Differential amplifier design

Discussion in 'Homework Help' started by boks, Oct 10, 2008.

  1. boks

    Thread Starter Active Member

    Oct 10, 2008
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    0
    1. The problem statement

    http://i36.tinypic.com/hugkyb.jpg

    2. Relevant equations

    According to my book, if R3 = R2 and R4 = R1, I can use the following formula:

    Vo = (R2/R1)(V2 - V1).

    3. The attempt at a solution

    We want R2/R1 to equal 5. This means that R3 and R2 must be 5*3,3 = 16.5 k(ohms).

    However, I don't know what to do with the inner resistance of V2 and Vo. Any suggestions?
     
  2. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    R3 = 5*3.3 = 16.5 k(ohms)

    But how about the inner resistance of V2, and the 22k(ohms) resistance? Don't I need to take them into consideration?
     
  3. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
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    It's 1.2 Mega ohms, not milli ohms.
     
  4. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    No, 1.2M = 1200K
     
  5. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    Then I get negative resistance.
     
  6. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    Forgot all we said. Your calculations are right but on your final answer (5*(V1-V2)) you have o subtract the voltage drop across the 1.2M resistor due to the current through R1+R2.

    If you want i can tell you in a few hours the complicated answer because now i am busy.
     
  7. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    Ok before i was busy and my mind was on my job so i wrote some stupid things and i deleted my posts.

    According to your circuit diagram, the output voltage will equal

    Vo=(V2-V1)*(R3/R4) (1)

    if R4=R3 and if R2=R1 and not as you said.

    Thus 5=R3/R4=R3/3.3K thus R3=16.5K

    But now R3 is not equal to R4 anymore so we cant use equation 1 to calculate the output voltage.

    We will use the general equation for the output voltage of the differential amplifier which is :

    Vo=V2((1+R3/R4))/(1+R1/R2))-V2(R3/R4) (2), according to your schematic

    Now, to take the desired equation for the output voltage we need to equate ((1+R3/R4))/(1+R1/R2))=5 because (R3/R4) equals 5 (we calculated it before) and to be able to take 5 as a common factor.

    Thus, R4=3.3K , R3=16.5K
    lets say that R1=0 but because V2 has an inner resistance of 1200K then we can say that R1=1200K

    Thus, we only need to calculate R2

    5=((1+R3/R4))/(1+R1/R2))=((1+16.5/3.3))/(1+1200/R2))=6/(1+1200/R2)

    thus R2=5*1200=6000K=6M

    If we apply our resistor values to equation (2) we get:

    Vo=5*V2-5*V1=5*(V2-V1) as desired
     
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