Find equations for: (Stuck)

Question

So i've been set a task to complete these questions, and I keep coming back to this and having major problems...

 

The question asks:

 

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

 

Find equations for:

 

a) dG/dVout

 

b) d²G/dVout²

 

*Out is small text

Answer 1

I assume the log is log₁₀.  I will use just V for V_out, since it is easier to type.  Just evaluate the derivatives, using

 

d/dx log_ax = 1/[x ln(a)] 

 

and the chain rule.

 

G = 20 log(10V)

 

(a)

 

dG/dV = [20/(10V ln10)] (10) = 20/(V ln10)

 

(b)

 

d²G/dV² = (20/ln10)(-1/V²) = -(20/ln10)/V²