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QUES: Design a BJT based inverter operated from a 1.5 V supply.With the input connected to the 1.5 V supply through a resistance equal to RC, the total power dissipation should be 1 mW and forced β should be 10. Use VBE = 0.7 V and VCEsat = 0.2 V

I tried solving this but I am not sure that total dissipation will be due to Rc only or both Rc and Rb. Please help. Below is my solved design.

enter image description here

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    \$\begingroup\$ Total power dissipation needs to include the power consumed in the transistor itself. This can be computed from knowing the VCEsat and the current through the transistor. Most accurate is to use the sum of base current and collector current in this calculation. \$\endgroup\$ May 28, 2020 at 12:05
  • \$\begingroup\$ I am little confused. So, Can you please just tell me whether the above design in the image is correct or not? @MichaelKaras \$\endgroup\$ May 28, 2020 at 12:07
  • \$\begingroup\$ So are you saying that dissipation will be only due to Rc? \$\endgroup\$ May 28, 2020 at 12:09
  • \$\begingroup\$ I am not going to analyze your design or calculations but I can say that your total power calculation needs to take into account the fact the the transistor in saturation has some bulk resistance and thus dissipates some power. (i.e. This is why VCEsat is not a value of zero. \$\endgroup\$ May 28, 2020 at 12:10
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    \$\begingroup\$ I read that part to mean that the resistance of Rb and Rc are meant to be the same. \$\endgroup\$ May 28, 2020 at 12:15

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It's a bit of a tricky problem. You seem to understand that you can consider the base and collector circuits independently, so that's a good start.

The phrase "the input connected to the 1.5 V supply through a resistance equal to RC" means that the base current flows through the series combination of the previous stage's Rc plus this stage's Rb. That's the only way you can meet the forced beta constraint. Here's the circuit:

schematic

simulate this circuit – Schematic created using CircuitLab

The total power dissipation is specified as 1 mW, and the supply voltage is 1.5 V. This means that the total current consumption of both circuits can only be 0.6667 mA.

The "forced β" is specified as 10, which means that 10× the base current flows through the collector. This means that Ib must be 0.0606 mA and Ic must be 0.6061 mA.

This should be enough of a hint to let you complete the problem.

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Your answer shows you understand how to do this. The problems are with the question with vague and incorrect specifications. (showing inexperience)

"With the input connected to the 1.5 V supply through a resistance equal to RC"

Wrong. The input is Rb and the output is the collector thru Rc pullup to 1.5V

"the total power dissipation should be 1 mW "

Vague: Total is the sum of which parts? Pd for Q1 ? Q1+Rc? Q1+Rc+Rb
Technically Rb & Vbe power comes from the driver. So assume total power Pd=Vcc*Ic=1mW

This is an inverting NPN switch. FYI saturated BJT transistors drop towards 10% hFE max linear, because this is where they are usually rated @ Ic/Ib=10 for Vce=Vce(sat) but this threshold of hFE reduction rises with current towards 2V at rated current but probably even lower than 0.1V @ Ic < 1mA.

Remember this.

If Ic=1.00mA, Vbe = 0.600V
@ room temp (diode exponential law within 1%)

NOT Vbe=0.7V

which might occur @ Ic=50 mA approx which depends on bulk resistance and chip size now. (common error in assumptions, but not a big deal)

You're good to go now.

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