What sets the MAG of a BJT?

[ezalys]

Suppose you design ideal matching networks on the input and output of your transistor so ALL we're concerned with is the transistor and the packaging. What semiconductor physics or parasitics or whatever sets the MAG figure in the datasheet? I tried doing a few back of the envelope calculations... one by looking at the y parameters of the hybrid-pi model and looking at the unilateral gain... this showed a dependence on the early voltage and beta (specifically, I get beta*va/(4 vt) ), but this figure was way too high (40 dB). I also tried calculating the maximum stable gain given the parasitic base-emitter capacitance and the barkhausen criteria (resulted in something looking like G = 1/(C_be Z0 omega)^2)... plugging in some sensible values gave a gain of somewhere between 20-30 dB, which seems better, but from what I understand, you can just add an inductor to resonate with this capacitance to stabilize the transistor and this is no longer a limit. When MAG is measured, is this considered? For whatever limits this MAG, could you point me to a reference where this is modeled somewhat concretely? I realize this might just be one of those things that just is really hard to model, but as a physicist, this makes me feel icky and I really feel the need to have some back of the envelope calculation to ballpark this with some numbers.

[tec5c]

While I don't directly know the answer to your question it has me interested, so I have done some reading around and have come across this article. http://users.cecs.anu.edu.au/~Gerard.Borg/engn4545_borg/transistors/transistors.html
The section on small signal RF design mentions MAG and associated parameters, however, I think you are after a deeper understanding than what this article provides.

Please, keep this thread updated with any info as you come across it 

[T3sl4co1l]

MAG?  Magnetically Actuated Gramophones?

Tim

[tec5c]

MAG?  Magnetically Actuated Gramophones?

Tim

 

I know you're just pulling our legs here Tim. MAG = max. available gain. Otherwise I may need to rethink some things/life. 

[T3sl4co1l]

Hmm, is that a well-defined property?  You can get infinite gain by pushing arbitrarily close to instability (hence the superregen radio)...

That assumes that you're evaluating over all possible input and output coupling impedances.

It may be more practical to speak in terms of maximum stable gain, and gain-bandwidth?

Gain-bandwidth is easily modeled with an ideal transconductance amplifier that has an RC output characteristic, and infinite isolation.  The R is due to BJT Early effect (or MOS channel length modulation, or electric field feedback in the vacuum tube, etc.), in parallel with the load resistance, and C is the output capacitance.  You can resonate the C with L, but to reach a higher and higher center frequency, you need smaller and smaller L, which drives the Q up (Q = R / sqrt(L/C) ).  Thus the bandwidth fraction (in terms of center frequency) drops, but it drops at the same rate that center frequency rises -- the bandwidth remains constant.  Bandwidth is inversely proportional to R, so it's also a gain-bandwidth tradeoff.

Maximum stable gain is rather more involved -- I don't know the proof very well myself, but it has to do with solving for the stability criterion over all input and output impedances.

The heart of it is this: if isolation is less than (feedback is more than) maximum device gain, then there will be some condition where the feedback, phase shifted appropriately, will result in oscillation.  You then have a conditionally stable amplifier.  As you go to ever-higher gains, the stability region, the locus of input and output impedances where it remains stable, continues to shrink.

Tim

[rfeecs]

MAG is a theoretical figure of merit like Ft.  It doesn't have much practical use except to get an idea of how much gain you theoretically could get if both input and output are perfectly matched.  Typically one matches to optimize output power or IP3 or noise figure or efficiency... so gain is seldom the only concern.

MAG is not measured.  It is calculated by first measuring S-parameters.  It is then calculated from the S-parameters.  See the equation on the last page:
http://www.hparchive.com/Application_Notes/HP-AN-95-1.pdf.

The MAG calculation is based on making a simultaneous input and output match for a two port.  No power is reflected, all power is transmitted, so gain is maximized.  This requires that the two port be unconditionally stable at the frequency of the calculation.  Stability again is calculated from the S-parameters.

The MAG depends only on the device, not the matching networks theoretically used to do the matching.  Since these theoretical networks are lossless, they contribute nothing to MAG apart from doing an impedance transformation.

Note that MAG is based only on matching input and output ports with no external feedback applied.  In the real world, feedback might be applied to neutralize the device or even positive feedback might be applied and both of these can give a gain higher than the MAG.

If you refer to the model from wikipedia for example:


MAG is limited by the resistances at the input.  They reduce the voltage available across Ce, which reduces the effective transconductance.  The output resistance has a similar effect.  The collector-base feedback also reduces the gain.  If there were no parasitic resistances and no feedback capacitance, MAG would be infinite.

[ezalys]

T3sl4co1l and rfeecs, that was exactly what I was looking for. Thank you!