# An ideal world

I’m still trying to figure out the purrrfect combination of resistors for the opamp-section of the new STM32 board.

The circuit is the same as my previous experiments with signal conditioning:

Gain is still:

`G = - R₂ / R₁`

and the level shift is still:

`S = R₄/(R₃+R₄)·(1+R₂/R₁)·Vref`

The output voltage still becomes:

`Vout = G·Vin + S = -R₂/R₁·Vin + R₄/(R₃+R₄)·(1+R₂/R₁)·Vref`

Having learnt to use LTspice a little since last, I thought it best to simulate the circuit before putting the iron to the solder. And it works just as it’s supposed to ..until the typical drive circuit from the CCD is connected. Which, in case you spent your life with something meaningful and hence forgot, is here:

Then it looks like this:

The green trace is the output from the CCD. The blue trace is the input for the opamp. The red trace is the output from the opamp. The blue trace is clipped. Having read some excellent posts on HaD I didn’t understand about transistor biasing, I thought this could be remedied by adjusting the resistor values around the 2SA1015, and sure enough:

By replacing the 150R resistor to gnd and the 2k2 resistor to +4V with 50R and 150R respectively, everything is back to what it’s supposed. (If any clever ee-geniouses knows if this is not a good idea, please let me know asap). The circuit now looks like this, well in LTspice it looks like this:

And the simulation like this:

No clipping this time 🙂 But of course as my good friend Kensha’s dog Feynmann would say, it’s nothing without an experiment. And so I soldered up the opamp with the resistors (and changed the two on my TCD1304-board).

And of course it didn’t work.. Well it sort of did. The input doesn’t clip (and I tried with the CCD in an unaltered circuit, and the clipping is real with the old resistors). It’s just that I didn’t measure the output from the CCD’s drive circuit with adequate precision before, and so the gain and the level shift needs adjusting.

Which is why I’m writing all this, so I won’t forget about my latest findings. So back to the algebra:

The CCD’s drive circuit delivers output from just above 1.45 V to just under 3.10 V when connected to the opamp (this will sure change with R₁ and R₂).

So anyway, the gain should be (the ADC range is actually 0-3.3V, but playing it safe I’m aiming for a signal range of 3.2V):

```3.2V = G(3.10V - 1.45V)
G = 3.2V/(3.10V - 1.45V) = 1.94```

So I will try R₂ = 750R and R₁ = 390, once I get some more time on my hands.

With an input of 3.10V I’d like an output of 0V (slightly above, to keep the ADC happy), so the next equation becomes (the gain is actually negative, because the opamp is in inverting mode, so observe the signs):

```Vout = G·Vin + S
S = Vout - G·Vin = 0.05V + 1.94·3.10 V = 6.064V```

To find nice resistor values for R₃ and R₄, we need to look at S’ dependence on those:

```S = R₄/(R₃+R₄)·(1+R₂/R₁)·Vref
6.064V = R₄/(R₃+R₄)(1+1.94)·Vref
6.064V/(2.94·Vref) = R₄/(R₃+R₄)
6.064V/(2.94·Vref)·(R₃+R₄) = R₄
6.064V/(2.94·Vref)·R₃ = R₄(1 - 6.064V/[2.94·Vref])
R₃ = R₄·(1 - 6.064V/[2.94·Vref])/(6.064V/[2.94·Vref])```

Vref is 4.65V, so this all then becomes:

`R₃ = 1.254·R₄`

So I will try with R₃ = 620R and R₄ = 510R  ..but not tonight. I deserve TV now.