Linearily of Derivative Circuits At High Frequency

To get to a higher frequency, is it possible to just use a smaller cap and/or resistor on op amp derivative taking circuits?

Bret Cahill

Only to a point -- then your performance is limited by the op-amp.

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Tim Wescott Wescott Design Services

Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at

Thanks.

What do you mean by "get to a higher frequency"? Do you mean "continue to be accurate at a higher signal frequency"?

The size of the cap scales the constant K in

OUT = K * (dIN/dt)

but has nothing to do with how high a frequency the circuit will work at. The opamp determines that.

The "pure" opamp differentiator, just a cap, a resistor, and an opamp, seldom works. It tends to be unstable and oscillate.

Interestingly, its dual, the opamp integrator, has problems of its own.

Do you have any specific performance goals in mind?

John

The derivative circuit needs to be linear to < +/- 1% over a range of frequencies.

One solution is to move everything to lower frequencies which takes a lot more time limiting use of the computer for hours/run. There's no reason why SPICE calculations should take more time at low than high frequencies. The time/step setting doesn't seem to help.

Is there any on line calculator that uses a faster computer?

Bret Cahill

What range?

John

Spice gets slow if there is a very wide range of time constants in a circuit. It also slows down a lot if you use semiconductor models of things like opamps. Behavioral models are faster. Ideal models are fastest.

The fastest way to analyze most circuits is to not use Spice at all.

John

What problems do you see with an integrator? These always seem to work just fine for me. I find the State Variable filter a bit 'scary'. Whoever first thought of putting to integrators in a row had a lot of 'guts'. But I love the outcome.

George H.

But that requires an imagination, no? Does growing up with Gameboys and hi-tech toys stifle imagination or something? Or modern schooling says you hafta simulate?

Grant.

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A couple of decades.

Thanks.

It's valuable as a double check.

Bret Cahill

Ok, lets keep playing this game.

WHICH decades?

John

Any two that are next to each other.

The problem may have been coming from some other part of the circuit. Everything was below 100 hz.

Bret Cahill

There are issues with dc offsets. If your signal has a dc offset then that will get integrated over time successfully reducing your headroom.

e.g., In(t) = dc + f(t), Out(t) = dc*t + F(t). It may work fine for some initial amount of time but eventually won't function at all. This is true for all integrators and this is where choppers come into play.

They integrate their own voltage offset and bias current, of course. For something like a magnetic field probe coil, that gets to be the dominant error. Some cute periodic auto-zero becomes necessary. Chopper amps are great, but noisy.

We're just finishing up a product that jams 32 brutaly-pipelined

8-pole lowpass filters into one FPGA, sample rate 500 KHz per channel. The cutoff range is 50 KHz down to 1 Hz, and original concept, classic DSP butterfly stages, blew up mathematically. At 1 Hz we had allowable coefficients errors like one part in 10^40, and 2-pole stage gains like 10^17. This wasn't good. I suggested simulating a state-variable lowpass digitally, and that worked, using the 48 bit MACs in the Xilinx FPGA. The nice thing about state-variable filters is that you can make the 2-pole stage gains exactly 1, and the coefficients scale pretty much linearly on frequency.

I like SV analog filters, but sometimes a Sallen-Key is better, because the DC gain is 1 and doesn't depend on resistor accuracy.

John

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Yeah, I forgot about that. Lately I've only been using integrators that are inside a control loop. So the DC offset is not an issue.

George H.

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" I like SV analog filters, but sometimes a Sallen-Key is better, because the DC gain is 1 and doesn't depend on resistor accuracy."

I was measuring the DC gain of SV filters we are using a few months ago. I was amazed at how accurate they were. I can't recall the exact numbers, (My notebooks at work and I'm on vacation.) but gain error was much less than the 0.1% resistor tolerance. They all used the same 10k 0.1% Sumuso (sp) resistors, I guess the resistors matched much better than 0.1%. It's hard for me to measure things to much better than 0.1%. I need another digit on my voltmeter.

Say has anyone looked at the resistor values from 0.1% Sumuso (sp) resistors? I wonder if they have the same bimodal distribution that was claimed for the old 10% tolerance carbon resistors. (where the 5% resistors were selected from the middle of the normal distribution.) For those who don't know the better Sumuso resistors also come in 0.05% tolerance.

George H.

Susumu. They are fabulous, come from Digikey, and cost 1/10 of the Vishay stuff.

The actual available values are bizarre. Maybe they made what specific customers wanted, then put them on the market. Or used a random number generator.

We tested some of the 0.05% parts, for TC. We got numbers like 5 and 8 PPM/K.

John

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Ahh Susumu, Thanks for the correction. I wonder if the 0.1% are rejects from 0.05% batches. (The 0.1% cost something like 1/5 as much.) Maybe I'll try and measure some.... Say If I put them in a bridge I can measure differences with a lot more resolution. Is there any easy way to swap chip resistors into some test jig? I'll need to keep the variations in the test jig resistance down below 0.1 ohm or so.. (for 10k ohm samples).

George H.

I think the only fair thing to do is solder them to real surface-mount pads on a board, especially to measure TC. You never know how stresses might effect things when you get to single digits of PPMs.

John

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Hmm If I want a quick measure of say 10 or 20 of them that sounds like a lot of work. Unsoldering surface mount is always a bit of a PITA. I use solder wick and then push with the iron...

Maybe I could stand the R's on end, solder one end to a PCB and touch solder a bit of wire to the other end.

The Sumusu data sheet does list TC's at the few ppm level. Resistors are pretty amazing. What's the TC of a piece of copper?.. one part in

10^4 or something like that. Oh they also sell 0.02% resistors. I wonder what they cost?

George H.