Hi @Moto, I spent some time with this, and also ChatGPT and Wolfram to see if the circuit could be solved symbolically. ChatGPT does a good job of determining the node equations and putting them into a form for entering into wolfram. And then you have 3 equations and 3 unknowns, and Wolfram will then solve for whatever you want. But the resulting equations got really unwieldy. I think there’s got to be some simplifications to help. BTW, asking ChatGPT to solve the system of equations was not good. It never got the right answer.
In short, I need to study more. If anyone wants to take a crack, please do.
Great @matt! Can you publish the chatgpt prompts you used and the resulting equations?
I do have a chatgpt 4 subscription and have had miserable luck with computations unless I ask it to explain each step at an atomic level. I’ll be interested to see how you structured it.
Which (I think) is the same result arrived at by ChatGPT4
In any case, ChatGPT does well on simpler circuits. And its ability to solve symbolically (that is, using R4 instead of 100K) is pretty impressive to me.
In any case, it tends to make a lot of mistakes, but fewer mistakes than I would using pencil and paper. But I’m pretty rusty in KVL and KCL.
That netlist capability of chatgpt is cool. I was unaware of it. Thx for the detail. I hate to be stupid but, you assume away R3 in the original diagram because R1 is small compared to it, right? Why do you omit R6 in you final simplified schematic?
Or is the simplified diagram just (R5+R6)||50k?
The QA40x measures the apparent impedance of the DUT. This is normally so close to the actual DUT impedance we don’t care. But this is not always the case, as you have seen.
The equation in my post predicts what you should measure with the QA40x in its current form at the time of writing, “Za” in Matt’s equation.
Matt rearranged it to back out the actual impedance of the DUT, Rd, given the other parameters. Using his equation you should get something closer to the DUT. He said he will add it to the plug-in.
I’ll do a blog post on how I found that. But basically, just finding the voltages at the nodes across the DUT and sense resistors, writing them in an expression that gives the apparent DUT impedance, and simplifying it; just following what Matt did.
What equation are you using for the calculated column here? Could you also add a column for what the QA40x measures and a corrected column using the backed out Rd impedance?
My 2 cents, the values you measured don’t agree with the LTSpice model nor the analytical expression. But there is still some doubt about comparing apples to apples. I was going to run the experiment myself following what you did, but I have not managed to do anything for a week. The can of worms might go deeper!
I used matt’s new formula to calculate the dut impedance from my measurements. My calculations agree very closely with the 27k resistor I used for the dut.
The only really odd one is using the 99.6ohm sense resistor.
What doesn’t agree with the model?
I’d say the new formula @matt came up with works unless you start to get the ration of sense to dut too large as in the 99.6 ohm sense case.
Just to be clear those dut numbers I show above were with @matt new formula.
I just re-arranged Dan’s formula. The 1.188 release HERE has the ability to apply the formula IF you check the User Analyzer Input Z Compensation. I haven’t spent any time on verifying it yet, but please try if you have a setup in place and let me know what you see. If that box is unchecked, the plug-in should work precisely as before.
@matt it doesn’t work for me. The same 27k resistor now shows around 19k with the box checked.
I don’t think you want @Dan formula as from what I understood from him, that describes apparent impedance which is your old way of calculating.
I used the one you got from chatgpt and wolfram and that gave me the correct answers in the table I previously posted.
I used (V1-V2)/Rsense=V2/Rdut + V2/50000
Where Rsense= value of sense resistor and Rdut = impedance of dut.
V voltages are as described in what @matt wrote above.
I’ll make a summary. Matt’s equation (not the one from ChatGPT) agrees with the LTSpice model but the data you collected seems not to agree with that.
So assuming your measurements are correct, something must be wrong with the LTSpice circuit we are using to derive the equation? Could that be the case?
Here Rsense is the value of the sense resistor, Vdut is the voltage across the device under test, and Vsense is the voltage across the sense resistor.
My measured voltages agree with the Tina model to about 1mv if I use 150ohms for the qa402 dac which I left in the Tina model but did not use in the netlist analysis.
The equation above yields correct results for Rdut to about .2% using your pcb and a sense resistor of around 10% of the value of Rdut. I will do more measuring today though.
After more measuring, its clear that the sense resistor needs to be above say 5% of the value of Rdut to get really good results. In any case though the results for calculating Rdut are much better than what is in the software today.
I did validate that the Tina simulated numbers provide very good results using the formula given above.
