What is the voltage gain for this circuit?

[kelvin56484984]

Homework Statement

assume β=200,Vt=26mV,Vbe(on)=0.7V
Find the voltage gain Vo/Vs

How to find the Rth , Vs ,then find the voltage gain?
I try to draw the circuit diagram below

Homework Equations

The Attempt at a Solution

Vth=[R2/(R1+R2)]*15
Vth=1.63V

Which method should I use to find Rth?
Rth=R2//R1
=5.53k ohm
or
I see this formula Rth=0.1Re(1+β) on my book
Rth=0.1Re(1+β)
=10.3k ohm

I assume Rth=R2//R1
Vth=Rth*Ib+Ie*Re+Vbe
Vth=Rth*Ib+(1+β)*Ib*Re+0.7
Ib=8.57μA

Rπ=Vt/Ib
Rπ=26m/8.57μ
Rπ=3.03k ohm

Assume my small signal model diagram is correct
Vb=ib*Rπ
Vo=-βib*Rc

But how to find the Vs
then I can find the voltage gain(Vo/Vs)?
=[Vo/Vb]*[Vb/Vs]

 

[gneill]

Vs is arbitrary, representing some small signal. The gain will be a ratio, so the particular value of Vs is not important. What may be important, though, is the frequency of Vs.

Notice where Vo is on your circuit diagram: It's not the voltage at the collector! What effect do you think the 20 μF emitter bypass capacitor is going to have? You may need to take a closer look at how the capacitors in the circuit are going to affect things, and perhaps examine the emitter circuit in more detail for your small signal equivalent.

Your circuit diagram shows the source resistance labelled with a capacitance value. Presumably that was meant to be associated with C_C1. Is there a resistance value for the source resistor?

 

[kelvin56484984]

Thank you
the resistot with wrong label is the internal resistor of the signal generator
I think it can be neglected during the calculation since the value is not given

 

[kelvin56484984]

Thank you
the resistor with wrong label is the internal resistor of the signal generator
I think it can be neglected during the calculation since the value is not given
And the voltage is at the collector

 

[gneill]

Is the given circuit diagram not correct? It shows Vo connected to the emitter.

 

[kelvin56484984]

Is the given circuit diagram not correct? It shows Vo connected to the emitter.

Yes , I make some mistakes when drawing the circuit
Vo should be at the collector