Answer to Question #97351 in Calculus for Matthew Plowman

Question

The gain of an amplifier is found to be G=20log(10Vout):

The gain of an amplifier is found to be G=20log(10Vout):

Find equations for:
a) dG/dVout ?
b) d^2 G/dV out^2 ?

Answer 1

$a)\\ dG/dVout = 20* 1 * 10 / ( 10 * Vout * ln10 ) = 20 / ( Vout * ln10 );\\ b)\\ d^2G/dVout^2 = ( -20* d( Vout* ln10 ) /dVout ) / ( Vout*ln10 )^2 = -20*ln10/( (ln10)^2 * Vout^2 ) = -20 / (ln10* Vout^2);$