Operating point importance; BJT transconductance

Selection of the operating point (Q-point)

The Q-point (ICQ, VCEQ) is the dc condition when no signal is applied. A signal makes the instantaneous operating point move along the load line around Q. For faithful amplification:

• Q must be in the active region, in the middle of the load line (VCEQ ≈ VCC/2), so that the positive and negative output swings are equal and not clipped.
• If Q is too near saturation (VCE small), the negative half-cycle of the output is clipped (saturation clipping).
• If Q is near cut-off (IC small), the positive half-cycle is clipped (cut-off clipping).
• If the Q-point is unstable (because of changes in β or temperature), it can drift later into a region where clipping or distortion occurs; hence stable bias circuits are used.
• The Q-point also sets gm = ICQ/VT, rπ, the gain and the input resistance.

 IC
 IC(sat)|\
        | \  Q too high (saturation clipping)
        |  \
   ICQ  |   *Q  (best: centre)
        |    \  Q too low (cut-off clipping)
        +-----\---- VCE
             VCEQ  VCC

Transconductance of the BJT

gm = ∂iC/∂vBE at the Q-point: the small-signal change in collector current per unit change in base-emitter voltage.

In the active region, iC = IS exp(vBE/VT). With vBE = VBE + vbe and vbe ≪ VT:

iC = IC exp(vbe/VT) ≈ IC (1 + vbe/VT)
ic = (IC/VT) vbe

gm = IC / VT

At room temperature VT ≈ 25 mV, so gm = 40 IC. For IC = 1 mA, gm = 40 mA/V. Then rπ = β/gm and re = α/gm.