# BJT single stage amplifier we write gm=Ic/VT

1. Feb 20, 2014

### pforpashya

For BJT single stage amplifier we write gm=Ic/VT where VT is Thermal voltage whose value is 26mv. Now if we have a Darlington pair i.e. two transistor connected in CC-CC mode what will be overall gm.

Will the collector current Ic be divided by 52mv or 26mv. (Because in gain equation gm comes)

as their are two forward active PN junctions ...the cumulative change in VT is 52mV?

is this correct?

can someone through light on "why we have to include Boltzmann constant in calculation of VT"
in simple words?

2. Feb 20, 2014

### cabraham

Each device has gm value equal to its own Ic divided by VT, where VT is 25.7 mV for each device. For a Darlington, if the input device is no. 1, and output device is no. 2, then Ie1 = Ib2, Ic1 = α1*Ie1, Ic2 = β2*Ib2, or Ic2 = α2*Ie2, .

This should get you started.

Claude

Last edited: Feb 20, 2014
3. Feb 20, 2014

### pforpashya

ok. thank you for your reply. to find overall gm (i.e. gm2 as gm1 of first pair in darlington is very small) of the device should i divide Ic2 by VT1+VT2 i.e. 52mV?

4. Feb 21, 2014

### Jony130

Yes you should use 2*Vt if you want to find voltage gain.

The small signal gain for CE amplifier is equal to

$\Large \frac{Vout}{Vin} =-\frac{Rc (\beta 1+\beta 2+\beta 1 \beta 2)}{(1+\beta 1) (re1+re2+re2 \beta 2)}$

Where

re1 ≈ 1/gm1
re2 ≈ 1/gm2

5. Feb 21, 2014

### pforpashya

Thanks alot...I have to solve one unsolved problem on darlington pair before saturday. I hope i will get right answer as i have to just multiply gm by output resistance of darlington pair.

6. Feb 21, 2014

### pforpashya

can someone through light on "why we have to include Boltzmann constant in calculation of VT"
in simple words?