Thevenin Potential Homework: Simplifying a BJT Amp Frequency Model

[sandy.bridge]

Homework Statement

Hey guys,

There is an example in the textbook regarding simplifying the frequency model of a BJT amplifier. It ends up determining the potential across the highlighted resistor I attached. The formula that the textbook is rather different than the one I determined to be the Thevenin, and hence I am looking for some sort of explanation. I plugged in some values to determine if they were equivalent, and they were close, but not exact. I believe there was approximatedly 0.0016 V difference for the particular values I had chosen. The textbook gives
$$V'_{sig}=V_{sig}\frac{R_3}{R_3+R_{1}}\frac{R_{4}}{R_{4}+R_2+(R_{1}//R_3)}$$

I do not understand how they ended up with $R_1//R_3$. I analyzed the circuit two different ways. I used potential dividers and I also determined the current passing through that leg. Each time my results were vastly different; however, they do give the same results upon evaluation.

 

[NascentOxygen]

To get the textbook result, replace the source and R1 and R3 with the Thevenin equivalent, giving a source of Vsig.R3/(R1+R3) and having impedance R1 // R3

This Thevenin equivalent is then loaded by the series resistances R2 and R4.

If I nominate some values, e.g.,
R1=4
R2=2
R3=5
R4=3

That expression gives Vsig‘ = 0.2307 Vsig

I'll recheck.

 

[NascentOxygen]

I checked using potential dividers with loading taken into account, the result with the above figures is also 0.2307

 

[sandy.bridge]

Finally! I was staring at that for a good hour attempting to determine how they got that. Thanks a bunch!

 

[rezeew]

Dear student,

Thank you for reaching out with your question regarding the simplification of the frequency model of a BJT amplifier. It is common for different sources to use different formulas or methods for simplifying circuits, as there can be multiple valid approaches to solving a problem. However, it is important to understand the reasoning behind each formula in order to fully grasp the concept.

In this case, the textbook formula you have provided is using the concept of equivalent resistors in parallel. This is represented by the notation "R_1//R_3", which means that R_1 and R_3 are in parallel. This is a common technique used in circuit analysis to simplify complex circuits and can be derived using Kirchhoff's circuit laws.

It is difficult for me to determine the exact reason for the discrepancy in your results without seeing the specific circuit and values you have used. However, I would suggest double-checking your calculations and making sure you are using the correct values for each resistor. It is also possible that there may be some slight differences in the assumptions or approximations made in the textbook example compared to your analysis.

I hope this helps to clarify the use of parallel resistors in the formula and provides some guidance for further analysis. Keep up the good work in your studies!

Best,