# BJT small signal analysis without beta???

#### Synia

Joined Aug 25, 2011
3
Hi all

I am currently working on a question that states, for a BJT similar to the one below,

If all thats given is:
vc = 5V
ve = 4V
vb = 4.7V
ie= 10uA

Is there a way to calculate what R1 and R2 are? Without β being given?

It would be great if anyone can help, i've been stuck on it all night! And is beginning to suspect the question is wrong...

#### MrChips

Joined Oct 2, 2009
20,911
This is a common collector a.k.a. emitter follower configuration.
Try writing out the equations using variables for Re and beta. Ignore R1 and R2.
You will probably find that the voltage gain is unity.

(With the information supplied you can determine Re.)

#### t_n_k

Joined Mar 6, 2009
5,455
I'd be surprised if ie (Ie?) is actually 10uA ....

What is the actual problem asking you to solve?

#### jp1390

Joined Aug 22, 2011
45
For this case, the BJT is in forward-active and there should be little current pouring into the base, relative to Ie and Ic.

With that being said, it would be a fair assumption that R1 and R2 create a voltage divider, with the current flowing through both resistors being significantly larger than the base current.

We know that Vcc = 5 V and Vb = 4.7 V:

$$Ratio = \frac{V_{b}}{V_{cc}} = \frac{4.7}{5} = 0.94 = \frac{R_{2}}{R_{1} + R_{2}}$$

Rearranging:

$$R_{1} = \frac{R_{2}(1 - 0.94)}{0.94} = 0.06*R_{2}$$

From here you can just pick a value for R2 and you will get your R1 value. This choice also determines the current flowing through them, so make sure that it is not too small as compared to the base!

#### Synia

Joined Aug 25, 2011
3

This is actually part of a low voltage FM radio transmitter design i have been given to do. The voltages and current are worked out by my partner from other parts of the circuit, and i am currently just trying to find what value to put into R1 and R2 that the circuit work properly....

@jp so how do i work out how much current is flowing into the base?

#### jp1390

Joined Aug 22, 2011
45

This is actually part of a low voltage FM radio transmitter design i have been given to do. The voltages and current are worked out by my partner from other parts of the circuit, and i am currently just trying to find what value to put into R1 and R2 that the circuit work properly....

@jp so how do i work out how much current is flowing into the base?
Well normally beta is between 40 - 100 for general purposes, so pick a value within that range and you can figure out the base current. From there you can figure out how large R1/R2 have to be in order to have the base current negligible to the current through R1/R2.

#### hobbyist

Joined Aug 10, 2008
887
Is your RE value around 400K ohms?
To give 4v. @ 10uA. for IE.

#### PRS

Joined Aug 24, 2008
989
Re-check your parameters. Ie = 10uA is ridiculously low.