# Amplifier equations

Discussion in 'General Electronics Chat' started by Sparky49, Sep 27, 2012.

1. ### Sparky49 Thread Starter Well-Known Member

Jul 16, 2011
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Hi everyone,

I reading up on amplifiers, however I've come across something which I don't understand.

If you take a look at the picture, you'll see a amplifier with feedback setup. I have written the equations next to it in order, however, looking at the last one, I am not sure why a j-notation has come into play.

Could someone please expain? I'm sure this is very easy.

Many thanks,

Sparky

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2. ### Sparky49 Thread Starter Well-Known Member

Jul 16, 2011
822
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If you feel you need any extra information - like text around it, just say I will help.

3. ### Ron H AAC Fanatic!

Apr 14, 2005
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Why do you (or they) say that Vi=0? In general, it can be any value. And β*Av≠-1, in the general case. That's absurd. Did you leave out the context of the development of this equation?

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4. ### Sparky49 Thread Starter Well-Known Member

Jul 16, 2011
822
421
All I can find is:

"When considering oscillator design, the important characteristics which must be considered are the range of frequencies, frequency stability and the percentage distortion of the output waveform. In order to achieve these characteristics two necessary requirements for oscillation are that the loop gain (BA) must be unity and the loop phase shift must be zero.

Consider Fig 1.5. We have" and so follows.

I agree, I don't see why Vi must be zero. :/ I'm missing something for sure.

Perhaps if I scanned the pages? I would send them by pm to avoid copyright issues.

5. ### ErnieM AAC Fanatic!

Apr 24, 2011
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If:

BAv = -1 + j0

then:

BAv = -1

and de j go away!

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6. ### Ron H AAC Fanatic!

Apr 14, 2005
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OK, it makes sense in the context of oscillators. However, I think the minus sign in the first equation should not be there. I believe β*Av should be +1 +j0, not -1+j0. The reason for the j0 is to indicate that there must be zero degrees phase shift around the loop.
I'm still confused about "vi=0". If Vi=0, there can be no Vo.

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7. ### Sparky49 Thread Starter Well-Known Member

Jul 16, 2011
822
421
So should the equation above read:

BAv - 1=0

I agree about Vi=0 it puzzled me.

8. ### Ron H AAC Fanatic!

Apr 14, 2005
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OK, now I get it:
Vi=β*Av*Vi
Vi*(β*Av-1)=0

Here's the part we missed:
Either Vi=0 or β*Av-1=0
Since Vi≠0,
(β*Av-1) must =0.
Therefore, β*Av=1. This must be at zero phase shift for oscillation to occur, so

β*Av=1 + j0

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