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The transconductance is defined e.g. for BJT by 

gm = dIc/dVBE with VCE=const  (1)

where Ic is the collector current and VBE is base-emitter voltage, and from (1) we can deduce

gm = d( Is*exp( VBE/(m*VT) ) )/dVBE, 
   = Is*exp( VBE/(m*VT) ) * 1/(m*VT),
   = Ic * 1/(m*VT),    (2)

and then the normalized transconductance is defined by 

gm,norm = gm/(Ic/Vt)  (3)

where Vt is the thermal voltage, Is is the saturated current, m is the linearity factor related to the technology. In my master thesis, I focus on the variation of gm,norm with changing the doping profiles of transistor, the target is to improve the gm,norm by design the transistors. I can understand that, with a higher gm,norm the transconductance of the device is better. But why do not we use the gm directly? Is there any superiority using normalized transconductance rather than transconductance? Can someone tell me also the meaning of transconductance in the circuit design? Thanks a lot!

X.J
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  • 'm' as you use it is often called 'n' instead and is the emission co-efficient. It's a simplified model value constant. But it actually is a variable. Have you looked up MEXTRAM modeling, yet? Finally, how exactly do you imagine that you will improve \$g_m\$ on the BJT? You won't create a lower emission coefficient than 1. So you are stuck on that point. \$V_T\$ is basic physics of matter and the equipartition rule of energy. I don't think you will change physics much. So you are stuck on that point, too, though perhaps you could come up with a way of unequal partitioning? (I doubt it.) – jonk Feb 03 '18 at 20:01
  • Thanks for you fast comment, Jonk. What you said is right. It is not very realistic that by changing the 'm' as you called 'n' and \$V_T\$ to improve the \$g_m\$, because they are normally constant for a technology and at a special temperature. As I said the target is to improve the \$g_{m,norm}\$, which is about but smaller than 1 at low current, and decreases at high current. So what I do exactly is to improve the \$g_{m,norm}\$ at high current e.g. operating point of peak \$f_T\$. I can achieve it, but I don't understand why people use \$g_{m,norm}\$ rather than \$g_{m}\$ here? – X.J Feb 03 '18 at 21:36
  • Besides, what your meaning about MEXTRAM modeling, what should I focus on when I look about it? Thanks!! – X.J Feb 03 '18 at 21:45
  • Are you being tasked to improve \$g_m\$ at high and or low collector currents? (I suspect you are asking about a ***nominal*** \$g_{m}\$, and not ***normal***, meaning one that is in the usual range of operation.) Before I write anything more, I want you to read my answer here about the three regions of collector current operation for the BJT [Dependence of transistor current gain on operating conditions](https://electronics.stackexchange.com/questions/305693/dependence-of-transistor-current-gain-on-operating-conditions/305720#305720). I need to know more about what you are discussing. – jonk Feb 03 '18 at 21:56
  • MEXTRAM is a better BJT model. If you are out to make improvements, you'd be a LOT better off examining and studying MEXTRAM and using math approaches to examine how and where improvements can be made. These will lead to ideas for the investigation of specific areas of solid state physics in the BJT to study further as possible segues to improving the device. But frankly, I think you are up against some basic physics limits. I'd be very, very interested in ideas you develop here and why and how you got there. – jonk Feb 03 '18 at 21:57

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