We now appreciate the application of the h parameter transistor model to the study of AC transistor operation. The hybrid pi model of the transistor, which is more versatile than the h parameter model (as will be shown later), can be related to the h parameters. This is particularly important, as manufacturers typically supply values for the h parameters in their transistor specification sheets, and NOT the hybrid pi model parameters. Therefore one needs to be able to derive the hybrid pi model parameters from the h parameters.

For the CE BJT amplifier, the h parameter model is shown below

As h_re is typically a relatively small quantity and 1/h_oe is very large, the above model can be simplified, with only a minor effect on any calculations made.

The corresponding simplified hybrid pi model is

B' is NOT physically accessible BUT represents the internal base node @ the junction, separated from the external node B by r_bb' g_m = transconductance of the BJT transistor.

Comparing the 2 models, it can be seen that

• h_ie = r_bb' + r_b'e.....(1)
• h_fei_b = g_mV_b'e = g_mr_b'ei_b
  where g_m = |I_c| / V_T
  OR
• h_fe = g_mr_b'e ..........(2)
  For a BJT
• g_m = |I_c|(mA) / 26 @ room temperature ..(3)

What about h_oe and h_re ?? How do they relate to the hybrid pi model ? To answer this question, we must return to the complete h-parameter model.

The corresponding complete hybrid pi model (@ LOW frequencies) is

Note the effect of h_oe in the h parameter model is represented partly by r_ce (i.e. the finite output resistance of the transistor). The effect of h_re in the h parameter model (showing some feedback from the output back to the input) is represented by r_b'c (C = output, B' = input)

h_re = V_be / V_ce|_ib=0 = V_b'e / V_ce = r_b'e / (r_b'e + r_b'c) r_b'e / r_b'c....(4)

Under these conditions i_c = V_ce / r_ce + V_ce / (r_b'e +r_b'c + g_mV_b'e

But from (4) for i_b = 0, V_b'e = h_reV_ce

Therefore, h_oe = i_c / V_ce = 1/r_ce + 1/r_b'c + g_mh_re

As g_m = h_fe / r_b'e, h_re r_b'e / r_b'c

Therefore h_oe = 1 / r_ce + (1 / r_b'c)(1 + h_fe)...(5)

SUMMARY

If the CE h paramaters @ LOW frequencies are known @ the collector current I_c, the hybrid pi model circuit parameters can then be calculated from the following equations, in the order given (derived from equations (1) - (5) above)

g_m = |I_c|(mA) / 26 @ room temperature ...(6)

r_b'e = h_fe / g_m ....(7)

r_bb' = h_ie - r_b'e ...(8)

r_b'c r_b'e / h_re ...(9)

1/r_ce = h_oe - (1 / r_b'c)(1 + h_fe) ..(10)

Example

Typical values of h parameters for a BJT transistor @ room temperature & I_C = 1.3mA are (M&G App8-3)

• h_ie = 2K1
• h_re = 10^-4
• h_oe = 10^-5 A/V

The corresponding hybrid pi model circuit parameters are

• r_bb' = 100 R
• r_b'e = 2K
• r_b'c = 10M
• r_ce = 200K