Overall Gain

Can anyone help me anwser this question:

Find the overall gain, in dBs of the amplifier.

Sorry I have no attempt shown. I am completely stuck. Could anyone point me in the right direction? Thanks.

Is this related to finding the input coupling factor and the output coupling factor?

 

I'll give you an outline to work with. Feel free to ask more questions.

Start by finding Vin(A1) using Rin(A1).
find Vout(A1)
Then find Vin(A2) using Rout(A1) and Rin(A2)
Find Vout(A2)
Find Vout(final) using Rout(A2)
Calculate total gain

 

Okay, I know the Vin = (4000/6000).Vs in case. How do I find Vin if I don't know Vs.

 

that's exactly it. gain is just a ratio of Vo/Vs, so Vs and Vo will drop out of your equation at the end.

 

You can actually do each step independently if you'd like. Your total gain will end up being:
( Vin[A1] / Vs ) * Av[A1] * ( Vin[A2] / Vout[A1] ) * Av[A2] * ( Vo / Vout[A2] )

 

Hi, so this means the gain for amplifier 1 is 0.67? Do I just add this to the gain of amplifier 2 to get the overall gain?

 

I'm not quite sure what you mean by 'amplifier 1' .

The gain from the input to Vin[A1] is 0.67 . The gain of A1 is 10. Since they are in series, you multiply the gains together to get the total gain, as I showed in my previous post.

 

Sorry for asking so many questions as I am having difficulty grasping this.

0.67*10 = 6.7

Vout[A1] = 6.7 and Vin[A2] = (3.5/5.7) = 0.61

Av[A2] = 20

Is this all correct so far?

 

Gain = 20log(base10)(Vo/Vi)

Can you use this? What would you use as Vout and Vin?

 

Vin[A2] / Vout[A1] = 3.5k / (3.5k + 0.5k) = 7 / 8

Otherwise you are correct thus far.

I see that your problem requests the gain in DB, therefore you will take your final gain ratio and use it as Vo/Vin for your Gain equation. That part of it is just a unit conversion.

 

I have no idea how to find the final gain ratio using the previous calculations?

 

Here are the equivalent circuits for the transfer functions of
Vin[A1] / Vs
Vin[A1] / Vout[A1]
and Vo / Vout[A2]

 

Hi, thanks for all your help so far. These diagrams make it easier to interpret. Can you walk me through the rest, or is that asking to much, as I am really finding it difficult to get my head round using all the calculations to get it in the form 20log(base10).(Vo/Vi)

 

Once you have:
Vin[A1] / Vs
Vin[A1] / Vout[A1]
and Vo / Vout[A2]

just put it into the overall gain equation from before:

Then you just have to take the log and multiply by 20

 

Okay so I need to find the log of:

((0.67)*(10))*(0.875/6.7)*(20)*(Vo/Vout[A2]) Is this right? How do I find (Vo/Vout[A2]?

 

You're close. I think mainly because there is a typo in my previous post:

This should be: Vin[A2] / Vout[A1]

and the value of that is simply the 0.875 that you calculated.

Vo / Vout[A2] is voltage division using the output resistor and Rout[A2], just like in the other steps.