AC analysis of common base BJT

[fastcharlie2]

I have to find the output voltage and phase. I started by doing the DC analysis with the capacitor as an open and then I don't know how to do the AC analysis with the inductor ans capacitor at the input. Any help is welcome
What I got is Vout=Vin[Rc/(re//100 +Xc +XL)] but I check my answer with LTspice and my it does not look the same.

 

[fastcharlie2]

My work up to now is
I took the capacitor as an open and did a KVL from the 2V sourece to the 1.2kohm.
-Vb+Vbe+Ie(100+1.2k)=0
Ie=(2-.70/(100+1.2k)=1mA
Ie is approximate to Ic, Ic=1mA
Then a KVL at the output
-10V+1k x Ic+Vout=0
Vout=9V

The only thing I know for AC analysis is re=25mV/Ie=25ohm

 

[Laplace]

Remember when you learned about imaginary numbers, how to perform manipulations in complex algebra, and how to calculate the magnitude and phase of complex variables? Well, a problem like this is where you use all that learning. Start by representing the capacitance and inductance as imaginary functions of frequency, then use the resulting impedance to write the circuit node or loop equation(s), solve for Vout/Vin and draw a Bode plot for the magnitude and phase.

 

[LvW]

Fastcharlie2
1.) Your calculation of the DC current is correct.
2.) I recommend to split calculation of the AC gain of the circuit into two parts:
a) gain between emitter and collector (classical formula involving only re=1/gm and Rc)),
b) Input damping between signal input and emitter node. This is a simple LC series resonant circuit with damping - followed by application of the voltage divider rule (to get the voltage at the emitter node). During this calculation It is important to consider the input resistance at the emitter node with re=1/gm=25 ohms.

 

[fastcharlie2]

I got it like this for the AC small signal but what do I got to do next?

 

[Laplace]

Here is my attempt at analyzing the common-base amplifier using the simplified hybrid-pi model. I don't remember ever having done this before as common-base is rarely used except for high-frequency RF circuits. Initially tried using Vπ from the model in the node equations but switched over to Vbe because it was confusing.



Derived Vo/Vs as the transfer function T(f). Note that for the Bode plot I slightly offset the component values so the result is not the exact answer for this problem.

 

[fastcharlie2]

Thanks for the explanation! I download Mathcad as well it helps minimize the math error on long transfer function like this. Can I do an imaginary node to get the voltage between the inductor and the capacitor or this has to be doing loop analysis?