# Find the voltage gain of operational amplifier

Discussion in 'Homework Help' started by ADCapacitor, Mar 25, 2016.

Feb 3, 2016
42
0
Find the voltage gain and Io

Vi=V+=V-
I1=(V-)/R1
I1=0.5mA

Node V-
Vi-0/R1+Vi-Va/R2=0
Va=-50mV

NodeA
[Va-V-/R2] + Va-0/R3 + Va-Vb/R4 =0
Vb=-0.2V

NodeB
Vb-Va/R4 + Vb-0/R5 +Vb-VO/R6=0
Vo=-0.55V

Av= -Vo/Vi
=-0.55/50m
= -11V/V

Io= Vo/RL
=-0.55/100
=-55mA

thank for the help

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2. ### Jony130 AAC Fanatic!

Feb 17, 2009
4,174
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And Vin is ?? Also there is some thing wrong with your answer because voltage gain cannot be negative.
Also notice that if Vin = 1V the voltage at V- is also equal to 1V and from there we can find Va using only KVL and KCL

Va
= VR1 + VR2 = Vin + IR1*R2 = 1V + (1V/100Ω)*200Ω = 3V.

Vb = VR3 + VR4 = Va + VR4 = Va + (IR3 + IR2)*R4 = 3V + (3V/200Ω + 1/100Ω)*200Ω = 8V

And if you use the similarly approach we can find that Vo/Vin = 21V/V

Feb 3, 2016
42
0
Vin is 50mV

I use KCL in the above calculation
current goes into the resistor R2 =current out the resistor R3 +R4
Vin-Va/R2= VA/R3+Va-VB/R4

But why
Va = VR1 + VR2 = Vin + IR1*R2 = 1V + (1V/100Ω)*200Ω = 3V.
and
Vb = VR3 + VR4 = Va + VR4 = Va + (IR3 + IR2)*R4 = 3V + (3V/200Ω + 1/100Ω)*200Ω = 8V

4. ### Jony130 AAC Fanatic!

Feb 17, 2009
4,174
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fir Vin = 50mV the voltage at VA node is equal to:
Voltage drop across R1 + voltage drop across R2 = VA = VR1 + VR2
Voltage drop across R1 = Vin because V+ = V-
Voltage drop across R2 = current through R2 resistor times R2 resistance. And the current through R2 is equal to Vin/R1 because R2 is in series with R1. So, the same current must be flowing through these two resistors.
Therefore VA = VR1 + VR2 = 50mV + 50mV/100Ω *200Ω = 150mV

And VB node is equal to VR3 + VR4, Also notice that VR3 = VA and VR4 = I*R4 = (IR2 + IR2)*R4 do you agree with this ?

Feb 3, 2016
42
0
sorry, but I still don't understand...
I find an example which is similar to this question

short R5
V+=V-
0-Vi/R1 + 0-Va/R2=0
Va=-0.5V

Then, I follow the same method to find the Va
Vi-0/R1+Vi-Va/R2=0
Va=-50mV
What's problem here?

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6. ### Jony130 AAC Fanatic!

Feb 17, 2009
4,174
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$\frac{Vi}{R1}+\frac{(Vi-Va)}{R2}=0$

Try solve this for Va

$\frac{50mV}{100\Omega}+\frac{(50mV-Va)}{200\Omega}=0$

Feb 3, 2016
42
0
Thank you
I think I forgot the negative sign , lol
Va sholud be 150mV
Then I can use the same way to find Vb,=0.4V ,Vo=1.05V
then I get the Av=21, Io=10.5mA

8. ### Jony130 AAC Fanatic!

Feb 17, 2009
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Very good, but you still do not have the right answer for Io. I can assure you that Io is not equal to 10.5mA . By Io I mean the op amp output current. 10.5mA is a current that is flowing through R7 resistor.

Feb 3, 2016
42
0
May be Io is equal to I7-I6 ?
(Io+I6=I7)
And I6=Vb-Vo/R6
I know the I6 and I7 ,then I get Io?

10. ### Jony130 AAC Fanatic!

Feb 17, 2009
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Why you think that Io is a difference between I7 and I6 ?

Feb 3, 2016
42
0
Because Io and the current flowing out the resistor R6 are flowing into node Vo?
So I guess Io which is equal to I7-16

12. ### Jony130 AAC Fanatic!

Feb 17, 2009
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Note that for Vin = 50mV we have Vo = 1.05V and Vb = 0.4V. So in which direction IR6 current is flowing ?

Feb 3, 2016
42
0
Thank you
I get it
So Io is Vo/R7 +Vo-Vb/R6 ?

14. ### Jony130 AAC Fanatic!

Feb 17, 2009
4,174
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Yes, that right but also do not forget about parentheses.