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!