Now to the non-inverting op amp circuit. With this one we'll send the input signal to the non-inv input but still set up a voltage divider from the output to the inverting input, so as to reign in the open loop gain (A) again.
The Non-Inverting Op Amp Circuit
----------------------------------------
Gnd ------- R1 --------- Vtap --------- Rf ---------- Vo
Op Amp: +in = Vin; -in = Vtap; out = Vo
Onc again, we use our friend the VDR, which says
Vtap
=
R1(Vo)
---------
R1 + Rf
Next, use the general eq for the op amp/comparator
Vo = A(Vp - Vn)
Now, this time, make Vp = Vin and Vn = Vtap and substitute.
Vo
=
A(
Vin
-
R1(Vo)
---------
R1 + Rf
)
Make a common denominator on the right by saying
Vo
=
A(
Vin(R1 + Rf) - R1(Vo)
--------------------------
R1 + Rf
)
And then lose it via
Vo(R1 + Rf) = A(Vin(R1 + Rf) - R1(Vo))
Now expand both sides.
VoR1 + VoRf = AVinR1 + AVinRf - AVoR1
Then group.
VoR1 + VoRf + AVoR1 = AVinR1 + AVinRf
Factor out Vo and Vin.
Vo(R1 + Rf + AR1) = Vin(AR1 + ARf)
Solve for Vo.
Vo
=
Vin(AR1 + ARf)
------------------
R1 + Rf + AR1
(Notice we didn't take the simplification that Vo/A=0 this time, as we saw that we'll get both the ideal and real at the end anyway.)
Now factor A from the numerator
Vo
=
VinA(R1 + Rf)
------------------
R1 + Rf + AR1
Then, to make it easier to understand, do our trick of multiplying by 1=A^-1/A^-1.
Vo
=
Vin(R1 + Rf)
------------------
(R1 + Rf)A + R1
This is the general equation for the non-inverting op amp circuit.
Once again, we see that, with A not equal to infinity, as the ideal assumption goes, the output decreases because the denominator increases by (R1 + Rf)/A, just as was the case with the inverting op amp.
Likewise, setting A = infinity, the general equation goes to the familiar ideal equation:
Vo
=
Vin(R1 + Rf)
---------------
R1
Finally, note that it is impossible to set a closed loop gain of less than one, since the eq can be adjusted to
Vo
=
Vin(
1 + Rf/R1
)
Also not one last thing. What if Rf = 0 (a short) anr R1 = infinity (an open)? Can you see that the equation then just becomes
Vo = Vin (1) = Vin
This is called the voltage follower configuration. Its advantage is its use as a high-impedance buffer. It presents a high impedance to the input source and a low impedance (a characteristic of an op amp circuit, generally) to the load.
There ya go, both circuits
The VDR rocks! Many more complex op amp circuits can be understood and designed simply by knowing the VDR and the general op amp/comparator eq, Vo = A(Vp - Vn).
Take care!