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Low output MC - Math Question ??

Calculators Ready... I'm presently using a low output- .3mV
MC cartridge with the Manley Steelhead phono stage. I prefer the sound of the cartridge thru the MM section (no step-up transformer) to the MC section w/ step-up. The MM section has a maximum gain of 65db. However, there is not enough gain in the MM section to allow me to run the Steelhead direct into the amps, so I must use a pre-amp (ARC REF 2Mk.1 w/ 18db gain) to achieve the correct gain structure. BTW- This combo sound pretty good! Now the Math Question- What is the relationship between cartridge output and db gain? Specifically how high of a cartridge output would I need to run into the Steelhead MM section set a 65db gain to realize 80+db of total gain, so as to have enough gain to drive the amps directly??? Hopefully I have not oversimplified this equation because of a lack of information.
fbhifi

Showing 1 response by herman

herman
2,280 posts
 
voltage gain = inverse log (dB gain / 20)
inverse log X is 10 raised to the power of X

You are looking to make up the difference of 15dB from the 80dB MC stage to the 65dB MM stage.

15dB divided by 20 = .75
take the inverse log of .75 = 5.6
.3 mV times 5.6 = 1.7 mV

So .3 mV amplified 80dB will have the same output as 1.7 mV amplified 65dB.

80dB is a gain of 10,000. So 10,000 times .3 mV = 3V
65dB is a gain of 1,778.. So 1,778 times 1.7 mV = 3V
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