# Why is the Voltage Gain 54 dB instead of 50 as stated in the problem?

Here I'm trying to find the overall voltage gain. I did everything correctly, except out of nowhere, the gain in dB was 54dB, not 50dB. I don't know why. Here's the solution:

And here's the figure (or problem statement)

Can someone explain why?

• Just looks like a typo. The professors who write textbooks and the grad students who proofread the problem sets at 3 AM are not infallible. – The Photon Sep 20 '16 at 17:33

could be a typo... quick analysis....

• Voltage gain, Av remains ~50dB or 49.7 @16Ω assumes Av=no load
• (negligible load loss -0.3dB @16Ω)
• Current gain, Ai=Av*Rin/Rout or in log format Av(dB)+Ar(dB)
• where Rin/Rout= 1M/{1kΩ:16Ω} = {1000:62,500} = {60dB:96dB}
• Power gain, Ap(dB)=Ai(dB) + Av(dB) = {50+60;49.7+96} for {1kΩ:16Ω}