BJT current mirror/amplifier - Page 1
Forum section: electronics / beginners

author: Solstickan
author_rank: Newbie
timestamp: October 07, 2019, 05:18:11 pm
content: Hello,I am having some difficulties with an assignment I was given. I'm supposed to determine the values for R1and R2such that the currents I1=1 mA and I2=10 mA. The only parameters given is that VCC=+5 V, Vee=-5 V, UBE=0.7 V and the transistors has a high beta value. The voltage drop across R2can be omitted.I've been working at this all day, but I have not for the life of me figured out how to get a determine the values for R1and R2if you don't know the value of R3. The current I2is going to depend on the value of R3, and for all we've learnt this type of configuration is going to allow the current I2to be less than or equal to the reference current I1, not higher than the reference.The only progress I've been able to make is through KVL that R1is approximately 9.3 kOhms to get I1to be 1 mA. But after that it stopped short, I'm really confused as to how you should find the resistor values without knowing the value of R3.Any hints or tips would be greatly appreciated!Thank you.

author: Marco
author_rank: Super Contributor
timestamp: October 07, 2019, 05:46:43 pm
content: Just say R2 value is large enough to drive T2 into saturation, 1 kOhm would do for instance, R3 being approximately 100 Ohm to generate the 10 mA ... because otherwise you'd have to use a large signal model for the transistor to even begin to calculate this and you haven't been given enough parameters to do that.In theory you could use the small signal model for transconductance together with integration to get a highly simplified large signal model to determine R2, but ehhh.

author: magic
author_rank: Super Contributor
timestamp: October 07, 2019, 06:01:48 pm
content: Quote from: Marco on October 07, 2019, 05:46:43 pmThat may actually doBut something is telling me that the expected solution was to use the Ebers-Moll equation to calculate how much voltage needs to be dropped on R2 such that the two different VBEs cause the desired currents to be produced. But as Marco says, you would probably need to know some parameters of the transistors. Or maybe they will cancel out once you solve the equations?In such case R2 voltage is very significant, but R3 isn't as long as R3 is less that 100Ω.

author: rfeecs
author_rank: Frequent Contributor
timestamp: October 07, 2019, 06:47:19 pm
content: Clearly VBEcan't be the same for both transistors.The circuit is similar to, but a little different from a Widlar current source:https://en.wikipedia.org/wiki/Widlar_current_sourceConsider how much VBEneeds to increase to give a 10x increase in current. This gives the voltage across R2 so that should allow you to find the solution.

author: Marco
author_rank: Super Contributor
timestamp: October 07, 2019, 09:43:53 pm
content: The formula for that is nonlinear though. If I2 was something like 1.1 ma you could at least use the small signal model for gm ... it's a strange problem, it feels like it should be a simple operating point problem based on extremely simplified assumptions, but isn't.

author: rfeecs
author_rank: Frequent Contributor
timestamp: October 08, 2019, 01:52:36 am
content: Quote from: Marco on October 07, 2019, 09:43:53 pmWell Widlar made a lot of simplifying assumptions. Among them that the ideality factor n=1. That makes the solution very simple. You can see that from the Wikipedia article and the patent. So that gives the familiar 60mV/decade rule for a pn junction voltage vs current. In reality it's within a factor of 2 or so.Yes, the strictly accurate solution is a nonlinear mess. So it all depends what the instructor was trying to get at when he assigned this problem. It's not totally clear as stated.

author: Jay_Diddy_B
author_rank: Super Contributor
timestamp: October 08, 2019, 02:33:50 am
content: Hi,You should end up with something like this:R1 was chosen to set the current in Q1 to 1mAR3 was chosen to set Q2 collector midway between ground and -5VR2 was chosen to cause a 60mV difference in Vbe based on the 60mV/decade 'rule' proposed by rfeecs.The transistors in the model are perfectly matched and at the same temperature.Regards,Jay_Diddy_B

author: Jay_Diddy_B
author_rank: Super Contributor
timestamp: October 08, 2019, 02:47:28 am
content: Hi,The model can be modified to step the value of the emitter resistor and measure the current ratio:The result is:Reading of this graph, 64will give you 10:1Regards,Jay_Diddy_Bratio mirror.asc(1.4 kB - downloaded 77 times.)

author: floobydust
author_rank: Super Contributor
timestamp: October 08, 2019, 03:38:44 am
content: Using Spice is cheating, they always want the derived equation for homework.I found the "low-level current mirror" analysis here by Dr. Leach, Fig. 5https://leachlegacy.ece.gatech.edu/ece3050/notes/bjt/bjtmirr.pdf

author: Jay_Diddy_B
author_rank: Super Contributor
timestamp: October 08, 2019, 04:04:44 am
content: Hi,Dr. Leech gives us:The OP circuit is similar so the analysis is:Putting in all the numbers gives us Re =60Regards,Jay_Diddy_B

author: Solstickan
author_rank: Newbie
timestamp: October 08, 2019, 06:18:38 am
content: Thank you all so much for your answers!I will see what I can do with them!

author: magic
author_rank: Super Contributor
timestamp: October 08, 2019, 06:22:45 am
content: Quote from: Marco on October 07, 2019, 09:43:53 pmIt feels like anonlinearoperating point problem based on some unspecified/unknownmoderatelysimplified assumptionsThe moral of the story is that OP shouldn't have skipped that lecture