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AC Analysis common emitter configuration

Discussion in 'Electronics Homework Help' started by studentLab, Apr 21, 2014.

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  1. studentLab

    studentLab

    11
    1
    Apr 21, 2014
    Hello and great day for all. Im asking for advice in this circuit. How to calculated Av for ac analysis in correct way.
    [​IMG]

    Av1 =( R3//R6//R7// Beta(re +R9) ) / re+R9

    Av2 = R8//R9 / re +R9

    Using that formula i cannot get same with multisim simulator for Av1 and Av2
     
  2. LvW

    LvW

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    Apr 12, 2014
    I see two small errors:
    * First expression: Denominator (re+R4)
    * Second expression: Numerator R8||R11 (instead of R8||R9).
     
  3. duke37

    duke37

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    Jan 9, 2011

    I am not familiar with your // convention. All computer programs that I have used from algol onwards have just used brackets.

    To look at Q2 in a simplified way, the voltage gain is the collector resistor/ emitter resistor.

    The collector resistor is shunted by the load resistor, R11 so gain is 1.03k/1k = 1.03

    Similarly, Q1 has a collector load of 1.2k so the gain is 8.

    These calculations assume that the transistors have infinite gain and that the capacitors have zero reactance.
     
  4. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

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    Jan 21, 2010
    R1 // R2 probably means 1/(1/R1 + 1/R2), i.e. R1 in parallel with R2
     
  5. LvW

    LvW

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    Apr 12, 2014
    Comparing in post#1 the circuit diagram with the formulas I think that the meaning of "//" is clear: parallel connection.
     
  6. studentLab

    studentLab

    11
    1
    Apr 21, 2014
    YEs im sorry my bad, it parallel. I fix the equation following LvW, and i get nearly same with simulator.

    * ICq1 = IEq1
    IEq1 = Vb1 - Vbe1 / R4 + R5
    = 2.16 - 0.7 / 1k + 0.150k
    = 1.27mA

    * r'e get from r'e = Vt / ICq1 = 26mV / 1.27mA = 20.47 ohm.

    Av1 =( R3||R6||/R7|| Beta(r'e +R4) ) / r'e+R4

    Av1 = (3.6k x 10 / 3.6 + 10) || R7 || Beta(r'e +R4) ) / r'e+R4
    Av1 = (2.647k x 2.2k / 2.647 + 2.2k) || Beta(r'e +R4) ) / r'e+R4
    Av1 = (1.2k x (100x(20.47ohm + 150ohm)) / (1.2k + (100x(0.02047k + 0.150k)) / r'e+R4
    Av1 = (1.2k x 17.04k) / (1.2k + 17.04k) / 0.02047k+0.150k
    Av1 = 1.12k / 0.17k
    Av1 = 6.59


    Av2 = R8||R11 / r'e +R9
    Av2 = ((3.6k x 1.5k) / (3.6k + 1.5k)) / 0.02047k + 1k
    Av2 = 1.06k / 1.02k
    Av2 = 1.04
     
    Last edited: Apr 22, 2014
  7. studentLab

    studentLab

    11
    1
    Apr 21, 2014
    Thank you duke37, it help me understand how to find voltage gain. But why simulator give 6.++ instead 8 for Av1?
     
  8. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

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    Jan 21, 2010
    The simulator probably assumed something other than infinite gain in the transistor.

    Assuming infinite gain for the transistor only works when the calculated stage gain is small compared with the actual transistor's gain.

    The same thing is true for op-amps (that you may or may not have covered). However their open circuit gain is far higher than a single transistor and thus higher stage gains can be accurately predicted using the simple model that assumes infinite gain.
     
  9. studentLab

    studentLab

    11
    1
    Apr 21, 2014
    Im confuse there diffrent formula to get Av:
    Av = Vc / Vb
    Av = Vout / Vin
    Av = Rc / Re

    In my DC analysis calculation:
    VB1 = 2.16v
    VC1 = 7.43v
    VE1 = 1.46v

    If i use
    Av1 = VC1/VB1
    = 7.43v / 2.16v
    = 3.44

    Av2 = Av1 since VB1, VC1 = VB2, VC2.

    Av2 = 3.44

    So in AC analysis i must use Av = RCtotal / REtotal right?

    And when should i use Av = Vout / Vin?
     
  10. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

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    Jan 21, 2010
    In the DC analysis, RE is 1150 ohms.

    In the AC analysis, RE is 1000 ohms because the 150 ohm resistor is shunted by the much lower impedance of the capacitor (let's call it zero ohms)
     
  11. LvW

    LvW

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    Apr 12, 2014
    @studentLab:

    1.) The gain of a circuit is a small-signal value (dynamic, differential) - hence, you must NOT use the ratio of DC values.
    2.) The expression Av=Rc/Re is a rough estimate only. The correct formula is Av=Rc/(re+Re) with re=1/gm=Vt/Ic,
    As you can see the rough approximation is valid for re<<Re only.
    3.) The expression Vout/Vin is just the definition for gain and must be transferred to another formula (like the one in 2.) which contains parts values of the reöevant circuit.
     
  12. studentLab

    studentLab

    11
    1
    Apr 21, 2014
    Thank you steve and LvW, it help me to understand better in this Av calculation. Only 2 month start studying Analog Measurement subject.
     
  13. duke37

    duke37

    5,364
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    Jan 9, 2011
    Gain of Q1
    The simplified calculation assumes infinite transistor gain and neglected re. You calculated re as 20R so the emitter resistance is nearer 20 + 150 = 170
    Gain calculation = 1200/170 = 7.0 which is very near the simulation of 6.9.

    To get even closer, you could look at the effect of the reactance of the capacitors.

    A good simulation saves a lot of work but even that is an approximation.
     
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