What is the Iout calculation for a BJT circuit with infinite gain?

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SUMMARY

The calculation of Iout in a BJT circuit with infinite gain (β→∞) involves using the BJT exponential transfer characteristic. With β approaching infinity, the base current (IB) for each BJT is zero, leading to the relationship IC = IE. The equation Ic = Is * e^(VBE/Vt) is utilized to compute the base-emitter voltage (VBE) for each transistor, starting with I1 to find VBE1, followed by I2 for VBE2, and so forth until VBE4 is determined. Ultimately, Iout is calculated as ic4.

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Hi!
Here is my task:
Calculate Iout if all BJT's have identical characteristics with β→∞, work on same temperature in forward active mode. Use BJT exponential transfer characteristic.
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Since β→∞, IB for every BJT should be zero amps and IC=IE. Equation for BJT exponential transfer characteristic is Ic=Is*e^(VBE/Vt) but I don't know how to use it in order to find Iout. Any idea? Iout should be I1*I2/I3.
 
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Using ic1 = is exp(Vbe1/VT), compute Vbe1. Note ic1 = I1.
Then using I2, compute Vbe2.
Etc. until you get to Vbe4. Finally, compute ic4 = Iout.
 
Done. Thanks a lot!
 

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