Level shifting a 11.3V-12V signal down to 0-5V with an Inverting Op Amp Level Shifter (Vout=-m*Vin-b)

Question

I want to invert, difference, and amplify the 11.3-12V decaying (upwards to 12V) signal from the metal detector coil in the circuit at https://www.lammertbies.nl/electronics/pi-metal-detector into a 0-5v range signal compatible with microcontroller ADCs.

I looked at Level shifting a +/- 2.5V signal to 0 - 5V and the answers there, especially the https://electronics.stackexchange.com/a/37096/30711 which contains the only example of an inverting level shifter I've found, but since I want amplification and the input signal is not centered on zero, my use-case seems a couple steps more complicated.

^{simulate this circuit – Schematic created using CircuitLab}

I figure that this will clip with 0+-2.5V on the output, but I'm not quite sure how to inject an offset to push it up an additional 2.5v.

Do I sum in another voltage on the negative input?

Or would I adjust the positive input to something else?

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For clarity, I'd like for the circuit to do approximately V_out = (12-V_in) * 7. I make plenty of sign and order of operations errors in my day job, and I'm curious how to translate this operation into an opamp. My attempt above seems like it would do V_out=(12-Vin)*7+(12V+0V)/2

Some completely fabricated curves of simulated input and desired output are below.

# R code:
x=0:30/1000
y1= 12-0.7* ifelse(x < 0.010,1,exp(-200*(x-0.010))); plot(x,y1,'l',col='black')
y2= 12-0.7* ifelse(x < 0.008,1,exp(-250*(x-0.008))); lines(x,y2,'l',col='red')
y3= 12-0.7* ifelse(x < 0.012,1,exp(-150*(x-0.012))); lines(x,y3,'l',col='blue')
y1= 7*0.7* ifelse(x < 0.010,1,exp(-200*(x-0.010))); plot(x,y1,'l',col='black')
y2= 7*0.7* ifelse(x < 0.008,1,exp(-250*(x-0.008))); lines(x,y2,'l',col='red')
y3= 7*0.7* ifelse(x < 0.012,1,exp(-150*(x-0.012))); lines(x,y3,'l',col='blue')

Simulated sample transient input voltages:

Simulated sample transient output voltages:

Answer 1

ok:

$$ output = ( 12V - input ) * ( 5/0.7 ) $$

^{simulate this circuit – Schematic created using CircuitLab}

R1,R2 gives the needed -7.14 gain

R3,R4 gives the needed bias to give 0V out when in is 12V (by symmetry)

use 1.1K in series with 300 ohms for R1 and R3

a good thing about ther LM358 is that its output goes to the negative supply, but unfortunately the input can only go to withing 2v of the positive supply.

there;s also a problem in that the output is not limited to 5V if the input goes out of range. but ther LM358's waek output stage is unlikely to be able to do any damage.

That power supply requirement is a pain. So, can better be done?

Yes!

^{simulate this circuit}

Here I've added 2k resistors pulling fown on the inverting and non inverting inputs.

This reduces the input votlage to the op-amp to arounnd 7V (I have not done the arithmetic) allowing it to operate off a 12V supply. or even lower.

Because it's symmetical this change does not alter the operating point of the amplifier output.

Answer 2

If input signal drifts with the power rail then output accuracy should be maintained.