Help me with calculating voltage and decible gain please?

[Derringer]

here's two mock circuits
1st the BJT


2nd the FET


I'm mostly interested in finding decibel gain but I don't know the darn equations !!!
I'm pretty sure that dB gain can be found looking at the voltage gain ... i.e. 20*Log10(Voltage Gain) ... right?

but how to find the voltage gain? and what to do with the FET circuit?

Also, how does C1 effect the decibel gain (gain with it in the circuits? gain with it not in the circuits?)

so please hit me up with the equations or links that will teach me the equations (I'm not afraid ... when I know what equations to use, math and I are good friends  )

Thanks!

[R.G.]

Conversion to db is the simple thing; for voltage ratios, the db is just as you've said, twenty times log ten of the ratio.

However, calculating the gain of circuits, even simple ones, requires more than a simple answer to a question in a forum. There are some approximations for simple circuits, such as the gain of any circuit with unbypassed emitter/source resistance being about equal to the collector/drain resistor divided by the unbypassed emitter/source resistor, but that ignores a subtler modelling of the devices. For a bipolar, for instance, you must take into account the internal Shockley resistance on the emitter inside it, and for a JFET, the ratio has to be significantly lower than the input voltage times the transconductance for the device gain to support the feedback that makes the two resistors carry the same currents.

I suggest getting a copy of "The Art of Electronics" and spending a couple of hours reading. Then a couple of months.

[Derringer]

cool

yeah, I was hoping for a simple plug and play equation ... but no dice huh?

I have a copy of TAOE and I'm just barely out of the "couple of hours reading" stage now, headed into the "couple of months" stage. So much of it is still over my head. I suppose with re-reads and practice it will come.


Thanks R.G.

[darron]

http://www.muzique.com/schem/gain.htm

may also help

[MohiZ]

Learn about small signal analysis and the hybrid-pi equivalent circuit for BJTs and the equivalent circuit for FETs. They are easily understandable, but you have to know some basics first. I'll give you some plug and play equations, although they will vary depending on the circuit. I'm pretty new to this as well, so someone correct me if I'm wrong but:

For BJTs: Once you know the voltage at the base (the voltage divider R1 and R2 in your mockup), you know that the emitter is usually about 0,7 volts below that voltage. Then, based on ohm's law, you know the current that has to be flowing through the emitter resistor to lift the emitter voltage to that value. The collector current is about the same. The transconductance of the transistor is then: gm = Ic/25,4mV. Then the gain is A = -R3/(1/gm + R4), and with the bypass cap A = - Rc * gm, as long as the frequency is high enough...

NOTE! The equations are just approximations. I assumed the gain of the transistor is not known because it varies. It could be calculated more accurately if the gain and the exact voltages were known, but I think these equations are good enough for normal use, since all the resistors have tolerances anyway and so forth.

The FETs are harder because you have to actually know the pinch-off voltage and zero gate-source voltage drain current to be able to calculate this.

[MohiZ]

For your FET circuit example:

Gain without the bypass cap: A = - (R2*gm) / (1 + R3*gm)
With bypass cap: A = - R2 * gm

Where gm = 2 * sqrt( K * Id ), where Id is the drain current of the FET (depends on bias point), and K = Idss / Vp^2, where Idss is "Saturation Drain Current" (found on the datasheet) and Vp is the pinch-off voltage of the FET (also found on the datasheet). These values are highly variable from device to device, though. Then there's also the internal drain-source resistance of the FET, which I left out of the equation because it's much larger than the drain and source resistors you've chosen.

[Derringer]

nice dude

thank you!

[Transmogrifox]

Here's a really quick and dirty approximation I use sometimes when I'm trying to determine whether it's "a lot of gain" or "not a whole lot".
BJT's (for number 1)
A= R3/(R4+25);
For bypass cap
A=R3/25;

JFETs:
A=R2/(R3+100);
For bypass cap
A=R2/100;

This just makes some really broad generalizations based on what I get using the equations from MohiZ above on typical bias conditions.  My purpose for doing it that way is just so I can pull resistor values out of my head to get something onto a breadboard that will work.  I tweak by ear from there. 

I wouldn't recommend it if you're designing something that has to meet a pre-defined specification.

[Derringer]

thank you


and just to follow up ...

I had found through bit-torrent sharing a pdf version of the Art of Electronics a while ago. That particular version went straight from the table of contents to chapter 2. I thought nothing of it till I recently looked at the T.O.C. to find that there was important information in chapter one!

I just found this link today that has an online re-print of the "Student Manual for the Art of Electronics." It has chapter one material.

http://www.scribd.com/doc/6135061/The-Art-of-Electronics-Student-Manual