account the panning law(s) and keeping the loudness constant as I move the faders.

A technician at Grace Design shared the following approximate values for the different Matrix switch settings, but I wondered if you could explain how the switch works and how these switch values relate. Also, am I correct in thinking that the different attenuation values attempt to maintain equal loudness to the 50:50 mix or 100 Mid, so that the L-R signals for all switch settings sound equally loud in a mix?

Here is the table of the approximate M-S width attenuation:

 M-S Ratio (%) Mid Gain (dB) Sides Gain (dB) 100:0 0dB -∞dB 70:30 -3dB -10.5dB 66:34 -3.5dB -9.2dB 62:38 -4.1dB -8.4dB 58:42 -4.7dB -7.4dB 54:46 -5.4dB -6.7dB 50:50 -6dB -6dB 46:54 -6.7dB -5.4dB 42:58 -7.4dB -4.7dB 38:62 -8.4dB -4.1dB 34:66 -9.2dB -3.5dB 30:70 -10.5dB -3dB

From Jazzbeat via email

SOS Technical Editor Hugh Robjohns replies: The switch you describe on the m201 is essentially just a ‘crossfader’ which adjusts the relative balance of the Mid and Sides signals, increasing one while decreasing the other (and vice versa) in a proportional way. The ratios have been chosen not to maintain equal loudness, but to ensure that the decoded outputs never exceed a nominal maximum level.

As you’ll recall, the decoder equations are L=M+S and R=M-S. So, if there is no Sides signal, just Mid, when decoded that Mid signal appears equally at both the left and right outputs, so the switch provides 100 percent Mid. If a sound source is at the full extreme of the stereo acceptance area it will appear hard left or right in the decoded stereo image, and so M=S (or M=-S). Consequently, the switch reduces both the Mid and Sides signals by 50 percent, so that the sum is the same level as the previous case. And other positions maintain the same proportional balance.

The ratios and the way they all sum to 100 percent are easy to see when expressed in percentages, but faders are marked in decibels, so the table from Grace simply provides that translation for you. Decibels are calculated as 20 times the log of the ratio, and the percentage is a ratio (by definition). As an example, the 50 percent ratio translates into decibels as: 20*Log(50/100) = -6dB. So, if you want to match the Grace ratios on your console faders, simple move them to introduce the equivalent amounts of relative attenuation.

This arrangement switches between two ladders of resistors, and is calculated to provide an overall load resistance of 15kΩ.

As for the actual mechanics of the switch, it is just a ganged switch with two chains of resistors linking each set of contacts to form two potential dividers, one for the Mid signal, and one for the Sides signal, but configured to work in opposite directions so that as the Mid attenuation increases, the Sides attenuation reduces (and vice versa). To keep the diagram simple I’ve reduced the number of ratio options compared with Grace’s table, but the principle is just the same, and I’ve calculated the appropriate resistor values to give an overall load resistance of 15kΩ.