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## Homework Statement

1. Given the above circuit, derive an exact equation for ##I_{out}## in terms of ##I_{REF}, V_{BE1}, V_{BE2}, \beta_1, \beta_2, R_{E1}, R_{E2}## and ##V_{CC}##. Do not make any assumptions.

2. Simplify the equation from part 1 by assuming ##V_{BE1} = V_{BE2}## and that both ##\beta##s are very large.

## Homework Equations

## The Attempt at a Solution

I am unsure how to attempt this problem.

I started by trying to find an expression for ##I_{REF}##, which I found to be:

$$I_{REF} = \frac{V_{CC} - [ V_{E1} + V_{BE1} ]}{R_{REF}} = \frac{V_{CC} - I_{E1} R_{E1} - V_{BE1}}{R_{REF}}$$

Then I thought about finding an expression for ##I_{out}##:

$$I_{out} = \frac{V_{CC} - V_{out}}{R_L}$$

I can't really see a way to relate these equations. I'm not even sure this is the right approach.

I have seen another approach for a different kind of current mirror that uses the equation ##I_C = I_S e^{\frac{V_{BE}}{V_T}}## to obtain ##V_{BE1}## and ##V_{BE2}##. Then it relates ##I_{out}## and ##I_{REF}##. The only difference was there was no emitter resistor in the first transistor, but there was still an emitter resistor in the second transistor. I'm wondering if this approach should be used instead.

Any help with getting this one going would be appreciated.