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I need some help with understanding the Op Amp amplifier?

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Wall-ED

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In my textbook it says that the gain of a Op Amp = Vout/Vinp, so if we considered the V input to be 9 and Gain to be 2, then V out would be 18.
Great, but then when we did some experiment on it practically, the professor added a note that the V out can never be larger than V in. So I'm kind of confused....it would be great if you helped.
Also, if I have a 1.27V coming out of a terminal of an IC (Nand gate) and I need to operate a LED with V gamma = 2v. How can I use a transistor or a capacitor to increase that 1.27v to larger than 2v? Is it even possible?
 
The gain of an inverting opamp stage is -[Rf (the feed back resistor) / Rin (the input resistor)]. G = Rf/Rn.

Suppose Rf=1Ω; Rin= 1meg, then gain is -0.000001
Suppose Rf=100kΩ; Rin= 100K, then gain is -1
Suppose Rf= 1meg; Rin= 10K), then gain is -100 , which means 1mV in makes -1V out.

I think you misunderstood your instructor, or he/she doesn't know what they're talking about.

What kind of logic Gate puts out 1.27V? Sounds like you have seriously overloaded that output pin. Are you trying to connect the LED anode to the pin, cathode to ground? Are you putting a resistor in-series with the LED? What logic family? What supply voltage?
 
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This is going to have to be a partial answer because I can't understand some of your sentences.
1) If Vout can never be higher than Vin, it wouldn't be an amplifier, would it?
2) I don't know what Vinp is.
3) Vout can never be higher than the power supply voltage.
4) if your nand gate is putting out 1.27 volts, something is wrong. The output should be zero or supply voltage. What is your supply voltage to the nand?
5)I don't know what a V gamma is, but I think it's the voltage the LED needs.
6) a transistor wired as a common emitter amplifier will drive the LED.
 
this is the circuit that I was working on and trying to light the Led.
**broken link removed**

I measure the output V at F, and it is 1.27 volts. Which is not enough to light the LED. So I wanted to know if I could use a transistor to increase that voltage..
 
Using a pair of 10k resistors to make 5 volts is not a power supply. If you try to use that to drive the nand and a LED, a 10k resistor is in series with the LED.
 
Connect the 100Ω resistor to +5V, connect the cathode of the LED to the output pin of the Nand gate, try all four combination of inputs at A & B, and report back what happens. Oh, and power the circuit from a real 5V supply; get rid of the two 10K resistors.
 
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Do you have three 1.5V AA,C, or D cells? 4.5V is close enough. Do you have a 5Vdc cell-phone charger, they make ideal little power-supplies for projects?
 
Well I did it the same way explained in the picture, but I removed the 100 ohms resistor. It lit but it is very dim and unstable, here's a picture.
**broken link removed**
 
I think the circuit is working, but you really need a 5 volt supply. Do you have a 78L05 chip? That would work with a 9v battery. Or you could use a zener diode (about 5.6 volts) and an npn transistor as an emitter follower to make a 5v supply.
 
I knew it! He is using antique 7404 and 7400 ICs that use a lot of supply current and the output high current is very low to light an LED.
The 5V power supply is as joke.
 
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