Non-inverting amplifier with negative supply rail

Question

^{simulate this circuit – Schematic created using CircuitLab}

The formula Vout = Vin * (1 + R2 / R1) is not valid for this case? because for example I'm feeding 2.567V to non-inverting input and getting 2.976V at the output! I'm certainly doing something wrong somewhere...

How to calculate the output of non-inverting amplifier with negative supply rail?

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Edit:

What I want from this configuration is to provide -1.25V to LM338 linear regulator to get 0V at its output, James mentioned in his answer to remove R3 from the first schematic and I did that with minor gain modification:

^{simulate this circuit}

At 1V the output is 0V and when non-inverting input is 0V the output of opamp is at 1/4 of Vref 1.250V.

• What's this configuration name? is it an inverting configuration?

• What's the equation to calculate output?

Answer 1

Remove R3 and it'll work as you require.

Edit

When input is 0V, the output is -1.25V. Perhaps missing the minus sign off was just a typo. Also assuming Vref is still +5V and that's a dash not a minus sign.

That is a non-inverting amplifier, the input voltage goes into the non-inverting input. If the input is +ve with respect to Vref then the output is +ve with respect to Vref. If the input is -ve with respect to Vref then the output is -ve with respect to Vref. It's a more rarely seen non-inverting amplifier because Vref isn't at 0V.

You'd probably have trouble finding a 4k resistor. I'd recommend R1=12k and R2=3k to get your 4X ratio. (E24 series).

Equation is:-

Vout = (Vin - Vref)(R2/R1) + Vin

where in your case Vref =+5V

You seem to perhaps be designing a variable voltage power supply, are you using a PIC to control it?

Answer 2

Since this looks like a good homework problem I will only give you a general method.

First, you need to know the voltage at the non-inverting input. Since it is variable in this case let's call it \$V_S\$.

Second, you need to determine how much current flows from R1 and R3 toward the inverting input. The inverting input must be at the same voltage as the non-inverting input, which is \$V_S\$. So you have a simple circuit problem, with the 5V source, R1, R3, and a virtual short to \$V_S\$. Analyze the circuit to find the current flowing toward the virtual short to \$V_S\$, expressed as a function of \$V_S\$ and the values of R1 and R3.

Third, you know that the current flowing toward the virtual short does not actually flow into the inverting input...there is no current into the inverting input for an ideal op amp. So, that same exact current must flow to the output through R2. Set up a simple KVL problem with the virtual source of \$V_S\$ at the inverting input, R2, and \$V_{OUT}\$. The only unknown here is \$V_{OUT}\$, so you can use a little algebra to find the formula for \$V_{OUT}\$ as a function of \$V_S\$ and the resistor values.

Answer 3

Superposition is your friend here. Instead of trying to analyze the circuit all at once (though that certainly is possible), break it into 2 familiar problems:

1) A non-inverting amplifier with \$G = 1 + \frac{R_2}{R_1||R_3}\$

2) An inverting amplifier with \$G = -\frac{R_2}{R_1}\$

Then the total output is the sum of the individual outputs. The negative supply rail has nothing directly to do with the output, except that a negative rail is required to get a negative output. However, if all you're trying to do is get -1.25V at the output, just remove R3, ground the non-inverting input, and apply 1.25V to the inverting input.