Why are V(rms) measurements frequency dependant?

[sourcecharge]

So, I've got this great new add-on for my current measurements, the uCurrent. 

It is going to allow me to measure DC current up to 999.99 mA with a 0.05% accuracy with only 10 milliohm added impedance.

The problem is that in order to measure AC current, the VAC from the meter must be used. 

I have measured a signal from my FG and have found that the V(rms) is changing from 45hz up to 10khz.

My meters (Mastech 8040), and all of the meters I've seen so far, seem to all have the error problem that is listed in the accuracy table specifications.

They all have an error that is frequency dependent.

Why is this?

Can it be solved like a uCurrent add-on to get an accurate VAC measurement that would cancel any frequency dependence?

Is there a meter that is already out that can accurately measure VAC across a broad range of frequency up to say 1 Mhz, or even non frequency dependent?

I know that I could just use low turn on diodes to find a Vp, and reverse calculate it, but I'm not sure even it that would be non frequency dependent. 

Would this be possible as a realistic piece of equipment so that this is not necessary?

[JS]

Because of frequency reaponse of the DMM chipset. When using an onboard TRMS converter inside the DMM chipset is uaual to get reasonable specs up to 1kHz and then starts to be less accurate. Better DMM have a dedicated IC to make the TRMS conversion and get good specs up to 100kHz or so. Compare BM235 and 121GW, EEVBlog's DMMs and you'll see. BM235 is using the chipset and only specified up to 800Hz, 121GW is using an external IC and specs go up to 5kHz. There are audio TRMS converters which do a good job over 20kHz depending on the level.


If you want to go higher you could use a dedicated  higher freq instrument. TRMS doesn't go much higher but you could build a higher freq measurement by just using a diode. μCurrent leaves you with a decent level to amplify a bit further and use a diode rectifier to get a value. If you use something like a voltage doubler you will be seeing something close to a peak to peak value.

JS

[sourcecharge]

I get what you are saying, and it makes sense.

How expensive would it be to make a high quality DIY type Vrms meter.

Basically, it would be only for AC Vrms.

It would output VDC so that normal 4.5 digit meters could be used, and use that 2032 battery.

It sounds like a lot of programing firmware, some pricey ICs, and a custom board, but I think it would be much cheaper than a 100000 count meter.


Where do I start?

[JS]

A single 2032 might not be enough, you usually want higher levels to get a bettee linearity. Start looking at a TRMS converter from a parametric search on your supplier. Once you pick one see what you need around it... With that approach no need for programming anything. What are the specs you are trying to get from it?

JS

[sourcecharge]

Well, I guess I just want a Vrms meter that's gives me the correct Vrms output without having to worry about frequency.

That might be asking too much...maybe 100khz bandwidth being a flat output? That might be asking too much too.

I took a look at PMIC RMS to DC converters, and digikey does not look like they have a good selection.

The AD8436 is in there, but I think the thing to do is to rip open a really really expensive 100000 count meter and check out what it's packing.

Maybe I'll find some toober videos that show their guts.

[Kalvin]

The analog RMS converter used in Fluke 8842A has accuracy around 0.5% or worse (from the Fluke 8842A manual). Similar accuracy can be achieved using an analog RMS converter from Analog Devices up to few kHz, and with additional 1% error up to 200 kHz with sufficient input signal level. The dynamic range an analog RMS-converter is around 60 dB (1:1000), so one will not get very many digits of accuracy, although the resolution might be a digit or so more. In order to get higher accuracy one could use LTC1968 up to 150 kHz and 0.1% accuracy. The RMS-converters are quite sensitive to the input voltage, which means that the [autoranging] input circuitry needs to track the input voltage so that the RMS-converter will see optimal input voltage with a sufficient crest factor margin.

Edit: The AD8436 looks pretty good.

[maukka]

Check out HKJ's DMM review page. The popup window on top of the DMM name will show the measured AC volt bandwidth.

Also Parametrek's DMM search engine has a couple brands crawled and there's several Uni-T's with a specified bandwidth of 100 kHz.

[Zero999]

The analog RMS converter used in Fluke 8842A has accuracy around 0.5% or worse (from the Fluke 8842A manual). Similar accuracy can be achieved using an analog RMS converter from Analog Devices up to few kHz, and with additional 1% error up to 200 kHz with sufficient input signal level. The dynamic range an analog RMS-converter is around 60 dB (1:1000), so one will not get very many digits of accuracy, although the resolution might be a digit or so more. In order to get higher accuracy one could use LTC1968 up to 150 kHz and 0.1% accuracy. The RMS-converters are quite sensitive to the input voltage, which means that the [autoranging] input circuitry needs to track the input voltage so that the RMS-converter will see optimal input voltage with a sufficient crest factor margin.

Edit: The AD8436 looks pretty good.

Don't some meters do the RMS calculation digitally? That might be more accurate, but it will could also use more energy, than doing it the analogue way.

[Kleinstein]

....
Don't some meters do the RMS calculation digitally? That might be more accurate, but it will could also use more energy, than doing it the analogue way.

Some of the bench-top meters measure do the RMS measurement digital. Keysight calls this true-volt.
This method has some advantages, like good linearity, temperature stability and also working well at a relatively low level, but it still has a limited bandwidth from the fast ADC used.

If one accepts a limited amplitude range (much like with the analog solutions) the 10 or 12 bit resolution ADC inside modern µCs can by used. The calculation is not that difficult: just root mean square and some extra compensations for an offset. I have made this once with an 8 bit AVR (10 bit ADC) - it works surprisingly good, about comparable to the low end analog chips and thus useful if the amplitude is more than about 2% of full scale and with a limed bandwidth (e.g. around 5 kHz).

One of the nasty points with the analog solutions is, that the bandwidth depends on amplitude - usually less bandwidth at low amplitude. This is one reason they don't work well over a large amplitude range. With higher frequency parts like in a square wave there can also be some nonlinearity / interaction of the harmonics - so not all waveforms wort equally well.

[sourcecharge]

I've been reviewing half a dozen spec sheets from meters and the best I found at a reasonable cost was the Siglent SDM3055 with 20khz bandwidth of 0.02% of reading and 0.05% of range error for 1 year.  Unfortunately it's still almost 500 bucks!

EDIT: Siglent SDM3055 has a 20khz bandwidth of 0.2% of reading and 0.05% of range error for 1 year.

So back to the DIY try.

I've been eyeing that LTC1968 rms to dc converter...at only about 9 bucks, it really looks like a winner.

Also, I guess I would need some kind of V reference?

Is the voltage reference for the rms to DC converter Vcc?

Or is it for the "the [autoranging] input circuitry needs to track the input voltage so that the RMS-converter will see optimal input voltage with a sufficient crest factor margin."

I found a good 10V reference from TI.

ref102 with only a +- 0.0025 error and 2.5ppm/C and at only about 11 bucks each, not bad right?

But if I need a 5V for the LTC1968, the MAX6325CPA has only a 1 ppm/C with only a +-0.02% error for about the same cost.

So what about this autoranging circuitry?

I'm guessing some kind of op amp multiplexing for the input and output....

Can't this be done with a switch like the uCurrent?  Maybe switch in and out different resistor networks?

What if, the circuit under test is measured first by the multimeter, then the add-on is switched to the resistor network required for the opamp to put out the correct voltage for the rms to dc converter, which also switches it for the output too as well?

Then the add-on is connected after it has been switched?

hmmm...

[Kleinstein]

The  LTC1968 looks like a good one. I don't see a need for a voltage reference here - the voltage reference would be needed for the measurement of the DC output only, which would be a normal DMM in voltage mode here.  The  LTC1968 would just need a reasonably regulated supply.

For the auto-ranging, there is no absolute need for this here. It could be done by hand too if there are suitable indications. The relevant numbers are the peak voltages - so one should have some extra circuitry to check the peak voltages. As a minimum this would be something like 2 comparators to check the upper limits and than use manual adjustment with try and error (use smallest range that does not indicate error from peak values).

The actual gain setting can be quite tricky for higher BW if it needs to be really accurate. This is because the divider would be not just resistors, but also with parallel capacitance that needs adjustment (a little like the compensation at scope probes). Also electronic switches have limited isolation when off.

[Zero999]

I've just quickly read through the data-sheet for the LTC1968. The reference is the common voltage for the AC waveform. The IC measures the difference between the voltage on its inputs. At least one input must be DC coupled to a steady voltage between the supply rails. If it's a single supply application, connect one pin to a potential divider with a bypass capacitor to 0V and the other input to the signal source, via a capacitor. See page 12.
http://www.analog.com/media/en/technical-documentation/data-sheets/1968f.pdf

The output of the LTC1968 is high impedance and needs a buffer amplifier, before going to the DVM. A decent, low offset, high input impedance, low bias current, op-amp is required for the buffer.

[Kalvin]

The analog RMS converter used in Fluke 8842A has accuracy around 0.5% or worse (from the Fluke 8842A manual). Similar accuracy can be achieved using an analog RMS converter from Analog Devices up to few kHz, and with additional 1% error up to 200 kHz with sufficient input signal level. The dynamic range an analog RMS-converter is around 60 dB (1:1000), so one will not get very many digits of accuracy, although the resolution might be a digit or so more. In order to get higher accuracy one could use LTC1968 up to 150 kHz and 0.1% accuracy. The RMS-converters are quite sensitive to the input voltage, which means that the [autoranging] input circuitry needs to track the input voltage so that the RMS-converter will see optimal input voltage with a sufficient crest factor margin.

Edit: The AD8436 looks pretty good.

Don't some meters do the RMS calculation digitally? That might be more accurate, but it will could also use more energy, than doing it the analogue way.

The RMS can be calculated digitally if you have a fast enough ADC = more energy required compared to analog solution due to ADC and DSP implementation. For a signal with 150 kHz bandwidth, one has to sample at least with 300 kHz - in practice somewhat faster say 500 kilosamples/second. For 1 MHz signal one should probably sample at 3 Ms/s.

In order to get high signal dynamic range with sufficient room for crest factor, the ADC has to have as many bits as possible, say 16 bits with 3-4 bits reserved for crest factor (ie. for the peak values of the signal compared to the RMS of the signal https://en.wikipedia.org/wiki/Crest_factor) leaving 12 - 13 bits RMS for computation.

At low signal levels the resolution will suffer due to the quantization. In order to compensate the quantization effects one may need to either increase the sample rate with oversampling or increase the number of bits of the ADC from 16 bits to 20 - 24 bits, for example, which will increase the cost of the ADC. Alternatively one may arrange the input signal level so that it will be kept as high as possible without clipping (autoranging or manual ranging) in order to get as many significant bits as possible for best accuracy and resolution.

After sampling the computation is quite straight forward requiring some DSP computation. There are nice algorithms available for computing the RMS: https://www.embedded.com/design/configurable-systems/4006520/Improve-your-root-mean-calculations

My guesstimate  is that getting 3.75 digits for resolution is quite the practical limit with one can achieve with a signal bandwidth of > 100 kHz with a typical 16-bit ADC and optimal signal level with crest factor of 10. Probably one could achieve one extra digit with a state-of-the art, fast 24-bit ADC. One can obtain better estimation on resolution/accuracy and effects of different signal levels by performing some simulation and running mathematical/numerical analysis for the quantized signals.

[JS]

The RMS can be calculated digitally if you have a fast enough ADC = more energy required compared to analog solution due to ADC and DSP implementation. For a signal with 150 kHz bandwidth, one has to sample at least with 300 kHz - in practice somewhat faster say 500 kilosamples/second. For 1 MHz signal one should probably sample at 3 Ms/s.

In order to get high signal dynamic range with sufficient room for crest factor, the ADC has to have as many bits as possible, say 16 bits with 3-4 bits reserved for crest factor (ie. for the peak values of the signal compared to the RMS of the signal https://en.wikipedia.org/wiki/Crest_factor) leaving 12 - 13 bits RMS for computation.

At low signal levels the resolution will suffer due to the quantization. In order to compensate the quantization effects one may need to either increase the sample rate with oversampling or increase the number of bits of the ADC from 16 bits to 20 - 24 bits, for example, which will increase the cost of the ADC. Alternatively one may arrange the input signal level so that it will be kept as high as possible without clipping (autoranging or manual ranging) in order to get as many significant bits as possible for best accuracy and resolution.

After sampling the computation is quite straight forward requiring some DSP computation. There are nice algorithms available for computing the RMS: https://www.embedded.com/design/configurable-systems/4006520/Improve-your-root-mean-calculations

My guesstimate  is that getting 3.75 digits for resolution is quite the practical limit with one can achieve with a signal bandwidth of > 100 kHz with a typical 16-bit ADC and optimal signal level with crest factor of 10. Probably one could achieve one extra digit with a state-of-the art, fast 24-bit ADC. One can obtain better estimation on resolution/accuracy and effects of different signal levels by performing some simulation and running mathematical/numerical analysis for the quantized signals.

No need for that much adc and dsp, you can do oversampling and decimation after rectification so the resolution and frequency response can be much better than what you said... You could sample at 1kHz and still get a response up to MHz if the sampling is short enough lthe adc frequency resppnae is the limit, not the sampling frequency) and after averaging you get the resolution under one LSB, useful if the ADC linearity is gpod enough but you don't need the data and computation to deal with greater ADCs. Using a pseudorandom sampling frequency makes for a better frrquency response, minimizing the comb filter at multiples of the sampling freq.

JS

[Zero999]

The RMS can be calculated digitally if you have a fast enough ADC = more energy required compared to analog solution due to ADC and DSP implementation. For a signal with 150 kHz bandwidth, one has to sample at least with 300 kHz - in practice somewhat faster say 500 kilosamples/second. For 1 MHz signal one should probably sample at 3 Ms/s.

In order to get high signal dynamic range with sufficient room for crest factor, the ADC has to have as many bits as possible, say 16 bits with 3-4 bits reserved for crest factor (ie. for the peak values of the signal compared to the RMS of the signal https://en.wikipedia.org/wiki/Crest_factor) leaving 12 - 13 bits RMS for computation.

At low signal levels the resolution will suffer due to the quantization. In order to compensate the quantization effects one may need to either increase the sample rate with oversampling or increase the number of bits of the ADC from 16 bits to 20 - 24 bits, for example, which will increase the cost of the ADC. Alternatively one may arrange the input signal level so that it will be kept as high as possible without clipping (autoranging or manual ranging) in order to get as many significant bits as possible for best accuracy and resolution.

After sampling the computation is quite straight forward requiring some DSP computation. There are nice algorithms available for computing the RMS: https://www.embedded.com/design/configurable-systems/4006520/Improve-your-root-mean-calculations

My guesstimate  is that getting 3.75 digits for resolution is quite the practical limit with one can achieve with a signal bandwidth of > 100 kHz with a typical 16-bit ADC and optimal signal level with crest factor of 10. Probably one could achieve one extra digit with a state-of-the art, fast 24-bit ADC. One can obtain better estimation on resolution/accuracy and effects of different signal levels by performing some simulation and running mathematical/numerical analysis for the quantized signals.

No need for that much adc and dsp, you can do oversampling and decimation after rectification so the resolution and frequency response can be much better than what you said... You could sample at 1kHz and still get a response up to MHz if the sampling is short enough lthe adc frequency resppnae is the limit, not the sampling frequency) and after averaging you get the resolution under one LSB, useful if the ADC linearity is gpod enough but you don't need the data and computation to deal with greater ADCs. Using a pseudorandom sampling frequency makes for a better frrquency response, minimizing the comb filter at multiples of the sampling freq.

JS

Yes, you should be able to use a lower sample frequency, than the bandwidth of the signal, because the waveform will more than likely be repeating and you want an average over a long time period, to do RMS calculations anyway.

[sourcecharge]

The  LTC1968 looks like a good one. I don't see a need for a voltage reference here - the voltage reference would be needed for the measurement of the DC output only, which would be a normal DMM in voltage mode here.  The  LTC1968 would just need a reasonably regulated supply.

For the auto-ranging, there is no absolute need for this here. It could be done by hand too if there are suitable indications. The relevant numbers are the peak voltages - so one should have some extra circuitry to check the peak voltages. As a minimum this would be something like 2 comparators to check the upper limits and than use manual adjustment with try and error (use smallest range that does not indicate error from peak values).

The actual gain setting can be quite tricky for higher BW if it needs to be really accurate. This is because the divider would be not just resistors, but also with parallel capacitance that needs adjustment (a little like the compensation at scope probes). Also electronic switches have limited isolation when off.

Well this is what I got so far, it's nothing fancy, but it will work in the ranges for the LTC1968 for 50mVrms to 500mVrms so that it can operate within the 0.1% error tolerance up to 150kHz.

It should give the add-on the ability to measure between 50uVrms to 500Vrms, with the output of the meter between 50mV DC to 500mV DC.

Any more additional components, and I think I would be increasing the error.

Basically, it's got the MAX4239 op amps like the uCurrent, and a resistor network that are switched between outputs.

The additional switch to the input of the 1st op amp is needed to limit the voltage on the input leg for higher voltages.

I was going to run the MAX4239 along with the LTC1968 with some type of voltage regulator at 5V and a 9V battery, but I'm not sure if the op amps still have the same characteristics when run at 5V vs 3V. 

I have discounted the op op amp LMV321 and all of the required capacitors that is on the uCurrent in this schematic, but they will be in the final design. 

I will also try to find 0.01% or better resistor tolerances.

I have not included the LTC1968 because B2 doesn't have even 1 rms to DC converter let alone this specific one, but the datasheet shows that one of the inputs to the converter needs to have a series capacitor and a capacitor on the output of the DC conversion.

I have included the datasheet for the LTC1968 and a 10V reference that I was going to use for a DC calibration for my bench meters.

I also got what I think are the most relevant graphs from the LTC1968 together to show the linearity.

Anyone have any thoughts, suggestions, maybe what switch to use, and maybe cheap improvements that don't increase the error?

The ranges for this network using the LTC1968 are of the following:

Closed Switch(es)- (while all other switches are open)
XSW8 and XSW1- Input: 50   uVrms   to    500  uVrms   Output: 50mV DC to 500 mVDC
XSW8 and XSW2- Input: 500 uVrms    to   5     mVrms   Output: 50mV DC to 500 mVDC
XSW8 and XSW3- Input: 5     mVrms   to   50   mVrms   Output: 50mV DC to 500 mVDC
                XSW4- Input: 50   mVrms    to  500 mVrms    Output: 50mV DC to 500 mVDC
                XSW5- Input: 500 mVrms    to   5      Vrms    Output: 50mV DC to 500 mVDC
                XSW6- Input: 5       Vrms    to   50     Vrms    Output: 50mV DC to 500 mVDC
                XSW7- Input: 50     Vrms    to   500   Vrms    Output: 50mV DC to 500 mVDC


EDIT: The resistor network shown is not available at digikey, but 20M, 2M, 200k, 20k + 2k + 200 (22200) are available at 0.01% 5ppm/C at about a total of 70 bucks.

[sourcecharge]

So, just checked the pricing at digikey and the only resistors with a greater tolerance of 0.1 were through hole types, and they were pricey.

Total cost of just the resistor network before tax and shipping, 196 bucks.
 

[Zero999]

So, just checked the pricing at digikey and the only resistors with a greater tolerance of 0.1 were through hole types, and they were pricey.

Total cost of just the resistor network before tax and shipping, 196 bucks.
 

That's because you've used weird values. 9×10^x is not a common resistor value, so it will be expensive, especially in 0.1% tolerance or better.

You would have more luck if you used standard E24 of E96 values. If you divide all of the precision resistor values in that circuit by 5, then it would give you much more widely available resistor values.

[David Hess]

The RMS can be calculated digitally if you have a fast enough ADC = more energy required compared to analog solution due to ADC and DSP implementation. For a signal with 150 kHz bandwidth, one has to sample at least with 300 kHz - in practice somewhat faster say 500 kilosamples/second. For 1 MHz signal one should probably sample at 3 Ms/s.

The only thing which matters is the sampling bandwidth; the sample rate is irrelevant except for uncertainty.  The RMS calculation is just the standard deviation.  Reducing the number of samples does not change the standard deviation so operating the analog to digital converter below the Nyquist frequency is completely acceptable.  Another way to look at it is that aliasing folds the signal over inside the Nyquist bandwidth but the standard deviation of the entire signal is still there to be measured.

This can also be done in the analog domain.  Use a sampler to capture the input and feed the sampler's output to a standard analog translinear RMS converter.  Now the input bandwidth is limited by the sampler and not the analog RMS converter.  The Racal-Dana 9301 and HP3406 sampling RF voltmeters worked this way to make RMS measurements into the GHz range.  Some old analog sampling oscilloscopes had a sampling output which could be attached to a low frequency RMS voltmeter to do the same thing up to 10+ GHz and beyond.

As far as the original question, most DSOs can do what is needed if their accuracy is acceptable.  Just be careful because not all DSOs compute the RMS function correctly.  This is likely to be a problem if they make measurements on the processed display record (this destroys the standard deviation) like the often recommended Rigol DS1000Z series.

If you want to build something simple without using the sampling and standard deviation method, then I suggest using the AD637 or LTC1967 RMS to DC converter IC.

[Tomorokoshi]

Is there a meter that is already out that can accurately measure VAC across a broad range of frequency up to say 1 Mhz, or even non frequency dependent?

Additionally, the Hewlett Packard 3403C True RMS Voltmeter can be coaxed to an accuracy of 10% at 100 MHz. At 1 MHz it can be good to around 3% depending on the input voltage level. These use a thermopile converter.

http://www.hpl.hp.com/hpjournal/pdfs/IssuePDFs/1972-03.pdf

http://www.analog.com/media/en/technical-documentation/application-notes/an106f.pdf

They show up on ebay for $100 to $200.

[Kleinstein]

The max4239 is not that suitable to amplify small AC signals. It has a rather limited BW and quite some higher frequency noise. With amplification it's usually better to separate the DC part out, so that no AZ OPs are needed.

The simple divider with 900 K will not work well without compensating caps. Normal mechanical switches may not offer sufficient isolation when off and the later OP stages driven to saturation may give quite some higher frequency components if really fast.
So the proposed circuit is not really good for higher frequencies - maybe up to a few kHz. With AC 0.1% resistors should be good enough - even with adjustment the caps will not be that accurate and stable.

When using the digital method there is no need for that much ADC resolution: for a single RMS reading there will be quite a lot of ADC samples (usually at least in the 10000 range) used and in a kind of oversampling way this will give a resolution for the RMS value that can be quite a bit higher than the ADC resolution. For a simple DIY test something like the STM32F3...  µC with a reasonable fast (a few MSPS) 12 Bit ADC would be a good start.

[sourcecharge]

Ya, I wasn't thinking..

digikey has a 20M, 2M, 200k, 20k, 2k, and a 200 good through hole resistors...and those come out to be about 70 dollars (I think).

I didn't want to decrease the impedance too much so I just did the calculation this time with what was available.

These resistors are 0.01% tolerance and it looks like they are meant for this application.

The 0.1% error of the LTC1968 is good only up to 150khz, which should be plenty for what I was hoping for..not sure if it is though...

The max4239 has a BW of 6.5Mhz, and with only a 10x gain, that means the adjusted BW at the last op amp should be

BW(tot) = 6.5Mhz/10 x (2^(1/3)+1)^(1/2) because I am using three with all the same gain.

That gives a BW of 977khz.

The uCurrent has proven to me that these op amps can amplify DC, but you are saying that these can't do small AC signals?

Why?

Regarding the switches, what about isolation relays coupled with a simple switch that turns the relays on and off with 5V?

Not too sure what to do regarding the caps, what are the caps going to help with?  Do you think by using the high resistance values of 20M..etc..will limit that problem?

[sourcecharge]

I've just quickly read through the data-sheet for the LTC1968. The reference is the common voltage for the AC waveform. The IC measures the difference between the voltage on its inputs. At least one input must be DC coupled to a steady voltage between the supply rails. If it's a single supply application, connect one pin to a potential divider with a bypass capacitor to 0V and the other input to the signal source, via a capacitor. See page 12.
http://www.analog.com/media/en/technical-documentation/data-sheets/1968f.pdf

The output of the LTC1968 is high impedance and needs a buffer amplifier, before going to the DVM. A decent, low offset, high input impedance, low bias current, op-amp is required for the buffer.

I was thinking about simply using another MAX4239 in unity gain for the buffer op amp, is that reasonable?

[Kleinstein]

The max4239 is not unity gain stable. For the output the unity gain stable version max4238 would be better.

The problem with the max4239 at the input is having quite some noise, especially at the higher frequencies (e.g. the AZ frequency). So it would likely not make much sense to have that much amplification. The BW calculation is also a little off - it should be a little below 650 kHz. So at 150 kHz the loop gain would be somewhere around 5 and thus significant errors could start to appear.

The capacitive problem is that the 20 M resistor will have some parasitic capacitance in parallel. To make the divider work well, there should be a parallel capacitive divider with the same rations. So the smaller resistors would need correspondingly larger caps in parallel.  If there is some parasitic 1 pF at the 20 M , the 200 K should have some 100 pF and so on.  As an additional complication the OPs input and switch will also have some capacitance, that changes with the switch setting. So to make is reasonably work in all settings the capacitance should be large compared to the load capacitance - so one has to add larger caps, including one with the largest resistor. So it may be more like 10 pF, 100 pF, 1 nF , ....
The higher frequency divider would be set by the caps, not the resistors.

Also a 2 M resistor will have quite some noise by it's own, which would limit the use of smaller ranges. There is a good reason, why bench DMMs usually use a 1 M  resistive divider for the AC ranges. Those 20 M dividers are more made for DC.

For the higher frequency isolation relays are not per se better than manual switches.  For good attenuation, one usually uses more than just a single switch and avoids to send the signal to amplifiers that are not needed / used.

[Zero999]

Ya, I wasn't thinking..

digikey has a 20M, 2M, 200k, 20k, 2k, and a 200 good through hole resistors...and those come out to be about 70 dollars (I think).

I didn't want to decrease the impedance too much so I just did the calculation this time with what was available.

These resistors are 0.01% tolerance and it looks like they are meant for this application.

The 0.1% error of the LTC1968 is good only up to 150khz, which should be plenty for what I was hoping for..not sure if it is though...

The max4239 has a BW of 6.5Mhz, and with only a 10x gain, that means the adjusted BW at the last op amp should be

BW(tot) = 6.5Mhz/10 x (2^(1/3)+1)^(1/2) because I am using three with all the same gain.

That gives a BW of 977khz.

The uCurrent has proven to me that these op amps can amplify DC, but you are saying that these can't do small AC signals?

Why?

Regarding the switches, what about isolation relays coupled with a simple switch that turns the relays on and off with 5V?

Not too sure what to do regarding the caps, what are the caps going to help with?  Do you think by using the high resistance values of 20M..etc..will limit that problem?

Why do you want 0.01% tolerance resistors, when the LTC1968 isn't that good?

The low resistor values makes no difference to the input impedance, when the op-amp is configured as a non-inverting amplifier.