Non inverting amplifier Caclulations

Discussion in 'Homework Help' started by LDC3, Aug 14, 2013.

  1. LDC3

    Thread Starter Active Member

    Apr 27, 2013
    920
    160
    Since this is a new topic, you should really start a new thread.
    You're good until you say you have a problem at:
    4 = 12Ω / R1
    Multiply both sides by R1 gives
    4 * R1 = 12Ω ----> R1 / R1 is equal to 1
    Now divide by 4
    R1 = 12Ω / 4 ----> 4 / 4 gives 1
    and find your answer.
     
    screen1988 likes this.
  2. WBahn

    Moderator

    Mar 31, 2012
    17,777
    4,804
    I agree with LDC3 that a change in topic deserves a new thread -- it becomes confusing otherwise. I'll report your post above to the mods and see if they will split off these three posts into a new thread.

    There are many different amplifier condigurations, so you really need to provide a schematic or, if all else fails, a details verbal description of the circuit topology. Don't for people to guess what your topology is and, even worse, which specific resistor you are referring to when you talk about "R1".

    I'm assuming this is the circuit you are talking about:

    [​IMG]

    This is just fine.

    Yep, this is where you mess up. Most of the time, if you are tracking units, this mistake (which is one we all make from time to time) will mess up the units and allow you to catch it. But since the 4 is dimensionless, the fact that you multiplied by it when you should have divided by it doesn't mess up the units. But since it usually will, tracking the units will let you catch this type of mistake immediately in most cases and the very experience of seeing how often you make the mistake immediately upon making it will train you to stop making it as often. So your general algebra skills will be improved by religiously paying attention to units -- just not in this particular case.

    As yourself how you got from

    4=12Ω/R1

    to

    R1=12Ω*4=48Ω

    Well you first multiplied both sides by R1

    R1*4 = R1*12Ω/R1 = 12Ω*(R1/R1) = 12Ω*1 = 12Ω

    But then you divided the left side by four and multiplied the right side by four. But that doesn't maintain equality! What ever you do to the one side you must do to the other. So divide BOTH sides by 4:

    R1*4 = 12Ω
    (R1*4)/4 = 12Ω/4
    R1 = 3Ω

    You basic algebra skills are presently pretty weak. That's fine, we were all there at one point. But what you need to do is to work your problems in sufficient detail with small enough steps so that you have absolute confidence in each step that you take. That way, you are less likely to make a mistake and, when you do (not if, but when), you will be in a good position to walk back through your work and spot exactly where you made it.

    Getting back to the circuit, let's look at it from the standpoint of working the problem without invoking some memorized or looked-up formula. How hard would it be?

    Let's work from your description in which you said that Vout changes to be whatever is needed to make the voltage at the inverting input equal to the voltage at the non-inverting input.

    Let's not even assume that we can just through the voltage divider equation at it.

    If we define I as being the current flowing in R1 from the inverting input to ground, then we have Vn (the voltage at the inverting input) is

    (1) Vn = I*R1

    We can rearrange this by dividing both sides by R1 to isolate I

    (2) I = Vn/R1

    By KCL, the current flowing in Rf from Vout to Vn is the same current flowing in R1 from Vn to ground, so

    (3) Vout = Vn + I*Rf

    By substituting (2) into (3), we get

    (4) Vout = Vn + (Vn/R1)*Rf = Vn + Vn(Rf/R1) = Vn(1 + Rf/R1)

    If the opamp does it's job, this is equal to Vp (the voltage at the non-inverting input) which is equal to Vin, so we have

    (5) Vout = Vin(1 + Rf/R1)

    And, finally, our gain is defined to be

    (6) Av = Vout/Vin = 1 + Rf/R1

    So that's where that equation comes from.

    If you were just wanting to get the value of R1 knowing Rf=12kΩ and the gain of 5, then you can follow this same reasoning path and get the answer pretty quickly.

    You know that Vn = Vin and that Vout = Av*Vin.

    You know that I=Vin/R1 and that Vout = Av*Vin = Vin+I*Rf = Vin + Vn*(Rf/R1), so you have

    Av*Vin = Vin + Vin*(Rf/R1)
    Av = 1 + Rf/R1
    Av-1 = Rf/R1
    R1 = Rf/(Av-1)

    R1 = 12kΩ/(5-1) = 12kΩ/4 = 3kΩ

    Notice that I didn't plug in values immediately. Instead, I worked with the symbols until the very end and then plugged them into the final result. This has a number of advantages. First, if gives you a lot more insight into what is happening and why the system behaves the way it does (or at least how that behavior is dependent on various parameters). Second, if you make a mistake it is MUCH easier to find, fix it, and patch up the work that follows. Third, it makes tracking the units easier because now you can think in terms of the units assocaited with the symbols and not have to track the actual units associated with the values. If nothing else, these keeps you from having to deal with all of the prefix multipliers until the very end. Finally, is largely separates the algebra from the arithmetic and let's you focus on doing each properly in turn, instead of doing them both properly when they are all mixed together.
     
    screen1988 likes this.
  3. Ross44

    New Member

    Aug 11, 2013
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    Moderator edit: This thread was split from here: http://forum.allaboutcircuits.com/showthread.php?t=88173

    Question.
    A non-inverting amplifier has a voltage gain of 5. If the value of the feedback resistor is 12kΩ what must the value of R1 be?

    A. 7kΩ
    B. 6kΩ
    C. 4kΩ
    D. 3kΩ
    E. None of the above


    in order for me to find R1, do i rearrange the forum?
    voltage gain=5
    5= 1+ Rf/R1

    5-1=12Ω/R1
    4=12Ω/R1

    but this is where i mess up.

    R1=12Ω*4=48Ω

    but if i did 12/4= 3Ω which is one of the Options!

    Where did i mess up
     
    Last edited by a moderator: Aug 14, 2013
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