OpAmp Adder x2

[MrAl]

Hello again,

You keep insisting on changing this back to something that is not as good. I have so far mentioned that the resistor R30 should be higher like 100k several times now. If you change the other resistors too then you loose the advantage of being able to use a higher reference voltage. It's not just the higher impedance of the resistors, it's also the relationship of the impedances between resistors. So one needs to be 100k and the others 10k. That's about the best you'll get, and it's not all that hard to understand or to accomplish. So adjusting the reference will then be centered around 2v instead of 0.2v. If there was no advantage then we could have used 1k resistors and adjusted the reference to 0.020 volts, but that's ever worse than 0.2 volts.
But do it any way you want to if you still dont understand why we are doing this

 

[ADWSystems]

I'm not insisting on changing back, I'm working on finding out the answer to a specific question. Although a different question than post #1, it is the same topic. The original question was the impact of the two direct adder circuits in parallel. We have now progressed to what effect does changing the resistance of R29 have on the gain and R30/31/32 when they are close in value (ie., R30=10k and R29=is in the range of 1k to 20K)? Based on previous designs with the hysteresis of comparators and non-high impedance source for Vref, I'm expecting there to be an effect.

I understand the advantage of using the higher reference voltage. I understand the reasoning of using the higher reference voltage. I understand why to do it. I understand 98% of what you have said (there were a few items two posts back I don't follow yet). I had the idea for using the higher reference voltage and the lower reference voltage before I made the first post. I considered the 0.02V reference then gaining both at once But I didn't like the idea of trying to set 20mV and 50mV values in the field was a bit scary. Plus the controller needs sensor x10 separate from the thresholds.

 

[MrAl]

Hello again,

Ok i understand now what you want to know. The short answer is 'yes', but there are ways around this, and one of them is to make R30 equal to 100k, leave the other ones alone except change the second stage gain to 2.1 and that's about it except for the error calculation which you'd like to know.

In the following R29a is the resistance of the upper portion of the pot and R29b is the resistance of the lower portion of the pot. We can then just set R29b and calculate R29a from:
R29a=R29-R29b

To start, first we set Vin=0 and adjust R29 to provide 0.2 volts output. This leads to a value of R29b:

R29b=(sqrt((3600*G^2*R31^2+((4-120*G)*R29+(4-120*G)*R28)*R31+(4*R29+4*R28)*R30+R29^2+2*R28*R29+R28^2)*R32^2+(((4-120*G)*R29+(4-120*G)*R28)*R31^2+((8*R29+8*R28)*R30+2*R29^2+4*R28*R29+2*R28^2)*R31)*R32+((4*R29+4*R28)*R30+R29^2+2*R28*R29+R28^2)*R31^2)-60*G*R31*R32+R29*R32+R28*R32+R29*R31+R28*R31)/(2*(R32+R31))

With the values i suggested, this leads to a value of R29b of 1688.9475 Ohms.

Now to see the output error, we can calculate the output with Vin=0 and with Vin=1 and we get:
Vin=0, Vout=0.200
Vin=1, Vout=10.206596

The equation that includes the two pot values is:

Vout=G*((R29b*Vref*R31+Vin*A*R28*R30+R29b*Vin*A*R30+R29a*Vin*A*R30+R29b*Vin*A*R28+R29a*R29b*Vin*A)*R32)/(R28*R31*R32+R29b*R31*R32+R29a*R31*R32+R28*R30*R32+R29b*R30*R32+R29a*R30*R32+R29b*R28*R32+R29a*R29b*R32+R28*R30*R31+R29b*R30*R31+R29a*R30*R31+R29b*R28*R31+R29a*R29b*R31)

Now you see the error is about 0.007 volts at full scale which is a tiny percentage of full scale, and about 3 percent of the offset.
If this isnt good enough, then we could do a simultaneous solution of both the correct pot setting and R31, and doing so we'd come out with roughly the same value for the pot setting and the value of R31 would change by about +20 ohms (roughly), and that represents 0.2 percent (two tenths of one percent, not 20 percent) so now we are down below the tolerance of the resistors.
But if you wanted to adjust that resistor too you could do that too. To accomplish this you would adjust R29 and then R31 and then R29 and then R31 again. But since the percentage is so small i dont think it would pay to bother. It's up to you though.

Does this make sense now? I think i addressed your second question a bit better this time, but no problem if you have more questions. I could also do a more exact analysis tomorrow sometime for the error and resistance percentage change required.

 

[MrAl]

Hello again,

Ok it appears that if R30 is 100k we would then have a small error as noted before so if R31 was increased by 13 ohms that would take care of that.
If R30 is 50k then R31 has to be increased by 26 ohms. But this is still a small amount.
So it looks like if R30 is 10k we'd have to change R31 by even more.

 

[ADWSystems]

13 ohms. 26 ohms. 1% of 10k is 100 ohms. Until the error gets above that, I'm not going to worry about it. That's why I have been concerned about R29 vs R30.

But what happens if R30 is held steady 10K and R29 is varied?

 

[MrAl]

Hi again,

When you say R29 is varied do you mean the 2k pot is adjusted or do you mean we can lower the value of the pot itself to a lower value like 1k? Because if we can lower the pot to say 100 ohms, then the max change we'll see is 100 ohms and that is less percent of 10k than 2k is for sure. So the impedance from the left side of R30 to ground is subject to much less change.

I could take another look at the 10k for R30, but it appears that 10k can work too if R31 is also varied to make up for it, but then we run into the other problem of having to adjust R29 to a very low voltage value which just isnt a good idea.
If R31 is not varied then we see 0.2v out for 0v in, but then around 10.25v out for 1v in instead of 10.20v.

Note this is a linear circuit and so it responds in linear way which means we can get it to work exactly for two different test points regardless of what values we use, and expect in between test points to respond along a straight line that joins the two original set points. So in theory we should be able to get it to work with just about any value for R30. The choice can then be based on other factors like the non ideal components which work better with some values than other values. What this means is the impedances themselves are best set based on the non ideal components rather than on how they related to the adjustment procedure unless you are looking for a super simple adjustment procedure as well. The adjustment procedure we'll probably have to use here is a little more involved than with an isolated pot for example.

The adjustment procedure so far looks something like this...
1. Apply 0v input.
2. Adjust output for 0.2 volts with R29.
3. Disconnect R28 from +12v, connect that end of R28 to ground.
4. Apply 1v input.
5. Adjust output for 10.00 volts.
6. Reconnect R28 to +12v.
7. Test for 0v in and 1v in and one point in between.
8. Possibly adjust R31 for better accuracy (probably not needed though).

Another possibility is to just adjust the output for 10.2 volts with R28 still connected, but if R31 is to be adjusted it is best adjusted with the top of R28 grounded.

Using the 'other' op amp section for the pot isolation helps to simplify the adjustment procedure but it introduces another op amp section, which means two for the two channel circuit. The adjustment procedure would then not involve having to disconnect R28. But another way to avoid that is to decrease the impedance of the pot itself, if that is possible.