Author Topic: BJT current mirror/amplifier  (Read 1813 times)

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Offline SolstickanTopic starter

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BJT current mirror/amplifier
« on: October 07, 2019, 05:18:11 pm »
Hello,

I am having some difficulties with an assignment I was given. I'm supposed to determine the values for R1 and R2 such 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 R2 can 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 R1 and R2 if you don't know the value of R3. The current I2 is going to depend on the value of R3, and for all we've learnt this type of configuration is going to allow the current I2 to 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 R1 is approximately 9.3 kOhms to get I1 to 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.
 

Offline Marco

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Re: BJT current mirror/amplifier
« Reply #1 on: October 07, 2019, 05:46:43 pm »
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.
 

Offline magic

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Re: BJT current mirror/amplifier
« Reply #2 on: October 07, 2019, 06:01:48 pm »
Just say R2 value is large enough to drive T2 into saturation
:-DD

That may actually do ;D

But 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.
 

Offline rfeecs

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Re: BJT current mirror/amplifier
« Reply #3 on: October 07, 2019, 06:47:19 pm »
Clearly VBE can'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_source

Consider how much VBE needs to increase to give a 10x increase in current.  This gives the voltage across R2 so that should allow you to find the solution.
 

Offline Marco

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Re: BJT current mirror/amplifier
« Reply #4 on: October 07, 2019, 09:43:53 pm »
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.
 

Offline rfeecs

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Re: BJT current mirror/amplifier
« Reply #5 on: October 08, 2019, 01:52:36 am »
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.

Well 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.
 

Offline Jay_Diddy_B

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Re: BJT current mirror/amplifier
« Reply #6 on: October 08, 2019, 02:33:50 am »
Hi,

You should end up with something like this:






R1 was chosen to set the current in Q1 to 1mA
R3 was chosen to set Q2 collector midway between ground and -5V
R2 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
 

Offline Jay_Diddy_B

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Re: BJT current mirror/amplifier
« Reply #7 on: October 08, 2019, 02:47:28 am »
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, 64 \$\Omega\$ will give you 10:1

Regards,
Jay_Diddy_B
* ratio mirror.asc (1.4 kB - downloaded 54 times.)
« Last Edit: October 08, 2019, 02:49:22 am by Jay_Diddy_B »
 

Offline floobydust

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Re: BJT current mirror/amplifier
« Reply #8 on: October 08, 2019, 03:38:44 am »
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. 5 https://leachlegacy.ece.gatech.edu/ece3050/notes/bjt/bjtmirr.pdf
 

Offline Jay_Diddy_B

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Re: BJT current mirror/amplifier
« Reply #9 on: October 08, 2019, 04:04:44 am »
Hi,
Dr. Leech gives us:




The OP circuit is similar so the analysis is:




Putting in all the numbers gives us Re =60 \$\Omega\$

Regards,
Jay_Diddy_B
« Last Edit: October 08, 2019, 04:06:42 am by Jay_Diddy_B »
 

Offline SolstickanTopic starter

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Re: BJT current mirror/amplifier
« Reply #10 on: October 08, 2019, 06:18:38 am »
Thank you all so much for your answers!

I will see what I can do with them!
 

Offline magic

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Re: BJT current mirror/amplifier
« Reply #11 on: October 08, 2019, 06:22:45 am »
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.
It feels like a nonlinear operating point problem based on some unspecified/unknown moderately simplified assumptions ;)

The moral of the story is that OP shouldn't have skipped that lecture :-DD
 


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