Mid-Band Voltage Gain Equations

[DODGEVIPER13]

Homework Statement

Problem picture is attached also some of my work is attached.
The problem states derive midband voltage gain v0/vi expression in terms of circuit parameters. From the expression you just derived calculate numerically the midband gain value?

Homework Equations

The Attempt at a Solution

I really only need help with part b finding the mid band voltage gain. So far I have V0=gmvpi(Rc||Rl) and vpi=-Vs((Rpi/(Ri+(Rb||Rib))). Then Vo/Vi = voltage gain but my professor told me I was wrong how should I proceed? I have also uploaded my work for a and shown some of b

 

[rude man]

Your high-pass corner frequency calculation is correct: 3.2 Hz.

The mid-band gain is when you assume the input capacitor → ∞ but without the 50 pF collector capacitor hooked up.

You won't ever get the rolloff frequency if you don't incorporate the collector 50 pF capacitor in your equivalent circuit.

I dn't have time to figure out where you went wrong in your computation of Vout/Vin. Maybe tomorrow. Offhand your V_π calculation looks strange.

 

[DODGEVIPER13]

Ok I recalculated the gain V0=gmVpi(Rc||Rl) and Vi=-Vpi((Ri+Rb||rpi)/(Rb||rpi)) so V0/Vi = -gm(Rb||rpi)(Rc||Rl)/(Ri+Rb||rpi) = -39.531

 

[rude man]

Ok I recalculated the gain V0=gmVpi(Rc||Rl) and Vi=-Vpi((Ri+Rb||rpi)/(Rb||rpi)) so V0/Vi = -gm(Rb||rpi)(Rc||Rl)/(Ri+Rb||rpi) = -39.531

If that's your mid-band gain it's way off.

To get an approximate idea of the gain (the input capacitor shorted and the collector capacitor gone), imagine a small voltage change ΔV_i. Now, ΔV_i is almost equal to ΔV_b and ΔV_b is almost equal to ΔV_e. So the emitter current change is ~ (0-ΔV_i)/R_E ~ collector current change which is Δv_c/RL + Δv_c/R_c. Now solve for Δv_c/Δv_i & what do you get?

Sorry, I don't have the time to check your math. Maybe someone else will.

 

[DODGEVIPER13]

Ok so I know you don't have much time but does this sound ok for my approach. Ic=beta(Ib) and Ie=(1+beta)Ib so Ie=.906 mA, Ic=0.9 mA, and Ib=.006 mA. Then deltaVi=-9.06 V and delta Vc=1.285 V so Vc/Vi=-0.1418 this seems off?

 

[rude man]

Ok so I know you don't have much time but does this sound ok for my approach. Ic=beta(Ib) and Ie=(1+beta)Ib so Ie=.906 mA, Ic=0.9 mA, and Ib=.006 mA. Then deltaVi=-9.06 V and delta Vc=1.285 V so Vc/Vi=-0.1418 this seems off?

That number is right on the money. Good going!

 

[rude man]

If you ever get into this stuff professionally you will almost never use equivalent circuits. You will follow the sort of argument I offered. Basically one assumes beta goes to infinity, ib = 0 etc. A good circuit will never depend on the value of beta since it can vary all over the place even for the same type number, like 2N2222.

The exception might be integrated circuit designers who can assume well-matched transistor pairs due to proximity, common process, etc.

 

[DODGEVIPER13]

Ok man cool yah I don't plan too well if I do it will be a mixture of this and power maybe electric vehicles or something