### Author Topic: Precision amplitude measurement using differential amps with precision offset  (Read 3120 times)

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#### robrenz

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##### Precision amplitude measurement using differential amps with precision offset
« on: July 23, 2013, 10:52:20 pm »
If I measure the peak to peak voltage of a sine wave on a scope using a differential amplifier with precision offset capability like a 7A13 or a preamble 1855. Using comparison mode where I drive the min and max of the wave to the center graticule line and read the total offset voltage used.  Does that eliminate any frequency response attenuation effects on the signal since the signal is in theory not amplified at all when crossing graticule zero?

As an example if I feed a 1Vpp sine wave into the scope at a frequency high enough to cause a -3db drop in amplitude. If I now use the differential comparison mode to measure the Vpp I am driving a peak that is 3db down to the graticule center. But now the actual voltage going to the vertical amp of the scope is zero when the peak is touching the graticule zero. So in my inexperienced mind it should be accurate since there is no signal amplification at graticule zero.

Any insight from the more knowledgeable is appreciated.

#### alm

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##### Re: Precision amplitude measurement using differential amps with precision offset
« Reply #1 on: July 24, 2013, 04:18:19 am »
Can't claim I've ever tried it, but my \$0.02:

First, both the diff amp and the scope will have a roll-off. The frequency response of the amplifier will be an issue anyhow, so this is only useful if the scope is the limiting factor. Let's assume this is the case for argument's sake. Let's also assume that the scope is bandwidth limited, not slew rate limited.

The differential amplifier in comparison mode will add/subtract a DC offset to the signal. The spectrum for the signal before and after the amplifier will look exactly the same (assuming an ideal diff amp), except for the magnitude of the peak at DC. The roll-off of the scope will only affect the high frequencies, so a 50 MHz sine on a 50 MHz scope will still have its amplitude reduced by - 3 dB. If we split the signal from the diff amp in a DC part and an AC (50 MHz sine) part, the DC part will not be affected and the AC part will be attenuated. Changing the DC part will do nothing to change the roll-off of the AC part.

Now if the scope is slew-rate limited, especially an analog scope, then using only the center graticules may help slightly. You don't need a differential amp for that though: the vertical attenuation and position control will do just fine.

#### quantumvolt

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##### Re: Precision amplitude measurement using differential amps with precision offset
« Reply #2 on: July 24, 2013, 04:46:49 am »
According to  http://en.wikipedia.org/wiki/Tektronix_analog_oscilloscopes : "The 7A13 differential comparator amplifier can subtract a DC voltage from the input and amplify around that voltage ...". So it adds the offset before amplification (while the vertical position control adds it after ... methinks). If there is no frequency response attenuation before the amplifier, you should be able to place the peaks at 0 V and read out the peak value as the offset.

#### robrenz

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##### Re: Precision amplitude measurement using differential amps with precision offset
« Reply #3 on: July 24, 2013, 05:29:55 am »
First, both the diff amp and the scope will have a roll-off. The frequency response of the amplifier will be an issue anyhow, so this is only useful if the scope is the limiting factor. Let's assume this is the case for argument's sake. Let's also assume that the scope is bandwidth limited, not slew rate limited.

I forgot about the diff amp attenuation,   that is why I asked if I am missing something.

Now if the scope is slew-rate limited, especially an analog scope, then using only the center graticules may help slightly. You don't need a differential amp for that though: the vertical attenuation and position control will do just fine.

I think that the advantage of using the diff amp is by using a much lower V/div I can get a much higher accuracy adjustment of the peaks touching the graticule center while using the comparison voltage for the pp measurement. As an example using 1mV/div while measuring a 10Vpp sine wave will give much 1000x more accurate alignment of the trace peak to the graticule than doing the same thing at 1V/div.  And that comparison voltage can be measured externally with an accurate meter.

"The 7A13 differential comparator amplifier can subtract a DC voltage from the input and amplify around that voltage ...". So it adds the offset before amplification (while the vertical position control adds it after ... methinks). If there is no frequency response attenuation before the amplifier, you should be able to place the peaks at 0 V and read out the peak value as the offset.

That is what I thought, I just forgot about the diff amp attenuation still being part of the measurement.

#### robrenz

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##### Re: Precision amplitude measurement using differential amps with precision offset
« Reply #4 on: July 24, 2013, 06:59:42 am »
The differential amplifier in comparison mode will add/subtract a DC offset to the signal. The spectrum for the signal before and after the amplifier will look exactly the same (assuming an ideal diff amp), except for the magnitude of the peak at DC. The roll-off of the scope will only affect the high frequencies, so a 50 MHz sine on a 50 MHz scope will still have its amplitude reduced by - 3 dB. If we split the signal from the diff amp in a DC part and an AC (50 MHz sine) part, the DC part will not be affected and the AC part will be attenuated. Changing the DC part will do nothing to change the roll-off of the AC part.

I have thought about it some more.  I agree on the diff amp attenuation being part of the system.  Stating here what I think is correct relative to the scope behavior only.  I realize I am probably missing something again.

If we assume a diff amp that has no attenuation at 10MHz feeding a scope that is 3db down at 10MHz. We measure a 2Vpp sine wave at 10MHz with comparison voltage of 0.  The scope shows a sine wave whose amplitude is 3db down when viewed at .2V/div as expected. Now we set the comparison votage to 1.0V which shifts the signal sent to the vertical amp by 1.0 volt making the peak be zero volts at the amplifier input and therefore 0 at the scope vertical amplifier (analog scope) I am making an assumption that at zero volts there can be no attenuation because there is effectively no amplification occurring at a zero input. So even though the entire sine wave is attenuated on the screen the peak that is touching the center graticule line (0 volts) is not attenuated and will need exactly 1.0 volts to touch the center graticule line not the -3db 0.707V.

I will test this as soon as I get a chance, just thought I would get some guidance first.

#### alm

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##### Re: Precision amplitude measurement using differential amps with precision offset
« Reply #5 on: July 24, 2013, 09:18:37 am »
For an AC signal with a relatively large DC offset, roll-off of higher frequencies is an AC (small signal) phenomenon, and is mostly independent of the DC (large signal) behavior. The small signal / large signal analogy is not perfect, but may provide some insight in why DC and AC can behave differently. Just because there would be no current flowing into the scope input at 0 V DC does not mean the same applies to AC. Something still has to spend energy to move the system from the previous -1 V state to the new 0 V state. The charge in the plates of the CRT has to change, VBE of transistors will change, all kind of parasitic caps will have to be (dis)charged. The amplifier will still have to go up and down by 2 V 10M times per second. If it has trouble keeping up, then the signal will tend more towards the mean, -1 V in your example. So it would go from -1.7 V to -0.3 V.

You can easily simulate this. You can model a scope as a basic RC filter with reasonable accuracy (low bandwidth DSOs and analog scopes will usually have an approximately Gaussian response). Feed it an AC signal using any DC offset you desire, and look how the output signal changes. A bandwidth-limited op-amp (active filter) will work just as well. Then you can do the same with a scope if you have fast enough signal sources.

One thing that might work is use the fast overdrive recovery of the 7A13 (although I doubt that it's fast enough for a 10 MHz signal) to only show a small portion of the signal at high vertical sensitivity. That would help. Assuming the high sensitivity of the 7A13 does not limit its bandwidth .

The other thing that might make a difference is slew rate, if the scope is actually slew rate limited.
« Last Edit: July 24, 2013, 09:26:40 am by alm »

#### quantumvolt

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##### Re: Precision amplitude measurement using differential amps with precision offset
« Reply #6 on: July 24, 2013, 10:26:46 am »
If your goal is as the title says "Precision amplitude measurement using differential amps with precision offset", maybe you can just forget the scope. Your unit has either a meter or a digital scale with resolution 1 mV. And bandwidth 105 MHz. So if you are in this range all you need to do is to add a negative offset until a peak detector on the output of the diff amp shows no activity anymore ... methinks. This will imo even work for higher frequencies if you know and correct for the slope of the frequency response of the diff amp?

#### robrenz

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##### Re: Precision amplitude measurement using differential amps with precision offset
« Reply #7 on: July 24, 2013, 12:58:44 pm »
Thanks alm and quantumvolt for your input. It is helping me get a better grasp on this.

My current simulation and electronic skills will keep me from doing a simulation.

Here is a test someone could do that has a signal generator fast enough to take their scope to the -3db point. Input a sine wave with a DC offset of 1/2 the sine PP voltage so the bottoms of the sine waves are touching the baseline. now increase the frequency to the -3db point.  If all the attenuation is a shrinkage toward the baseline with the bottoms of the sine waves still stuck to the baseline. Then my thought that 0 volt input has comparatively minimal attenuation has some merit.

Here is a test that I just did to (I think) prove the diff amp comparison voltage pp measurement method eliminates amplifier gain accuracy from the measurement.  7A13 with the 0.4PP square wave of the scope into the "A" input at 0.1V/div dc coupled.  "B" input set to Vc comparison voltage. The square wave is 4 divisions high with the bottom on the baseline. Now dial in 0.4V comparison voltage and the top of the square wave is on the baseline. So the comparison voltage equals the height of the square wave.  Set the comparison voltage back to zero and set the "A" attenuator to uncalibrated and adjust so the 0.4V high square wave is only 2 divisions high instead of 4 (equivalent to -6db attenuation).  Base of square wave is still on the baseline.  Now adjust the comparison voltage until the top of the square wave is on the baseline and guess what, 0.4 volt same as the actual signal.  So (I think) the signal gain accuracy has no effect on this method.
« Last Edit: July 24, 2013, 09:01:27 pm by robrenz »

#### alm

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##### Re: Precision amplitude measurement using differential amps with precision offset
« Reply #8 on: July 24, 2013, 09:41:30 pm »
If your goal is as the title says "Precision amplitude measurement using differential amps with precision offset", maybe you can just forget the scope. Your unit has either a meter or a digital scale with resolution 1 mV. And bandwidth 105 MHz. So if you are in this range all you need to do is to add a negative offset until a peak detector on the output of the diff amp shows no activity anymore ... methinks. This will imo even work for higher frequencies if you know and correct for the slope of the frequency response of the diff amp?
This is essentially an AC version of a differential voltmeter (no idea if anyone ever made such a beast). And it requires a peak detector with enough bandwidth. And yes, you can correct for frequency response errors if you first measure them. Which requires access to something like a leveled signal generator, or a normal signal generator and power meter. Don't rely on datasheet specs. The -3 dB point is guaranteed to be at least 105 MHz, but don't be surprised if it turns out to be 120 MHz. Multiplying the amplitude at 105 MHz by sqrt(2) will most likely overestimate the amplitude, for example.

So (I think) the signal gain accuracy has no effect on this method.
Gain errors will not affect this measurement, as long as the gain is constant over the bandwidth of this signal. This is quite different from the roll-off of higher frequencies.

The way I analyze this: I split the signal into an AC and a DC component (cf Fourier transform). Then model the scope as a low-pass filter. Since a low-pass filter is linear, we can apply superposition and first apply the low pass filter to the AC (attenuated) and DC (unaffected) components individually, and add these two together for the final signal. Now you can argue that a scope is not well described by a passive low-pass filter, that you can only solve by measuring. If I have some spare time then I'll see if I can set something up next weekend, but no promises. It would be much more instructive if you could do this yourself.

#### robrenz

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##### Re: Precision amplitude measurement using differential amps with precision offset
« Reply #9 on: July 24, 2013, 09:53:18 pm »
Thanks alm, I have been thinking about the scope BW only, not the vertical amplifier BW also. I now realize I can do some testing using the 7A22 which has a 1MHz BW limit and drive it with my 20MHz FG.  I was stuck thinking I needed at least 150MHz sig gen to do any testing on a 100MHz scope.

#### robrenz

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##### Re: Precision amplitude measurement using differential amps with precision offset
« Reply #10 on: July 25, 2013, 03:28:54 am »
Sure enough, you were right alm.  The bandwidth attenuated sine signal (AC) stays centered on the DC offset voltage as its amplitude decreases with higher frequency.  So my take away of all this is the precision offset diff amp pp measurement method will work fine as long as you are in the flat frequency response region of your diff amp and scope. And the accuracy of your vertical gain setting is not important with this method.

And a DC offset does not negate the dynamics of an ac signal just because it crosses 0 volts.

Thanks for your patient help.
« Last Edit: July 25, 2013, 03:35:47 am by robrenz »

#### alm

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##### Re: Precision amplitude measurement using differential amps with precision offset
« Reply #11 on: July 25, 2013, 03:39:21 am »
It's always nice to have experimental verification. I concur that the method works fine for measuring amplitudes if the vertical accuracy of your scope is the limiting factor, since it allows you to use the scope as just an AC null detector. An AC equivalent of the differential volt meter that people used in the days before accurate DMMs.

Smf