# About BJT, JFET & MOSFET transconductance

For BJT, the term "gm" refers to base-emitter conductance. But when we are talking about FETs and MOSFETs, where is this "gm"? Between gate-source junction for JFET? Drain to source conductance for MOSFET?

And what "gmb" means when talking about MOSFETs?

In general $g_m$ in simple term is a "gain" for any transconductance amplifier. And because transconductance amplifier is nothing more then a voltage controlled current source (VCCS) the gain expression is $g_m = \frac{I_{out}}{V_{in}}$.

For example if is $g_m = 1\:Siemens$ any change in the input voltage by $1V$ will change the output current by $1A$ (1 Ampere per Volt).

For BJT the transistor $I_C$ current is a controlled via input$V_{BE}$ voltage.

So, you plot $I_C$ vs $V_{BE}$

The $g_m$ is the slope of this curve

In MOSFET & JFET we have the same situation.

The output current $I_D$ is controlled via $V_{GS}$ voltage.

Hence again the slope of a $I_D = f(V_{GS})$ is a $g_m =\frac{dI_D}{dV_{GS}}$

The MOSFET in general is a 4 terminal device. The Gathe, Soure, Drain and the Body. And we can control the $I_D$ via the gate terminal or via the Body. And this is why you have $g_{mb}$

• Nice. From the first picture; the small vgs represents input AC (actually triangular) and Vgs represents DC biased quiescent point, right? May 1, 2017 at 19:35
• Yep, you're right.
– G36
May 2, 2017 at 5:14
• So, input AC voltage vgs changes DC biased Vgs just a little bit (if we are looking onto the slope)? Even if vgs is ten times higher/bigger than Vgs, Vgs changes just a little bit with input signal? May 2, 2017 at 7:46
• If Vin is lower then Vt the MOSFET is OFF and if Vin>> Vgs at DC. The MOSFET is in saturation. Hence $$V_{INmin} = V_T$$ and $$V_{INmax}= V_T+ \frac{-1+\sqrt{1 + 2KR_DV_{DD}}}{K*R_D}$$ In real life the range is even smaller.
– G36
May 2, 2017 at 18:20
• But if DC Vgs is biased above Vt, Vin does not need to be necessary above Vt. May 2, 2017 at 18:33

In the bjt ic=gm*vbe refers to base-emitter conductance.

Similarly, in field effect transistors, and MOSFETs in particular, refers to gate-source conductance.Transconductance is the change in the drain current when we have small change in the gate/source voltage.id = gm*vgs

gmb: refers to transconductance which appears when we have the body effect.This occurs when VBS<>0(Voltage in the Bulk and Voltage in the source).

Notice:The terminal of bulk should usually be connected to the lowest potential of the circuit(ground or -VSS).This gmb provides a second current in the circuit with value ib=gmb*vbs

If body effect appears in your circuit your small signal model is the above

• But if bulk is connected to source, body effect cannot occur, right? Because if bulk and source are connected together there is no voltage difference, so no Vbs, right? May 1, 2017 at 19:16
• All you refer is right May 2, 2017 at 9:17
• But bulk is always connected to source, right? Or not? May 2, 2017 at 11:05
• The terminal of bulk should usually be connected to the lowest potential of the circuit(ground or -VSS).In the most CMOS process bulk shouldn't connect in the source May 2, 2017 at 14:57