# Help with differential amplifier question. Not sure where to start

#### HunterDX77M

Joined Sep 28, 2011
104
I guess I would start with the DC analysis, but the resistor across the Current source is really throwing me off. I wanted to get ICQ first, but I'm not sure how I would go about getting it. Could anyone point me in the right direction?

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#### WBahn

Joined Mar 31, 2012
26,521
The resistor across the current source is merely modeling the fact that the current source is not ideal. An ideal current source would 500uA flowing between the emitters and the Vee supply regardless of the emitter voltage. But, in reality, the actual current flowing is slightly greater than that and is also a function of the emitter voltage. In this case, there is simply an additional 1uA of current for every 1V by which the emitter voltage is higher than the Vee supply.

When you make the small signal model for the circuit, you will turn of the current source (set it equal to zero current) and be left with the resistor to ground (not Vee, since both supplies are also turned off -- set to zero volts between their output and ground).

Note that the input voltage is not referenced to ground and this will cause a problem as you try to analyze the circuit, particularly since the current source is not ideal. When doing the DC analysis, you keep the DC sources on and turn the small signal sources off (which, in this case, is only the input signal). That will short the two bases together and therefore require that equal current flow in each, but how much current will depend on the voltage relative to ground, which you have no way of knowing since they are floating relative to ground. If you absolutely have to, you can assume that the common-mode voltage of the input is 0V, but you are changing the circuit from what is given and should make a note of that.

#### mlog

Joined Feb 11, 2012
276
Like WBahn I have a problem with this circuit, because there is no bias current path through the B-E junctions.

#### WBahn

Joined Mar 31, 2012
26,521
I'm embarassed to admit this, but I didn't spot that particular glaring problem. Perhaps I can claim that I latched onto the first problem I saw just didn't go any further looking for other problems. I KNOW that had I done the analysis I would have seen that the bias current was zero and that the ideal current source would have pulled the emitter voltage down to -500V and the base voltages would have been pulled down to no more than one diode drop above that.

#### Ron H

Joined Apr 14, 2005
7,014
I'm embarassed to admit this, but I didn't spot that particular glaring problem. Perhaps I can claim that I latched onto the first problem I saw just didn't go any further looking for other problems. I KNOW that had I done the analysis I would have seen that the bias current was zero and that the ideal current source would have pulled the emitter voltage down to -500V and the base voltages would have been pulled down to no more than one diode drop above that.
Yesterday I started a post to comment on the lack of a common mode reference/base current path to ground, but after reading your post #2 more carefully, I decided not to post because I thought you had pretty much covered it in your second paragraph.

#### HunterDX77M

Joined Sep 28, 2011
104
Umm, now I'm just confused. What is the problem that everyone has now?

#### t_n_k

Joined Mar 6, 2009
5,455
As drawn in the attachment schematic no means exists for the correct biasing of Q1 & Q2. It's a confusing oversight by the person drafting the problem itself.

#### mlog

Joined Feb 11, 2012
276
Umm, now I'm just confused. What is the problem that everyone has now?
Keeping in mind that current flows from positive to negative, start at the base of the transistor on the left (or the right, for that matter), move down to the emitter, and then back to the same base without retracing your steps. What path is there? Answer: None. You can't get there by move "upstream" through the other transistor's emitter-base junction. There is no loop.

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#### HunterDX77M

Joined Sep 28, 2011
104
As drawn in the attachment schematic no means exists for the correct biasing of Q1 & Q2. It's a confusing oversight by the person drafting the problem itself.
I see. Perhaps I should contact him.

#### t_n_k

Joined Mar 6, 2009
5,455
Frankly, I wouldn't sweat on that issue. The emitter current per transistor is probably meant to close enough to 250uA it doesn't matter about small differences of a couple of uA. Just include the 1MΩ to ground for AC analysis. Since you aren't given the DC supply it's difficult to know how to use Va in the analysis.

#### WBahn

Joined Mar 31, 2012
26,521
I see. Perhaps I should contact him.
I would highly recommend it. Just bringing something like that to his attention will probably get you some brownie points.

The usual way of dealing with this is to split the input voltage into two supplies connected in series. One supply has +Vdm/2 while the other supply has -Vdm/2. Then, between the two supplies, a third supply, Vcm, is connected to ground. The Vcm then sets the common-mode voltage while Vdm is the differential-mode voltage and both are independent of each other.

#### WBahn

Joined Mar 31, 2012
26,521
Frankly, I wouldn't sweat on that issue. The emitter current per transistor is probably meant to close enough to 250uA it doesn't matter about small differences of a couple of uA. Just include the 1MΩ to ground for AC analysis. Since you aren't given the DC supply it's difficult to know how to use Va in the analysis.
That's the problem. It's usually fine to assume that the collector current equals the emitter current (at least in a configuration like this) and, without Va, the base voltage doesn't have an effect. But now it does. It still shouldn't be significant and the output resistance should still be able to calculated very close without it, but you still have to make assumptions about the emitter voltage that aren't supported by the problem statement.

#### WBahn

Joined Mar 31, 2012
26,521
Yesterday I started a post to comment on the lack of a common mode reference/base current path to ground, but after reading your post #2 more carefully, I decided not to post because I thought you had pretty much covered it in your second paragraph.
I certainly remarked the lack of the common mode reference, but my last 15+ years as an ASIC designer has been working with CMOS, so I've gotten out of the habit of thinking about supporting a base current, but very much in touch with looking for floating gates.

#### t_n_k

Joined Mar 6, 2009
5,455
Just bringing something like that to his attention will probably get you some brownie points.
I recollect my university lecturers ("professors") were largely indifferent to their undergraduate students and any mention of brownie points would have caused their faces to glaze over even further.

There were a few who were interested but they tended to be those who had small specialist classes for students typically in their final year of study.

I imagine present day teachers are encouraged to engage more with their students but I also imagine that time poverty, economic pressures & cut-backs are forcing the "sausage factory" mentality to prevail.

Still let's not discourage the inquisitive student from seeking to engage their teachers. Student & teacher alike might be encouraged by the conversations.

#### WBahn

Joined Mar 31, 2012
26,521
I recollect my university lecturers ("professors") were largely indifferent to their undergraduate students.
<snip>
Still let's not discourage the inquisitive student from seeking to engage their teachers. Student & teacher alike might be encouraged by the conversations.
I sometimes tend to forget that I was fortunate enough to attend a smaller engineering school (about 3000 total enrollment with sixteen different departments) and only a handful of freshman courses had large sections (seldom over 100) and most had class sizes of 20 to 35. It certainly makes a difference. My major department generally graduated only a dozen students a year, so we became very close to many of our professors.

Even so, I have taught classes with total enrollments well over 100 (and as many as 80+ in one section) and the situation I found was that very few students would ever come with questions like this and the ones that did invariably stuck in my mind with a favorable impression and I'm sure that I probably looked a bit harder on their papers (if they weren't too far out in left field) to see if I could justify a couple more points of partial credit.

On the rare occasions that a student came in with a subtle problem or something that I didn't have a quick answer for, we could get involved in a discussion for quite some time exploring it and those are some of my more memorable and enjoyable times teaching.