Common Emitter Gain question

[H. Neary.]

I have a circuit that I understand the DC gain, but I don't understand the
AC gain.

the top resistor on the base from Vcc is 18k, bottom is 18.2k into a 2n3904
with an Re of 562 and an Re of 1k, vcc is 9v.

There is a cap in parallel with Re that is 100uf and my input freq. is 1kHz.

The DC gain should be Rc/Re which is a little less than 2. But when I scope
the input and the output, it's like 100 times.

I understand that cap is bypassing all the AC to ground, but why the higher
gain?

Work out Xc, then work out the gain using Xc in parallel with Re.

HTH

HN

 

[Peter]

I have a circuit that I understand the DC gain, but I don't understand the
AC gain.

the top resistor on the base from Vcc is 18k, bottom is 18.2k into a 2n3904
with an Re of 562 and an Re of 1k, vcc is 9v.

There is a cap in parallel with Re that is 100uf and my input freq. is 1kHz.

The DC gain should be Rc/Re which is a little less than 2. But when I scope
the input and the output, it's like 100 times.

I understand that cap is bypassing all the AC to ground, but why the higher
gain?

 

[Peter]

I tried that and my gain is like 629 when my gain is clearly 100 because I'm
looking at the input which is 1mV rms and my output is approx. 100mV rms.

 

[H. Neary.]

I tried that and my gain is like 629 when my gain is clearly 100 because I'm
looking at the input which is 1mV rms and my output is approx. 100mV rms.

Sorry, it was obviously more complex than my simplistic approach. I'll
dig out my old text books if no-One provides an answer. I know that ac
gain in common emitters was something that was done to death on a few
of my courses in analogue electronics. Strange really, I seem to have
spent the whole of my career without having needed the theory once

HN

 

[TimPerry]

Sorry, it was obviously more complex than my simplistic approach. I'll
dig out my old text books if no-One provides an answer. I know that ac
gain in common emitters was something that was done to death on a few
of my courses in analogue electronics. Strange really, I seem to have
spent the whole of my career without having needed the theory once

HN

http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/npncegain.html

http://www.ecircuitcenter.com/Circuits/trce/trce.htm

take a look at these sites.

do you have a load resistance? if so it parallels Rc

dont forget about the resistance in the emitter junction (r ej). its small
but adds in series to the ac resistance.

 

[bushbadee]

Maximum common emmiter gain is 40 X Vcc

That occurs near saturation.

 

[Peter]

I don't think it's 40 x Vcc

I think what I was missing was that I needed to include re' in the equation
too and also consider the resistors on the base of the transistor (r1 and
r2)

 

[bushbadee]

re depends on the current flowing'
At 1 Ma it is about 25 ohms.
The value of 40 Vcc is for a grounded emmitter configureation
Close to saturation the current is limited by Rc.
This means that as Rc gets bigger the current drops and re also gets bigger
in proportion to Rc.
Because they track, both drop out of the equation and the gain is 40Vcc.
If there is a substantial externam emmitter resistance which is a lot bigger
than re than the gain is Rc over Re.
If Re is not a lot bigger than re then the effects of re must be considered,
but remember re is a moving target varying with current. and the gain varies
with the current flowing.