Offset amplifier's input to prevent opamp clipping

Question

We can do this:

1. With AC coupling and biasing op-amp input.
2. Summing using buffered resistor
3. Using sum and difference inherited in OpAmp and sum signal with desirably created virtual ground

1 is good but I want DC coupled circuit. 2 is good but I my circuit have variable resistance and low summing resistor attenuate signal and use power. High resistor in the other hand create noise. 3 seems to be good but I don't know how to apply it in the circuit below.

^{simulate this circuit – Schematic created using CircuitLab}

I've heard unity non inverting input is reference, I don't know why but if this is then input is shorted to reference and the only variable is reference then there is no way to use virtual ref on it, Then 3 is not implementable without summing. But the opamp must be able to sum two signal not the summing mention in 2. using buffered resistor. OpAmp designed to summ and difference but why I can not do that?

Answer 1

Amplifying a signal around Ground with a single supply is a nice application for a JFET. As they have a negative turn on voltage, you can easily make an op-amp with a very large input offset voltage. The offset voltage will be roughly the pinch-off voltage of the JFET + 0.7 V.

When you wire it up as a voltage follower, it will add its offset to the input:

^{simulate this circuit – Schematic created using CircuitLab}

Answer 2

You want the 1.5V input mapped to 6V output, with gain 1.

First, we can mirror the input around the average of these two voltages, performing the mapping but with gain -1. The "mirror" - or simply the reference voltage is:

$$V_{ref1} = {1.5+6 \over 2}{\,\rm V} = 3.75{\,\rm V}.$$

The first stage is an inverting amplifier with gain -1 and 3.75V reference voltage.

The second stage should restore the overall gain to +1 by inverting the voltage again, this time around the midpoint

$$V_{ref2} = 6{\,\rm V}.$$

^{simulate this circuit – Schematic created using CircuitLab}

With a relatively stable 12V supply, we can derive the reference voltages from the supply voltage using a resistive divider:

^{simulate this circuit}

The R5, R6 and R7 resistors are 1% types from the E96 series.

The waveforms at IN, A and B/OUT look as follows: