Unified Robotics I: Actuation

Operational Amplifier

Non-Inverting Amplifier

So far, we have been looking at inverting op-amp circuits. We’ll now turn our attention to the non-inverting op-amp circuit.

Figure 7-1 - Non-Inverting Op-Amp Circuit

Notice that the input voltage vin is this time connected to the non-inverting input. We again have two additional resistors in the circuit. The feedback resistor R2 again connects the output to the inverting input, but this time the other resistor R1 acts to form a voltage divider with R2.

Before going on let’s examine whether the feedback is still negative. We’ll start by assuming the supply voltage vin is positive as shown and therefore the output voltage vowill be positive (and possibly large). Since the resistors R1 and R2 form a voltage divider, some portion of the output voltage vo will appear across the resistor R1; let's call the voltage v1.

We know that the differential input voltage Vi is given by the equation: vi=vin-v1. It should be apparent that as vo (and therefore v1) get larger then vi will get smaller (given a constant vin). Thus vi is driven towards zero and we indeed have negative feedback.

What would happen if there was positive feedback?

    • A) Nothing
    • B) vo → 0
    • C) vo → ∞
    • D) The Op-Amp will burn out
    • E) No clue?
  • Show Answer
    • C) vo→∞

Now that we know the feedback is negative we can use the analysis techniques we have seen previously. More specifically, we can use the summing point constraints which are that: vi = 0 and ii = 0. If we apply KVL around the left most loop as shown we can see that vi=0 and therefore vin=v1. Since ii=0, R1 and R2 form a voltage divider which gives us:

v1=(R1vo)/(R1+R2).

Putting it all together we can finally see that the gain is given by: Av=vo/vin=(R1+R2)/R1=1+R2/R1. As you can see, the gain in this case is always going to be a positive value. It is again, however, influenced by the ratio of the resistors R2 to R1.

There are a couple of interesting things to note about the op-amp circuits that we’ve been studying so far. The first is that the input resistance of the circuit is theoretically infinite (resulting in ii=0). The implication of this is that the op-amp places no load on the circuits that are driving it. Also note that the load resistance RL has not shown up in either of the voltage gain equations developed so far. This means that the output voltage is independent of the load resistance. The implications of this fact is that the output resistance Ro is zero.

It’s important to remember that we have been dealing with an ideal op-amp in each of these analyses and real op-amps made behave somewhat differently. The good news, however, is that real op-amps don’t behave all that much differently from the ideal op-amp model so we are justified in using that as the basis for our analyses.

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