# 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? – Keno May 1 '17 at 19:35
• Yep, you're right. – G36 May 2 '17 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? – Keno May 2 '17 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 '17 at 18:20
• But if DC Vgs is biased above Vt, Vin does not need to be necessary above Vt. – Keno May 2 '17 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? – Keno May 1 '17 at 19:16
• All you refer is right – elecV1 May 2 '17 at 9:17
• But bulk is always connected to source, right? Or not? – Keno May 2 '17 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 – elecV1 May 2 '17 at 14:57