op-amp basics

[redepoch7]

So I'm reading up and trying to understand op-amps.

I'm sure it's simple but it's just not sinking in.

I was following the example at this site...
Inverting Amplifier

I was just wondering if someone could explain the math in the formula for the relationship between gain/Rin/Rf/Vin/Vout?

In example #1 they seem to drop the - sign... why is that? Does it have something to do with it being on the inverting input?

Example:


But then the answer to the problem is not negative. it's just 10.

-Rf/Rin = 100k/10k = 10.

Shouldn't it be -100k/10k = -10 ???

[J M Fahey]

Sorry redepoch but that seems to fit more into some Electronics 101 forum than this one.
Technical questions are gladly answered , if possible, but some basic knowledge is assumed or answers need to be *very* long and stray away from the main point.
Just not to leave you "dry", that equation is not read as "negative resistor 1 divided by (implied positive) resistor 2 equals stage gain" *but* as "resistor 1 value divided by resistor 2 value (which will give us a unit-less value, that's to say a pure mathematical number) is the stage gain; the negative sign meaning that the instant value of the output voltage is the opposite polarity/has the opposite sign of the instant input voltage , meaning that if we apply +1VDC to the input, we will get minus "x" volts in the output, and if we apply some signal wave at the input, the output one will have, besides a different value that depends on the resistors ratio, the opposite phase.
As you see, long phrases are very simplified, still being quite clear in meaning for both members of a conversation, if both share the same codes.
Congratulations on your interest in Electronics, but go step by step, in the long run it's the shortest way.

[Jazz P Bass]

Op Amps Defined

Read this.

[Steve Conner]

Shouldn't it be -100k/10k = -10 ???

Yes, the gain should technically be -10.

But the minus sign is often dropped, because as JM says, it just means that the amplified signal is turned upside down ("inverted", as the name of the circuit suggests) and that's often no big deal.

Or sometimes, it's the very reason why the circuit designer used the inverting amplifier, because he wanted to turn his signal upside down, so the minus sign is left out as it's stating the obvious.

Or whatever...

The most important things to remember about op-amps are the two golden rules as listed in that tutorial:

1. The inputs don't draw any current
2. The inputs are always at the same voltage (because the output does whatever it needs to to make that happen)

You can derive all of the gain equations from those. Of course they only hold for linear op-amp circuits, not comparators, fuzzboxes and so on, and they assume that the circuit is working properly. In fact that's a common test when troubleshooting op-amp circuits, you look to see whether the + and - inputs are sitting at the same voltage.

There are other exceptions to the rules, and purists would argue that both are false (due to offset voltages, bias currents, finite loop gain, and so on) but at a superficial level they work, and you have to start somewhere.

This semester I'm doing the labs and tutorials for Electronics 101 at the university where I work, and the students all struggle with this stuff too. I don't think they've even got as far as op-amps yet.

[Robert M. Martinelli]

I was just wondering if someone could explain the math in the formula for the relationship between gain/Rin/Rf/Vin/Vout?

To complement the good info already provided by Steve and the other "fellows solder fume breathers" ( credits ----> Enzo ) :

The key point in understanding op-amps theory of operation ( and to answer the above question of yours ) is to consider the amp's input as a "virtual ground".

If you look at the "basic inverting amp" schematic, by considering the amp's input as a virtual GND, the algebraic sum of the currents flowing into that point has to be zero. This means that If, the current through the feedback resistor Rf, has to be equal ( but with the opposite sign ) to Iin, the current flowing through the input resistor Ri ( As Steve rightfully said, the amp's input does not draw any current ). By applying Ohm's law we therefore have ( for DC ).

If = Vout / Rf

and

Iin = Vin / Ri

remembering that Iin = -If,

Vout / Rf = - Vin / Ri

Solving for Vout yields

Vout = - Vin * Rf / Ri

where it's plain to see that Rf / Ri represents the stage's gain factor ( multiplication factor ).

The same applies to AC signals, only, you have to use "impedance" ( Zf and Zi ) instead of "resistance".

I hope this answers the above question of yours.

Best regards

Bob

[nigelwright7557]

I was just wondering if someone could explain the math in the formula for the relationship between gain/Rin/Rf/Vin/Vout?

In example #1 they seem to drop the - sign... why is that? Does it have something to do with it being on the inverting input?

Example:


But then the answer to the problem is not negative. it's just 10.



Shouldn't it be -100k/10k = -10 ???

Vout = (feedback resistor divided by input resistor) * input voltage.

For an inverting amp the output is the opposite sign to the input.

The max frequency out is the bandwidth/ (feedbackresistor/input resistor)