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The Resistance seen by the Op-Amp in our circuits.

The Op-Amp Circuits under test.

Thankfully we are through with the heavy meals of Op-Amp theory for awhile. Tonight’s post will be a full meal but nothing like the last one. We will not have to loosen our belts, walk around the parking lot a few times and move the seat in the car back to get under the steering wheel after eating this one. (Yeah that happened to me once in my younger days after going to a Mexican buffet restaurant. I was kind of dumb back then.)

First, I would like to introduce a short-hand way of writing a formula for electricity.   When two resistors, for example R1 and R2 are in parallel we can write  R1 || R2 to show the two are in parallel.   Another kind of quick way of thinking of this that will also simplify your life is if R1 || R2 the total resistance will be less than the lowest of the two resistors.   If both resistors are exactly the same value the total will be 1/2 of that value.  If the lowest resistor is less than or equal to one-tenth the value of the higher resistor, a good estimate is to assume the total is equal to the lowest.  If the lowest is exactly 1/10 of the highest, then the total will be 90.9% of the lowest. This is less than a 10% error and no calculator is necessary with simply saying the lowest value.  Remember many resistors come with a 10% tolerance.

Now we will look at the resistance seen by the op-amp in our two circuits.    The easiest on to understand is the non-inverting amplifier.  The output is feeding two resistor strings and both go directly to ground.  The amplifier is seeing a total load of: R load || (Rf + Rg).

The inverting amplifier circuit is not much harder to understand if you remember that if the non-inverting input is at 0 V then the inverting input is also at 0 V.  The amplifier is seen total load of: R load || Rf.

Now that we know what the amplifier will see, what is acceptable?  There really is two answers to that question, desirable and bad.   Desirable for the amplifier we are using is shown on the “output voltage swing vs load resistance” graphs on the data sheet. (If you have not downloaded the data sheet yet, it is available here:  MC4558 data sheet). The output voltage swing starts decreasing significantly if the load resistance is less that 2KΩ and this would be the bottom limit for any design I would do with this amplifier driving the load.

However, if we wanted to get closer to the smoke test limit another way of looking at things is the following.  The data sheet states the output resistance of the op-amp is 75Ω and it also states that the maximum power dissipation for the op-amp is 680 mW. P= V*V/R  so square root of (P*R) = maximum V dropped across the amplifier.  0.68 * 75 =  51  and the square root of 51 = 7.14V drop.  Going back to our graphs that is about a 450Ω for +/- 15 Volt power supplies.  (Use the point where the 8 V line crosses because 15 V – 8V = 7V drop).   I would not feel all warm and fuzzy going this low, because we do not know if all the voltage is dropped across that 75Ω part of the circuit and the 680 mW dissipation is probably for both amplifiers within the package. But I guess if you really wanted to try and “if you got ’em, smoke ’em”, you could try.  Again I would be looking for alternatives.

In the next post on op-amps I will summarize all of what we have determined and make recommendations for various situations.   After that we will talk about temperature measuring devices and why an op-amp circuit is necessary to “linearize” the output before we jump into digital.

Very soon I will put up some links that go into a lot more detail than what I have about op-amps.  The manufactures of these circuits put out a lot of application notes in pdf format.

Once we get past the temperature measuring device, I will talk about temporary energy storage devices, capacitors and inductors.  Not too long after we introduce them in DC circuits, we will have to switch into AC because many of you probably are more interested in actual time varying signals than you are with pure DC.   There is lots of “fun” in our future.  As always I hope to deal with some practical circuits and not just theory as we progress.

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