Possible webpage title: What is the Maximum Gain of an Op-Amp?

[DefaultName]

Homework Statement

http://img440.imageshack.us/img440/9996/untitledbq0.png

Homework Equations

Please see picture.

The Attempt at a Solution

Please see picture.

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I have a strong feeling this is incorrect. I think I'm missing something important here... I don't know what R1 is, so I'm a little lost.

 

[AlephZero]

You haven't used two facts you were given in the question:

1. The output voltage can't exceed the power supply voltages, i.e. =15 <= V0 <= +15
2. The output current from V0 must be less than 200 mA.

Those two conditions limit the values that V0 can have. When you know the maximum value of V0, you can find the the maximum gain of the circuit.

When you know the gain, you could then find R1 and R2 to give that gain, but the question doesn't ask you to do that.

 

[DefaultName]

You haven't used two facts you were given in the question:

1. The output voltage can't exceed the power supply voltages, i.e. =15 <= V0 <= +15
2. The output current from V0 must be less than 200 mA.

Those two conditions limit the values that V0 can have. When you know the maximum value of V0, you can find the the maximum gain of the circuit.

When you know the gain, you could then find R1 and R2 to give that gain, but the question doesn't ask you to do that.

"2. The output current from V0 must be less than 200 mA."

Does that mean that I_o = -200mA when the op-amp is operating at it's saturation point?

Also, should those two facts I overlook affect my KCL equations? I'm believing not, but I already made an error so I'm not quite sure.

 

[berkeman]

I'm missing something here (it wouldn't be the first time, however). The gain of the overall amplifier is set by the values of the two resistors, which you indicate as given in the problem statement and equal to each other.

Given that the overall gain of the circuit is set by the external resistors as +2, and given that 2V across the load resistor of 40 Ohms demands less than 200mA max that the opamp can source, then the max gain of the opamp itself could be infinite, it would seem.

Is that really the whole problem statement word for word?

 

[ravenprp]

Yes, it is stated word by word.

"The gain of the overall amplifier is set by the values of the two resistors, which you indicate as given in the problem statement and equal to each other."

The sum of the resistances equals 90.

 

[berkeman]

Oh, that's what I missed. The sum of the resistors is 90k, they are not 90k each. Okay, so you need to figure out whether you run out of output current or output voltage range first.

Except, they didn't give you a datasheet showing the output voltage range of the opamp, so I guess you need to assume the ideal, which is the +/- rails.

 

[AlephZero]

"2. The output current from V0 must be less than 200 mA."

Does that mean that I_o = -200mA when the op-amp is operating at it's saturation point?

Also, should those two facts I overlook affect my KCL equations? I'm believing not, but I already made an error so I'm not quite sure.

I would take it to mean the limits on the output current are +/- 200 mA. You need to do a KCL at the output to find the limits for V0. (For practical purposes R1 and R2 don't affect this much becase R1+R2 = 90k ohm and RL = 40 ohm).

If you think about the directions of the current in the resistors (or as Berkeman implied, if you recognise the circuit is a non-inverting amplifier) then you can decide whether the output voltage is positive or negative when VS = +1V. If you decide wrong, you will probably finish up with negative values for R1 and R2 which doesn't make sense.

You need two equations connecting the two unknowns R1 and R2. When you know the V0 corresponding to VS = +1V, you can get one equation from KCL at the input (node V1). The other equation is R1 + R2 = 90k.

 

[trevie1970]

looks like a gain of 8 to me.. if you understand the maximum current drawn is 200mA then I x R = 200mA x 40 Ohms = 8 volts therefore gain of 8 is known. then r1 and r2 ratio can be worked out. 10k 80k respectively. this is not taking into account the feedback current which is probably around 77uA. R2/R1 = 80k/10k = Gain of 8

 

[Redbelly98]

looks like a gain of ___ to me.. if you understand the maximum current drawn is 200mA then . . .

Hello Trevie,

Welcome to Physics Forums. Actually, the goal was to get DefaultName to figure that part out.

 

[trevie1970]

yea, sorry, I didn't realize until I had posted the answer?

 

[Redbelly98]

Never mind!

This thread is over a year old ... don't worry, no harm done