The NPN BJT is biased in saturation model with and . What is the approximate ratio of the electron concentration at the base near the emitter to the electron concentration at the base near the collector () ?

[ans]

Question

The NPN BJT is biased in saturation model with and .  What is the approximate ratio of the electron concentration at the base near the emitter to the electron concentration at the base near the collector ()  ?

[ans]

BlackTom AI · Accepted Answer

The problem asks for the approximate ratio of electron concentration at the base near the emitter (n_BEs) to that near the collector (n_BCs) in an NPN BJT saturated with given VBE and VBC values.

A common way to relate carrier concentrations in forward-biased junction regions of a BJT is to use the thermal-voltage model, where carrier concentrations in a forward-biased region vary roughly as exp(qV/displayed as) exp(V_forward / V_T). Here, V_T is the thermal voltage (~kT/q), about 25 mV at room temperature.

Optionally, we can express the ratio as:

n_BEs / n_BCs ≈ exp[(V_EB − V_CB) / V_T]

where V_EB is the emitter-base forward bias (0.47 V) and V_CB is the base-collector forward bias (0.23 V). Note that V_EB − V_CB = 0.47 − 0.23 = 0.24 V.

Plugging in V_T ≈ 0.025 V gives:
Exponent ≈ 0.24 / 0.025 = 9.6
n_BEs / n_BCs ≈ e^9.6 ≈ 1.3 × 10^4 (on the order of 10^4).

Since the problem asks for an approximate ratio and provides 1e4 as the answer, this aligns with the expected magnitude, acknowledging that exact values depend on the precise temperature and model details. The key idea is that a larger net forward bias difference between emitter-base and base-collector junctions drives a larger electron concentration near the emitter side of the base.

If one were to consider slight variations in V_T (e.g., using 25 mV vs 26 mV) or rounding, the result remains in the 10^4 range, justifying the given answer of about 1e4.

Therefore, the approximate ratio n_BEs / n_BCs is on the order of 10^4 (around 1e4).

EESM5200 (L2) Part I: Topic 12 - Non-ideal Effects in BJT

The NPN BJT is biased in saturation model with and . What is the approximate ratio of the electron concentration at the base near the emitter to the electron concentration at the base near the collector () ? [ans]

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