Combining Signals of Hall Sensor & Rogowski Coil

[Glenn Emmers]

Dear all,

I'm trying to combine the singals of both a hall sensor and a rogowski coil.
The proposed circuit is given in the following figure:

This should be the physical form of the implementation given in the following figure:

I can somewhat see a summing amplifier formed by A2, where the gain is determined by selecting R2, Rcoil and Rhall. I imagine C2 adds the low pass properties to this system. I simply don't see what the purpose of the lower opamp is. Can someone explain me how this circuit works and how I can determine the components C3, R3, Ri, Ci and maybe also C2, with Vcoil and Vhall being known
(Vhall will be in the range of 300 microV and Vcoil in the range of 2microV).

Thanks in advance!

Kind regards,
Glenn

More information can be found in the attached file:

 

[Tom.G]

Overall, the HOKA paper says you can create a very wideband amplifier stage by having a high frequency stage and a low frequency stage (DC in this case) and combining the outputs. The circuit implements the high frequency stage with C3 R3 A2 (C3 R3 being a highpass filter). This handles the impulse signals from the Rogowski coil.

R1 C1 A1 are of course an integrator, or low pass filter, to handle the DC component of the Hall sensor. If you look at the 2 op amps as a single opamp, with A1 being just a narrow bandwidth input stage within the compound op amp, it makes more sense; Sort of like putting a capacitor from C-B of a single transistor stage to reduce its bandwidth.

I don't follow all the math, but sections II & III state that the time constant Tv ≥ 100T_H is required to approach 'ideal' operation, where T_H is the Hall sensor time constant.

Hope this helps.

Cheers,
Tom

 

[jim hardy]

I simply don't see what the purpose of the lower opamp is.

The purpose of the lower amplifier is to keep the output of the upper amplifier Vo centered at whatever is the recent average of flux.
That would be the DC component of flux. That DC component is reported by the Hall sensor.

Focus on the input node V2 for a moment.
The coil being inductive can produce no DC voltage for to have DC would require a flux that's changing in one direction forever . That's because Faraday's law takes the derivative of flux and derivative of a flux that's not changing anymore is zero. ...

So the coil can detect only changing flux. I think of it as the AC component of flux.
Accordingly there's an AC coupled amplifier, the upper one A2. Its purpose is to pass the AC components of flux , at least the ones too fast for the Hall sensor.
Observe C3 blocks DC from reaching A2's - input pin. That's why it's an ACcoupled amplifier.
Since C3 blocks DC from A2's - input pin, that A2 minus -input pin must be at zero volts average .
That's the heart of this gizmo , and the answer to your question -- looky here >>
>>since an operational amplifier circuit must hold its inputs equal A2's positive +input pin must also be at zero volts average.<<<
Hmmm.. What puts it there?

The Hall sensor can detect constant flux and produce DC. (as well as low frequency AC)
And the lower amplifier A1 can follow DC, in fact it is an integrator. So its output V5 will be the time integral of V2.

Now take a look at A1 . Its output V5 is the time integral , which is also the average, of V2..
At steady state V5 must be zero we established that up above in the "looky here" sentence fragment ,
recall V5 is at A2's + input pin which must be at zero to match its - input pin..
So how does the circuit force V2 to average zero so that V5 will stay there too ?

AHA ! Look at this markup of your circuit
See R2 up top?
Whatever DC voltage is present in Vhall , left side of R1H, will be exactly balanced by DC voltage of opposite polarity in Vo on right side of R2. They'll inject equal and opposite DC currents into that node V2 through their respective resistors.
Any AC components of course average to zero anyway, that's math.
SO - V2 can average zero.
Integrator A1 will make sure it does by applying miniscule voltages to A1's + input, forcing Vo cancel any DC at V2.
A1 is intentionally made quite slow so as to not interfere with whatever AC components of signal the slow Hall sensor is able to reproduce. That's explained in the text of that article you linked.

Here's your picture marked up.
When working an opamp circut in my head i a;ways first trace out how it achieves DC balance, then trace out the AC path.

DC balance: any DC in VHall propagates through the integrator A1, then amplifer A2 , finally through R2 cancelling out DC.
If R2 and R1h ae equal, Vo's average value will be same as that of VHall but with opposite polarity.

AC balance: At high frequency the gain of A2 is essentially C3/C2...
Remember that Faraday is a derivative function which is naturally high pass. A Hall sensor is rather slow and resembles a low pass.
Time constants R3C3 and R2C2 are carefully chosen to give a smooth transition from low pass frequency response of the slow Hall sensor to high pass frequency response of the much faster coil.

Any help ?

The algebra will be tedious but enlightening .

It took me a while to figure this one out. For me the trick was working first the DC balance then the AC.
Cascaded opamps are pretty common but it's not intuitive at first how such a circuit works.

When you've got this one it'll be a powerful tool in your bag of tricks.

old jim

 

[Glenn Emmers]

Thank you for your reaction! My insight in the problem has defenitely become better thanks to your responses. I still have a couple of questions though.

In reality I want to connect 4 hall-sensors to the node of V2 and just one coil. I want the amplitude of the sum of the 4 hall sensors to be the same as the amplitude of the coil after amplification. The way I understand it, is that the amplification by both chains is determined by R2, R1H and R1C. Because the output voltage is supposed to be about 5V for the 300μV input for 4 Hall sensors and the 2μV for the rogowski, I selected the following magnitudes for the following resistors:
R1C = 50Ohm
R1H = 1880Ohm
R2 = 100kOhm

Because of the requirement that Tv ≥ 100T_H with T_H being 3μs for the hall sensors I selected and assuming Tv = R2C2, I figured C2 should be 10nF to be sure. I'm wondering if this could be correct.

Since circuit design is not really my field of expertise, I'm not really sure about what transferfunction to solve in order to determine R3, C3, Ri and Ci.
Is it a correct assumption that the time constant R3C3 can be one decade higher than R2C2? And what would be reasonable values for these components? The problem is that I have no idea about the order of magnitude.

For Ri and Ci to dimension the low pass filter, I assume I have to be looking at the characteristics of my Hall sensor in order to determine both these components. But I don't really know which property to look at and again what reasonable values could be.

Thanks in advance,

Glenn

 

[jim hardy]

does this not give enough information ?
If the authors' algebra is rigorous

The way I understand it, is that the amplification by both chains is determined by R2,

yes the feedback resistor for the A1&A2 block . It certainly sets the DC gain for Hall. Surely it'll show up in the TF for coil

R1H

Input resisitor for Hall's AC and DC components.

and Ci.

sets rate of integration.
C2 shows in their equations, sets low pass time constant for A2
but not C3 or R3 ? I wonder why..

here's their clue on R2 and C2

. A low-pass is inserted at the output of the Hall sensor signal with the same time constant Tv. As long as TV > 100 TH the behavior of the evaluation circuit is only slightly altered compared with the ideal one. Having the same low-pass block in the coil and Hall signal path, it can be shifted as well as part of the amplification block past the addition block as shown in Fig. 3. As a result the matching of the parameters of the low-pass becomes easy as long as the given inequality is respected

needs to be long compared to your Thall , 100X longer is what they chose.

Their fig 5 on page 2123 from gives us a clue as to corner frequency

looks like they picked 100 hz. That suggests they had a 10 khz Hall sensor.
I've not yet worked out the transfer functions of their circuit. I'd start by solving Vo / V2 for A1 and A2 separately, each without the other.

My instinct says set R1C1 and R3C3 equal to each other and equal to R2C2 for starters.
But I'm not comfortable giving that advice - don't do anything irreversible based on it.
............

Now

Because the output voltage is supposed to be about 5V for the 300μV input for 4 Hall sensors and the 2μV for the rogowski,

you say you have only 2 microvolts from your rogowski coil ? To make that into 5 volts requires gain of two million and that's way too much for a single stage opamp.
Since it's a coil and takes derivative of flux,
and derivative of flux is also derivative of current,
i'd expect a term like volts per amp per unit of time.

Can you educate us on what they meant by that 2 microvolt term you gave us ? How many amps per microsecond does it take to give 2 microvolts?
How many amps per microsecond will you want to measure ?

 

[jim hardy]

History of this concept is interesting.
In early 70's i used a Tektronix current probe that used a Hall sensor plus coil to provide DC to 50 mhz, astounding for its time.
Here's a nostalgia article about the device
https://www.edn.com/design/test-and-measurement/4442795/Teardown--The-Tektronix-P6042-current-probe-is-a-classic

and its instruction manual (sadly no schematics) http://bama.edebris.com/manuals/tek/p6042/ click p6042pdf

Rogowski was an 1800's fellow. I think you'll enjoy this.
http://www.rocoil.co.uk/Chattock.pdf
I'll look in my 1901 Thompson book for him.

haven't abandoned you.
Just thinking about Bode plots trying to get a feel for how to match the crossover points of highpass Rogowski coil and lowpass A2 amplifier so they'll intersect the flat part of the Hall sensor.

plenty of folks here on PF who could do it in a heartbeat I'm sure -
but i plod along, have to get that 'feel' before i leap...

old jim

 

[Tom.G]

Here is a link to a PDF of the Original TEK P6042manual. It has the usual TEK thoroughness of Use, Calibration, Schematic, Parts List, Exploded Views, etc. http://www.atecorp.com/ATECorp/media/pdfs/data-sheets/Tektronix-P6042_Manual.pdf

Here is the partial schematic for the TEK P6042. From: http://www.pa4tim.nl/?p=3135

Probe:

Amplifier:

All the above found with: https://www.google.com/search?&q=tektronix+p6042+schematic

 

[jim hardy]

Thanks @Tom.G !

That's the instrument i had. It was really handy around the plant for non intrusive measurement of current.
We had a problem with asymmetric thyristors adding small amounts of DC to the AC drive for relay coils which made them run hot and burn up, sometimes tripping the plant.
The DC capability of the probe let us detect that and fix them preemptively.

So - the HOKA technique was around in the sixties, perhaps under another name. But the math has become much more elegant.
I suspect the reason there are three frequency adjusts in this old Tektronix is because the core is ferrite not air.
It was an impressive device in its day. Saved us literally millions of dollars in plant downtime.

But that's not helping you size your time constants, is it ?

We need to find the frequency where your Rogowski coil voltage approaches that of your Hall device.
I think that's where R2C2 should be set , to keep the transfer function flat as di/dt replaces i(t) as the dominant input .
Then you'll be able to have R1c and R1h same order of magnitude.

Is there a HOKA expert in the house?old jim.

 

[Tom.G]

Anyone know what the expansion is of the "HOKA" acronym? A Google search shows only shoes!

Found it. The first two letters of the first two authors last names; Hofer-Noser and Karrer.

 

[jim hardy]

Glenn

do you have particulars on your Rogowski coil ? Inductance ? volts per amp per second ? 2 microvolts at what current and frequency ?
Likewise on the Hall ? millivolts per amp ? 300 mv equal how many amps ?

 

[Tom.G]

Vhall will be in the range of 300 microV and Vcoil in the range of 2microV

I just realized that you are trying to process signals with a 43dB range, at the same time. That means the Rogowski coil signal will be buried -43dB down in the noise!

Even if digital processing is contemplated, you may be better off handleing and processing the signals seperately and combining them, if needed, appropriately weighted at the output.

 

[Glenn Emmers]

Hey guys, thank you so much for all the effort you're putting in!

I have some more information for you guys.
- The hall sensors I'll be using will be these: http://www.farnell.com/datasheets/1676927.pdf
- For the rogowski: The actual rogowski hasn't arrived yet so I haven't been able to do the measurements just yet. But I calculated the parameters to be about this:

- Mutual inductance (M) = 40nH
- Resistance = 10.141 Ω
- Inductance = 8.019 μH
- Capacitance = 40.7nF

This gives the following bode plot for a second order model of the Rogowski coil (mind the frequency is in rad/s):

I don't expect to measure too much DC values, neither will de frequency deviate a whole lot from 50 Hz. I'm trying to use this technique to get a somewhat accurate measurement of a relatively low current of 100A using multiple techniques. So maybe it's easier to simply amplify both signals seperately and process them digitally, than to try to find the right time constants in order to get this wide bandwith? In fact I don't really need such a wide bandwith, but which would be a nice extra?

I did create something in spice though and got some good results with the following setup:

I just realized that you are trying to process signals with a 43dB range, at the same time. That means the Rogowski coil signal will be buried -43dB down in the noise!

This is a very useful remark! Is it possible to amplify this branch before combining these signals?

 

[Tom.G]

Is it possible to amplify this branch before combining these signals?

I sure hope so, because that is what I had in mind.
Now that I got the wisecrack out of the way, Yes. It just makes it slightly more complicated if you need very accurate relative timing data between the two channels. In that case you will have to match the circuit delays. If you need high timing accuracy and will be doing digital processing, pay attention to simultaneous A-to-D sampling versus sequential sampling if using multiple input channels (as opposed to combining the signals in analog.)

 

[jim hardy]

I just realized that you are trying to process signals with a 43dB range, at the same time. That means the Rogowski coil signal will be buried -43dB down in the noise!

I didnt know what to make of his 300,000 to 1 ratio of Hall to Rogowski signals. Hall is flat, Rogowski is linear with frequency, so to give a ratio infers a frequency.

Bode plot time.

Take a high pass coil 20 db.decade up
and a low pass Hall flat out to several khz then 20 db per decade down
^^^^^^^ that's a draft i saved. Struggling with a germ of an idea that wouldn't come out until i saw your Bode plot.^^^^

Aha ! I was trying to use words to describe a Bode plot solution but your picture is worth a thousand of them
You answered your own question. Simplicity is the goal... Bode plots are great.

This gives the following bode plot for a second order model of the Rogowski coil (mind the frequency is in rad/s):

Thanks for the Bode plot

e = l di/dt ? 40 nanohenries gives 40 nanovolts X radians per second X amps ?
hall gives 3.125 mv per gauss , can you estimate the field where your Hall sensors will be mounted ?

Then you can estimate where they cross and set LP breakpoint there.. You have some adjustment of where they cross with Rhall and Rcoil, they shift Hall and coil vertically on your Bode pot.

Hope i got tthat right. I've never built one of these...

Make sense ?

old jim

 

[jim hardy]

At frequency below the breakpoint your Hall signal dominates. Coil signal is very small
Above that frequency your coil signal dominates , it becomes larger than the Hall.

So you don't have to handle such a wide range of input signal as you thought. Just whatever is your measurement range.

Keep us posted ?

 

[jim hardy]

Thanks @Tom.G
My annotation to Bode plot was just sketched to show the concept. Trying to wrap my alleged brain around the math of this thing.

Authors mentioned LP filter breakpoint is two decades or more below Hall corner frequency . I drew it too close.

Will have a go at transfer function tonight.

old jim

 

[jim hardy]

Well ! I sure learned a lot on this one.

The circuit that your authors used is a little bit different from what I'm used to. How they arrived at it is not clear but it does make sense.
They published an earlier paper wherein they used a more traditional summing amplifier . It's at
https://pdfs.semanticscholar.org/f39a/25945d67d3d3f0ffc778a038e07fad64af52.pdf

( i had to lookup what is a PT1 element - in my day we just called it ' lag' )

and clearly that's what their evaluation circuit immediately above is.

Now anyone who's searched for op-amps finds that it is difficult to find in one device both precision and speed .
They describe in that second paper troubles with DC offset and drift.
So what i think they did is combine a high speed amplifier, A2, and a slower but more precise A1 to achieve best of both words.

Observe in the link you posted that C3 in series with inverting input blocks DC to that pin.
But opamps must have at their input pins a path to signal common for their input bias currents . R3 serves that purpose.

I'd got hung up trying to calculate a transfer function for the circuit that included R3 and C3.
But in reality they are effectively inside the amplifier , as I've drawn them below,
so only affect the amplifier's open loop gain at frequency lower than R3C3 breakpoint.
Above that frequency they can be ignored.
Below that frequency A1 provides response , extending open loop gain all the way down to DC.

That for me solves the R3C3 riddle. It let's A2 do what A2 does well, follow fast signal from Rogowski coil;
and relieves it of the need to do what it cannot do well, track DC signal from the Hall sensor.
Accordingly, RiCi and C3R3 can be set to a low frequency. I think they should be set the same, i'd try just a very few hertz.


So rather than fight the algebra, treat A1-A2 combination as a single op-amp configured as a low pass summer, where R2C2 sets its breakpoint.
Node V2 is its summing junction. Look more traditional now?

There's a TI device made for use with Rogowski coils. Its datasheet delves into setting the lowpass filter R2C2.
http://www.ti.com/lit/ml/tiduby4a/tiduby4a.pdf
Don't get confused - in that document when they say 'integrator' they mean the lowpass which is our R2C2 NOT our DC tracker RiCi. Sorry i don't have all your answers yet. This is new to me, too. But the technique is somewhat reminiscent of chopper stabilized opamps from the 1950's...

old jim

 

[jim hardy]

I'd got hung up trying to calculate a transfer function for the circuit that included R3 and C3.
But in reality they are effectively inside the amplifier , as I've drawn them below,
so only affect the amplifier's open loop gain at frequency lower than R3C3 breakpoint.
Above that frequency they can be ignored.
Below that frequency A2 provides response , extending open loop gain all the way down to DC.

I am so accustomed to considering the two opamp inputs perfectly symmetrical that it took me days to realize what they'd done.
A2's + input is DC coupled
but they blocked DC from its - input, set that to zero with R3.
So it's a DC amplifer for its + input only
for its - input it is AC only
and nobody said we couldn't have different Avol plots for the two inputs - they'll diverge below R3C3 breakpoint.

That was my mental stumbling block.

http://www.analog.com/media/en/training-seminars/design-handbooks/Op-Amp-Applications/Section1.pdf
"Tradition !" ... old jim

 

[Tom.G]

I printed the HOKA paper referenced in post #1 and seemed to be getting a better handle on it. I also found, and printed, what appears to be an earlier version of the HOKA magazine article. It is a little different as to what details are included or missing. (attached below)
Between the two papers, there is enough detail to simulate the circuit if anyone cares to.

how I can determine the components C3, R3, Ri, Ci and maybe also C2, with Vcoil and Vhall being known

The conclusions I've reached are:
These are wrong! See post #27.[/color]

• 
  [*]T_V = R2C2 ≥ 100 x T_H
  [*]R3C3 = T_H (crossover freq between coil and Hall. determines what freq the coil starts to take over the from the Hall sensor)
  [*]Edit R_iC_i ≥ 3 x T_V (not critical. determines how fast output recovers from DC transient)
  [*]R_iC_i = T_V (this is the DC path for the Hall sensor and the DC feedback path for A2) end Edit (sleeping on the problem helps!)
  

T_H = Time constant of Hall sensor, reciprocal of corner frequency
T_V = Compensates for the 20db per decade rolloff of Hall sensor (this can be varied to adjust the mid - low freq response)

I'm about 85% confident in the above, so if you are comfortable with a simulator it could be advantageous.

Notes:
If you use an unamplified Rogowski coil, it needs to have a high load impedance (10's of kOhms) to act as intended; a low load impedance makes it act as a current transformer.

The amplified Hall sensors I've looked at have a temperature coefficient of +0.1% to +0.15% per degree C.

ARRGH! PDF Upload not working. Here is a link to the earlier HOKA paper.
https://pdfs.semanticscholar.org/1b89/88109a6d7b682292993829a537da079fcd94.pdf

p.s. I just looked at the datasheet for the Hall device, their is no frequency response data! You will need that to match to the Rogowski coil.

Edit
Hmm. Looks like it did after all.
end Edit

 

[jim hardy]

The conclusions I've reached are:

• TV = R2C2 ≥ 100 x TH

Agreed.
To get this thing working in my alleged brain i have to imagine a constant amplitude swept frequency sinewave test current applied to the sensor.
That makes it clear that Hall sensor's amplitude is flat out to at least some audio frequency, Kh X Sin(wt)
and coil's output is the derivative, Kr X ω X Cos(wt) , extra ω gives its amplitude a slope of +20 db/decade.
So coil signal is nil at low frequency but there's some frequency at which it will become larger than the Hall signal.
They have some control over the frequency where that happens by applying different gains to the two paths. R1h and R1c for OP..
So they pick an R2C2 and fine tune crossover point with R1h and R1c

In that article you linked;
In their 'ideal' implementation page 2 of 10 fig 2 they used TH for the breakpoint

for some reason they dropped it two decades to 1khz per page 5 of 10 (i suppose to reduce phase shift?)

and gains are adjusted to make that frequency be the point where Hall and Coil . signals becone equal amplitude .
Below that frequency the Hall sensor's flat response lies on the flat part of the LP's transfer function.At those low frequencies the Hall signal is larger and dominates.
Above that frequency the coil's +20db/decade response is brought back flat by the -20db/decade part of the LP's transfer function. Coil signal becomes now increasingly larger with frequency and overwhelms the Hall signal.

R3C3 = TH (crossover freq between coil and Hall. determines what freq the coil starts to take over the from the Hall sensor)

For ideal yes. For their practical implementation, Tv two decades lower

RiCi ≥ 3 x TV (not critical. determines how fast output recovers from DC transient)

I think RiCi should be very slow. because it's mostly a DC trim to take care of offset and drift in high speed amplifier A2..
See this schematic from yet a third article by sameKarrer(linked earlier): https://pdfs.semanticscholar.org/f39a/25945d67d3d3f0ffc778a038e07fad64af52.pdf

It handles the DC without an integrator. (from magnetorestrictive sensors not Hall but still proportional)
R5C2 looks to me like it violates a stability taboo. Maybe it is there to make the circuit faster? I'm unsure at this point..

Anyhow our ideas are converging.

Good to learn about these Rogowski devices. Now the first real one i encounter won't be so baffling.. What a great idea, and it's from the 1880's !

In another conversation with Dr D we both wondered what more would Ampere have found if he'd had today's electronics.. Indeed we stand on the shoulders of giants. It's humbling to contemplate and that's good.

old jim

 

[jim hardy]

R5C2 looks to me like it violates a stability taboo. Maybe it is there to make the circuit faster? I'm unsure at this point..

around page 25 here.
http://www.ti.com/lit/an/slyt087/slyt087.pdf

 

[Tom.G]

R3C3 = TH (crossover freq between coil and Hall. determines what freq the coil starts to take over the from the Hall sensor)

For ideal yes. For their practical implementation, Tv.

Consider the response at T_H/10. If R3C3 = T_V then both the Hall and the Rogowski will make significant contributions to the output. Wouldn't the overall bandpass then imitate a tuned circuit? Or did I miss something?

It handles the DC without an integrator. (from magnetorestrictive sensors not Hall but still proportional)
R5C2 looks to me like it violates a stability taboo. Maybe it is there to make the circuit faster? I'm unsure at this point..

Yeah, looks an awful lot like an oscillator! An apparent rational for the HOKA circuit was to avoid having to match multiple RC time constants. For flat frequency response, this circuit requires matching of R3C1 with R5C2.

 

[jim hardy]

Consider the response at TH/10. If R3C3 = TV then both the Hall and the Rogowski will make significant contributions to the output. Wouldn't the overall bandpass then imitate a tuned circuit? Or did I miss something?

I still think that R3C3 and RiCi should be both set slower than 1 hz. Their purpose is to correct DC offset.
1hz puts them three decades below R2C2.

A2 adds Vcoil and Vhall irrespective of their frequency.

Th/10 is a decade faster than Tv .
IF coil and Hall voltages are equal at frequency Tv,
THEN
at Tv X 10 , coil voltage is 10X Hall voltage (+20 db/decade)
and since one is a sine and one a cosine they add at 90 degrees so their vector sum is 10.05Vhall
and at that frequency R2C2 attenuates that sum by 20 db bringing it back to 1.005 Vhall .

RiCi needs to be very slow so that its lowpass keeps it from interfering with the AC signal
and R3C3 should be set to the same value so that A1 corrects the low frequency Avol rolloff they created in A2.
R3C3 caused the red-blue departure here (from post 18)

A1 with RiiCi pushes the red back up to horizontal.

That's my mental model as of this minute and it's evolving. Hope you don't mind my thinking aloud.

Those authors could have done a lot better job of explaining their circuit, i think. I find nothing like it in AN31...

Thanks ! old jim

 

[jim hardy]

I find nothing like it in AN31...

oops AN31 page 36 of 62

time to rethink A1.

 

[Tom.G]

See the Edit to my post #19. I've restated R_iC_i criteria to:

R_iC_i = T_V (this is the DC path for the Hall sensor and the DC feedback path for A2)
(sleeping on the problem helps!)

But I'm still a little uncomfortable with where all the breakpoints occur and interact.
Again, anyone up to doing a simulation of this thing?

@jim hardy Haven't digested your above post #23 yet. Will dig in a little later. (after I print it!)

 

[Tom.G]

@jim hardy In my post #22, I should have stated F_H/10 or T_H x 10, not T_H/10. Sorry to add to the confusion!

So far, I'm sticking with R_iC_i = T_V.

Edit: removed incorrect freq response image and text reference thereto.

 

[Tom.G]

Yup, twice I got egg on my face.

Correction to post #19: R_IC_I =T_V
Correction to post #25: same fix for R_IC_I =T_V and the Bode plot is wrong in #26, removed, see below.

I missed an inversion when doing the Bode plot in post #25 so I re-plotted using the values the OP has in the schematic in post #12 https://www.physicsforums.com/threads/adder-lp-filter.943146/#post-5970040. @Glenn Emmers got the RC values very close to what is needed. As you can see in the plot,

As Simulated in post #12 but it is slightly off. Swap R2C2 and R_IC_I.

• T_V = R2C2 ≥ 100 x T_H Wrong, see below.
  
• R3C3 = T_V
• R_IC_I = T_H (this is the DC path for the Hall sensor and the DC feedback path for A2 and wrongly the integrator for the Rogowski coil) Wrong, see below.

If R3C3 is set to T_V then the Transfer Function (TF) will rise 6db and look just like it should!

There are a few things that will be important in a practical implementation.

• The time constants of R_IC_I and R2C2 should be swapped. Make R_IC_I = T_V and R2C2 = T_H. This gets the high frequency coil signal out of A1 and into A2 where it belongs.
  
• Fix R3C3 time constant.
• R_I should be a much higher value so it doesn't act as a voltage divider on the summing node, 20 to 100 times the value of any of the input resistors.
• The selected Hall sensors can drive only about 0.5mA so if their expected output voltage is >0.9V, the input summing resistors will need to be a higher value.
• The Rogowski coil has a very low output signal and needs a high impedance load. It will need a fast preamp (gain≥100, perhaps) with an impedance of at least a few 10s of kΩ. (Low noise, low level preamps can be a challenge.)
• The usual stuff for low level, low noise; avoid ceramic caps in the signal chain, use metal film resistors, attention to ground planes and shielding, depending on the environment, the leads to the Rogowski coil might need triax cable with a driven shield.

 

[jim hardy]

Great work on the Bode plots @Tom.G
I added the sensor slopes to it in purple and gold, and how the circuit would sum them in brown.

one question though

could you multiply Rogowski by +40 db so it'd cross Hall at Tv
then shift R2C2 down by two decades so it'd attenuate Hall and flatten Rogowski ?

RiCi is still unsettled for me. I do agree it should be same as R3C3. But i don't yet grasp the details of Bob Pease's fast amplifier from AN31.

Hmmm... OP gave up on us ?

 

[Tom.G]

one question though

could you multiply Rogowski by +40 db so it'd cross Hall at Tv
then shift R2C2 down by two decades so it'd attenuate Hall and flatten Rogowski ?

Long Answer:
Well, let's see. OP says expected coil signal is 2uV; and that varies directly with frequency. Two decades lower frequency means a 20nV signal. To get moderately decent pulse waveforms down to 5uS pulse width, we choose maximum freq as 1MHz. With that bandwidth, the unity signal-to-noise ratio (SNR) would be with an opamp equivalent input noise e_n, of

e_n in units of (nv/√Hz),
20nV/√(10⁶),
20nV/1000, or 20pV input noise.

The lowest noise opamp at Maxim, the MAX410, has e_n = 1.5nV. It seems the technology has a few more centuries to go for that!

That MAX410 has unity gain at 28MHz, so you will get a closed loop gain of 2 to 3 at 1MHz. A few more wideband, noisier, stages could get you to that 40db you are after - assuming you can beat the input noise problem!

Ahh, that noise problem. Thermal noise also becomes an issue. To get down to that 20nV level the total resistance in the input circuit would have to be 1Ω and the entire input circuitry cooled to 7°K (-266°C), lower if you want better than unity SNR.
(thermal noise calculator at: http://www.daycounter.com/Calculators/Thermal-Noise-Calculator.phtml)

Short Answer:
No.

 

[jim hardy]

Ahhh ! How utterly 'Practical' ! i love it...

Paraphrasing Matt Hooper: "We need a bigger Rogowski coil"...

Thanks Tom !

 

[Tom.G]

@Glenn Emmers Considering the time/effort expended on this project, a commercially available Rogowski probe that covers your full frequency range should be investigated. Here are some links for wideband ones that may help. (No Hall device needed unless you need DC.)

Some explanation from the Government Printing Office:
(On page 175 et seq. of 428)
https://www.gpo.gov/fdsys/pkg/GOVPU...VPUB-C13-6fc54876ae3cb5ad69ab9d43094650f8.pdf
Here is a link to reference [7] in the above. It is behind a $30 pay wall so I haven't looked at it.
Review of Scientific Instruments 51, 1535 (1980); https://doi.org/10.1063/1.1136119

User Guide:
https://www.keysight.com/main/redir...ey=2925114&lc=eng&cc=US&nfr=-32553.1229528.00

Data Sheet:
https://www.keysight.com/en/pd-2877...23-mhz-3000-a?nid=-32553.1229528&cc=US&lc=eng

Selection Guide:
https://www.keysight.com/en/pc-1000000101:epsg:pgr/oscilloscope-probes?pm=SC&nid=-32564.0&cc=US&lc=eng

("Keysight" used to be "Agilent" used to be "Hewlett Packard")