2

"What would (ideally) be the DC voltage at the output in the following circuit?" That's how the question was formulated. Can it be found without having any information on \$V_A\$ or on \$\lambda\$? The only way \$v_o\$ could be evaluated would be by equating the currents through Q6 and Q7, but that would only yield \$v_o\$ provided that I have some information on either \$V_A\$ or on \$\lambda\$. Could anyone help me settle it?

enter image description here

peripatein
  • 399
  • 6
  • 16
  • How about posting a plot of the I_V charactieristic, for the gate-length(s) used in your amplifier? – analogsystemsrf May 27 '17 at 14:13
  • I just posted all the information given in the question. I have no other info. – peripatein May 27 '17 at 14:14
  • Oh, and in a previous section I was asked to perform a DC design that will result in each of $Q_{1-4}$ and $Q_{6,7}$ conducting a drain current of $200\mu A$ and all transistors operating at $V_{ov}=0.2V$. I managed that. – peripatein May 27 '17 at 14:17
  • Are Va and Vb given, Hint its easy for the two cases of Va>Vb or Va < Vb – sstobbe May 27 '17 at 15:19
  • current mirror and differential V I/O determine inverse transfer function with k n/p ratios for RdsOn but matched Vth – Tony Stewart EE75 May 27 '17 at 15:22
  • Initially A and B are stated to be grounded. Under this condition I am asked to perform a DC design that will result in each of Q1−4 and Q6,7 conducting a drain current of 200μA and all transistors operating at Vov=0.2V. I did that. Then I am asked to find the DC voltage at the output (ideally). That's all the information I have. Can the output DC voltage be determined without having any information on lambda? – peripatein May 27 '17 at 16:21
  • For the case of Va = Vb, you know Q7 will mirror Q8 for 200 uA. Q6 will mirror Q4 at 100 uA, so Q7 rails the output to Vss – sstobbe May 27 '17 at 17:42
  • Wait, Q6 and Q4 are both expected to conduct a current of 200uA! That was the requirement and my DC design (finding the right W/L's) assured of that – peripatein May 27 '17 at 17:48
  • I see, it helps to put that right in the question, and the @ so a user gets notified you write a comment, yes if Q6 and Q4 have the same current then there isn't a great answer. In reality any mismatch or noise on the diff pair will send the output to one of the rails in open-loop mode – sstobbe May 27 '17 at 18:10
  • @sstobbe Later in the question the value of lambda is stated.. Do you figure I could use that here to evaluate the output voltage or since the word "ideally" was included channel modulation would be irrelevant here? – peripatein May 27 '17 at 18:13
  • Personally if you do choose to do a complete small signal analysis, I would leave it to the end as the result is strictly academic. But it is a good question to think through, Q5 is going to have a smaller Vds than Q8, that is certain for the grounded case, so with Q5 having less drain current what ends up happening to Q6? – sstobbe May 27 '17 at 18:38
  • @sstobbe that's the thing, I don't think it's expected to be that complicated. What am I missing here? This section appears before the section mentioning lambda and asks for the "ideal" output voltage.. I believe lambda was inadvertently omitted as the question is nearly similar to question 2 here -- http://web.eece.maine.edu/~hummels/classes/ece343/docs/2010_test2_solution.pdf – peripatein May 27 '17 at 19:32

1 Answers1

3

The OP provided a sample solution to the problem as,

enter image description here

Turning to spice, we can determine the complete hypothetical solution as,

enter image description here

Spice estimates the output to be, $$ Vo \simeq -50 \textrm{ mV} $$

The practical aside is if M4 is 1% larger than expected, the input offset voltage causes the output to rail.

sstobbe
  • 2,992
  • 1
  • 11
  • 12
  • how do I find it in my problem given that I was asked for the ideal output voltage without specifying lambda and that the current is 200uA through Q1-4 and through Q6-7? I can give you the W/L's I found, should that help, as they are different than the ones here – peripatein May 27 '17 at 20:20
  • You have it in the solution you provided, just assume $ \lambda_N = \lambda_P$, and it divides out. – sstobbe May 27 '17 at 20:26
  • So say I found $(W/L){1,2,7,8}=25, (W/L)_5=50,(W/L){3,4,6}=100$, how would that affect the output voltage? Mind you that I also have no idea what the value of lambda is, unlike the question above – peripatein May 27 '17 at 20:37
  • It won't divide out as the W/L's are different.. Moreover, why does the question specifically ask for the "ideal" solution? What does "ideal" mean here? rds equals infinity? – peripatein May 27 '17 at 20:51
  • Spice solution for full opamp -92 mV, just the matched output stage 0 V. – sstobbe May 27 '17 at 20:56
  • kn = 4kp, it divides out – sstobbe May 27 '17 at 20:57
  • Yes, when Q6 & Q7 each have 200mV Vov the output is zero for equal lambdas. Also the ideal case is like balancing a ball on a pin as physical analogy... – sstobbe May 27 '17 at 21:07
  • but how do I know that the lambdas are equal? Do I assume that as that what "ideal" would imply? – peripatein May 27 '17 at 21:12
  • Well you could assume lambda is 0 and your amplifier has infinite gain. You are free to decide which one you prefer. – sstobbe May 27 '17 at 21:17