Nikolai,

Thank you for the appreciation of my "puzzle". I would be glad if it can be really classified as a "brain teaser":)

Your second situation - an emitter-coupled amplifier with a single-ended input, is another (third) example in addition to my two. It is an excellent answer to my question, for which I (nobly) envy you:)

But I have to confess that I have difficulties with understanding your first situation. In my opinion, even when the common-mode source resistance is very low, the emitter current source should not be replaced by a simple ohmic resistor. Or maybe you mean something else?

I think the use of a current source (in an itegrated circuit) is much better than a resistor (of great value, of course).

Dear Cyril,

welcome,

Hope you are well!

I think you love the common emitter differential amplifier circuit as you return to it again after the long discussions about it.

To remember, the role of the emitter tail either VEE and RE or a current source IE substituting them is to keep the emitter current IE fixed with the variation in the common mode voltage or at least nearly fixed with that voltage.

The ideal solution for this problem is using ideal current source for IE. Using ideal current source would lead to constant IE while varying the common mode voltage since the common emitter point potential will adjust its potential to absorb any changes in the common mode mode VCM applier at the bases of the transistors.

If we use instead VEE and RE to mimic the current source, one has to make RE as high as possible while realizing the required emitter bias current IE, which means to raise VEE. Since VEE is limited then RE will be also limited.

In this case if the common mode voltage changes, it will basically affect also some change in the emitter current IE even if this change is small.

If i understood the question , we have at least two cases where this circuit can perform as if it built with constant current source. What are these cases??

Some cases are:

- The case where VCM= 0, the amplifier works in differential input mode only,

- The common mode voltage is much less than VEE such its effect on IE is very small and can be neglected.

- The differential output rather than single ended output can help cancel the common mode changes in IE provided that there is symmetry of the circuit.

Best wishes dear colleague.

How many great answers! A real constellation of ideas:)

Josef, of course, you are right that "the use of a current source is much better than a resistor"... but here we try to explain exactly when and why... That's why I suggested to look at cases where this is not (absolutely) necessary...

Abdelhalim, welcome to the right place at the right time:) Your first case - "VCM= 0, the amplifier works in differential input mode only", is just like mine. Regarding your second case - "VCM is much less than VEE", I'd clarified - the variations of VCM are much less than VEE... I would accept even your third case - "differential output rather than single ended output can help cancel the common mode changes in IE" although we assume here the usual single-ended output...

Nikolai, your case - "if it's fixed (doesn't even have to be =0)", is exactly what I meant as a third case. And how nice you said it - "RE does the same job as an equivalent current source"...

Let's list the collection of cases in which we can use a simple ohmic resistor instead of the more sophisticated current source (I have put the authors in brackets):

That's fine, but there is a danger that the discussion will be exhausted and to cease:)

So I have fabricated another (fourth) situation where (only imagine!), using an ohmic resistor, the long-tailed pair works equally well in both differential and common mode!

Naturally, i thought about constant VCM, but in this case if VCM is sufficiently large and RE is relatively low, the potential of the common emitter point will be moved upward causing a remarkable change in IE compared to its nominal value at VCM=0 and therefore i restricted it it by relatively small values of VCM.

Best wishes

I agree with you, Abdelhalim... but you know that we here a little fantasize and imagine some unlikely situations, just to show the circuit phenomena:)

So we can assume large but constant VCM... and by adjusting RE and RC so that to obtain the desired operating point...

Dear Cyril,

Okay, well!

I copied a part of your answer above: So I have fabricated another (fourth) situation where (only imagine!), using an ohmic resistor, the long-tailed pair works equally well in both differential and common mode!

Do you mean to use RE without VEE such that we operate the emitter coupled differential amplifier with only a unipolar power supply?

Best wishes

Dear Abdelhalim and Nikolai,

For the 4th situation I was inspired by The Adventures of Baron Munchausen:)))

Abdelhalim, I do not mean a unipolar power supply... I rather mean a special kind of VEE ...

Nikolai, students with original answers really get good bonuses for the exam:)

Dear Colleagues,

I made this simple analysis concerning the long tailed emitter pair.

By reference to the circuit in the question brought the respected colleague Cyril, one can write the following input loop equation:

VEE+ VCM = VBE + IERE,

We have further the relation between VBE and IE in the active mode of operation of the transistor:

VBE= Vt ln IE/2ISE, where Vt is the thermal voltage and ISE is the resverse saturation current of the emitter junction. The factor 2 is due to IE is divided equally between the two transistors.

So this equation shows that if the variations in IE is small then the variations in VBE will be much less.

Till now all this analysis is normal. Now let us assume that the bias voltage VEE is fixed and we want to observe the variations in IE due to changes in the common mode voltage VCB. This can be accomplished by differentiation:

RE dIE/dVCB = 1, where VEE is considered constant and VBE is almost constant.

So dIE/dVCB = 1/RE,

To make IE constant independent of VCB, then according to above equation one has to make RE tending to infinity.

This can be implemented satisfactorily with two methods:

The current source to get IE and make RE very large ideally infinite,

and increasing both Re and VEE to set at the same time the value of IE.

It remains the special cases invoked by Cyril and we discussed some of them.

Now let us suspect the Cyril fourth methd where one has to choose VEE to satisfy IE= constant with VCB,

An other way of thinking is to let VEE vary with VCB such that we can keep IE constant for any value of RE and VEE.

By inspecting the loop equation above, one can satisfy this required condition by splitting VEE into a fixed part VEEf and a variable part VEEv, and make the VEEv= - VCB, which is some sort of cancellation.

So, the solution may be to let VEE decrease by the same amount of increase of VCB.

Best wishes

Exactly, Abdelhalim!

Thank you for the perfect analysis that makes us think again about these great ideas...

Yes, that was my (more precisely, Baron Munchausen's:) idea - to make VEE follow VE... or to say it more "professionally" - to bootstrap RE...

Of course, you can think of the combination "varying VEE" + "constant RE" as of a kind of constant current source... but the teasing here is that the common element in the emitters (which we see) is an ohmic resistor.

I have written a few stories dedicated to this technique for creating constant current sources:

http://www.circuit-fantasia.com/circuit_stories/inventing_circuits/current_source/current_source_philosophy/current_source_philosophy.htm#step5

http://www.circuit-fantasia.com/circuit_stories/understanding_circuits/current_source/transistor_source_capacitor/transistor_source_capacitor.htm

http://www.circuit-fantasia.com/circuit_stories/understanding_circuits/current_source/transistor_source_diode/transistor_source_diode.htm

http://www.circuit-fantasia.com/circuit_stories/understanding_circuits/current_source/widlar_op-amp_current_source/widlar_op-amp_current_source.htm

I think all the above contributers have thoroughly analysed the long tailed pair circuit. I would simply add, that in practice, the nearer "infinity" the dynamic value of Re can be made, the better will be the "common mode rejection ration (CMRR)" which is a practical expression of how much better a long tailed pair is over a single ended amplifier. Best wishes with your work!

What is the purpose of a differential pair?

We want (expect) that it amplifies the voltage difference between both inputs only! "Only" means that it must not react upon the common mode part of the signal which might exist "behind" both voltages.

This property is very important for applications where one input is grounded. Therefore, we want the common mode gain as low as possible. An ideal current source (infinite dynamic source resistance) can fulfill this desire.

However, there is no ideal current source.

Hence, there will be always a finite CMRR - even if both legs (transistors and collector circuitry) would be ideally symmetrical.

A simple large ohmic resistor RE as "current source" is allowed only if (a) the supply voltages are large enough to cope with the DC drop across RE and (b) if we can live with the "relatively large" common-mode gain.

Regarding the purpose of the differential amplifier.

When analyzing the differential amplifier is important to explain the physical operation at differential and common-mode input signal. Then, the formulas for differential and common-mode coefficients are obtained. Finally, the CMRR is defined. In my opinion, the role of an current source can be most accurately demonstrated. Of course, during the laboratory exercises, the students experimental testing a differential amplifier at differential and common-mode input signals.