Differential Amplification

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vkorakakis

Differential Amplification

Post by vkorakakis » Thu Oct 28, 2004 4:10 am

Hi,

I have been reading your page on:

"What is the function of the CMS and DRL electrodes. Ground, Reference or what ?"

Am I right in thinking that you do not have any hardware differential amplification (i.e. between a measurement electrode input and CMS). In this way, each channel input is amplified, filtered, digitised and sent to the PC, as well as the CMS value, where they are subtracted from each other in software?

I'm sorry if this is obvious (or wrong), but I want to understand what your system is doing. I initially thought you had a monopolar arrangement (where each channel is input through an instrumentation amp with CMS), and then at a later point an arbitrary channel could be used as a reference to subtract two channels in software).

Thanks

vk

vkorakakis

Differential Amplification

Post by vkorakakis » Thu Oct 28, 2004 5:23 am

Hi,

I've gone over it a bit more...! I think I am correct that there is no differential amplification between CM and a channel input...

But you drive the CM to the ADC reference - Is it not feasible to use the CM as the actual reference voltage? i.e. keep the CM driver circuit to keep the CM within a reasonable input range (i.e. so the range fits within the ADC input), but use CM as the actual reference voltage. In this way you are effectively using the ADC as a differential amp with the exact value of CM rather than a fixed reference value that CM is driven towards/approximating? Alternatively, you could pass the value of CM in as an additional channel through the ADC so that the software could subtract an exact value.

These thoughts are just my way of trying to work out the fundamental processes....

vk

Coen
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Post by Coen » Fri Oct 29, 2004 5:00 pm

Let me explain by starting with the most simple setup, and then making thing more complicated step-by step until we end up with the actual ActiveTwo configuration. The initial goal is to measure the potential difference (voltage) between two electrodes.

1) The most simple setup is to use one Ground (GND) electrode, and one measuring electrode (E1). Electrode E1 is connected to the high-impedance input of an amplifier, the GND electrode is connected to the 0V of the amp. The amplifier amplifier E1 with respect to GND, the output signal is digitized and displayed.
This setup does not work very well because interference currents are flowing via the GND electrode (see http://www.biosemi.com/publications/pdf ... uction.pdf). Current through the GND impedance causes a voltage. This interference voltage is by definition called the Common Mode voltage. The CM voltage is added directly to the EEG signal, the Common Mode Rejection Ratio (CMRR) is zero. Even with an optimally isolated front-end (battery power, fiber coupling), the CM voltage will completely mask the EEG in this situation.

2) To improve thing, we replace the simple GND connection with a driven ground electrode circuit (Driven Right Leg). As the input of the DRL integrator we use an extra CMS (Common Mode Sense ) electrode. The GND electrode (called DRL from now on) is within a feedback loop, and its effective impedance is divided by the loop gain. Consequently, the CM voltage is reduced by the open-loop gain of the DRL circuit. The amount of open-loop gain is limited for stability reasons. Still, an open-loop gain of 100 at 50 Hz is easily attained. So, the CM voltage at 50 Hz is reduced by a factor of 100 (40 dB) with respect to situation 1. In other words, we have improved the CMRR to 40 dB.
In spite of this improvement, there are two remaining problems with this setup. First, 40 dB CMRR is not enough in most situations. Secondly, the location of the GND potential becomes dependent on the frequency. The reason is that the open-loop gain of the DRL driver decreases with frequency, So, for low frequencies (where open loop is gain is high) E1 is measured with respect to the CMS electrode, whereas for higher frequencies (where the open-loop gain is low), E1 is measured with respect to a location somewhere between CMS and DRL electrode (wandering toward the DRL for increasing frequencies).

3) To solve the two indicated problems, we now add a second measuring electrode E2 and corresponding amplifier channel. Instead of looking at the difference between E1 and GND/CMS/DRL as in situations 1 and 2, we look at the difference between E1 and E2. The difference between E1 and E2 can be calculated by analog electronics (use an instrumentation amplifier), or with digital electronics (subtract digital output words of analog-to digital converters).
This new setup solves the problems still present in situation 2. The CMRR is increased by a large extra factor depending only on the matching of the channels (40 dB extra in case of ActiveTwo). Also, the location problem of the GND point (somewhere between CMS and DRL) is eliminated: E1 and E are both measured with respect to the same point, we only look at the difference between E1 and E2, so the exact location of the GND point doesn't matter anymore.

Finally, I'll comment on the to suggestions for modifications of the setup given in the second post

- Why not use the output of the CMS signal as the actual reference ?
This is indeed an alternative (analog) method for increasing the CMRR. The problem with this method is that in a multichannel system, the CMS buffer will have to drive many parallel instrumentation amplifier inputs (up to 256 in our case). This proved to lead to several stability problems.

- Why not thread the CMS as just another channel ?
This is the same as asking: why not us one of the measuring electrodes as CMS signal?. This is indeed possible and would spare an electrode (no separate CMS anymore). For example: E1 could be use both as channel 1, and as input for the DRL integrator. There are two reason why we prefer an extra separate CMS. First, the concept of having one special channel that always have to be connected is confusing (for example: several users do not use channel 1, or do not always use channel 1). Secondly, an important design principle in the ActiveTwo is optimal equality of the channels. With this suggestion, one channel would be very slight different form the others (one active electrode has to drive both the ADC and the DRL integrator, all others only drive the ADC, load by stray capacitances would be slightly different). This would jeopardize the perfect symmetry that we want to achieve in the design.

Best regards, Coen (BioSemi)

vkorakakis

Differential Amplification

Post by vkorakakis » Mon Nov 01, 2004 10:44 pm

Hi Coen,

Thanks for your response - that answered perfectly my questions. It is great to find people who know their topics totally, and who are prepared to put the time and effort into their users/customers.
Best regards

VK

max
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Post by max » Sun Jul 20, 2008 10:41 am

[quote="Coen"]...Consequently, the CM voltage is reduced by the open-loop gain of the DRL circuit. ... the open-loop gain of the DRL driver decreases with frequency[/quote]

Dear Coen,
can I understand this in the way, that for high sample rates the interferences aren't reduced as much as for low sample rates?
Cause the raw data of my measurements (measuring one person with different sample rates) contain more 50Hz voltage for higher sample rates. And I just want to make sure that the reduced open loop gain might be the explanation for this fact.

And I'm sorry, but I have to ask a question about referencing again (like millions of users before me :roll: )
My raw data measured with a sample rate of 2kHz seems to be perfectly clean (no CM voltage at 50 Hz at all).
In another link (I'm not allowed to post the URL) I found your explanation, that a valid measurement only appears after subtracting the reference to get rid of the interference. And here you explain the importance of referencing because of the wandering of the GND point.
Are these the only two reasons which make a referencing important? My EEG signals look quite unpolluted and the distance of the wandering of the GND point doesn't seem to be that long. So what if I use the unreferenced raw data? Would this be valid? (I used bipolar referencing before, but in this way (and with a monopolar reference as well) the result is always a mixture of both channels (of course). I also tried the linked reference, but I only measure with 8 channels. And according to some literature I read, linked reference should only be applied when at least 20 electrodes where used.)

Thanks a lot
max

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Post by Coen » Mon Jul 21, 2008 4:36 pm

The selected sample rate does not influence the DRL circuit. As explained above, the DRL circuit offers less CM rejection at higher frequencies. Because a higher sample rate means a higher bandwidth, you may see higher harmonics of 50 Hz in recordings made with a higher sample rate. However, if all other boundary conditions remains the same, the mere change of the sample rate cannot make a difference to the amount of 50 Hz interference in the data.

Referencing is important to prevent distortion of the signal (because of the wandering GND point), and to achieve sufficient CMRR, especially at high frequencies. Without referencing there is zero CMRR for frequencies above 5 kHz. (40 dB @ 50 Hz, 20 dB at 500 Hz).

The fact that your signal "look" OK, proves the effectiveness of our setup with battery power supply and fiber optic coupling of the front-end. Because of this setup, low frequency (50 Hz) interference may well be absent in many situations. Still, referencing is essential to prevent signal distortion (which is difficult see in the EEG waveform), and to reject high frequency interference (50 Hz harmonics, radio transmitters, mains spikes).

You seem to suggest that the referenced result is a "mixture of both channels", and that the unreferenced result would be principally different in this respect. This is not true. The measurement result is always a voltage, that is the difference in electrical potential between two measurement points. In case of a (bipolar) referenced result, the EEG voltage is the potential difference between the locations of the two selected electrodes. In case of the unreferenced result, the EEG voltage is the potential difference between a single electrode and a point somewhere between CMS and DRL (the exact point being frequency dependent). In case of a mastoid reference, the EEG result is the potential difference between a single electrode and a virtual point in the center of the head (at the midpoint of the line from the left to the right mastoid).

A statement that the mastoid reference can only be used with at least 20 electrodes can of course not be true. Please post the literature references to which you are referring, I would be interested to know the source of such nonsense. With a properly designed measurement system, a certain electrode cannot "know" how many other electrodes are measuring simultaneously. With the ActiveTwo system, you can very well measure 1 channel (or 8 or 256) with respect to the average of the left and right mastoids.

Best regards, Coen

max
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Post by max » Tue Jul 22, 2008 3:04 pm

Hi Coen.

Thanks a lot for the fast reply and your help.
As I just changed the sample rate for my measurements (measured the participant for about 1 minute, then switched off the A/D box, changed the sample rate, restarted and measured again with the new sample rate at exactly the same conditions) it is probably the bandwidth which causes the higher harmonics of 50 Hz.

I’m sorry, but it seems I mixed something up with the names of the different reference options. I used the names you listed on http://sccn.ucsd.edu/pipermail/eeglabli ... 00930.html

- Monopolar: select one of the electrodes as a reference, calculate the
voltage between every other electrode and the reference electrode (V1 =
E1-REF, V2 = E2-REF, etc.)
- Bipolar: select pairs of electrodes (V1 = E1-E2, V2 = E2-E3, etc.)
- Linked reference: Use the average of several potentials (electrodes) as a reference. Calculate the the voltage of every electrode with respect to this reference. For example, use the average between ears as a REF, thus REF = (EA1+EA2/2), then V1 = E1 - (EA1+EA2/2), etc.”

And it seems I misunderstood the explanations given there. By ‘linked’ I meant the average reference scheme with an average over all electrodes. In three different books I found three different minimum numbers of electrodes which seem to be necessary for an average reference, but all of them are bigger than eight:
Davidson, Jackson & Larson (2000). Human Electroencephalography. In Cacioppo, Tassinar & Berntson, Handbook of Psychophysiology, Second Edition Page 34, penultimate sentence.
The other two books are written in German.

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