Small transistor signal analysis

[Sebastie]

Transistor small signal analysis

Hello all,
I would want to study a low noise preamp with small signal analysis, but I don't really know I can do.
I would want to calculate the gain of the amplifier.

I tried to deduce the equivalent schematic in small signal analysis, but I don't know how I can start with this two stage, do I separate them ? and how ? What is the method to do the analysis with multiple stages like this ?

Another question, how can I deduce the 1/y11 and 1/y22 values ?

I hope that you coudl help me
Thanks

Original schematic :
Small signal analysis :

 

[FvM]

The equivalent circuit looks correct.

As a first step you'll need to determine the DC operation point to determine the actual transistor parameters. AN exact analysis requires to solve a nonlinear equation system, so you'll most likely use some simplifications for the calculation, e.g. constant Vbe and current gain.

Secondly, the small signal analysis can be always be performed by general linear network methods you'll find in your text books. In most cases, an estimation of both transistor stages' voltage gains and overall feedback factor will be sufficient. It can be derived from an intuitive view.

 

[jeffrey samuel]

The equivalent circuit looks correct.

AN exact analysis requires to solve a nonlinear equation system, so you'll most likely use some simplifications for the calculation, e.g. constant Vbe and current gain.

Secondly, the small signal analysis can be always be performed by general linear network methods you'll find in your text books. In most cases, an estimation of both transistor stages' voltage gains and overall feedback factor will be sufficient. It can be derived from an intuitive view.

can you explain a little more sir

 

[Sebastie]

Hello FvM,
Thanks for your reply.

For the 1/y11 parameter, I found on the net this expression :

1/y11=Beta*VT/Ic
the problem is that the Beta of the transistor is specified in the datasheet with a value comprise between 100 to 630... How can I found the good value ?

1/y22=(VA+VCE)/IC
what is the VA voltage ?

source : https://users.ece.gatech.edu/~alan/ECE3040/Lectures/Lecture20-BJT Small Signal Model.pdf

 

[FvM]

You'll notice that neither the exact beta nor VA (https://en.wikipedia.org/wiki/Early_voltage) have much effect on the overall gain in the present circuit. y22 is often ignored in simplified analysis, for beta you can assume some medium value.

can you explain a little more

I don't intend to retell the text books.

 

[LvW]

Hi Sebastie,

an ac small-signal model depends on the used dc operating point.
Therefore, the calculation must start by roughly calculating the quiescent currents through both transistors.
This task looks complicated - but in principle you only have to combine several equations that can be read out of the circuit diagram.
In this context some simplifications are necessary:
Ie=Ic, Ib=0, Vbe=0.7 volts, I(R4)<<I(R3)=Ic,2

Then we can write:

false: V1-Ic,2*R3=Ve,2=Vb,2+0.7=Vc,1+0.7 >>> Ic,2/Ic,1=R2/R3
correct: V1-Ic,2*R3=Ve,2=Vb,2+0.7=Vc,1+0.7=5-Ic,1*R2+0.7 >>> Ic,1=(Ic,2*R3 + 0.7)/R2
Vb,1=Ve,2*16/(16+56)
Vb,1=Ve,1+0.7)
Ve,1=(Ic,1+Ic,2)*R6
_______________________________________
After combining these equations I arrive at an approximate value Ic,2=1.388mA.

Perhaps you can re-check this calculation?

As a second step you can use transconductance g=Ic/VT (without using h21=beta).

Good luck.

Sorry for the correction.

 

[Sebastie]

Hello and thansk a lot for your replies.
I'm going to hazve a look on calculation.

I made an error with the small signal schematic : the R1 and R4 are referenced to the ground not to the emitter of T1