# Overall Gain

Discussion in 'Homework Help' started by cheyenne, Mar 28, 2008.

1. ### cheyenne Thread Starter Active Member

Dec 6, 2007
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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?

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2. ### veritas Active Member

Feb 7, 2008
167
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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

3. ### cheyenne Thread Starter Active Member

Dec 6, 2007
48
0
Okay, I know the Vin = (4000/6000).Vs in case. How do I find Vin if I don't know Vs.

4. ### veritas Active Member

Feb 7, 2008
167
0
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.

5. ### veritas Active Member

Feb 7, 2008
167
0
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] )

6. ### cheyenne Thread Starter Active Member

Dec 6, 2007
48
0
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?

7. ### veritas Active Member

Feb 7, 2008
167
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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.

8. ### cheyenne Thread Starter Active Member

Dec 6, 2007
48
0
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?

9. ### cheyenne Thread Starter Active Member

Dec 6, 2007
48
0
Gain = 20log(base10)(Vo/Vi)

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

10. ### veritas Active Member

Feb 7, 2008
167
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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.

11. ### cheyenne Thread Starter Active Member

Dec 6, 2007
48
0
I have no idea how to find the final gain ratio using the previous calculations?

12. ### veritas Active Member

Feb 7, 2008
167
0
Here are the equivalent circuits for the transfer functions of
Vin[A1] / Vs
Vin[A1] / Vout[A1]
and Vo / Vout[A2]

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13. ### cheyenne Thread Starter Active Member

Dec 6, 2007
48
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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)

14. ### veritas Active Member

Feb 7, 2008
167
0
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

15. ### cheyenne Thread Starter Active Member

Dec 6, 2007
48
0
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]?

16. ### veritas Active Member

Feb 7, 2008
167
0
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.